Program Information
- ISBN
- 9780544470279
- Copyright Type
- Proprietary
Math
KindergartenPublisher: Houghton Mifflin Harcourt
Copyright: 2015
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
Grade |
TEKS Student % |
TEKS Teacher % |
ELPS Student % |
ELPS Teacher % |
Kindergarten |
100% |
100% |
N/A |
100% |
Grade 1 |
100% |
100% |
N/A |
100% |
Grade 2 |
100% |
100% |
N/A |
100% |
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 % |
---|---|---|---|---|
Kindergarten | 100% | 100% | N/A | 100% |
The materials concentrate on the development of the primary focal areas for the grade level. The materials spend the majority of concept development on the focal areas as outlined in the Texas Essential Knowledge and Skills (TEKS), and they strategically and systematically develop students’ content knowledge. There are practice opportunities for students to master the content.
Evidence includes but is not limited to:
Throughout all modules, the materials contain planning documents such as unit plans and the TEKS for Mathematics Correlations that clearly state the focal areas of a unit; these focal areas align with the grade-level TEKS. The materials clearly and consistently showcase focal areas of the curriculum that are aligned to the grade-level TEKS; the Process Standards are combined with the content strands in the majority of the modules. For example, in the Teacher Edition, at the beginning of each unit, there is an outline that shows teachers a broad scope and sequence as well as all of the modules that fall under that focal area. The “Engage, Explore, Explain, Elaborate, Evaluate” (5E) lesson plan design in the materials informs the teaching and learning of math concepts.
The lessons begin with activating prior knowledge and progress to higher-order critical thinking and problem solving throughout the units, ensuring students master the full concept. The materials include inserts that outline the primary focal areas for instructional emphasis with a narrative and a graphic depicting vertical alignment. The lesson design permits instruction in each grade to focus on skills in greater depth while simultaneously building a foundation for the next grade, establishing an effective learning progression. In addition, the materials provide various practice opportunities through the use of additional resources such as “Response-to-Intervention (RTI) Tiered Lessons,” “Enrich” lessons, STEM activities, and the “Grab-and-Go” activities found in the digital resources. The materials explain that students will be able to apply mathematical skills in a variety of ways in order to be mathematicians. The introduction explains that through using manipulatives, models, and rigorous questions, students are able to move beyond a basic level of learning to develop deep conceptual understanding and then practice, apply, and discuss what they know.
Modules 1–8 focus on representing, counting, writing, and comparing whole numbers. Modules 9–14 focus on composing and decomposing numbers, addition, and subtraction. Module 17 identifies 2D shapes, while Module 18 identifies 3D shapes. These key focal areas are spiraled in most of the modules after they are taught; for example, Module 1 teaches “Count, Write, and Represent numbers through 4.” This is scaffolded through to “Counting, Writing, and Representing the whole numbers through 20” in Module 8.
In Module 9, the center activities consist of a bus stop game that could be played at an actual bus stop, a literature piece, and a subtraction activity involving various objects that extend beyond the classroom walls. The lesson cycle for each module contains opportunities for students to practice the concept, utilizing manipulatives prior to moving to the abstract.
In Module 11, lessons provide scaffolding to activate prior knowledge and continue to build on the concept being taught. The lessons begin with activating prior knowledge about terms used when adding. The teacher then uses hands-on activities to introduce the concept of joining. Each lesson introduces a different strategy for addition up to 5. Additionally, the opportunities to practice in the lessons as well as the additional materials available in the resources promote rigor and guide the students to build their “toolbox” with varying strategies for problem-solving and critical thinking. In Module 11, students learn to use at least three strategies to solve addition problems.
In Module 17, students distinguish triangles from non-triangles and explain their selections using evidence-based justifications. The “Explain, Elaborate, and Evaluate” portion of this lesson illustrates how students utilize two-dimensional shapes and two-color counters in counting sides and vertices and communicate mathematical ideas within whole-group and small-group discussions, center activities, and through independent practice.
The provided materials include concepts sequenced from concrete to representational to abstract (CRA) as is grade-level appropriate. Materials include a variety of appropriate content and grade-level types of concrete models and manipulatives, pictorial representations, and abstract representations. However, materials do not clearly support teachers in understanding and developing students’ progression along the CRA continuum.
