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MathGrade 2 | 2020
Publisher: Accelerate LearningSeries includes:
The quality review is the result of extensive evidence gathering and analysis by Texas educators of how well instructional materials satisfy the criteria for quality in the subject-specific rubric. Follow the links below to view the scores and read the evidence used to determine quality.
Section 1. Texas Essential Knowledge and Skills (TEKS) and English Language Proficiency Standards (ELPS) Alignment
TEKS Student %
TEKS Teacher %
ELPS Student %
ELPS Teacher %
Section 2. Concept Development and Rigor
Section 3. Integration of Process Skills
Section 4. Progress Monitoring
Section 5. Supports for All Learners
Section 6. Implementation
Section 7. Additional Information
|Grade||TEKS Student %||TEKS Teacher %||ELPS Student %||ELPS Teacher %|
The materials concentrate on the development of the primary focal areas for the grade level. Ample teacher materials provide rigorous delivery of instruction with high-engagement activities in the focal points. Throughout the scopes, the materials spend the majority of the year focusing on the concept development of the primary focal areas for second grade as outlined in the TEKS. Eight of the fifteen scopes focus on concept development in place value, solving problems with addition and subtraction, identifying and creating two-dimensional shapes and three-dimensional solids, and principles of length measurement. The program has a “Scope and Sequence” that outlines the TEKS covered in each scope and the suggested pacing of each scope. The remaining scopes, which are also aligned, spiral throughout the second-grade curriculum. The pacing of the Scope and Sequence allows students to systematically develop content knowledge and build on knowledge learned in previous units. The materials allow students to practice skills in primary focal areas in multiple settings. These settings include whole group instruction, games, interactive activities, stations, and small group instruction. The content increases in rigor across the course of the school year.
Evidence includes but is not limited to:
The materials devote a majority of lessons to the focal areas, as outlined in the TEKS. The primary focus of eight out of fifteen scopes is on place value, addition and subtraction with multi-digit whole numbers, measuring length, and applying understanding of 2D shapes and 3D solids. According to the suggested pacing guide, these eight scopes account for 19 out of 35 instructional weeks within the school year. The eight scopes centered around the focal areas are: “Represent Numbers to 1,200,” “Numbers on a Number Line,” “Compare and Order Numbers,” “Addition and Subtraction Strategies and Algorithms,” “Addition and Subtraction Problem Solving,” “Creating 2D Shapes,” “3D Solids,” and “Length.”
The scopes are clustered by TEKS alignment. The “TEKS Unwrapped” section dissects the strands and uses verbs and nouns to explain what the students should be doing; several planning documents are located in the “Teacher Toolbox.” The toolbox also includes a Scope and Sequence and a “Lesson Planning Guide.” “Benchmark Assessments,” which should be administered three times a year, are also included. These assessments cover focal area concepts and allow the teacher to adjust small group instruction accordingly to ensure that students master the focal area concepts. Within each scope, a homepage details TEKS and student expectations based on what students learned in the previous grade level and what students will learn in the upcoming grade. The “Scope Overview” provides a vibrant graphic organizer that showcases the content for the module. It clearly notes the unit’s focal points and aligns with the scope and sequence of the second-grade TEKS. The “Elaborate” tab notes the spiraling of these key focal areas for each module. Each scope contains one spiral review activity.
Materials showcased in the modules directly build upon materials previously taught in first grade. For example, in first grade, students identify shapes; in second grade, students determine the shapes used to make up a 3D solid. In addition to following the provided scopes, the Scope and Sequence suggests that teachers and students focus on addition and subtraction fact fluency from October through May. This is in addition to focusing on daily numeracy from September through May. This indicates that materials focus heavily on whole numbers and addition and subtraction concepts throughout the entire year, even when the scopes have an alternate focus. “Daily Numeracy” is used every day, within every scope of the materials. The goal of Daily Numeracy is to have a 15-minute meeting with the class to share connections and mental strategies about concepts they are currently learning or spiraled concepts. Each activity includes a slideshow that has multiple prompts for teachers to choose from. Numeracy and fact fluency activities spiral multiple focal areas in second grade throughout an entire school year. In scopes that are not centered around focal areas, such as “Fractions,” “Money,” “Multiplication and Division,” “Area,” “Time,” “Data Analysis,” and “Personal Financial Literacy,” there are opportunities for spiraled practice and “Fluency Builders.”
The materials, specifically the “New Teacher Navigation Guide,” provide the philosophy behind the publisher’s approach to students’ mathematical learning. The publisher takes the constructivist approach to mathematical instruction, meaning that students follow the “concrete, representation, abstract” (CRA) process while acquiring knowledge and skills. The materials state that they provide “an interactive curriculum that encourages your students to rely on critical thinking, compelling reflection, and collaborative exploration within each scope.” The scopes also provide opportunities for students to engage in intentional discourse to broaden student mindset and encourage educational growth.
The “Teacher Toolbox” provides a document stating the mathematics instructional philosophy. The philosophy document references research that has been conducted and discusses how the research influenced the elements of the materials. For example, cited research states that there is a disconnect between performing procedural skills and knowing when to use them in everyday situations. Due to this research, the materials rooted student learning in real-world scenarios. Within every scope, the “Hook” activity, the “Explore” activities, and the “Problem-Based Tasks” all incorporate real-world learning. For example, there are problem-based tasks in the “Identify 3D Solids” module; students work in groups to complete a real-world challenge to name, draw, and discover real-life 3D objects. There is also a problem-based task in “Compose and Decompose Numbers to 120”; students complete a task as if they are an equipment manager for a high school football team. Materials provide multiple opportunities to practice in a variety of ways, including through paper-pencil tasks, hands-on manipulatives, and interactive games. Technology and hands-on tasks allow teachers to easily assess student performance in each module.
“Content Support,” at the beginning of each scope, provides teachers with an overview of the upcoming scope, the TEKS covered, and what students need to know to show mastery. This section provides information about what students learned in the previous grade and how it applies to the current scope. It also highlights misconceptions many students have before learning the content introduced in the new scope. The program also explains the TEKS and skills necessary for students to show mastery of the scope and provides content-specific vocabulary to introduce during whole group lessons. Included sample questions model what students should be able to answer by the end of the scope to demonstrate mastery. For example, in the “Multiply and Divide” scope, the Content Support section explains what students learned in previous grades and the misconceptions students may have before learning how to multiply and divide. This section explains that by the end of this scope, students will be able to model, create, and describe contextual multiplication and division situations. This explanation helps teachers understand the goal of the tasks in the scope. In the “Coming Attractions” section, the program explains how students will build on their knowledge of fractions in third and fifth grade.
Students have various opportunities to practice the content and skills in different modalities and contexts. For example, in the scope on length, students measure length using concrete objects to inverse relationships, measure length using formal measuring tools, and then engage in a math chat and use strategies to solve problems with length. An example of students making real-world connections is within the Personal Financial Literacy scope, in the Problem-Based Task portion. Students make life connections to highlight ways to make income and choose how to use their income. The activity congratulates students on getting a new job that earns money; students must also share how they would spend their money. These problem-based tasks appear in all the units throughout the instructional material. Each scope has a variety of whole group lessons, practice problems, games, digital games, station options, and small group intervention activities. Each lesson plan includes step-by-step instructions for how teachers can implement the activity in the classroom and all of the necessary materials. In each scope, a “Parent Letter” lists several ways students can practice their new learning at home and in other settings, using authentic methods.
An example of a skill that builds upon rigor is in the scope related to comparing and ordering numbers. Students engage in a Hook activity: They compare and order whole numbers up to 1,200 by relating the concept to a game of laser tag. Students watch a phenomena video and use mathematical vocabulary to compare and order scores based on laser tag games. This gives students a real-world example to connect with the concept while engaging them in the activity. In one Explore activity, students use base-ten blocks and store ads to generate numbers that are greater than or less than a given number. Students have the opportunity to use manipulatives in order to support their learning. In the Elaborate component, students play a game called “Roll of the Dice”; they roll three dice and create a three-digit number, and then compare their number with a partner’s number. Students then write a comparison equation using mathematical symbols to compare the two numbers. This activity incorporates the same concepts, but in a game using number sentences instead of manipulatives. Also in the Elaborate component, students participate in a problem-based task; they read scenarios about feeding animals at the zoo and apply their knowledge of comparing and ordering numbers to solve the problems. Students also have the opportunity to play virtual games, such as “Mountain Goat” and “Dragon Battle,” to practice the concepts in a virtual format. Finally, students complete a STAAR-based assessment that tests their ability to apply the concept of comparing and ordering numbers to 1,200 using STAAR-formatted questions.
The materials sequence concepts from concrete to representational to abstract (CRA) within the school year as well as within each scope. The materials include a variety of opportunities for students to use CRA materials while learning specific concepts. The “Content Support” section provides teachers with guidance on prior knowledge from previous grade levels. There are different activity ideas based in the CRA model to teach new skills. The program provides rationale for the materials used. There are suggestions for supporting students as they progress through the CRA continuum. The materials used in the CRA model increase in rigor over the course of the school year. Each lesson plan states whether students will be using manipulatives, pictorial representations, or abstract representations. The plans also provide teachers with facilitation points on how to teach each skill and give instructional support for students struggling to move across the CRA continuum. Both the usage of materials and the information written for teacher support show a clear progression in the CRA continuum within the instructional materials.
Evidence includes but is not limited to:
According to the program’s “Math Philosophy,” students progress through the CRA models in each “Explore” activity. When students first learn a new skill, the program incorporates carefully selected concrete materials to develop their understanding of the new concept or skill. As students gain understanding with physical models, they begin to draw a variety of pictorial representations that mirror the work they did with concrete models. Then, students learn to use symbols and algorithms to represent their concrete and pictorial models. Each Explore activity follows one of the components in the CRA approach. In the first few Explores of a scope, students use concrete materials to learn the new skill. Then, students begin drawing pictorial representations. By the final Explore activity, students are working to represent their models with symbols and algorithms.
The materials change with the content taught in each scope and increase in rigor over the course of the school year. For example, students learn how to use an open number line to plot numbers in the “Numbers on a Number Line” scope. Later in the year, students apply their knowledge of number lines to use them as an aid to add and subtract numbers up to 1,000. All of the scopes use models, manipulatives, and representations, including scopes that teach focal areas for second grade. Before teaching any Explore, the program includes “Skill Basics” lesson plans. In these lessons, students learn necessary skills for the scope, including how to use any model or manipulative. For example, in the “Represent Numbers to 1,200” scope, students learn how to use concrete models to compose and decompose numbers to 1,200. In the Skill Basics lesson, students review the value of flats, rods, and units and how to represent numbers to 120 in a pictorial model. During the Explore lessons, students apply their knowledge of place-value blocks to represent numbers to 120; then, they move towards representing numbers beyond 999.
The materials include a variety of concrete models and manipulatives, pictorial representations, and abstract representations to introduce and practice mathematical concepts. For example, in the scope on measuring length, students have access to various concrete manipulatives, such as centimeter cubes, inch tiles, rulers, yardsticks, meter sticks, measuring tape, and color tiles. Before starting this scope, the materials recommend that students complete the Skills Basics lesson on how to use measuring tools, so they can apply the skills to the concept. Later in the scope, students complete a problem-based task in which they apply the knowledge and skills they have learned about measuring length to a real-world challenge. In the task, students select the best-fitting measuring tool (inch cubes, ruler, yardstick, and unit of their choice) to measure various objects around a classroom. Students have the choice to select the tool that they prefer, whether it is concrete or representational. Afterward, the Explore 1 activity focuses on length; students use concrete objects such as color tiles and centimeter cubes to find the length of objects. In the STAAR-based assessment at the end of the scope, students use pictorial models as well as concrete objects to determine the length of different pictures.
The materials support teachers in identifying where student understanding is along the phases of the CRA continuum. The materials also provide guidance and instructional suggestions to help students move through the phases of the CRA continuum.
Each scope provides “Content Support” for teachers on the homepage of the scope. The Content Support section provides guidance on the use and progression of the materials. Teachers can find what students learned in previous grade levels and how their background knowledge applies to the current scope. The section also explains common misconceptions that students may have about the materials before beginning the scope. Within these sections, teachers receive suggestions and guidance on supporting students through the CRA continuum. For example, in the scope focused on addition and subtraction strategies and algorithms, the materials explain that students will have previously worked on this concept with numbers up to 5 in pre-kindergarten, up to 10 in kindergarten, and up to 120 in first grade, using concrete objects, generating pictorial models, and in both written and spoken number sentences. The support document explains that mental math strategies may be a struggle for some students who may still prefer to see concrete representations of addition and subtraction problems. The support document also states that this scope is focused on the operations of addition and subtraction and that students will move away from concrete representations as they utilize algorithms, properties of operations, and mental math strategies to solve problems.
Within the scopes, the materials provide opportunities for the teacher to assess where students are in the CRA continuum. Each Explore activity provides teachers with details about procedures and facilitation points as a guide to help support students as they work through the CRA model. By reading the description of the lesson, teachers are able to determine which part of the CRA model the students are working on. For example, in the scope focused on creating 2D shapes, the “Accessing Prior Knowledge” activity asks students to create various 2D shapes using chenille sticks. This allows the teacher to assess which students are still at the concrete phase and which students are ready to move to the representational phase. In an Explore activity focusing on decomposing 2D shapes, students explore how to decompose shapes into other shapes by cutting, partitioning, and dividing. Materials provide suggestions on how to support students who may be struggling. One suggestion is to provide students with pattern blocks that compose the shapes, and then model how to place two or more pattern blocks on top of the picture in order to decompose the original shape. In the “Show What You Know” component, the materials recommend providing manipulatives to students as needed and using the manipulatives that were used in the corresponding Explore activity.
Skill Basics lesson plans give students a necessary foundation in skills before they progress through the CRA model. For example, in the “Length” scope, Explore 1 guides students to measure using concrete objects such as color tiles, centimeter cubes, and different sizes of paper. Students apply the knowledge from the lesson to an “Exit Ticket,” where they independently use centimeter cubes to measure objects on a handout and record how long the object is. Before Explore 3, in a Skill Basics activity, materials explicitly teach students how to use measuring tools such as a ruler and measuring tape. In Explore 3, students use formal measuring tools to measure objects in centimeters and inches. If students are struggling to use the ruler, the lesson plan states that students can continue to measure to the nearest inch.
The materials include supports for students to build their vertical content knowledge by providing prior knowledge activities and foundation builders for students who have gaps in their prior knowledge. They also provide supports for teachers to understand the prior knowledge students should possess and how the concepts will be applied and further integrated in future grade levels. The materials also include tasks and problems that connect multiple concepts as appropriate for the grade level. The materials provide opportunities for students to engage in math talk and discover math as they explore relationships and patterns within and across concepts. The materials are organized in a way that provides students with opportunities to examine relationships and patterns within and across different concepts. Some activities require students to interconnect different mathematical ideas to problem solve. The program provides teachers with a scope overview, Scope and Sequence, and vertical alignment to show which TEKS are introduced in that grade level and how they progress in future grade levels. The “Content Support” and “TEKS Unwrapped” sections at the beginning of each scope provide teachers with a deeper understanding of students’ background knowledge, expectations for the current grade level, and how the concept develops in future grade levels.
Evidence includes but is not limited to:
Each scope begins with an “Accessing Prior Knowledge” activity where students apply prior knowledge to a vertically-aligned standard. The activity either assesses students’ knowledge of skills taught in a previous grade level or skills taught in previous units. As students progress through the materials, the program incorporates previously learned skills and applies them to new concepts. As the program progresses, scopes utilize familiar models and strategies from previous units and introduce new models and strategies that students apply to the new skill. The materials contain tasks that measure students’ prior knowledge and direct teachers on building from the knowledge that students have. These tasks are at the beginning of every scope and occur before materials present a new concept or idea. For example, in the scope focused on addition and subtraction problem solving, students engage in the Accessing Prior Knowledge activity on the first day. In the activity, students solve addition and subtraction word problems and record their thinking with pictures and number sentences. This activity measures students’ prior knowledge based on what they learned in first grade and gives the TEKS that the prior knowledge is addressing from first grade. The Content Support documents for each scope provide teachers with the related background knowledge that students should possess with regard to the content in the scope. The “Coming Attractions” section shows how students will apply that knowledge in future grades.