Evidence includes but is not limited to:
Throughout the materials, in order to understand whole numbers, Modules 1 and 2 include two-color counters, MathBoards, stones, connecting cubes, and five-frames; Module 3 includes two-color counters, connecting cubes, number and symbol tiles, number cards, sets of blocks, five-frames, MathBoards, and dot cards. For addition and subtraction, Module 9 uses MathBoards, two-color counters, connecting cubes, and paper bags. The lessons all include step-by-step instructions for how to administer the concrete models and manipulatives. Although many concrete models and manipulatives repeat themselves over the course of the entire curriculum, there is plenty of variety. Because these manipulatives repeat themselves throughout the curriculum, students have previous experience with the concrete models and manipulatives. Additionally, there are paper-and-pencil opportunities for students in each lesson. As skills are spiraled in and built upon, students are using these manipulatives in more complex ways. Students are using the counters; for example, students represent numbers in a ten-frame. Next, they build numbers with counting cubes and then write numbers. The use of the ten-frame is spiraled back in as students begin exploring addition and subtraction and represent equations with the connecting cubes. However, the materials do not explicitly state how these manipulatives should be used, and kindergarteners have likely not had prior experience using these tools.
Throughout the modules, the materials do not explicitly provide guidance about what tools should be available to students at different points in their development and how to push students to use increasingly sophisticated tools as appropriate along the CRA continuum. There is some evidence that the materials do support teachers with instructional suggestions to help students to progress through learning new concepts, knowledge, and skills; however, there is a lack of direct instruction on how or when to move students along the CRA continuum. For example, every model in each grade level includes a “Show What You Know” section to assess students’ understanding of the concept. This section directs teachers to provide intervention using the “Response to Intervention” materials or to provide enrichment through the enrichment materials based on the students’ responses, but there is no explicit reference to utilizing the CRA continuum.
Across the modules, there is a spiral usage of manipulatives. The materials introduce number representation and addition and subtraction with two-color counters. In Unit 1, the modules begin with an exploration of the counters so that students have opportunities to manipulate the materials prior to application. Later in Module 1, students transition into utilizing connection cubes and continue to use the counters, connecting cubes, and Math Boards in Modules 1 through 14 to join, separate, count, add, and subtract numbers. Materials introduce students to representations with concrete support as early as Module 1, through direct teaching. Students begin paper-and-pencil type activities in Module 1 but continue to have the manipulative accessibility embedded within the lessons. This lesson implementation continues, progressively adding more manipulatives, such as play coins in Module 15, attribute blocks in Module 17, and three-dimensional shapes in Module 18. Additionally, students have access to pictorial representations as part of each lesson within each module, as depicted in the colorful practice workbook, work mats, “Daily Assessment Tasks,” and “Homework and Practice” pages. Students practice representing, comparing, and counting numbers throughout Modules 1 through 8 using counters; students then transition to using the counters within ten-frames when they begin composing and decomposing numbers. Since students have already had practice with five-frames as early as in Module 2, students have established prior knowledge of this format when transitioning to ten-frames. When students begin Module 11, “Adding Up to 5,” they have already manipulated counters; they transition to using the addition and subtraction symbols. The materials utilize manipulatives for application after students have had opportunities to familiarize themselves with the models.
In Module 4, in the “Making Connections” section, students begin by counting up to 5 by using their fingers, and then think of other ways they can show the number 5. As a whole class, students use five-frames and counters to demonstrate the number 5 and one more. This is continued in the “Explore” section. In the “Elaborate” section, students manipulate two-color counters to identify different ways to represent 6 with two different numbers, such as 2 and 4. In the “Homework and Practice” section, students draw counters on a ten-frame as they count each rocket ship, and then select the right number to match the number of counters in three different ten-frames. The lessons provide instructions for RTI, for students who need additional support, and enrichment for students who understand the concepts; however, there is no direction or instruction for teachers in reference to moving along the CRA continuum.
In Module 9, the lesson invites students to share what they know about modeling numbers; teachers ask, “What number is one more than 1?” and “What number is one more than 2?” The lesson recommends using the “Interactive Digital Lesson,” where students are guided through the process of modeling numbers using items such as cubes or their fingers. The “Explore” section scaffolds through modeling numbers to composing numbers, using both counters and five-frames, up to the number 3. Materials instruct students on how to use the counters and five-frames; teachers tell them how to place the red and yellow counters, asking questions such as, “How many yellow counters are there? Write the number. How many red counters are there? Write the number. What is 0 and 3? 3. Point to the number. There are 3 counters in all.” As the lesson progresses, the teacher digs deeper by asking, “Two children are sitting on a rug. One more child joins them. How many children are sitting on the rug now? How can you solve this problem?” The lesson contains “Dig Deeper” recommendations, such as asking students how they can solve this problem and guiding students to suggest acting out the problem or using manipulatives. The lesson ends with a higher-order thinking skills (HOTS) question: “Sasha wants to have 3 counters. She has 2 yellow counters. How many red counters does she need to have 3?”
In Modules 9–14, the introduction recommends that students complete the “Show What You Know” independently as a pre-assessment test. The materials then recommend a “Diagnostic Interview Task,” using two-colored counters, to have students demonstrate what they understand. The “Vocabulary Builder” lists strategies to help build students’ vocabulary, such as visualizing and drawing representations for the vocabulary words. In Module 14, “Differences within 7,” teachers instruct students on how to use pictorial models to solve subtraction problems by crossing out the pictures to show subtraction.
The provided materials support coherence and connections between and within content at the grade level and across grade levels. The resources include supports for students to build vertical content knowledge by accessing prior knowledge and understanding of concept progression. The included tasks connect two or more concepts, and they provide opportunities for students to explore relationships and patterns within and across concepts. The materials mostly support teachers in understanding horizontal and vertical alignment; however, there are not always sufficient explicit details or directions to indicate why the materials build, especially for teachers less familiar with the TEKS for the grade level or grades above.
Evidence includes but is not limited to:
Throughout all modules, kindergarten materials contain tasks that direct teachers to build on students’ prior knowledge before presenting a new concept or problem aligned to a grade-level focal area. Each lesson in each module begins with an “Essential Question” and a “Making Connections” piece that links the new skill or concept to previously learned material or students’ prior knowledge. All lessons within the curriculum have an “Are You Ready?” section that guides teachers to assess children’s understanding of the prerequisite skills for each lesson; this is located in the “Assessment Guide,” which instructs the teachers where to go in the guide. Each lesson contains a “Go Digital” resources section, which has a “Digital Management Center” specifically designed for the teacher’s use; it organizes program resources by TEKS, Tier 1 intervention lessons (provided in the “RTI Guide”), and “Soar to Success Math” online lessons that teachers can use to help build those skills. At the beginning of each unit, there is a “Vocabulary Reader.” At the very bottom of every page in the Teacher Edition, the “Vocabulary Builder” section explains to teachers the prior knowledge students should be coming in with. Kindergarten materials build students’ vertical content knowledge through task familiarity; materials utilize common manipulatives and models from previous units and continue to do so as students progress into subsequent grade levels. The materials are organized so that skills and concepts build in rigor over the course of a unit, throughout the year, and over consecutive years. The materials follow the same format in all grade levels and utilize the same models; for example, they use five-frames for representing numbers, counting, adding, and subtracting in kindergarten and then in first grade. The materials teach the same or similar strategies to scaffold in higher grade levels, such as using number lines, counting on, modeling, and acting out to solve problems. The problem-solving model is the same throughout all grade levels; the content changes, but the format remains the same. While the kindergarten materials build upon concepts and materials used throughout kindergarten and what students may have learned in prekindergarten, there is little evidence of a direct connection to what students will learn in the first grade. Also, the materials don’t explicitly state how to include the application of concepts outside of the mathematical classroom; students receive real-world examples and problems to explore and solve throughout each module. The only indication that shows students will use these skills in the future is found in the “Math Tutor on the Spot” section, which provides students with help in solving the HOTS (higher-order thinking skills) question included in each lesson. This section, which appears in every lesson across grade levels, states: “With these videos and the HOTS problems, children will build skills needed in the TEXAS assessment.” Materials give no further guidance or direction.
At the beginning of the year, in Module 5, focusing on modeling, counting, and writing numbers to 10, students use their knowledge of representing numbers; they use counters in a ten-frame. In the middle of the year, in Module 10, students again connect their knowledge of numbers; they compose and decompose numbers to ten. At the end of the year, in Modules 11–14, they once again connect their sense of numbers; they add and subtract.