The materials provide tasks that help students recognize and make connections among mathematical ideas. In the scope related to area, students engage in an Explore activity to use concrete models of square units to find the area of rectangles. In this activity, students make connections to addition, measurement, two-dimensional shapes, and basic concepts of multiplication and division. In the scope focused on multiplication and division, students engage in an Explore activity where they use concrete objects to model, create, and describe contextual multiplication situations in which sets of objects are joined. Students use counters and story mats to create a concrete model of scenarios represented on cards. This activity helps students connect the concepts of repeated addition, number sentences, and using the equals sign to show equality on both sides of an equation. The activity also connects to the concept of skip counting.
Each scope contains a “Life Connections” activity, located in the “Elaborate” section. Life Connections activities introduce students to careers and real-life experiences that highlight the mathematical concepts being learned in class. Each scope also has a “Math Story” in the Elaborate section. Math Stories support literacy and expand students’ ability to identify the information they need to solve math-related problems. The stories are interactive and prompt students to answer questions as the teacher reads. In the “Math Today” section, students explore connections and applications of math and other cross-curricular content through interactions with authentic, real-world events.
The materials include tasks that require students to understand how mathematical ideas interconnect and build on one another. For example, in the “Represent Numbers to 1,200” scope, students use place-value skills learned in first grade to count organized sets between 120 and 999. They extend their knowledge of place value to represent numbers between 0 and 1,200. In the “Numbers on a Number Line” scope, students apply their knowledge of place value to locate the position of a given number on an open number line and name a whole number that corresponds to a specific point on a number line. In the “Compare and Order Numbers” scope, students continue to build their knowledge of place value in order to generate numbers that are greater or less than a given number, use place value to compare and order numbers up to 1,200 and use their knowledge of place value to determine if a number is 10 or 100 more or less than a given number to 1,200. Place-value skills introduced in kindergarten progress into first grade when students are expected to represent, compare, and order numbers to 120. The scopes in second grade build on that knowledge by providing students opportunities to make connections and examine relationships and patterns in place value.
The materials also provide opportunities for students to examine relationships and patterns within concepts and across concepts. Within the “Hook” activity for every scope, the teacher asks, “What do you notice?” and “Where can you see math in this situation?” Students are given this question so they can relate mathematics across concepts and with new understanding. Each scope has a “Spiraled Review” activity that reviews previous or current grade-level content based on the focal points for each grade level. For example, in the “Fractions” scope, students complete a spiraled review activity titled “Arcade Party.” The teacher first reads a story problem to set the stage for the activity. Then, students answer questions related to the story problem. The questions in this activity review locating points on an open number line, generating numbers greater than or less than a given number, writing numbers in standard, word, and expanded form, and determining the value of points on a number line. All these skills were taught in previous scopes.
The materials include a grade-level scope list, a Scope and Sequence, and a vertical alignment chart. In the grade-level scope list, teachers can find what TEKS are covered in each scope. The Scope and Sequence shows teachers how to pace each scope over the course of a school year; it is organized by week and includes the scope name and which TEKS to introduce. The vertical alignment chart gives teachers an overview of how each standard progresses from kindergarten through third grade. The Content Support document for each scope provides information on how the content in the current scope builds over time. The document begins by highlighting the prior knowledge that students should have when entering their current grade level. This includes what students should have mastered in their previous grade level and how that relates to what students will be learning in the current scope. The support document then gives an in-depth overview of what will be covered in the current scope: terms to know and major concepts and examples. Finally, the Content Support documents provide an overview of Coming Attractions, which highlight how students will continue their growth and understanding of the concept in future grade levels.
The materials meet some of the guidance bullets; however, some of the guidance bullets are only partially met. The tasks are designed to engage students in the appropriate level of rigor as identified in the TEKS and as appropriate for the development of the content and skills. The materials clearly outline for the teacher the mathematical concepts and goals behind the tasks. Each lesson plan provides teachers with the objective for the lesson, procedure and facilitation steps, prompts to use during the lesson, and instructional support for students struggling to meet mastery. The “Content Support” section provides teachers with students’ background knowledge, common misconceptions, and skills students need to demonstrate to meet mastery. The materials provide teachers with many prompts for questions to ask students and even possible student responses. In the STEMcoach in Action component, administrators and teachers are provided with professional development to guide teachers on how to begin the facilitation of quality classroom discourse. The "Building Scientific and Mathematical Understanding,” "Facilitating Questioning and Discourse,” and FAQ sections in the STEMcoach can be used to determine what the students, teachers, and administrators should both do and see in the classroom.
Evidence includes but is not limited to:
The tasks in the materials are designed to engage students in the appropriate level of rigor as identified in the TEKS and as appropriate for the development of the content and skill. Throughout each scope, there is an increase in depth and complexity. The design of the instructional materials begins with an “Engage” activity to hook students; the activity guides the teacher in asking thought-provoking questions. As lessons advance toward the “Explore” portions, there is a higher level of questioning and rigor. The Explore tasks in each scope are scaffolded in a way that guides students through CRA tools, models, and understanding, with increasing depth and complexity. Students use concrete and pictorial models to demonstrate their thinking in the Explore tasks; as they progress, students begin to demonstrate their knowledge through abstract models.
For example, in the “Addition and Subtraction Problem Solving” scope, the “Skee-Ball Scores” activity engages students by providing a short video about children playing the “SkeeBall” game. Students must take what they have learned so far to solve addition and subtraction problems. Strategies learned are used to integrate the use of a strip diagram to assist in solving. Students also use a number line to solve, and then note that the answer is the same for both strategies. Students use these strategies to assist them in representing and solving multi-step word problems. Second grade students follow the same scopes in sequence as they did in first grade, just with a larger number (1,200).
The rigor level of the tasks increases throughout the course of the year as students progress through the overall CRA process. For example, in the first scope focusing on representing numbers to 1,200, the majority of activities during the Explore lessons include concrete and pictorial models for students to use. In the middle of the year, when students are engaging in addition and subtraction problem solving, students begin the concept using models to solve problems, and then quickly move into pictorial models such as strip diagrams and number lines. At the end of the year, as students are engaging in the scope related to financial literacy, students use abstract representation in order to differentiate between deposits and withdrawals, evaluate lending decisions, differentiate between producers and consumers, and calculate the cost to produce a simple item.
The materials clearly outline for the teacher the mathematical concepts and goals behind each task. Each lesson plan provides teachers with an objective for the lesson, procedure and facilitation steps, prompts to use during the lesson and during the “Math Chat,” instructional supports, and ELPS strategies. There are explanations of the mathematical concepts and goals behind each scope that serve to build teacher content knowledge. For example, each scope includes a Content Support document to explain the TEKS that will be covered in the scope, background knowledge that students will be coming with, misconceptions and obstacles that the student may have during the scope, terms to know in the scope, specificity in content that the student will gain throughout the scope, and how the information learned in the current grade level will be reinforced and elaborated on in future grade levels. Additionally, each unit in the instructional materials contains a portion titled “Current Scope.” This section addresses the strategies and tasks that will be completed throughout the entire unit to teachers. It provides a summary of the intended outcome of each strategy or skill and a visual of key vocabulary and skills.
The materials guide the teacher in supporting student discussion and responding to student strategies as they use problem solving to support the development of skills. Each scope provides a section titled “Background Knowledge,” which gives the teacher a glimpse of the prior grade levels and what the students should have mastered. In every Explore activity, materials provide supporting questions to ask students during the activity; there are also questions to ask the whole class during the Math Chat after the activity has concluded.
The materials integrate contextualized problems throughout in order to provide students the opportunity to apply math knowledge and skills to new and varied situations. Hook activities include tasks posed in real-world contexts that are meaningful for students. Each Explore lesson has a scenario that is familiar to most students. For example, in Explore 1 of the “Personal Financial Literacy” scope, students explore how saving is an alternative to spending and how saving money over time can accumulate into larger amounts. The teacher sets the stage for the lesson by reading a scenario about earning an allowance for doing chores around the house. The teacher asks the class if they would rather spend or save their money. In groups, students take turns reading scenario cards that describe different ways students earn allowance and how much money they earn by doing the chore. Students decide whether to spend or save their money on something from a spending menu. At the end of the activity, students calculate how much money they have left over after earning money in different situations. The “Math Today” activities are located in the “Acceleration” section. In these activities, students explore real-world connections and applications of math content through media provided by the Associated Press.
The materials provide support to teachers on lesson modifications with relevant context for students who are English Learners (ELs). Within the Explore activities, materials provide modeling and sentence stems for teachers to support students as they work to respond. The materials also provide a parent letter to be sent home at the beginning of each scope, which provides information on the concepts being learned in class as well as a choice board of activities so families can practice the concepts at home.
The materials provide teacher guidance on anticipating student responses and strategies as they practice questions and tasks. Before the start of each scope, prior to teaching the concepts, the teacher can read about the misconceptions and obstacles that students can encounter. Throughout the materials, in each lesson, there are embedded sample guiding questions. “Instructional Supports,” provided throughout the material, include specific suggestions on how to help a struggling student. For example, if a student is struggling with subtraction, materials suggest using a number line to assist with solving. As students explore, teachers may ask the provided guided questions to ensure mastery. Within every “Accessing Prior Knowledge,” “Foundation Builder,” “Hook,” and “Explore” activity, the materials provide possible student responses next to the questions that teachers can ask. These student responses are typed in red so they can be spotted during the planning phase. Foundation Builders assist in reteaching skills not retained from the prior lesson. Materials provide suggested solutions to assist teachers in correcting the misunderstandings. Each Explore lesson introduces students to a new strategy that can be used to answer questions and tasks. The strategies introduced in the lesson plans are appropriate for the grade level and task students are expected to complete. By the end of the scope, students have learned multiple strategies they can use to problem solve. Students use different strategies they have learned throughout the scope on a “Skills Quiz” at the end of the scope.
In the Content Support section of each scope, there is a portion titled “Misconceptions and Obstacles.” This section outlines both common misconceptions and areas that students may struggle with as they progress through the scope. For example, one misconception listed is “Students may transpose 2D terms with 3D terms (e.g., the term side, used for 2D polygons, is used when referring to an edge on a 3D solid)”; one obstacle is “Students may mistakenly count vertices of a 3D solid more than once as they look at each face independently.” Teachers can find ideas on how to combat these misconceptions in the materials’ explanation of the current scope. For example, students are expected to compose 3D solids. Using their prior knowledge of what 2D shapes make up 3D solids, students use different manipulatives to compose their own solids.
The materials sequence anticipated strategies in order of strategy sophistication so that teachers know how to push students from one strategy to the next. The Explore lessons begin with students learning new concepts with concrete materials. In these early stages, students have opportunities to also use pictorial models by illustrating the concrete model they used to solve the problem. As students progress, they begin to move toward using only pictorial models and representing their answers in an abstract way. The Content Support section also provides two additional teacher guidance pieces: There is guidance for appropriate grade-level strategies and the sequence of the strategies.
The materials partially provide teacher guidance in preparing and facilitating strong student discourse grounded in the quality tasks and concepts. Each activity has an outlined facilitation piece that has step-by-step instructions as well as questions that teachers should ask. The “Home” page of each scope lists the overarching fundamental questions for that scope. The Explore activities provide possible student responses to teacher questions as well as questions that can be asked after the students have responded. The materials provide instructional support on how to support a student with misunderstandings, such as small-group intervention.
The provided “Teacher Toolkit” contains a section titled “Communicate Math,” which provides information on the importance of discourse within the math classroom and expectations for the K-2 classroom. Some of these expectations include modeling discourse interactions for students to have a clear understanding of what discourse is and what it sounds like; providing sentence stems to help scaffold language; including a variety of approaches to convey knowledge, strategies, justifications, and conclusions; allowing adequate wait time after asking a question or hearing a response; and ensuring each student contributes to the discussion with clear and organized thoughts and ideas. While these expectations are laid out for teachers to understand, the materials do not provide specific lessons on how teachers can teach these ideas to students. The “Daily Numeracy” component of the program encourages students to participate in a daily math talk. Daily Numeracy is a 15-minute class meeting where students share connections and mental strategies used to solve problems. The program provides slides with numeracy activities that reinforce skills such as counting, patterns, and guess-the-number. Teachers choose a topic they want to discuss with the class, show the slide, and use guiding questions to facilitate the discussion. The program provides teachers with how this should look in the classroom, examples of guiding questions, and how students should respond to the questions.
The materials include guidance for teachers on the structure and design of the “Fact Fluency” scope. The materials include a cohesive, year-long plan for students to develop fluency in an integrated way. There is a year-long plan for students to develop fluency; however, the fluency activities are completed in isolation as opposed to being integrated into the lessons. Fact Fluency is its own scope that can be used in daily instruction at the teacher’s discretion. The content in the Fact Fluency scope is sequenced in a way that allows students to make connections across and between strategies. The components of the Fact Fluency scope give students opportunities to practice the skill in multiple ways. Students are assessed at the end of the scope using an online assessment.
Although there are several fluency activities provided for each scope, there is no evidence of differentiation or guidance for teachers on how to evaluate or track student progress. The Fact Fluency scope is the same in grades K-2. This includes mini-lessons, stations, games, and assessments. Materials do not build upon skills in each grade level; instead, skills are retaught using the same materials. There is no evidence of grade-level fluency expectations, tools to monitor students’ fluency, or interventions/extensions for students who are struggling or who have mastered the fluency activities.
Evidence includes but is not limited to:
The materials include teacher guidance and support for conducting fluency as appropriate for the concept development and grade. Within the Fact Fluency scope, each set of facts includes a mini-lesson, fact fluency stations, fact fluency games, and an assessment related to the facts that are being focused on. The scope develops student automaticity with basic addition and subtraction facts by building on their conceptual understanding of addition and subtraction. The first-grade scope list suggests that this component should be paced from October through May. The scope and sequence does not provide a concise timeline of when new fact fluency skills should be introduced. Teachers can use the “Lesson Plan Guide,” located in the “Teacher Toolbox” as an aid to pace the Fact Fluency component. According to the Lesson Plan Guide, teachers choose between Fact Fluency or “Daily Numeracy” for the beginning of each lesson. Teachers should use one of the fact fluency stations or games during center rotations to reinforce skills that were taught in fact fluency mini-lessons. When students are participating in fact fluency stations, materials prompt them with directions and/or sentence stems so that they can discuss their fact fluency knowledge. For example, in the fact fluency station covering “plus and minus 10,” students use sentence stems such as “I am looking for a card that represents the sum/difference of ... and 10” “Who has the numeral that is ... plus/minus 10?” and “I need an expression that represents ….”
The instructional materials provide support and clear directions for when and how to conduct fluency activities. The “Scope Overview” of each scope states that the fluency component should be taught in the “Elaborate” portion of the lesson. The Scope Overview is an embedded diagram on the home page of each unit. Within the lesson, there is a “Fluency Builder” component that has games with step-by-step directions to conduct the fluency activity.
There are no strategic discourse opportunities in the Fluency Builder activities embedded within each scope; however, there is a separate unit within the materials, titled “Fact Fluency: Addition and Subtraction”; within it, a fluency mini-lesson activity provides opportunities for discourse.