In Module 8, Lesson 8, students solve a word problem to find out how many apples Kaelin has. Through the step-by-step process, they find out that Kaelin has 18, and Chase has 16. Materials then prompt teachers to ask students which set is larger and to clarify that this also means which set has more. Students discuss how they know which set has more. This word problem alone connects addition, subtraction, greater than, less than, and abstract concepts. Also in this module, a lesson titled “Count and Write 18 and 19” includes an Essential Question: “How can you count and write 18 and 19 with words and numbers?” Students have modeled, counted, and written numbers 1–17 using counters and ten-frames in a consistent manner. During the “Making Connections” piece of the “Lesson Opener,” students tell the teacher what they know about counting and writing up to 17; then, they count the number of legs on an octopus out loud, up to 17, starting with 10; finally, they write 18 in number form. Students have done this in previous “Lesson Openers,” beginning in Unit 1, with the corresponding numbers of study. Students utilize the ten-frame models as part of the “Explore,” “Explain,” or “Evaluate” portions of the lesson just as they have throughout Modules 4, 5, 6, 7, and 8.
In Module 14, in the “Go Deeper” section, materials prompt students to find the similarities and differences in number sentences. Through this, students can begin to understand the relationship between addition and subtraction, which correlates with the following first grade TEKS: “Students use properties of operations and the relationship between addition and subtraction to solve problems.”
In Module 15, the materials use real-life problems that require students to recognize and apply mathematics in contexts outside of mathematics. For example, in an “Enrich” activity, students draw an art piece to sell. They put a price on it between 1 and 5 pennies. The teacher gives each student 5 pennies and has them buy and sell one drawing each. Students exchange pennies for the drawing and then count how many pennies they have left.
In Module 15, students use their sorting skills when sorting coins; they continue to sort, using shapes, in Modules 17 and 18; in Module 20, students sort objects. Building on prior practice in sorting is essential in helping to solidify students’ understanding of building, creating, reading, and interpreting picture graphs.
In Module 16, the teacher asks students to share stories about a time when they saw or used eggs; students draw up to 20 eggs on their paper and then count and write down the number of eggs they drew. Later in the lesson, students play a game to increase their familiarity with numbers from 1 to 30; they repeatedly count forward to move along the game path. Students complete an activity card by showing sets of 10 objects using the ready-made “Grab-and-Go” differentiated centers kit.
In Module 20, students sort objects and create a graph. Teachers ask students to read the graph, asking questions such as “How many cubes are red?” and “Which color has few cubes?” This activity builds on the previous eight modules, where students learned to count, write, and represent numbers.
The provided materials are built around quality tasks that address content at the appropriate level of rigor and complexity. Tasks are designed to engage students in the appropriate level of rigor as identified in the Texas Essential Knowledge and Skills (TEKS), as appropriate for the development of the content and skills, and they clearly outline for the teacher the mathematical concepts and goals behind each task. Materials integrate contextualized problems throughout, providing students chances to apply knowledge and skills in varied situations. The resources provide teachers guidance on anticipating student responses and strategies; however, the materials do guide teachers on ways to revise content to be relevant to their specific students, the students’ backgrounds, and the students’ interests. In addition, there are embedded opportunities for discourse, but there are no rubrics for teachers to evaluate the quality of the discussions.
Evidence includes but is not limited to:
Throughout all modules, the materials begin with concrete models, allowing students to use tools and manipulatives to represent numbers. The materials guide students through CRA (concrete to representational to abstract) tools, models, and understandings, with increasing depth and complexity; materials provide increasing rigor throughout a given unit and across units over the course of the year. Each unit (which includes multiple modules) includes an introduction called “Introduce the Unit;” it describes and explains the overall concepts and the goals of the unit. This is exemplified in the “TEKS for Mathematics” section in the Teacher Edition (TE) as well as in the teacher professional development videos; the student edition lists the TEKS for each lesson in the top right-hand corner of the first page. Materials note multiple goals behind a task, emphasizing that the process is just as important for student learning as the product; they guide teachers to facilitate discussion on how differences in strategy relate to efficiency and how well strategies work for the problem type. The unit page explains each component of the lesson; unit pages also include “Essential Questions” that teachers focus on throughout each unit. Lessons follow a “5E” format (“Engage, Explore, Explain, Elaborate, and Evaluate”). Each lesson starts out with accessing prior knowledge and a “Making Connections” section; in the Explore section, the lesson dives into the on-level material. During the Explain portion, materials encourage moving students to Elaborate only if they master the previous teaching. There are enrichment questions in the higher-order thinking (HOT) problems, “Go Deeper,” and in independent practice, labeled “Homework and Practice.” The unit page also informs teachers that the “Diagnostic Interview Task” may be used for intervention on prerequisite skills. For each grade level, several sections throughout the TE unit pages direct teachers to students’ prerequisite skills, such as “Show What You Know,” “Quick Checks,” and the “Vocabulary Builder.” Each lesson includes TEKS and learning objectives to address; the “Common Errors” section lists possible misconceptions for each lesson in the TE.