The materials partially include a year-long plan for building fluency as appropriate for the concept development and grade. Fluency Builder activities are specific to the content being taught in each scope. Every scope includes Fluency Builder games related to the scope to help students work towards fluency with the concept being learned. The Fact Fluency scope provides students with multiple stations and games to practice different strategies learned in the scope. Each scope contains virtual games designed to reinforce the skills established by the standards in each scope and build fluency. Students engage in a “Spiraled Review” during each scope, which reviews previous or current grade-level content based on focal points. These spiraled reviews also provide additional fluency practice for students. Within the Fact Fluency scope, students engage in the mini-lesson, fluency stations, and fluency games in order to practice their fluency skills as appropriate to the grade level and skill. During the mini-lesson component, students engage in a game-type activity that introduces the fact fluency skill they are working on. During the activity, students respond to questions related to strategies they used, discuss different ways to solve problems, and describe the actions they took. The materials also provide students with opportunities to efficiently and accurately solve grade-level tasks by applying their conceptual understanding of number relationships and strategies. Each scope has multiple “Show What You Know” activities where students apply the different strategies they have learned throughout the scope to demonstrate their learning. Although there is a scope and sequence listed in the addition/subtraction fact table, no other scopes and sequences are evident. The materials provide a year-long plan for building fluency and include recording sheets tied to each fluency activity.
The materials partially integrate fluency at appropriate times and with purpose as students progress in conceptual understanding. Components of the Fact Fluency program can be integrated into different scopes; however, there is no scope and sequence for the Fact Fluency program. Therefore, teachers would have to use this at their own discretion. Fluency Builder activities specific to the content being taught in each scope integrate fluency activities within the development of conceptual understanding. Every scope includes fluency activities and games; these are used after the introduction of the skill and vocabulary. In the “Explore” and “Explain” portions of the scope, students have multiple opportunities to master the skill. The fluency activities in the Elaborate tab provide opportunities for the students to apply what they have learned and reinforce the skill in an interactive partner game.
The materials provide students with opportunities to efficiently and accurately solve grade-level tasks by applying their conceptual understanding of number relationships and strategies. Each scope has multiple “Show What You Know” activities, where students apply the different strategies they have learned throughout the scope to demonstrate their learning. When completing tasks at the Explore level, students are encouraged to share their thinking and strategies. Some prompting questions that students answer include “What strategies can you use to understand what is happening in the problem?” “Can you explain how you solved this?” “Is there a different way to solve this?” and “Is there a math tool that can be used to help solve this problem?”
The materials partially include scaffolds and supports for teachers to differentiate fluency development for all learners. The materials include assessments to assess students as they develop fluency skills in their mathematical understanding and reasoning. For example, at the beginning of every scope, an “Accessing Prior Knowledge” activity helps teachers determine where students are in their conceptual and fluency understanding. The Explore lessons are scaffolded in a way to increase fluency in each concept. Students begin by using manipulatives and pictorial models to explore new content. By the end of the scope, students move toward written strategies and algorithms. Teachers can use information gathered from the Explore activities to determine if students need differentiated supports for fluency activities. The instructional interventions provided for students struggling to meet mastery include small group intervention lessons. These lessons are to reteach skills introduced in the Explore lessons, not to support students’ fluency skills. In the “Acceleration” tab for each scope, there are “Math Today” activities and a “Connection Station” activity. These activities are designed to take the concepts learned in the scope and extend student knowledge of the concept and fluency.
If students are struggling to meet the fluency expectations for the grade level, the materials provide supports for teachers to scaffold activities within the scopes that relate to fluency. For example, during Explore activities, instructional supports help teachers support students who may be struggling with particular components of the activity. An example of this can be found in the scope related to representing numbers at least to 20. In Explore, if students are struggling to generate sets of concrete objects, the materials recommend giving students counting strips or ten-frames to help with organizing their counts. Additionally, materials provide interventions within every scope in order to support students who are struggling to grasp concepts. During these intervention lessons, supplemental aids support students as they acquire fluency skills.
The materials include embedded opportunities to develop and strengthen students’ mathematical vocabulary. The materials provide authentic opportunities for students to develop mathematical language. There are opportunities for students to listen, speak, read, and write using academic language. The instructional materials are designed so that the development of mathematical language is scaffolded and students are supported as they learn the new language. Students use their prior knowledge to apply vocabulary words within the “Foundation Builder” and “Hook” activities. There are embedded opportunities for students to develop and strengthen their mathematical vocabulary in “Explore” lessons, class discussions, and “My Math Thoughts” prompts. Materials provide tools and techniques such as vocabulary cards, sentence stems, modeling, and visual supports to assist teachers in encouraging academic talk with students in the Explore lessons and in the Math Talk sections. Students apply their mathematical vocabulary in the “Show and Tell” assessments, where they complete performance tasks and explain their thinking. The materials include supports such as picture vocabulary and anchor charts to support the use of academic vocabulary. Explore lessons are scaffolded in a way that guides students from using informal vocabulary to using formal vocabulary.
Students engage in daily math chats to strengthen their vocabulary knowledge. They also practice vocabulary through games played with other students. Additionally, the materials include guidance for teachers on how to scaffold and support students’ development and use of academic mathematical vocabulary in context. The “Content Support” document provides teachers with the terms to know in each scope. A parent letter informs parents about how vocabulary words can be applied in different contexts in the real world and at home.
Evidence includes but is not limited to:
The materials include embedded opportunities to develop and strengthen students’ mathematical vocabulary. The learning goals, or key concepts as they are referred to within the instructional material, address the development of mathematical vocabulary. Within each scope, a homepage outlines both the key concepts of the scope as well as fundamental questions that can be used to increase the use of mathematical vocabulary. Teachers can also obtain more information about scope-specific vocabulary in the Content Support section. In each activity, throughout all scopes in the materials, there is a teacher instruction page that provides guiding questions for the application of the vocabulary. Within each scope, the “Accessing Prior Knowledge,” Foundation Builder, and Hook activities often embed content-specific vocabulary into the questions and discussions in order to determine where students are in their vocabulary knowledge. Explore activities provide teachers with facilitation to attach academic vocabulary to the students’ experiences. Each Explore activity includes discussion prompts for the teacher to use to help guide students in communicating their thoughts using academic language. Each Explore lesson also has ELPS strategies that support English Learners to acquire new vocabulary. Each scope has a picture vocabulary presentation for teachers to use as a support tool to represent new vocabulary with pictures and student-friendly definitions. Students engage in math chats with every Explore activity, and vocabulary acquisition is embedded within those classroom conversations. The My Math Thoughts sections provide students with the opportunity to complete sentence stems using academic vocabulary that is given in a word bank. The questions and word problems provided throughout the My Math Thoughts activity use precise mathematical vocabulary consistently and frequently. Students’ knowledge of academic vocabulary is assessed in the Show and Tell assessments, where students must understand and use precise mathematical language as they respond to prompts.
The materials provide scaffolding suggestions to support students with the development and use of academic vocabulary in context. The design of the lesson follows the “5E + IA” design model; lessons start with “Engage” activities, which build on prior knowledge and develop an anticipatory set; lessons progress to Explore activities, where teachers use dialogue to introduce new vocabulary through hands-on learning and within the context of the mathematical concepts. This model is consistent throughout the instructional materials. The “Explain” portion of the 5E model dedicates several parts to the direct teaching of new academic vocabulary. In the “Anchor Charts” portion and the “Picture Vocabulary” portion, students have the ability to listen to new academic vocabulary in context with the new material.
The instructional materials include ELPS strategies, which include sentence stems for language development and the use of academic language. The sentence stems are consistently embedded in every Explore activity throughout the instructional materials. Following Explore activities, to scaffold the use of academic vocabulary, there are Math Chats. Teachers prepare sentence stems and place them in a visible spot for students to use during the chat. Within each scope, a Picture Vocabulary section is located under the Explain tab. This provides students with an academic math vocabulary word and a picture that represents the definition. The instructional materials provide the option for teachers to print picture vocabulary cards; they can be used on a math word wall. Teachers can also virtually assign the cards to students.
The materials provide multiple opportunities for students to apply mathematical knowledge and skills to solve problems in new and varied contexts. They provide opportunities for students to solve grade-appropriate real-world scenarios by applying their knowledge and skills. They also include opportunities for students to analyze and interpret graphs in real-world settings. Students have the opportunity to use mathematics efficiently in real-world problems through the “Engage” “Hook” activities, “Explore” activities, “Problem-Based Tasks,” “Life Connections” activities, the “Math Stories,” and “Spiraled Reviews.” Each Explore lesson is embedded with a new, real-world topic that is developmentally appropriate for grade-level students. The lessons require students to integrate knowledge from previous Explore lessons to problem solve. When students interact with the “Accelerate” activities, they are able to use their knowledge and skills and apply them to real-world scenarios that are related to cross-curricular content. The “Math Today” activity and the “Connection Station” activity also apply math to real-world events.
The materials include a variety of different activities that require students to solve math problems in real-world scenarios. In Problem-Based Tasks, students work collaboratively to apply the knowledge and skills learned in the current scope to solve open-ended, real-world challenges. Students have the opportunity to integrate knowledge and skills that have been previously learned within the current scope and in previous scopes in order to solve new problems. Within the “Data Analysis” scope, the materials provide students with opportunities to analyze data through real-world problems. Each activity that students engage in connects them to a real-world scenario in some context.
Evidence includes but is not limited to:
The materials include opportunities for students to integrate knowledge and skills together to successfully problem solve and efficiently use mathematics in real-world problems. Within each component of the “5E+IA” model, students engage with real-world problems in multiple contexts. Each scope in the instructional materials begins with an “Accessing Prior Knowledge” activity and a “Foundation Builder” activity. These activities ask students to solve real-world problems based on prior knowledge from early childhood outcomes and kindergarten guidelines. Within the Engage component, students participate in a Hook activity that relates the new skill to a real-world concept. Within each scope, Explore activities require students to solve scenario-based story problems using concrete and representational methods. Each Explore lesson is embedded within a new real-world context that is developmentally appropriate for first grade students. Each Explore lesson also has a different scenario that requires students to integrate knowledge from previous Explore activities to find a solution to the new problem.
Each scope uses the knowledge from the previous explore in order to support students to solve the problems in the new Explore activity. As students progress through the Explore activities within each scope and through the scopes throughout the year, they must integrate knowledge and skills to make sense of specific contexts and solve problems. For example, in the scope related to three-dimensional solids, students progress through five different Explore activities. Each scope uses the knowledge from the previous Explore in order to support students to solve the problems in the new Explore activity. Before students engage in the Explore activities, they complete the “Skill Basics” lesson to ensure they know how to label edges, faces, and vertices. Once students have completed this, they begin by sorting 3D solids, and then classify 3D solids. Next, students determine the relationships between triangular prisms and rectangular prisms as well as the relationships between cubes and rectangular prisms. Finally, students practice composing 3D solids. These Explore activities integrate the knowledge and skills from the previous activities in order to support students as they move through their conceptual understanding of sorting, classifying, and composing 3D solids. In addition to the Explore activities, a variety of activities require students to use their skills to solve different real-world scenarios. In Problem-Based Tasks, students work collaboratively to apply the knowledge and skills they have learned in the current scope to an open-ended, real-world challenge. Math Today lessons provide real-world videos and images that relate to the scopes. Parent letters in the scopes provide real-world opportunities for parents to complete activities with their child, such as using the tic-tac-toe boards.
The materials provide students opportunities to analyze data through real-world contexts. These can be found within the Data Analysis scope for second grade. This scope builds upon what was mastered in first grade. Students now chart data using intervals of 2, 5, and 10. They also use keys to represent items in picture graphs and create graphs with collected data using the TALK method. In second grade, students engage in four different Explore activities related to analyzing data in real-world contexts. In addition to the Explore activities, Life Connections include opportunities for students to analyze data from real-world contexts. Life Connections introduce students to careers and everyday life experiences that highlight the math concepts being taught in the scope. In the Data Analysis scope, students watch a video that highlights a scientist who analyzes data from space. After watching the video, the teacher facilitates a discussion with questions such as “How does an analyst use the data he/she is given to draw conclusions?” “Why is it important for the data to be shown and presented in an easy way?” and “How does a scientist use math when interpreting data?” After the discussion, students pretend to be a scientist from the video. Their job is to organize the data an astronaut brought back from space and to draw conclusions based on the data. When they are finished creating their graph, students write down one or two conclusions they drew from the graph to share with the class. This is the same Life Connections activity used in the first Data Analysis scope.
In this scope, students also participate in a Problem-Based Task to help their teacher determine which type of class pet to select. Students determine how they want to collect the data; then, they survey their classmates to vote for a class pet. Afterward, students display the data collected in both a pictograph and bar graph. Finally, students create two questions about the data using addition and subtraction.
The materials include cited research in the curriculum that supports the design of the materials and the teacher and student resources. Materials are supported by current and relevant research on how students develop mathematical understandings. The research is cited and is linked to the publisher’s design model and recommendations. The “Math Research and Philosophical Approach” document provides educators with an explanation of research used to design the program and where the research-based materials can be found within the program. The “Content Support” section provides teachers with research-based guidance for instruction that enriches their understanding of mathematical concepts. Cited research is current, academic, and relevant to skill development in mathematics. Teachers can find support in teaching the process standards in the “Teacher Toolbox.” A bibliography is present.
Evidence includes but is not limited to:
The materials include cited research throughout the curriculum that supports the design of teacher and student resources. The “Math Research and Philosophical Approach” document, located in the Teacher Toolbox, cites research to support the design of the teacher and student resources. Some of the topics in this document include conceptual learning, number sense, computational fluency, and learning in a real-world, relevant context. There is a research summary, excerpt, and “Math Element” for each topic of design. For example, the document describes the program’s concrete-representational-abstract (CRA) approach. First, it provides an explanation of the research studied regarding the CRA approach and how it benefits students learning. It states that when students are first learning a new skill, they should use carefully selected concrete materials to develop their understanding of the new concept. Next, students begin to use pictorial representations that mirror their work with concrete models. Finally, students learn to translate these models into abstract representations using symbols and algorithms. This summary of the CRA approach to learning is supported with citations from Special Connections, 2005.
The materials embed the “Process Standards” within every scope and activity. In the Teacher Toolbox, for every process standard, materials provide the research, the meaning behind the standard, and how to apply it within the materials. For example, the materials address the process standard related to communicating mathematical ideas and their implications. The materials provide information on understanding the standard, along with relevant research from the National Council of Teachers of Mathematics (NCTM) and Van de Walle. The materials cite the research provided from the field of mathematics and explain how that research applies to the components of the materials. After describing how the process standard can be used within grades K-5, at the end of the process standard description, materials provide a summary. This summary includes a research statement from Van de Walle in addition to the overall summary and views of the materials.
The materials provide research-based guidance for instruction that enriches educator understanding of mathematical concepts and the validity of the recommended approach. In the Teacher Toolbox, there is a “Research and Philosophical Approach” chart that links the research with sections of the publisher’s “Math Elements.” The summary of the “Fact Fluency,” “Explore,” and “Decide and Defend” portions of the program quotes Marilyn Burns’ book About Teaching Mathematics (2007). The discussion on using picture vocabulary to attach new worlds to prior knowledge and basic communication using academic vocabulary references Vygotsky (1962) and ACSD (2008). The embedding of the ELPS strategies and the Explore activities are supported by Francis, Rivera, Lesauz, Kieffer & Rivera (2006). For example, materials provide the rationale behind including conceptual understanding and number sense. They state that students are more likely to retain and apply mathematics if they understand how and why different procedures work. Establishing conceptual understanding and number sense routines helps students understand the “why” behind other mathematical concepts. This philosophy about conceptual understanding and number sense is justified with a citation of Marilyn Burns’ About Teaching Mathematics and Laney Sammons’ Guided Math. Additionally, the mathematics instructional philosophy document explains the program’s Math Elements that support conceptual understanding and number sense.
Also in the instructional philosophy document, materials provide the rationale behind the importance of teachers’ and parents’ content knowledge as it can be found in the instructional materials. The materials state: “The ability of teachers and parents to help students understand math is limited by their own basic understanding.” The materials explain that many parents and teachers learned math differently than how it is currently taught and that it is important to provide them with content knowledge. The materials cite research conducted by the NCTM as well as Marilyn Burns’ text About Teaching Mathematics to justify their philosophy about the importance of content knowledge for teachers and parents.
The cited research is current, academic, relevant to skill development in mathematics, and applicable to Texas-specific context and demographics. The research cited in the materials includes sources that are well-known for research and practice in the field of mathematics. Many pieces of cited research are published by the NCTM, which, according to their website, is the world’s largest mathematics education organization. Additionally, the research resources provided include many current articles and publications that address current mathematics teaching. For example, research surrounding the ideas of promoting equity within the mathematics classroom includes research published by Boaler and Staples in 2008, research published by Boaler in 2016, and research published by the NCTM in 2012. The materials were created by Rice University, located in Texas, after the success of the publisher’s science program. According to the “New Teacher Navigation Guide,” the materials were developed by teachers, for teachers.
A bibliography is present. Materials on research listed in the instructional philosophy document contain a bibliography citing several researchers and organizations, including Marilyn Burns, Jo Boaler, the NCTM, and Laney Sammons. There is also a bibliography that cites research presented throughout the instructional materials, which can be found in the Teacher Toolbox. Additionally, at the end of each component dedicated to the mathematics process standards, the materials cite the research and resources that were used in the rationale and explanation.
The materials guide students in developing and practicing the use of a problem-solving model that can be transferred across problem types. In “Skill Basics” lessons, students learn the problem-solving model they will use throughout the scopes and when solving problems. The materials also prompt students to variously apply a problem-solving model in context throughout the year. The “Content Support” and “Process Standard” documents provide teacher guidance pertaining to problem solving-models as well as support and prompt student reflection on approaches to problem solving. After each “Explore” lesson, the teacher facilitates a “Math Chat” where students discuss their learning and share how they solved the problem.
Evidence includes but is not limited to:
The materials guide students in developing and practicing the use of a problem-solving model that is transferable across problem types and grounded in the TEKS. The materials state that teachers should provide opportunities for students to analyze given information, formulate a plan or strategy, determine a solution, and justify and evaluate the process or strategy and reasonableness of a solution. Additionally, the materials state that students need multiple opportunities to share in pairs, small groups, or with the whole class in order to challenge or argue a solution or strategy. In prior grades, students learn multiple strategies to independently solve problems, such as pictorial models, number lines, ten-frames, and number bonds. In second grade, materials introduce students to a problem-solving model explanation sheet, where students are reminded about identifying the important information, using a plan or strategy, finding a solution, and justifying their answers. The teacher explains the model and models how to use it correctly. Teachers encourage students to use this as a reference when solving word problems.
Each Explore activity develops problem-solving skills. Each scope provides several Explore activities that focus on problem solving through the use of concrete and representational models. Students practice these skills in Skill Basics activities, which are embedded in each scope. For example, in Skill Basics, students practice using ten-frames, number lines, or hundreds charts as problem-solving tools. Each scope has a “Problem-Based Tasks” section that poses a real-world problem; students must analyze it, formulate a strategy with a group, create a problem-solving model, and then determine and justify their answer through dialogue with their group. Each Problem-Based Task also has a “Think About” question that requires students to reflect on the reasonableness of their response and elaborate on other ways that they could have solved the problem.
The materials prompt students to apply a transferrable problem-solving model. Within each scope, in the “Explain” tab, materials provide descriptions and examples of usable anchor charts. The class creates the anchor charts together and uses them as a reference tool throughout the scope. Each scope in the instructional materials includes an anchor chart example that models problem solving and can be used as a quick reference for students. In addition, each Explore activity in the instructional materials comes with a “Student Journal.” The journal prompts students to apply the problem-solving model they are learning within that lesson. In most instances, there is a template of the problem-solving model in the student journal. The Explore lessons include guiding questions for teachers to use to support students in learning the model.
The materials provide guidance to prompt students to reflect on their approach to problem solving. In the “Hook” activities within the “Engage” component of the materials, students are asked to consider what they already know, consider what information they need to find out, discuss solutions to the problem, and justify their responses. “My Math Thoughts” are journal prompts that provide students with the opportunity to write out their mathematical thoughts and ideas using several different avenues. These activities prompt students to reflect on their approach to problem solving. My Math Thoughts are in each scope, and students are tasked with using the problem-solving skills taught in the lesson to solve a problem before completing a reflection. The reflection asks students to circle how they feel about different problem-solving skills presented in the unit. The options that students can circle include “I got it!” “Almost there!” and “Not yet!” Questions on different levels accommodate all students as they reflect on what they are learning and how they use strategies to solve their problems. Reflective questioning suggestions include “What did you notice?” “Is there a different way to count out your crackers?” “Is there a math tool you could use?” Although it is not consistent throughout each piece of the instructional materials, there is an opportunity for students to reflect on the problem-solving model that they are using. This reflection seems to focus more on the student’s ability to use the skill as opposed to how effective the skill was as a problem-solving resource.
The materials provide teachers with examples of how to introduce and explain the correct use of the manipulatives. Within the scopes, the materials provide multiple opportunities for students to learn how to use the various mathematical tools that are available. This includes both hands-on and virtual manipulatives. Students can select whether they want to use hands-on manipulatives or virtual manipulatives. Students can also select which manipulatives they want to use when completing the “Math Thought” activities; on occasion, they can select the tools they want to use during “Explore” activities. Virtual manipulatives are available within most scopes for students to use when completing activities. Material lists are explicitly provided for each scope and each activity, although there is not a specific rationale behind why each manipulative was selected. However, the “Teacher Toolbox” provides information within the process standard regarding intentional tool selection that helps teachers understand why particular tools are selected for different scopes and activities.
Evidence includes but is not limited to:
The materials partially provide opportunities for students to select and use real objects, manipulatives, representations, and algorithms as appropriate for the stage of concept development, grade, and task. They provide students opportunities to learn to use grade-appropriate tools for solving tasks and understanding concepts. For example, in the scope related to representing numbers to 1,200, students are expected to use tools such as base-ten blocks during the Explore activities. The materials provide a “Skill Basics” lesson on how to use this tool in order to prepare students for the following scope activities. This lesson ensures that students use the tools appropriately for solving tasks and understanding concepts. During this lesson, the teacher introduces each type of block and what it represents in numbers. For example, the teacher says, “This is a unit. It represents one. It is just like one linking cube.” Then the teacher uses the base-ten blocks to model the number 231. Students have time to use their own base-ten blocks to create the number 231; they answer questions such as “How can we compose 231?” and “Is there another way to compose this number?” Students then have the opportunity to practice using the base-ten block tool in order to create other numbers and explain their process when using the tool. Students also practice taking a set of base-ten blocks, determining the number they represent, and writing that number in standard form.
Although students are not always allowed to select their own grade-appropriate tool for solving tasks, there is an embedded portion that allows for student choice. Many of the Explore activities are guided and provide teachers with instructions on which tool to provide for students; however, in the “Show What You Know” activities, students apply the knowledge and skills learned during the Explore using the tools that they select.
The materials provide opportunities for students to select and use technology (e.g., calculator, graphing program, virtual tools) as appropriate for the concept development and grade. Most scopes have virtual manipulatives that students can use during Explore lessons. Virtual manipulatives related to the scope are found under the Explore tab. Each virtual manipulative has a video tutorial teachers use to model the correct use of the manipulative. When applicable, Explore activities prompt teachers to “go digital.” This means that teachers can assign each student a virtual manipulative, rather than a concrete manipulative, to use as a support throughout the activity. For example, in Explore 3 of the “Represent Numbers to 1,200” scope, students explore counting collections with base-ten blocks and a place-value chart. The lesson includes virtual base-ten blocks and a virtual place-value chart that students can use to complete the task. The instructional materials also provide an “Interactive Practice” that allows students to use technology to solve virtual real-world problems that are designed to look like a game. The Interactive Practice combines math problem solving and technology in a real-world scenario.
The materials provide teacher guidance on tools that are appropriate and efficient for the task. The instructional materials have a Teacher Toolbox that contains a portion titled “Intentional Selection of Tools and Techniques to Solve Problems.” This portion provides teachers with some background knowledge of common tools used in various grade levels. Each scope also contains a “Content Support” section on the “Home” page. This section explains which tools are appropriate and efficient for the unit. Each Explore lesson contains a materials list, so teachers know which tools are appropriate and efficient for the task. The list states how many of each manipulative will be used in the activity and when to use them during the activity. For example, in Explore 5 of the “Three-Dimensional Solids” scope, students use manipulatives to create 3D solids. The lesson plan states that each group needs one piece of construction paper, one cup of mini marshmallows, one container of dough, thirty-five toothpicks, thirty-five coffee stirrers, ten chenille stems, and one roll of tape. Students read direction cards to find out which shape to build. For example, students are prompted to create a block with six vertices, nine edges, and five faces, with three faces that are rectangles and two bases that are triangles. Students choose from their set of manipulatives to build the solid.
The materials provide a variety of opportunities for students to select problem-solving strategies that are appropriate for the work, concept development, and grade. In addition, the instructional materials provide teachers with guidance, support, and general background knowledge on various strategies and their importance. Many activities ask students to reflect on their chosen strategy versus a different strategy; some even ask students to solve one problem using multiple different strategies. The “Content Support” section explains the different strategies students will learn throughout the scope and how to develop the use of those strategies across different activities. Students learn a variety of strategies throughout a scope that can be used to solve a class of problem types. The “Explore” lessons provide students with opportunities to apply multiple strategies to solve a problem.
Evidence includes but is not limited to:
The materials prompt students to select a technique as appropriate for the grade level and the given task. The “Daily Numeracy” component ensures that all students participate and engage as mathematical thinkers. The goal is to empower students to reason with numbers in an accurate, efficient, and flexible way. The class gathers as a whole group in a central location where the teacher displays a numeracy activity. The students think about what they see and how they will solve the problem mentally. Throughout, the instructional materials often guide students to use generalization and abstraction techniques as they explore new concepts and apply them to new contexts. For example, each scope has several Explore activities. These activities prompt students to use various problem-solving skills and techniques. “Math Chat,” embedded in each Explore activity as a closure, provides opportunities for students to share problem-solving techniques. The materials also support students in selecting techniques that are appropriate for their grade level. For example, because the instructional design follows the “5E” model, students are allowed to explore a variety of problem-solving techniques, including estimation and number sense, prior to completing the “Explain” portion of the lesson. The Explain portion of the lesson provides an opportunity for students to showcase their learning and to explain their mathematical ideas.
The materials support teachers in understanding the appropriate strategies that could be applied and how to guide students to more efficient strategies. The materials support teachers in understanding which strategies are appropriate for solving tasks within various scopes. Teachers have supports for their own understanding and for guiding students to understand which strategies are needed for problem solving. Materials also provide questions that help guide discussion with students as they self-select methods for solving. The materials and objectives progressively build to encourage students to solve more efficiently. The support document explains where students should be in their knowledge acquisition for the content and the strategies students should be using based on their current level of development and age. For example, in the scope related to addition and subtraction strategies and algorithms, the materials state that at this stage in development, students focus on the operations of addition and subtraction. They explain that students will move away from concrete representations as they utilize algorithms, properties of operations, and mental math strategies to solve problems. The Content Support document provides the teacher with mental math strategies that help students determine sums and differences without the use of pencil and paper. The document states that once students become fluent using the mental strategies, teachers can introduce the traditional algorithm, relating the steps in the algorithm to the steps in the strategies already learned. Students build the algorithm by using concrete and pictorial models; they connect the concrete model to the pictorial model to the abstract model in order to make meaning of the algorithm. The materials state that if students move too quickly through these models, they will lose their number sense, so it is important to take time to ensure that students are ready to move to the next model.
The “Mathematics Instructional Philosophy” document, provided within the “Teacher Toolbox,” explains that as students progress through the Explore activities within a scope, they transition from hands-on experiences with concrete objects to representational, pictorial models and ultimately arrive at symbolic representations using only numbers, notations, and mathematical symbols. The layout of the Explore activities and the sequence in which they are taught support teachers as they guide students towards increasingly efficient strategies.
The materials provide opportunities for students to solve problems using multiple appropriate strategies. In the “Addition and Subtraction Problem Solving” scope, students learn to solve a variety of one- and multi-step word problems using concrete objects, strip diagrams, number lines, and a problem-solving model. In Explore 1, students solve addition and subtraction word problems within 1,000 using a variety of strategies, including base-ten blocks and a place-value chart. In Explore 2, students use strip diagrams or number lines to solve one-step addition and subtraction word problems; they read each word problem and decide which strategy to use to best solve the problem. Students record their chosen model in their student journals. The skills learned in Explore 1 and 2 are applied to Explore 3 and 4, where students solve multi-step word problems using objects, strip diagrams, or number lines. These strategies are used to solve a variety of problems throughout the scope. Within the materials, students consistently come across problems that provide the opportunity to solve using multiple appropriate strategies. For example, every Explore activity opens with a scenario that is related to the concept that is being practiced. These activities include very little teacher-led instruction and involve students in discovering learning through solving problems. Students are not expected to use just one way of solving problems, and they have time to share their strategies with other students in the class.
The materials develop students’ self-efficacy and mathematical identity by providing opportunities to share strategies and approaches to a task. The materials are designed so that students complete most activities with a partner or in a group. Students share ideas and learn from each other as they explore new concepts. All students have an opportunity to participate and engage as mathematical thinkers during their collaborative work. The materials include tasks that support students in productive struggle as they learn concepts. The materials also support and guide teachers in facilitating the sharing of students’ approaches to problem solving. This is done through information provided in the “Content Support” document, which describes how to support students in selecting strategies to solve problems related to the concepts and provides the teacher with multiple question stems and prompts in order to support students both during and after activities. In addition, embedded “Facilitation Points” provide teachers with guidance and support. Materials provide sample responses as an added layer of support for teachers.
Evidence includes but is not limited to:
The materials support students to see themselves as mathematical thinkers who can learn from solving problems, make sense of mathematics, and productively struggle. The “Daily Numeracy” component ensures that all students participate and engage as mathematical thinkers. The goal of Daily Numeracy is to empower students to reason with numbers in an accurate, efficient, and flexible way. The class gathers as a whole group in a central location where the teacher displays a numeracy activity. Students think about what they see and how they will mentally solve the problem. Students use hand signals to indicate if they are still thinking, if they have one strategy, or if they have more than one strategy. Once everyone has at least one strategy, the teacher facilitates a conversation about the strategies the students came up with. The Daily Numeracy lesson plan describes the environment of the classroom as an accepting and safe sharing environment. Students should feel and believe that it is a risk-free environment where making mistakes and diverse thinking are expected parts of the learning process. Materials provide students with tasks to solve in order to struggle productively and learn the content through their experiences. Each scope begins with a “Hook”; it sets the stage for learning a new skill by presenting a problem that students cannot yet solve. Students then move to the “Explore” tasks, where they work in groups to explore concepts through problem solving. For example, in the activity titled “Chips in a Bag,” materials present students with a problem that they do not know how to solve. Through guiding and reflective questions, students share ideas and discuss information before solving. Afterward, independent activities such as journaling and exit tickets provide students opportunities to apply what they have learned.
The materials also provide opportunities for students to see themselves as does and thinkers through the use of scenario-based problem solving. Each unit or scope has scenarios that the teacher reads aloud or shares with the class; in these scenarios, students imagine themselves in the role of the problem solver. These scenario-based story problems are targeted to reach all students and provide opportunities for all students to see themselves as mathematical thinkers.
The materials support students in understanding that there can be multiple ways to solve problems and complete tasks. Within each component of the scope, students receive tasks that are designed to allow for multiple pathways to a solution. For example, within the “Engage” component, students complete the Hook activity where they listen to a scenario and answer a question using any preferred strategy. Students use their prior knowledge and conversations with a partner in order to determine a solution to the problem. Teachers also encourage students to share their thinking and strategies with their classmates.
“Life Connections” activities introduce students to careers and everyday life experiences that highlight the mathematical concepts they are learning in the classroom. For example, in the scope focused on data analysis, Life Connections highlights the career of a scientist who analyzes data from space. Students discuss why it is important for the data to be presented in a simple way, how an analyst uses data to draw conclusions, why an analyst’s job is important for astronauts and other scientists, and whether or not this would be a career that students are interested in. These activities relate the math skill to real-world activities and careers.