In Module 1, students progress to finding all the ways to create 10 using counters and ten-frames; this culminates in Module 6. As they extend this work to 20 in Module 8, students are expected to understand and verbalize the conceptual understanding behind these skills, explaining and demonstrating that numbers can be composed and decomposed in different ways. This is a precursor to understanding the relationship between addition and subtraction as well as algebraic relationships in writing expressions.
In Modules 1–8, “Numbers and Operations,” teachers guide students to use connecting cubes or two-color counters to model the numbers 1–20. As the unit and modules progress, students use picture representations to identify and count numbers 1–20. These may be pictures that they draw themselves or pictures that are provided for them in their student edition. Specifically, in Module 5, students see pictures of ten objects. Later in that same module, students draw their own ten objects and write the numbers 1–10. At the end of the unit, in Module 8, teachers guide students to think abstractly as they order and compare numbers up to 20.
In Module 3, students begin a lesson by reviewing counting up to 5. Students then make cube towers in the Explore section of the lesson. They make cube towers in order, using one cube, then two cubes, and so on up to five cubes. The Explain section has students “Share and Show” what they’ve learned and their reasoning behind how they know the cube trains are in order. In the Elaborate section, students move on to filling in blanks, using numbers 1 to 5. Finally, in the “Problem Solving” section, students must figure out which set has one more than a set of three blocks. This is much more advanced than the beginning of the lesson, which is just rote counting from 1 to 5. Tasks increase throughout any given module and unit. For example, in Module 3, students compare numbers through 5; they begin with counting and ordering to 5, then move on to greater than and less than, and finish with comparing by matching and counting sets of 5.
In Module 5, a lesson titled “Represent, Count, and Write through 10” begins with activating prior knowledge through the use of the “Lesson Opener” activities. For example, materials state: “Review counting objects and counting to 8 with children. What numbers do you say when you count to 8? Would you use counters and a five-frame to count 8? Why not?” The lesson then moves to Explore; materials introduce the Essential Question: “How can you show and count 9 objects?” Students use manipulatives or other strategies previously taught to work through a problem. The teacher reads the problem: “Daniel wins eight prizes at the fair. Then he wins one more prize. How many prizes does he win?” The teacher guides the students through the steps to solve the problem; the teacher gives each child nine counters, models counting to 9, and has children count to make sure they have nine counters. If needed, the teacher rereads the problem and directs students, “Place eight counters on the page. Now place one more counter. How many prizes did Daniel win? Count to be sure that you have nine. Now draw the counters to model the prizes. Is 9 greater than or less than 8? When you are counting, is a number always greater than or less than the one before it?” The next step in the lesson is Explain; teachers use the “Model and Draw” strategy to model their thinking process and how to solve a problem. The lesson progresses from conceptual understanding to procedural fluency in the Elaborate, Share and Show, and Problem Solving sections of the lesson, where students repeat practices building on rigor.
In Module 10, “Compose and Decompose Numbers Up to 10,” a discussion question embedded within the Elaborate portion asks, “There are six bananas on the snack table. Two bananas are green. How many bananas are yellow? How many bananas are on the table? How many are green?” Students count out the two bananas and mark them with an x. Teachers then instruct students to count the remaining bananas and determine if they put together or took apart (added or subtracted) for this problem. “Go Deeper” guides the teacher on how to proceed should a student exhibit mastery; “Differentiated Instruction” guides the teacher on how to proceed should a student experience difficulty. Also in Module 10, in the “Springboard for Learning” section, the materials remind teachers that children must ask themselves what the problem asks them to do. If the problem is a “put together” problem, children will add to solve it, thus leading to further application in problem-solving requiring addition.