Materials support and guide teachers in facilitating the sharing of students’ approaches to problem solving. In several instances, materials encourage the use of divergent solution strategies. This can be seen through the scripted scaffolding opportunities and teacher questioning as students problem solve. Facilitation Points and guidance in the lesson provide support for monitoring students as they develop solution strategies. Facilitation Points also provide sample student responses to guide students as they problem solve. Sample student responses are written in red throughout the instructional materials, where there are opportunities for students to engage in problem-based tasks and hands-on activities. For example, as students engage in Explore activities, materials provide question stems to give to students as they work and after they complete the activity. These questions prompt students to consider the strategy they are using, to determine why they used the strategy, and to consider whether or not there is another way to solve the problem. In the scope related to addition and subtraction strategies, students engage in an Explore activity where they practice representing and solving one-step word problems pictorially. As students work, the teacher asks provided prompting questions; materials also provide possible student solutions for the activity.
The materials provide students an opportunity to communicate mathematical ideas and solve problems using multiple representations. The materials prompt students to effectively communicate mathematical ideas, reasoning, and their implications using multiple representations. During “Explore” activities, students communicate mathematical ideas through concrete objects, pictorial models, numerical expressions, and verbal discussion. The materials also guide teachers in prompting students to communicate mathematical ideas and reasoning in multiple representations, including writing and the use of mathematical vocabulary. After each lesson, students communicate their ideas orally through a teacher-facilitated “Math Chat.” The materials guide teachers in prompting students to communicate mathematical ideas and use mathematical vocabulary. Each lesson plan includes prompts for teachers to use to guide students in their learning and to reflect on the activity once it is complete. Each lesson plan includes facilitation points that guide teachers in developing students’ mathematical vocabulary. The “Content Support” documents give teachers suggested prompts in order to engage students in discussion about their mathematical ideas.
Evidence includes but is not limited to:
The materials provide students opportunities to communicate mathematical ideas and solve problems using multiple representations, as appropriate for the task. Students communicate using multiple representations and precise mathematical language throughout the program. For example, in each scope, during Explore tasks, students draw representations and explain their thinking on their “Student Journal” pages. The “Facilitation Points” in the Explore lessons guide teachers in asking guiding questions, introducing new vocabulary, and recording ideas on the Student Journal page. These opportunities for students to use representations to organize and show their thinking are evident throughout the instructional materials.
In Explore 5 of the “Represent Numbers to 1,200” scope, students communicate their ideas with their partners, teacher, and class throughout the duration of an activity, as they determine whether a number is even or odd. Students pretend they are zookeepers and are feeding the animals. Each station has a story mat, which depicts two animals, and a given number of linking cubes, which represent the food. With their partners, students distribute the food evenly between the two animals and place any leftover cubes on the bottom of the mat. While students are working, they discuss how much food is given to each animal and if there is any leftover food; the teacher monitors the students and checks for understanding by asking guiding questions included in the lesson plan. These questions include “How many total pieces of food are there?” “How many pieces of food did you feed to each animal?” “How many leftover pieces of food are there?” and “Is the total number even or odd? How do you know?” As students work, they create pictorial models in their journals to communicate their ideas. Students record the total number of pieces of food, draw how many pieces of food each animal will eat, and write the number of leftover pieces of food. Then, students answer the question “Is the starting total even or odd? How do you know?” After the activity, the teacher facilitates a Math Chat using provided prompts. The prompts include questions such as “How many pieces of food were at each station?” “Are these numbers odd or even?” “What did you notice about the odd numbers when sharing the pieces of food between the animals?” “What did you notice about the even numbers when sharing the pieces of food between the animals?” “What rule can be applied to even numbers?” “What place value in a number determines if the number is odd or even?” and “When might we use even and odd numbers in real life?”
The materials guide teachers in prompting students to communicate mathematical ideas and reasoning in multiple representations, including writing and using mathematical vocabulary, as appropriate for the task. Prompts support students with multiple representations throughout the instructional materials. For example, in the Explore activities, students use concrete, representational, and abstract methods to solve various tasks. These activities are designed for student discovery, and, in turn, they rely heavily on the teacher’s prompting questions.
The instructional materials also have a portion designed explicitly for academic vocabulary and they provide vocabulary picture cards, which can be used for a word wall in the classroom. Students also have opportunities to use the academic vocabulary in Math Chats, guided by teacher prompts. Teachers receive guidance and specific questions in the Facilitation Points of the lessons. These questions are used to guide students as they participate and explore. Math Chat questions are used after students have completed the lesson so that they can share their findings and observations.
For example, in the scope focused on multiplication, students engage in an Explore activity where they model and describe multiplication. During the activity, teacher prompts support student reasoning as students are working. Some of the questions include “How did you solve this problem?” and “How did you figure out the total?” After the activity, during the Math Chat, more teacher prompts support students’ reasoning with multiple representations; they include “What did you need to know to solve each problem?” and “What did you notice about the different strategies used to determine the total number of each item?” In the scope related to comparing and ordering numbers, once students have completed a “Skill Basics” lesson, the teacher guides them through the Explore activity to practice comparing and ordering numbers using academic vocabulary and symbols, such as greater than, less than, and equal to. In the Math Chat, teachers use prompting questions such as “What does the < symbol mean?” “What does the > symbol mean?” and “What does the = symbol mean?” The materials also support teachers to guide students struggling with the concepts of greater than and less than. They recommend reviewing vocabulary with examples and non-examples, saying phrases such as “Greater means more. What does less mean?” Students receive sets of pictures or items and label them as greater than or less than and explain how they know. Materials encourage teachers to ensure that language and vocabulary are parallel throughout the entire lesson.
The materials provide opportunities for students to engage in mathematical discourse in a variety of settings. Students engage in whole group discussions during “Hook” activities as well as during “Math Chats,” after completing “Explore” activities. Students engage in small group discussions during “Problem-Based Tasks” and during some “Elaborate” activities, such as “Fluency Builders” and “Life Connections.” Students also engage in partner discussions during Explore activities, Fluency Builder games, and “Acceleration” activities. The materials integrate discussion throughout to support students’ development of content knowledge and skills as appropriate for the concept and grade level. Students actively engage in discussing their mathematical thinking in all components of each scope; teachers model mathematical language, which is built into the conversations. Materials guide teachers in structuring and facilitating discussions as appropriate for the concept and grade level. Teachers receive guidance through the “Teacher Toolbox”—specifically with the process standards and “Communicate” math component. Materials suggest hand signals, possible sentence stems, and questions for teachers to use throughout the scopes.
Evidence includes but is not limited to:
The materials provide opportunities for students to engage in mathematical discourse in a variety of settings. The materials intentionally provide opportunities for students to engage in mathematical discussions in a variety of different groupings. Students have multiple opportunities to engage in discussions with partners, small groups, and the entire class based on the activity and setting of the lesson. Each scope opens up with a Hook activity in which students are given an engagement piece to introduce the scope. Explore tasks encourage small group time to problem solve. Each lesson provides instructions on how the teacher should group students. Grouping possibilities range from pairs of student groups to groups with five students. While in small groups, the teacher facilitates the Math Chat questions to determine mastery. Throughout the lessons, students share their thinking with a neighbor and also have opportunities for whole group discussion. Intervention and acceleration tasks are conducted in small group settings, giving students the opportunity to engage with other students and the teacher and have mathematical discussions. In those small groups, students discuss the task with one another and respond to prompts provided by the teacher to move along their mathematical thinking. At the end of the lesson, the teacher orchestrates a whole group discussion with the class based on observations conducted during the small group. The teacher records individual student responses through conversations, journal responses, and “Show What You Know” assignments.
The materials integrate discussion throughout to support students’ development of content knowledge and skills as appropriate for the concept and grade level. Students have opportunities to discuss mathematical ideas throughout the program. Materials provide teachers with specific facilitation points and guiding questions that can be used to facilitate this level of mathematical discourse. Opportunities are embedded with discussions in all phases of concept and skill development. Each Explore lesson includes opportunities for discussion in all phases of the activity. At the beginning of the lesson, the teacher reads a scenario to the class. In groups or partners, students discuss how they will solve the problem. While students are working, the teacher monitors the students and asks guiding questions. At the end of the activity, the teacher facilitates a Math Chat using prompts included in the lesson plan.
For example, in Explore 1 of the “Numbers on a Number Line” scope, students locate and write the positions of numbers on an open number line. At the beginning of the lesson, the teacher reads a scenario about a family driving to the beach. Teachers prompt students to help the family mark the rest stops for the trip; in groups, students discuss the scenarios and explore the manipulatives for the activity. As students work, the teacher monitors the class and asks guiding questions to check for understanding. Questions include “Why did you place that rest stop number there?” “What helped you decide where to put that number?” and “What is the distance between those numbers?” At the end of the activity, the teacher facilitates a Math Chat where students discuss what they learned in the activity. Prompts include “Which number did you place on the number line first? Why?” “Which number did you place next?” “Did you move any numbers after placing other numbers?” and “What strategies did you use as you placed numbers on an open number line?”
The materials guide teachers in structuring and facilitating discussions as appropriate for the concept and grade level. In the Teacher Toolbox, there is a tab designated for communicating math. Within that tab, teachers have guidance to support students in the elements of discourse, making connections, questioning, representations, and writing. According to the materials, discourse is an oral exchange of ideas or a conversation between two or more students. It provides students the opportunity to share ideas with others in order to solve problems, increase learning, or express opinions. Discourse may take place around mathematical concepts, procedural knowledge, or problem-solving processes and solutions. Discourse can take place in a whole group setting, small groups, or partner groups. Materials provide teachers with clear expectations in order to facilitate discourse in the K-2 classroom. These expectations include the following ideas: modeling discourse interactions for students to have a clear understanding of what discourse is and what it sounds like; allowing students to use tools or models necessary to help with their expectations; providing sentence stems to help scaffold language; allowing adequate wait time after asking a question or hearing a response; ensuring each student contributes to the discussion with clear and organized thoughts and ideas; actively listening by making eye contact with the speaker and asking questions; including accurate academic math vocabulary; and presenting and explaining ideas, reasoning, and representations in pairs, small groups, or the whole class.
Each lesson plan includes prompts for teachers to use throughout the lesson, facilitations points on when to ask the prompts, and sample student answers to guide the discussion. The facilitation points instruct teachers to invite the class to a Math Chat to share their observations and learning after the activity. The “Daily Numeracy” component ensures that all students participate and engage as mathematical thinkers. The goal of Daily Numeracy is to empower students to reason with numbers in an accurate, efficient, and flexible way.
The teacher materials foster students to justify their reasoning. They also help teachers establish a math routine. Materials provide opportunities for students to construct and present arguments to justify mathematical ideas using multiple representations. Students are able to justify their thinking using concrete manipulatives, pictorial models, equations (when necessary), and oral explanations. Students have the opportunity to justify and defend their thinking frequently throughout the scopes, particularly when completing “Explore” activities. Students can also present and justify their thinking through activities such as “Math Thoughts” and the show-and-tell assessment. The materials also assist teachers in facilitating students to construct arguments using grade-level appropriate mathematical ideas. Question stems throughout the materials help teachers facilitate conversations with students that allow them to justify and defend their thinking. Additionally, in the “Daily Numeracy” scope, provided teacher tools such as hand signals and sentence stems support students as they defend and justify their thinking in a productive way.
Evidence includes but is not limited to:
The materials provide opportunities for students to construct and present arguments to justify mathematical ideas using multiple representations. Problem-solving activities lead students to justify their reasoning verbally and in written form. Students have the opportunity to complete a “Decide and Defend” activity in each scope. These activities are open-ended assessments that prompt students to reason mathematically and support their ideas with evidence. Students show their work using a pictorial model and justify their answers in writing. For example, in the “Compare and Order Numbers” scope, students must describe a counting rule that is used in a problem. The question states that two characters were playing a game where they each had to choose a rule and count according to that rule. The first player has the numbers 918, 908, 898, 888, 878, and 868. The second player has the numbers 432, 532, 632, 732, 832, and 932. Students have to determine the rule each player used and describe their reasoning for each player’s rule. Teachers use a rubric to assess each student’s understanding of the problem, computation, and reasoning.
The materials assist teachers in facilitating students to construct arguments using grade-level appropriate mathematical ideas. Provided procedure and facilitation prompts help teachers guide students to establish routines and encourage discussion. The “Teacher Toolbox” guides teachers on facilitating the process standard of displaying, explaining, and justifying mathematical ideas. According to the materials, this standard focuses on students validating their conjectures and conclusions with displays, explanations, and justifications, with emphasis on mathematical ideas and arguments. The materials also state that problems provide a context in which students may draw conclusions and support mathematical ideas or arguments with their evidence. In order to foster these justifications and explanations in the mathematics classroom, the materials encourage teachers to provide problems and tasks that engage and challenge students, providing productive struggle; provide a variety of tools and techniques for students to use to investigate their understanding of the mathematical ideas; and allow students’ work to be visible in written or oral form. Materials also state that teachers should support students’ conceptual growth by facilitating questions to help them organize their thoughts as they display and explain or justify their mathematical ideas using appropriate mathematical language. They should expect mathematical idea arguments and promote a productive discussion environment, and they should continually work toward helping students make real-world connections as they engage in the task.
The Daily Numeracy component ensures that all students participate and engage as mathematical thinkers. The goal of Daily Numeracy is to empower students to reason with numbers in an accurate, efficient, and flexible way. After students formulate at least one mental strategy, the teacher facilitates a conversation about the strategies the students came up with. Students first share their ideas with a partner, and then with the whole class. Students learn from each other as they listen and respond to their peers’ problem-solving strategies. To show that they agree with another student’s response, students put their pinky finger and thumb out and shake it back and forth. Teachers also invite students to respectfully disagree with another student’s response. The Daily Numeracy lesson plan includes prompts for teachers to use to guide students in justifying their answers. Some prompts include “Explain how you…” “How do you know your answer is reasonable?” “How can you explain this differently?” “Can you justify/defend how you...?”
Within the Explore activities in the scopes, teachers use the provided question stems to promote students in justifying their mathematical thinking and processes. Questions include “How did you solve this problem?” “Is there another way you can solve this problem?” “When is a good time to use this strategy?” and “What is similar/different between the way you solve the problem and how your neighbor solved the problem?”
The materials include a variety of diagnostic tools that are developmentally appropriate; for example, diagnostic tests (formal assessments) are given three times a year. The materials also include other formal assessments at the end of each scope, such as the “Show-and-Tell” assessment and the “Skills Quiz.” Additionally, the materials provide informal assessments to help guide teacher instruction, such as observations during prior-knowledge activities and an observation checklist for each scope. The materials provide guidance on the administration of formal and informal assessments. Students have the opportunity to reflect on their understanding of concepts within a scope during the “My Math Thoughts” activity, and the materials provide the opportunity for students to set goals and track and monitor progress on those goals or their mastery of various standards. Diagnostic tools are presented to measure all content standards.
Evidence includes but is not limited to:
The materials include a variety of diagnostic tools that are developmentally appropriate. Materials provide teachers with an array of assessments ranging from anecdotal notes and checklists to formal assessments administered three times a year. In second grade, there are formal assessment tools, such as the “Pre-Assessment,” “Mid-Year Assessment,” and the “Post-Assessment.” Students complete the Pre-Assessment to determine what they remember from the previous year’s standards. This allows teachers to identify knowledge gaps before attempting to build on that knowledge throughout the year. The second grade Pre-Assessment assesses students’ knowledge of skills taught in first grade, such as knowledge of place value, comparing numbers, solving contextual word problems, and describing attributes of 2D shapes and 3D solids. About halfway through the year, students complete a Mid-Year Assessment to monitor their progress and track growth. Finally, students complete an end-of-year Post-Assessment that evaluates all grade-level standards, including, but not limited to, knowledge of place value to 1,200, comparing numbers, using open number lines, and contextual division. Each assessment provides class performance analytics, standard analysis, item analysis data, and a personal quantile measure for each student, which can be used to inform instruction. The “Benchmark Assessments” home screen provides guidance on how the assessments function. Informal assessments are noted within the scopes and include facilitation points for the teacher. Students are able to show their knowledge in a variety of ways, such as journal entries, verbal communication, modeling with concrete manipulatives, formal assessments, exit tickets, and skill-builder assignments.
The materials partially provide guidance to ensure consistent and accurate administration of diagnostic tools. Each diagnostic tool includes facilitation instructions for teachers to follow as they administer formal and informal assessments. For example, the “Show What You Know” assessments are independent practice assignments that give students an opportunity to demonstrate their learning after scope activities. In the “Multiply and Divide” scope, students complete “Show What You Know, Part 1: Model and Describe Contextual Multiplication” after completing Explore 1. There are facilitation points for teachers to read to implement the assessment correctly. Teachers provide each student with a handout; students read a contextual multiplication word problem, draw a model using circles, and identify how many groups they made and the number of objects in each group. The facilitation points state that this element of the program can be used to assess whether intervention is needed for each student. The assessment also includes an answer key that teachers can use to accurately grade each handout.
At the end of each scope, students are able to demonstrate mastery of the concepts through various assessments, such as the “Decide and Defend” assessment, a STAAR-based assessment, and a “Skills Quiz.” The Decide and Defend assessment includes a rubric for teachers to use, but none of the assessments provide guidance for teachers on how to administer the assessment, when to administer the assessment, or how to score and use the data to guide further instruction.
Materials include an age-appropriate tool for students to track their own progress and growth. My Math Thoughts are a collection of journal prompts designed to allow students to explain their thinking and reflect on their learning. After students complete activities, they reflect on their learning by indicating how they feel about each skill taught in the scope. In the “Three-Dimensional Solids” scope, the skills listed are “I can classify three-dimensional solids based on attributes using formal geometric language”; “I can sort three-dimensional solids based on attributes using formal geometric language”; “I can identify spheres, cones, cylinders, cubes, and rectangular and triangular prisms”; and “I can compose three-dimensional solids when given attributes.” Students indicate if they know it, almost know it, or do not know it yet.
The materials include diagnostic tools to measure all content and process skills for the grade level, as outlined in the TEKS and Mathematical Process Standards. The instructional materials provide various diagnostic tools, including both informal and formal assessments. Formal assessments include the benchmark assessments that can be given three times throughout the year to track student progress: the Pre-Assessment, Mid-Year Assessment, and Post-Assessment. Each assessment provides a blueprint to the TEKS that will be covered on the assessment. For informal assessments, throughout the instructional materials, each component of the “5E” model provides an opportunity for students to show their understanding of a concept. For example, in the Explore section, there is a “Student Journal” that allows students to record their answers. In the “Evaluate” portion, there is a Skills Quiz that tests the mastery of the skill being taught in that unit.
The “Accessing Prior Knowledge” activities are brief probing activities to gauge students’ prior knowledge before they engage in new content taught in the Explore activities. For example, in the “Time” scope, Accessing Prior Knowledge assesses students’ prior knowledge from first grade, such as telling time to the hour and half-hour using analog and digital clocks. Students draw hands on an analog clock to show 2:30. Then, the teacher leads a discussion where the students describe the hands on a clock. The facilitation points state that if students struggle to complete this activity, the teacher should use the “Foundation Builder” activity to fill the gap in prior knowledge before moving on to other parts of the scope.
The materials support teachers with guidance and direction to respond to individual students’ needs based on informal assessments and observations in the classroom. The materials include guidance for teachers to analyze and respond to data. Protocols are included for formal and informal assessment, with guidance for teachers on how to use the data to drive instruction. Assessment and response routines are present within the scopes to address student learning needs. The materials include a variety of diagnostic tools for teachers to use throughout the school year. Assessments include informal assessments such as exit tickets or individual student worksheets. Formal assessments include “Benchmark Assessments,” “Show-and-Tell” assessments, and “Skill Quizzes.” Each assessment tool includes an answer sheet for teachers to use while they are grading. Some answer keys also state which standard individual questions assess. The materials provide callout boxes or instructions within our markdowns to guide teachers on how to use the data to plan instruction. For example, at the end of Accessing Prior Knowledge, teachers are prompted to move to the Foundation Builder if students are still not understanding the concept. The program’s lesson planning guides assist teachers in knowing when to administer different assessments and how to evaluate and respond to data. The materials include a variety of activities for teachers to use to address the results of student assessments. Each scope includes an “Intervention” section for students approaching grade-level expectations and an “Acceleration” section for students who have mastered grade-level expectations. Benchmark Assessments provide teachers with meaningful data that can be used to inform instruction; the data can be compared with other classes or schoolwide.
Evidence includes but is not limited to:
The materials support teachers with guidance and direction to respond to individual students’ needs in all areas of mathematics, based on measures of student progress appropriate to the developmental level. Within every unit, a “Content Support” document provides teacher guidance on scaffolding within the scope. A “TEKS Unwrapped” component breaks down the TEKS within the scope and provides implications for instruction and student misconceptions. Each second-grade scope begins with an informal assessment to assess prior knowledge. If a child is unable to complete the assessment or is struggling, teachers are guided to reference the “Foundation Builder” to help close the gaps. The Foundation Builder provides the teacher with possible misconceptions and suggestions on how to correct them. The Foundation Builder focuses on students’ thinking about the strategies used and how they solve problems.
Each “Explore” lesson plan includes instructional supports for teachers to use based on their observations of students as they are working. Explores provide teacher guidance on how to scaffold next steps or instruction based on student needs. The materials also include questions that allow for a variety of strategies for finding the correct answer. Some questions include “How did you solve this problem?” “Is there another way to solve the problem?” “What strategy is your favorite?” and “What was hard about solving this problem?” Students take assessments at the end of every scope to measure their knowledge of the content that has been taught. Materials guide teachers to use the results of the assessments to determine whether students need interventions or acceleration.
The diagnostic tools yield some meaningful information for teachers to use when planning instruction and differentiation. Benchmark Assessments include an answer key and blueprint for teachers to use to determine a students’ understanding of certain topics. The answer key provides teachers with the answers to each question and which TEKS each question is assessing. The blueprint document lists the topic of each question, the standard each question assesses, and the correct answer for each question.
Each scope has an “Evaluate” section. This section includes three diagnostic tools for teachers to use during the scope to assess students’ knowledge of the content being covered in the scope. The Skills Quiz is a short, standards-based assessment to determine students’ ability to compute efficiently and accurately. Teachers use an answer key to grade each student’s responses to determine if the student has any learning gaps on skills in the scope. The answer key provides teachers with correct answers. The Observation Checklist is a list of standard breakouts and where they are found in each Explore. Teachers use this checklist to record anecdotal notes throughout the scope. The Show-and-Tell Assessment is a quick assessment with a rubric. It can be administered individually or in small groups using teacher prompts and manipulatives. Teachers use the rubric to assess students’ knowledge of each standard taught in the scope. This rubric provides teachers with information about what standard each question assesses so that they can determine specific skills on which students may need intervention. Based on the results of these three assessments, teachers determine if students meet grade-level expectations, need small group intervention, or can move onto Acceleration activities.
The “New Teacher Navigation Guide” states that materials include “a robust student data system that allows you to group and organize students based on areas of content mastery, re-teaching needs, quantile scores, and response to individual questions.” While the guide provides information on the data analysis tools that teachers can use after administering the diagnostic assessments, material reviewers do not have access to seeing what this would look like for a teacher and therefore cannot give a review on this component.
The materials provide a variety of resources and teacher guidance on how to leverage different activities to respond to student data. The materials provide teachers with a variety of suggestions and activities to use to address the results of student assessments. Each scope has an “Intervention and Acceleration” tab, which includes lesson plans and activities based on student performance. The Intervention section of each scope contains supplemental aids and small-group intervention activities specific to the scope. The Acceleration section of each scope contains extension activities for students who have demonstrated mastery of the content being taught in the scope.
As students move throughout the scope, they complete a “Show What You Know” activity after each Explore, which provides the teacher with a quick assessment to measure student understanding of a concept. Based on these results, teachers have guidance on how to plan and implement activities for students moving forward. If students are demonstrating an understanding of the concepts, the teacher has the option to allow them to participate in “Fluency Builder” games, digital interactive practice, game-based activities, problem-based task activities, or “Math Stories” during center time. If students are demonstrating a lack of understanding within a concept, the teacher is provided with small group instruction lesson plans to use in order to support students in closing their gaps.
The materials provide some guidance for administrators to support teachers in analyzing and responding to data. The New Teacher Navigation Guide provides information about data analysis; it suggests using quantile information in order to analyze data for students based on the results of their pre-, mid-, or post-assessments. Administrators are provided their own Administrative Portal in order to analyze data and guide teachers with designing instruction in response to the data. Information on how to support data analysis is not provided to administrators. Materials reviewers do not have access to an example of student data based on information gathered from a diagnostic assessment.
Benchmark Assessments provide teachers with meaningful data that can be used to inform instruction in the classroom. The intent of each assessment is to evaluate students’ progress on standards they have already learned. When students submit their answers online, the teacher receives data, which includes standard-specific performance and a quantile measure. Quantile measures can be used to determine a student’s mathematical performance level, assess what content the child is ready for, and track student growth over time. This data can be analyzed for individual students, classes, and schoolwide. While this data is available, there is no guidance for administrators in supporting data analysis and planning future instruction.
The materials include routine and systematic progress monitoring opportunities. Progress monitoring accurately measures and tracks student progress; it is appropriate in frequency and content for students in second grade. Formal diagnostic assessments are conducted three times a year; they are appropriate in length and content. Informal assessments included throughout the materials provide teachers the opportunity to observe and make notes based on student growth and progress. These activities have an age-appropriate format and enable students to demonstrate learning through games, discussions, “Math Chats,” interactive games, and show-and-tell tasks. Progress monitoring occurs frequently enough to support the teacher in making adequate observations and guide instruction based on student needs.
Evidence includes but is not limited to:
The materials include routine and systematic progress monitoring opportunities that accurately measure and track student progress. The formal progress monitoring assessment is to be taken three times a year: at the beginning, in the middle, and at the end. These benchmark assessments consist of 25 multiple-choice and griddable questions. Each scope provides an “Exit Ticket” for each “Explore” task and an observation checklist that helps the teacher evaluate students as they work. Teachers administer the Exit Ticket at the end of each Explore lesson to gauge students’ understanding of the new content. These tickets assess skills taught in the scope. In addition, “Student Journals” and “Show What You Know” activities allow for progress monitoring via informal assessment activities. Each scope also contains a “Decide and Defend” assessment, which is open-ended and prompts students to reason mathematically and support their ideas with evidence; teachers grade student answers using a rubric.
The materials also include teacher guidance and checklists to track students’ content knowledge and skills through stations, small group work, whole class discussions, and partner activities. These informal assessments allow teachers to observe and document student learning and behaviors throughout the course of the scope. Continued progress monitoring over the span of multiple scopes provides teachers with data to identify each student’s content, skill level, and progress over time.
The frequency of progress monitoring is appropriate for the age and content skill. At the beginning of the year, mid-year, and at the end of the year, teachers administer a benchmark assessment. Benchmark assessments allow the teacher to formally monitor growth in a standardized way three times a year. The materials also include suggestions to frequently assess students in an informal fashion throughout each individual scope. These assessments do not always include students sitting down to do written tasks, often utilizing checklists or anecdotal notes based on observations. For example, teachers can assess students during the prior-knowledge activity within each scope in order to determine whether students are ready for the “Hook” activity and new learning experiences or if students need to complete the “Foundation Builder” activity to fill in gaps in prior knowledge. As students complete Explore activities within each scope, they complete an Exit Ticket as a form of informal assessment. This assessment guides the teacher to determine whether students are ready to move on to the next Explore concept or if they need additional support through small group instruction. This progress monitoring also helps teachers to determine when they need to reteach an entire class and when they need to focus on a small group of students.
The materials provide a variety of options for progress monitoring that are appropriate for the age and the content skill. For example, students demonstrate their learning through “Problem-Based Tasks.” These are independent or collaborative activities that allow students to solve a challenging, meaningful problem in a real-world context. As students engage in stations such as “Fluency Builder” games and “Interactive Practice” games, the teacher is able to make observations to determine whether students understand the skills they are working on. Students are able to demonstrate their skills through games, peer collaboration, and group discussions. The teacher is able to use an observation checklist to determine whether students are demonstrating mastery of concepts as they engage in activities. At the end of each scope, students complete a Decide and Defend activity, answering questions via verbal answers, written answers, and manipulation of concrete objects. The teacher can record anecdotal notes and make observations through these activities to determine whether students have mastered each TEKS or component within the TEKS and whether or not students need small group intervention or Accelerate activities.
The materials provide guidance and support that helps teachers meet the diverse learning needs of all students. Formative assessment and STAAR-based assessments provide teachers data to guide their instruction and meet the needs of all learners. The “Engage” portion of each unit houses material that serves as a prerequisite to the topic. Each scope provides targeted instruction and activities for students that need scaffolding, additional guidance, and enrichment opportunities. Each scope also has an “Intervention” section where teachers can find small group intervention activities as well as instructional aids for students to use throughout the unit. The materials also provide recommended targeted instruction for students who have mastered content through “Acceleration” activities. The “Accelerate” portion contains lessons that extend learning and make real-world connections; these activities are designed to engage students who have already mastered the content and are ready to apply it in a different way.
Evidence includes but is not limited to:
The materials provide recommended targeted instruction and activities for students who struggle to master content. The “Teacher Toolbox” includes interventions for teachers to address various developmental areas for students. These areas include adaptive development, cognitive development, communication development, physical development, and social and emotional development. Within each category, there are example behaviors and strategies so that teachers can support students with those specific behaviors. Students begin the year by taking an assessment to measure their progress on standards they have previously learned in kindergarten and first grade. Teachers use this data to address students who have not mastered previous concepts and to create small group instruction. Within each scope, content supports are provided to the teacher; they provide insights on background knowledge and what students have learned about each concept in previous grade levels, misconceptions and obstacles that the students may have or encounter during the scope, important terms to know, and what the skill will look like in the current grade level as well as future grade levels. Throughout the year, students take second-grade benchmark assessments to give teachers insights into their knowledge and where to guide instruction.
Each scope begins with an “Assessing Prior Knowledge” activity where teachers can identify potential learning gaps in the class. Each second-grade scope includes an Engage component, which contains instructional materials for pre-teaching prerequisite concepts in a section titled “Foundation Builder.” Throughout, the instructional materials break down multi-part questions into one question at a time and provide sample student responses. Examples show how to use multiple steps that build on one another to decipher and answer questions. For example, in the scope “Represent Numbers to 1,200,” students use base-ten blocks and a place-value mat to compose numbers up to 120. Teachers review the value of ten and one blocks before beginning. Next, the teacher calls out different numbers that students have to build on their place-value mat. Students also show different ways to represent given numbers. If students do not perform well in this activity, the program states that teachers use the Foundation Builder activity to fill in learning gaps before moving on to other parts of the scope. In the Foundation Builder, students work in groups to practice representing different numbers using linking cubes and learn how to use the linking cubes to represent numbers in a different way. In part two of the activity, students use a handout to draw pictorial models of different numbers. The lesson plan also includes possible preconceptions and suggested solutions for teachers to use during the scope.
The materials also include intervention lessons within every scope. These interventions are designed for small group instruction that either focuses on the skill that is being learned in the current scope or reviews a previously learned skill. All intervention lessons are hands-on and chunked into sections so the teacher can assess multiple times in the lesson. For example, in the intervention lesson contained in the scope focusing on three-dimensional solids, teachers ask guiding questions to gain an understanding of student prior knowledge and adapt the lesson format based on those notes. Materials provide a checklist to list student names in each group and anecdotal notes for each student.
Within learning activities, materials provide instructional supports for students who are struggling to master content. For example, when students are struggling with strategy errors, before passing out student journals, the teacher reviews the process of identifying place value, creates an anchor chart with the name of each base-ten block and the value of each block, and reviews the four ways to write a number. In another support example, when students struggle with regrouping, the teacher models regrouping using base-ten blocks as a concrete representation.
Materials provide recommended targeted instruction and activities for students who have mastered content. Within the “TEKS Unwrapped” portion of the instructional materials, a vertical alignment document details the trajectory into the next grade level. Every scope within the materials includes acceleration opportunities for students who have mastered the concept activities. In the “Math Today” activities, students view an image, read a paragraph related to the image, and then explore the connections and applications of math and other cross-curricular content. As students engage in these activities, the teacher can then pull small groups of students to work with students who have mastered the content and are ready for further projects or activities.
The small group lessons allow teachers to break down questions into progressive steps to scaffold student learning. The materials include recommendations for teacher-student dialogue and provide sample questions for teachers to ask regarding solution strategies. Videos show real-world examples to encourage and enhance learning outside the classroom. Student self-evaluations with age-appropriate language allow them to take ownership of their learning and engage in more rigorous tasks. Mental math strategies with the justification piece encourage students to not only solve the problem but also to explain their thinking. Throughout the year, students take second-grade benchmark assessments and STAAR-based assessments to give teachers insights on their knowledge and where to guide instruction. Students take the benchmark assessments three times a year (pre, mid, and post); STAAR-based assessments are given during each scope. Teachers use this data to address students who have mastered concepts and adjust instruction in order to provide them with acceleration activities.
The materials provide additional enrichment activities for all levels of learners. There are a variety of activities, produced in a variety of modalities, to ensure materials meet the needs of different types of learners. Under the Accelerate portion of the scope, the instructional materials include recommendations for student enrichment and project-based tasks. Within the “Elaborate” section of the instructional materials, there are activities to build fluency, complete project-based tasks, and create life connections. “Interactive Practice” opportunities include digital games that address skills using games and technology. “Math Stories” allow students to practice skills and concepts while embedding literature. “Problem-Based Tasks” allow students to work collaboratively to apply the knowledge and skills they have learned to an open-ended, real-world challenge. “Fluency Builder” games allow students to practice new skills in a game format with a partner, promoting partner work and verbal discourse. For example, in the scope covering length, students play a “Go Fish” card game to match a picture with the correct measurement in centimeters or inches. In each scope, picture vocabulary provides a visual alongside the vocabulary word. Materials also include virtual manipulatives such as place-value disks, base-ten blocks, number lines, Cuisenaire rods, color tiles, geoboards, pattern blocks, and clocks.
The materials provide a variety of instructional methods that appeal to a variety of learning interests and needs. Students are engaged in mastery of the content through the use of concrete objects, pictorial representations, abstract representations, exploration activities, partner games, real-world applications, connections to literature, and virtual games and manipulatives. The “Explore” lessons are designed so that students practice new content in multiple ways, such as through using manipulatives, working with a partner or in a group, or completing a task individually. The materials use developmentally appropriate activities such as picture vocabulary, anchor charts, and teacher modeling. The materials support developmentally appropriate instructional strategies, such as starting with concrete objects and moving to pictorial and abstract representations, engaging students in exploration, and giving students the opportunity to work in small groups. The materials also support flexible grouping and multiple types of practices; students have multiple opportunities to complete activities as a whole group, in small groups, with partners, or independently.
Evidence includes but is not limited to:
The materials incorporate a variety of different instructional approaches throughout every scope. Each scope begins with a “Hook” activity, which engages and motivates students. It also sets the purpose for learning the new content in the scope. Before teaching the corresponding Explore activities, teachers use the “Pre-Explore” lesson from the Hook to engage the students in the new content in a hands-on way. After teaching all of the Explore lessons, teachers use the “Post-Explore” activity in the Hook to revisit the activity and solve the original problem with the new skill. For example, in the “Numbers on a Number Line” scope, teachers use the Hook activity titled “Recording Reading Pages” to engage students in the new content. In the Pre-Explore activity, students watch a video of a student reading a book. The teacher prompts the students by asking what kind of math they see in the video. After the discussion, the teacher reads a scenario about three students who read up to different pages in a book and asks the students how their page numbers can be plotted on an open number line. In the Post-Explore activity, the teacher rereads the scenario to the class. Using five sticky notes and an open number line, the students write benchmark numbers on the number line and plot the given page numbers on their open number line. The class discusses what they have learned about number lines and how they used their benchmark numbers to help them plot the book pages.
The Explore lessons are designed so that students are able to practice new content in multiple ways. The Explore activities are all teacher-facilitated; students work in partners or groups, often using manipulatives or other instructional supports to solve a problem. Lesson plans list necessary manipulatives, reproducibles, and visual aids for each activity. For example, in the “Personal Financial Literacy” scope, the Explore Lesson 1 incorporates whole-group, partner work, and independent work. The teacher begins the lesson by reading a scenario about making the decision to spend or save the money students earn from their allowance. In groups of 3–4, students take turns picking “Allowance Cards,” which state the chore they completed and how much money was earned, and decide if they want to spend or save the money. After discussing how much money each student earned and what they decide to do with it, the students complete a Spending vs. Saving handout, where they record how much money they earned, how much they want to save, and how much they want to spend. When the activity is finished, students independently complete an exit ticket to demonstrate their knowledge of spending and saving.
The materials support developmentally appropriate strategies. There is clear guidance to support teacher understanding of developmentally-appropriate instructional strategies as they guide the students through the “5E+IA” process. The “Scope Overview,” found on the “Home” tab, displays a flowchart of how the 5E+IA portions work together to ensure all learners are supported. Also, on the Home tab of each scope, “Student Expectations” and “Key Concepts” provide an overview of the learning expectations. “Content Support” provided for each scope lists information such as background knowledge, misconceptions, obstacles, and strategies to support the teacher in delivering instruction. “Vertical Alignment” provides information to the teacher about the logical progression of the TEKS and how concepts are built upon for the next grade level. “What Should Students Be Doing?” found in the “TEKS Unwrapped” section ensures students are progressing appropriately. Each scope also contains step-by-step instructions for teacher modeling. Across the instructional materials, teachers find modeling and sample think-aloud questions, with sample student responses noted in red. For example, in the scope on multiplication, teachers ask the question, “Did you have a strategy that worked well to help your group solve these problems?” The “Picture Vocabulary” section, provided for each topic, provides added language support; it contains image or pictorial support for new academic language. “Foundation Builder” lessons are used at the teacher’s discretion before beginning a new unit. Teachers use this lesson plan if there are noticeable learning gaps after assessing prior knowledge. In these activities, teachers model important skills necessary for the upcoming scope while also giving students time to problem solve on their own. Students then begin the scope in the “Engage” phase; the teacher uses this component to increase student engagement through exploration and open-ended questions. Once student engagement has been obtained, the teacher moves into the Explore component, which gives students the opportunity to build their knowledge through hands-on activities that promote understanding of new concepts. In the “Explain” tab, each scope has a slideshow with picture vocabulary and anchor chart examples. Each Explore lesson plan includes teacher support for students struggling to master the material and ELPS strategies.
Within the materials, each “Explore” activity has ELPS strategies for teachers to use to support students in that lesson. However, these strategies are general and do not provide support for varying levels of English language proficiency. In addition to the ELPS strategies, each scope has a “Picture Vocabulary” slideshow, which includes a picture and definition of content-specific words for the scope. Instruction is sequenced in a way that supports all learners and allows for repetition. Students use discourse and manipulatives in each Explore lesson to learn new content. However, there is limited instruction on how to further scaffold the materials for English Learners (ELs). Small group instruction focuses on reteaching content taught in the Explore lessons through the use of hands-on experiences with manipulatives. These lessons do not focus primarily on language development. Most resources in each scope are translated into Spanish; however, there is no guidance for teachers on how to use these materials with ELs. There is also no evidence of a teacher guide that supports teachers on the use of effective strategies specific to ELs.
Evidence includes but is not limited to:
The materials partially include accommodations for linguistics commensurate with various levels of English language proficiency. The materials are sequenced in a way that supports students’ understanding of new academic vocabulary in an authentic manner. For example, the program supports the development of academic vocabulary for all students by introducing new terms within the context of an activity. This allows students to connect the term to a physical object or process and supports the retention of academic vocabulary. An extension of this is the Picture Vocabulary element, which can be used to support the development of academic vocabulary with visual supports. All “Foundation Builder” activities provide intentional support for students on English words with multiple meanings. Provided sentence frames help the teacher support students who are in the process of learning English. There are opportunities to act out word problems for students who cannot express their ideas verbally. For example, in the scope related to multiplication and division, students engage in an Explore activity where they model and describe multiplication sentences. Suggested support includes having groups of two or three students take turns to act out the problems with counters or read the problem out loud. The materials also suggest that if students are shy or not comfortable reading, they can be in a group of three and watch their teammates. They can give a thumbs-up or a thumbs-down based on how the problem was solved using counters. This is beneficial for students at the beginning levels of English language acquisition.
While the materials provide support throughout the scopes at different levels of support, they provide one example of support for each Explore activity; therefore, the support is not directly differentiated based on the level of support ELs need. All EL students receive the same support regardless of where they are in their progress of language acquisition.
The materials partially provide scaffolds for ELs. There is little evidence of research-based scaffolds in the materials to provide support to ELs. The only evidence of support is the ELPS strategies listed at the bottom of each Explore lesson. These strategies list the ELPS standards being taught in the lesson and explain how to support students during that specific lesson. The instructional materials do not explicitly address scaffolding for ELs; however, the instructional materials do include whole group, small group, and flexible grouping opportunities for the entire class. Although direct resources for scaffolding intentional and natural lessons are not noted, the Foundation Builder of each scope provides the teacher with words that often have a double meaning and can be a roadblock to understanding the mathematical meaning. The words can be found at the bottom of the facilitation instructions.
The Explore lessons are written in a way that makes scaffolding intentional and natural. However, these scaffolds are intended for the whole class and do not have additional supports listed on how to further scaffold for ELs. However, small group intervention activities include rich vocabulary conversations and hands-on manipulation of materials. For example, in the scope related to measuring length, students receive inch tiles, centimeter cubes, erasers, straws, books, and rules in order to determine the length of objects using concrete models and formal measuring tools. Students then estimate lengths and determine the solution to a problem involving length. Teachers instruct students to use mathematical vocabulary, such as measurement, inch, centimeter, ruler, length, and estimate. Students are able to use the manipulatives as they discuss their observations and processes in order to support English language acquisition. Materials provide Spanish versions of all student materials and resources for students who need support in their native language. While there is no specific assistance for teachers when using the Spanish version with students in their class, the Spanish version of the materials is identical to the English version, so teachers will be able to understand the questions that are being asked in each activity, journal, or exit ticket.
Materials partially encourage strategic use of students’ first language as a means to develop linguistic, affective, cognitive, and academic skills in English. Within the individual Foundation Builder activities for word meaning, aside from the supports and suggestions made in the individual Explore activities and picture vocabulary, there is no evidence that supports the use of students’ first language as the foundation of developing skills in English. In the Foundation Builder activities, the materials reference multiple-meaning words in English, such as the word face, and words that sound the same but that are spelled differently and mean different things, such as ate and eight. However, the materials do not reference words from a student’s native language that can be connected to new vocabulary words in English. Each Explore activity contains ELPS strategies at the bottom of the facilitation points to guide teachers in supporting ELs during the activity. Teachers can use the ELPS strategies, along with the sentence stems that the instructional materials provide, to support students with strategic use of their first language. Some student materials in the program are available in Spanish and could be used as support for students who speak Spanish; however, outside of these resources, there is no other evidence noted on supporting students in their native language.
The materials include year-long plans with practice and review opportunities that support instruction. The “Scope and Sequence” outlines how to implement the materials based on a 36-week school year. The Scope and Sequence also dedicates the final two weeks of school to reviewing focal skills taught during the school year. The content plan is cohesively designed to build upon students’ current level of understanding with clear connections between lessons and across grade levels. The activities in each scope build upon each other and provide students with skills to apply new knowledge to more complex tasks. The materials include a “Vertical Alignment Chart” to show how content builds in preceding and subsequent grades. The “Content Support” section also provides teachers with an explanation of how the content builds in subsequent grade levels. The materials provide students with opportunities to review and practice throughout the program. Each scope contains a “Spiral Review” activity designed to provide students with opportunities to practice previously learned skills. The “Foundation Builder” reviews a vertically-aligned skill before beginning the remaining scope activities.
Evidence includes but is not limited to:
The materials include a cohesive, year-long plan to build students’ concept development and consider how to vertically align instruction that builds year to year. They include a year-long plan of content delivery through the Scope and Sequence provided for each grade level. The Scope and Sequence includes 36 instructional weeks and contains all scopes that are included in the materials as well as one week devoted to establishing classroom procedures and one week at the end of the year devoted to reviewing focal areas for the grade level. Within the Scope and Sequence, the materials provide a pacing structure that follows a logical sequence and allows time for depth and focus. The Scope and Sequence provides one or two weeks of instruction for every scope within the materials. The amount of time spent on each scope is based on whether or not the scope is a focal point and whether or not it is a concept that is necessary for success with future concepts. Each scope also provides a week for the “Show-and-Tell” rapid assessment for that scope. This allows teachers to provide depth to each scope and enables students to have time to master the concepts within the scope.
The materials include Vertical Alignment Charts to help teachers see how the content builds from year to year. These charts, located in the “Teacher Toolbox,” include charts for kindergarten through third grade and fourth through sixth grade. The document provides teachers with a description of how the TEKS are organized and an explanation of each part of the mathematics TEKS. The Content Support section in each scope also describes how each skill will be extended in future grade levels.
The materials provide review and practice of mathematical knowledge and skills throughout the span of the curriculum. The instructional materials build upon previously taught content from both prior grade levels as well as previously taught units. Each scope within the materials contains the same opportunities for review. Every scope includes an “Accessing Prior Knowledge” activity, a Foundation Builder, a Spiral Review activity, and time built into the day for “Daily Numeracy” review activities. Each lesson begins with the Assessing Prior Knowledge activity; this is a brief probing activity, designed to connect learning from previous grade levels with new learning, to gauge students’ prior knowledge before engaging in the inquiry process. The Foundation Builder is designed to review the vertically aligned skill, as needed, before students complete the remaining scope activities. Spiral Review, found in the “Elaborate” portion of the instructional materials, suggests previous skills that students can continue to practice and review. Teachers have the option to spiral back to any skill they prefer. Daily Numeracy activities, included for each grade level, provide opportunities for students to mentally practice a variety of skills throughout the year. Each scope also contains elements that spiral back to previously learned content.
The materials include implementation support for teachers; administrators have access to the same planning documents as teachers. The “Scope and Sequence” document is aligned to the TEKS and outlines which essential skills are taught over the course of a school year; it also shows the order in which essential skills are presented. The “Vertical Alignment Chart” displays TEKS for kindergarten through third grade; it provides teachers with an explanation of the layout of the mathematics TEKS and shows how standards build upon each other. “Lesson Planning Guides” support teachers in using the program and materials as intended; they provide teachers with support in pacing lessons across a week and which lessons to teach on specific days. There are two lesson planning guides: one for scopes with one to three “Explores” and one for scopes with three to five Explores. The “Content Support” section provides teachers with an explanation of best practices for the current scope. Teachers find guidance on how to teach specific skills and what students should be able to do by the end of the scope to show mastery. Each individual lesson has an objective for the lesson, a materials list, preparation instructions, and procedure and facilitation points. The materials include lessons and activities for a full year of instruction and additional activities to use to extend learning or provide intervention for students. The materials include realistic pacing guidance at the unit and lesson level.
Evidence includes but is not limited to:
Materials are accompanied by a TEKS-aligned Scope and Sequence outlining the essential knowledge and skills that are taught in the program, the order in which they are presented, and how knowledge and skills build and connect across grade levels. There is a “Scope List” and a Scope and Sequence document for teachers to follow. The Scope List shows the scope name, the TEKS covered in the scope, and the suggested pacing for the scope. The Scope and Sequence shows teachers how to pace the program throughout the course of the school year and is written based on a 36-week school year. Teachers learn which essential knowledge and skills are taught in each unit by reading the title of the scope and the TEKS covered on the Scope and Sequence document. Essential skills taught in each scope are described within the title; the document details the order in which the essential skills are presented. Teachers can view the pacing of each scope by seeing in which week new concepts are introduced.
The Vertical Alignment and Content Support documents for each scope provide information on prior knowledge and what students are expected to be able to do in future grade levels. Content Support documents also provide information on key concepts within the scope, fundamental questions, misconceptions and obstacles that may come about, terms to know, important information on how to guide students using prior knowledge, and where students are developmentally.
Materials include supports to help teachers implement the materials as intended. Lesson Planning Guides support teachers in using the program to best fit their needs and use the program as intended. The guides include notes on pacing and how to respond to student performance and data. Teachers choose between two guides depending on the number of Explore activities in the current scope. One guide provides pacing suggestions for scopes with one to three Explores and the other for scopes with three to five Explores. These guides provide teachers with pacing for both whole group and small group instruction models; they are based on a 90-minute class period. The whole group plan lists activities to do with the whole class and various assessment and closure activities to complete each day.
At the beginning of each scope, there is a list of materials and a unit overview. Each scope has individual tabs for each logically planned part of the scope that ensures the CRA method is being used. Lessons progress through the “5E” model (“Engage, Explore, Explain, Elaborate, Evaluate”). After the Evaluate portion, materials provide “Intervention” and “Acceleration” lessons to appropriately meet the needs of all students. The Lesson Planning Guide, located in the “Teacher Toolbox,” provides the teacher with an overview of the week. The whole group and small group plans provide the teacher with the content taught each day and remind the teacher to assess and reteach as needed. The materials are designed on a digital platform and allow for work to be assigned to the student. The instructional materials are also available in PDF or printable files that can be downloaded and/or printed. Teachers can also create editable Google slides for activities such as the academic vocabulary and the Explore student journals.
The materials partially include resources and guidance to help administrators support teachers in implementing the materials as intended. The Teacher Toolbox provides Lesson Planning Guides for teachers and administrators to use as a reference when planning for their students. As teachers collect data and respond in small group interventions, it is noted that their pacing can be affected. The suggested pacing ensures that the CRA method is followed and that adequate time is spent in the individual scopes. The Scope and Sequence can be used as a tool to ensure that teachers cover all scopes within the 36 weeks of school. Lesson Planning Guides support teachers and administrators to best fit the program to their needs and to use it as intended. They provide notes on pacing and responding to student performance and data. Although this evidence is noted, there is no indication that this is solely meant to support administrators. Administrators have access to the same materials that teachers use to implement the program in their classrooms.
The materials include a school year’s worth of math instruction, including realistic pacing guidance and routines. The Scope and Sequence provides the names of each scope within the materials and suggested pacing time of how many weeks should be devoted to each scope. The Scope and Sequence provides suggestions for scopes to teach over the course of 36 weeks; it provides anywhere from one to four weeks at the end of the school year for teachers to review the focal areas with students before they move into the next year of school. The Scope List for each grade level provides more detailed information about the pacing and planning of each scope. This document provides the name of each scope, the specific TEKS that will be covered within the scope, how many Explore activities are included in the scope, and the suggested amount of time that should be spent teaching the scope. The materials provide teacher guidance on how to pace scopes based on how many Explore activities are included within the scope. The suggested lesson plans provide support for a 90-minute math block and reasonable suggestions about how much a teacher can execute considering the developmental level of the students. The units are connected and allow for depth and focus. The experiences do not skim lightly over focal areas; they support students in spending sustained time developing content and skills in grade-appropriate areas.
The materials provide implementation guidance to meet variability in program design and in scheduling considerations. The “Scope and Sequence” provides guidance on implementation that ensures the sequence of content is taught in an order consistent with the developmental progression of mathematics. Students learn prerequisite skills in earlier scopes before moving on to content with increasing difficulty in later scopes. The Scope and Sequence states that there is flexibility in implementing the scopes. The activities within each scope are sequenced in a way that allows students to begin with foundational skills and work toward a more abstract understanding of the content taught in the scope. The program provides guidance to allow easy implementation in a variety of school designs. Each lesson planning template included in the scope is designed for a 90-minute math block. The “Lesson Planning Guides” (LPGs) provide teachers with guidance on how to implement the materials in a whole group and small group setting.
Evidence includes but is not limited to:
The materials provide guidance for strategic implementation without disrupting the sequence of content that must be taught in a specific order following a developmental progression. The materials are flexible in the sequence of content and learning elements used during instructional time. The Scope and Sequence can be found in the “Teacher Toolbox”; while the program suggests a scope and sequence to be used, the scopes are modular and can be rearranged to fit the needs of a particular teacher, campus, or district. LPGs provide options; teachers choose which elements they want to implement based on their given instructional time. Within each scope, teachers use the LPGs to plan their instruction for the duration of the scope. The activities in each scope are sequenced in a way that is consistent with the developmental progression of mathematics. Each “Explore” activity builds on the previous Explore activity. The LPGs ensure the sequence of content is taught in an order consistent with the developmental progress of mathematics. By using the organized LPGs, teachers make sure that precursor skills are taught first. LPGs are written based on a 90-minute math block and list each activity that teachers implement for each day of the week. Teachers choose from two different LPGs based on how many Explore activities are in the scope they are teaching—one to three Explores or three to five Explores. Each LPG provides teachers with pacing for both whole and small group instruction.
Materials are designed in a way that allows LEAs to incorporate the curriculum into district, campus, and teacher programmatic design and scheduling considerations. The materials are designed to allow easy implementation into a variety of school designs, without compromising the validity of the materials or the structure of the program. The materials provide a 36-week scope and sequence but stress that the scope and sequence can be implemented in a way that meets specific campus needs. Teachers and campuses can determine how long to spend on each unit and how to use the review units at the end of the year. While the scope and sequence provides a suggestion to LEAs on how to structure the year and how much time to spend on each scope, there is still room for a campus to implement the materials in a way that meets the needs of the students and staff. Additionally, the materials provide lesson planning support to teachers. The lesson planning support documents are split up based on the number of Explore activities within the scope. Within these documents, LEAs are provided with suggestions on how to implement the scope using a 5- to 10-day structure. The materials make suggestions to teachers on how the components can be taught in a way that fits within the time limits of the scope. The materials also provide suggestions and support for teachers to teach the lessons in a way that caters to the needs of the learners within the classroom. Because the materials are online, LEAs have the flexibility to implement the program virtually. The program has recently created a section titled “Virtual Learning.” Therefore, the materials respond to needs that may be occurring in many classrooms around Texas due to COVID-19. They provide the opportunity for teachers to meet the needs of students both virtually and face to face.
The materials support the development of strong relationships between teachers and families. They also specify activities for use at home to support students’ learning and development. The materials include parent letters in both Spanish and English that can be sent home at the beginning of the year; there are also letters sent at the beginning of each scope that provide information on concepts that will be covered throughout the year or throughout the scope. The letters also provide background on the mathematical philosophy of the materials and suggested vocabulary that can support students while they are at home. Students have virtual access to different components of the materials, and parents are able to support their child’s growth while at home. The materials also provide a tic-tac-toe board of suggested activities that families can complete during each scope in order to support and grow student understanding of the concepts that are being covered in the classroom.
Evidence includes but is not limited to:
The materials support development of strong relationships between teachers and families. Materials provide an editable parent letter, found in the “Teacher Toolbox,” for teachers or administrators to use to share their choice of the program’s curriculum. The letter introduces the “5E+IA” model and shares an overview of the program philosophy. The letter also notes that the program is aligned to the TEKS. Parents receive contact information for the school if they have any questions or would like to give feedback on the program. There are also parent letters sent out for each individual scope to provide an overview of the upcoming scope and a choice board to extend learning at home. For example, the “Join and Separate” newsletter introduces parents to the new scope, explains what it is that the student will learn, and advises parents on how they can assist at home. It clearly states vocabulary words and definitions and sometimes provides clipart. The newsletter encourages parents to identify examples of their child’s learning in everyday tasks and thanks them for their support. All of these parent letters are also available in Spanish. The materials specify activities for use at home to support students’ learning and development. Each student has his or her own online account. Accounts provide students access to learning resources and assignments given by their teachers. Learning resources include picture vocabulary, virtual manipulatives, interactive practice games, and a visual glossary of math vocabulary. Home support materials are available in English and Spanish.
The materials provide appropriate suggestions and/or resources for home activities that support the curriculum and can be used easily by families. The parent letter provides a parent-friendly breakdown of the standards, a list of vocabulary words used throughout the unit, and a “tic-tac-toe choice board.” The choice board includes games and activities that use materials available in most homes and have instructions that are simple for parents and students to understand. For example, in the “Money” scope, the parent letter explains that students will be learning to determine when it is appropriate to use the cent sign versus the dollar sign. It also explains that students will count collections of the same type of coin or a mixed group of coins up to one dollar. There is a list of vocabulary words, including value, cent symbol, dollar sign, and decimal point, along with the words’ definition. Parents are encouraged to use these words at home with their children because students are expected to use them during daily “Math Chats.” The choice board includes eight different activities that parents and students can play at home. One activity is “At the Store,” in which families look at the cents part of prices of items at the store. Students determine which coins are needed to make the value of the cents in the price. Another activity is “All the Same,” in which families give students a value, such as 25 cents; students must make the given amount with only one type of coin.
The visual design of student and teacher materials is not distracting. The materials include appropriate use of white space and design that supports and does not distract from student learning. Student handouts are designed in a way that is easy for students to read; there is enough white space for students to complete their work. The pictures and graphics are supportive of student learning and engagement without being visually distracting. Teacher’s guides are designed with clear, designated places for important information. Each scope includes a tab for each component of the “5E+IA” model and a description of each activity. Lesson plans are designed in a way that allows teachers to easily locate important information.
Evidence includes but is not limited to:
The materials include appropriate use of white space and design that supports and does not distract from student learning. The materials are designed in a way that supports student learning. The images are aesthetically pleasing to look at and provide information in a simple yet purposeful format. The student documents within the program include plenty of white space for students to perform tasks and calculations in order to complete their work. Clear images are appealing to students and also support their understanding of the concept. Scopes are easy to identify within the materials; students can easily see where to locate the scopes and components within the scopes when they are working. Virtual manipulatives are colorful, easy to locate, and user friendly to help support student understanding of concepts.
Teacher guides are designed with clear, designated places for important information. When logging into the system, the components of the materials are easily found along the top in various tabs. The scopes are easy to identify; teachers see the specific content being covered, the grade level it is designed for, the TEKS that are aligned to the scope, and the domain it aligns to within the standards. Colorful sidebars give the teacher additional support and resources such as STEMscopes streaming, the “Teacher Toolbox,” visual glossaries, benchmark assessments, and professional development videos and support. Within the components of the Toolbox, tabs and sidebars are clearly defined and labeled to provide teachers information they need to support student learning. Colors are visually appealing and are not distracting; images do not take away from the information being provided to teachers. Information in the materials and different components are easy to locate and are clearly stated. Each scope is labeled with the topic, standard, and strand. The toolbar on the left-hand side of the screen can be used to search by keyword or filter scopes by grade level and/or strand.
The materials adhere to user interface design guidelines. Teachers are able to view the system status by referring to lesson plans that are added to their lesson planner; teachers can view which digital assignments have been assigned to each student. The materials in the program match the real world and are easily navigable by users. Teachers have control and freedom in the program and are able to take steps backward if they make an error. The materials in the program are consistent across grade levels. The materials provide error prevention by providing teachers with an explanation of the intention of use for each element in the program. The way the program is designed allows for recognition rather than recall. Consistency in each scope allows teachers to become familiar with each element in the program. The pictures and graphics included in the program are visually appealing with a minimalist aesthetic. The materials provide teachers with help and support. Teachers utilize the Teacher Toolbox for lesson planning guidance and descriptions on how each element in the program should be used.
Pictures and graphics are supportive of student learning and engagement without being visually distracting. The materials include pictures that are easily identifiable by students and support student learning. Images are included for students in order to support the task they are asked to complete. The images match what the problem or question is related to, are engaging for students, and are easy to see. The digital format of the materials includes colorful images that are visually appealing to students and easy to relate to the mathematics problems. In the printed materials, the images are black and white; they are still easy to understand and decipher. Images are the appropriate size and are not too small or too large. Images support learning and understanding. Fonts, graphs, and charts are clear and easy to read within the student materials. Manipulative images are provided when needed; they are not distracting, difficult to use, or difficult to understand. Student materials use white space appropriately.
The technology and online components included in the program are appropriate for grade-level students and provide support for learning. Most scopes have virtual manipulatives available for student use. Teachers are prompted to go digital in the lesson plans if there are virtual manipulatives available to assign to students. The virtual manipulatives align to the curriculum and support student learning. Each scope has “Interactive Practice” activities; these are games aligned to what students are learning, which provide them with extra practice with the skills that are being covered in the scope. Teachers also have the option to assign certain activities for students to complete virtually. This option replaces the use of paper-and-pencil activities. Materials provide teachers with guidance and support in using virtual resources throughout the materials.
Evidence includes but is not limited to:
The technology aligns to the curriculum’s scope and approach to mathematics skill progression. The materials contain technological components that enhance learning for students. Students interact digitally with tasks through virtual manipulatives, interactive games, and digital journals or assignments. As students engage in “Explore” activities, they have the option to use the virtual manipulatives that align with the manipulatives that are offered in the classroom. In the “Elaborate” component of each scope, interactive games enhance students’ knowledge of the concepts and provide a way to practice in a virtual format. These games are available to play through the materials’ website and app; they support the materials’ progression of math content and skills introduction and practice.
Many elements within the materials can be completed digitally. There is a PDF version of the materials that teachers can print, but students can also complete activities virtually. Students can digitally complete the “Show What You Know” activities from the “Explain” component of each scope. They can also digitally complete the “Problem-Based Task,” the “Math Story,” and the “Spiraled Review” from the “Elaborate” component from each scope. Skills quizzes and benchmark assessments can be assigned and completed virtually. When students take these assessments virtually and submit their work, they are provided with data and scores.
Due to COVID-19, materials have added additional components to support digital learning. Each grade level now includes virtual learning. Within the virtual learning components, students can interact with each scope. Students are able to watch videos that explain new concepts and model learning. Students are also able to use virtual manipulatives in order to support their conceptual understanding as well as virtually complete Explore activities.
Technology supports and enhances student learning, as opposed to distracting from it, and includes appropriate teacher guidance. The technology promotes and enhances student participation in the materials. Many of the student elements in the program can be completed digitally as an alternative to the paper-and-pencil version provided within the lesson plan. Assessments like the benchmarks can also be taken digitally. When teachers select this option, they are provided with whole-class data after the assessments are submitted and scored. The materials give teachers appropriate and sufficient guidance on how to use technology with students and how to support students with technology use. The procedure and facilitation instructions in the Explore lessons provide teachers guidance on how to use the virtual manipulatives during the activities. Virtual manipulatives are found under the Explore tab of each scope and can be digitally assigned to each student. Teachers know when they have the option to use the virtual manipulatives: Materials prompt them to “Go Digital” in the “Preparation” instructions of the Explore lesson plans. The instructions state that students can explore or present their solutions using virtual manipulatives during the activity. Lesson planning guides provide teachers with guidance on when to use the Interactive Practice games. For example, in the “Small Group Plan” guide, teachers use the Interactive Practice games as a math station.
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