In Module 16, materials direct the teacher to ask children to share stories about a time when they saw or used eggs; students draw up to 20 eggs on their paper and then count and write down the number of eggs they drew. Later in the lesson, students play a game where they increase their familiarity with numbers from 1 to 30, repeatedly counting forward to move along a game path. Students complete an activity card by showing sets of 10 objects, using the ready-made “Grab-and-Go” differentiated centers kit.
The materials develop fluency in an integrated way. There is guidance and support for conducting fluency practice and integrating fluency at appropriate times as students progress in their conceptual understanding. There is not a cohesive year-long plan that is explicitly laid out for fluency practice, and there is little scaffolding or support for teachers to differentiate fluency development for all learners.
Evidence includes but is not limited to:
Throughout all modules, the materials include some guidance for teachers on the structure and design of fluency practice; this guidance is found in the “Strategies and Practice for Skills and Facts Fluency – Primary, GK-3,” in the “Digital Resources.” This resource lists the lessons in kindergarten, 1st grade, 2nd grade, and 3rd grade, and how they match “Basic Facts” workshops and “Basic Facts Practice” worksheets. The workshops and worksheets are connected to concept development and expectations for the grade level. This is evidenced through the lessons listed in the “Math Expressions Correlation” section, which also provides opportunities to choose appropriate strategies for grade-level tasks. Students have opportunities to efficiently and accurately solve grade-level tasks by applying their conceptual understanding of number relationships and strategies; students do this in the scaffolded workshops from “Introduce It!” “Develop It!” and “Make it!” Materials provide support for conducting fluency practice with students; in the introduction, materials explain that basic facts workshops use number patterns, visual models, and prior knowledge to introduce and to develop the strategy for learning a specific group of facts. Materials provide further directions for children on how to create manipulatives to practice those basic facts independently or with a partner.
Throughout the year, the materials direct teachers to use the “Strategies and Practice for Skills and Facts Fluency” resource for additional practice to promote automaticity. While this resource makes connections to the development of conceptual understanding within the overview, materials do not explicitly embed these connections within the units or modules. Other than the correlation sheet, materials give no clear direction on how and when to conduct these fluency activities. The materials do not provide a year-long overview or scope and sequence for building fluency connected to the concept development and grade-level expectations that increase in complexity; however, the materials do contain elements that provide routines, complexity skill progression, and tracking of fluency progress. The materials provide some guidance for determining if students need differentiated supports for fluency activities. Teachers receive fluency support for English Learners. Fluency expectations for the grade level are not stated, and there is no explicit link or instruction in the Teacher Edition (TE) for fact fluency support. The “Practice for Skills and Fact Fluency – Primary, GK-3” resource has leveled lessons to support fluency, but the TE does not refer to this resource, and it is not correlated with specific lessons within modules. The workshop instructions are broken into three steps: “Introduce It!” “Develop It!” and “Make It!” The idea is for teachers to scaffold the lesson as the students develop the concept; however, the materials lack guidance for the teacher on how or when to move on and what to do for students who are struggling, even with the included “Tips.” In kindergarten, only one module pertains specifically to the fluency TEKS.
In Modules 1–6, materials cover Level 1 and portions of Level 2 of “Basic Facts Workshops.” The materials contain worksheets to help reinforce the fact fluency practice. The levels and worksheets are connected to specific lessons within the TE, as depicted in this resource.
In Basic Facts Workshop 1, “Readiness: Counting,” teachers ask, “Which number of letters in a name is the largest group in our class?” “Which number of letters is the smallest group in our class?” “How can we be sure?” This prompts dialogue and discussion among the class to support the point of this particular fluency lesson.
The Level 1 Basic Facts Workshop 11 utilizes the addition strategy “Using Doubles to Add.” The teacher makes six holes in a piece of paper that is folded in half and asks the students to count the number of holes in the paper. The teacher asks the students how many holes the paper will have after it is opened. The teacher writes the number sentence on the board and repeats this process a few times. The workshop also provides tips, such as, “It may take several rounds or practice before some children understand that the number of holes doubles when the paper is open.”
In Module 11, a lesson supports procedural fluency with “sums up to 5” by connecting the strategy to MathBoards and two-color counters. In this lesson, students use counters to “show” an addition story about birds. Students trace and then write the addends and then the sum for the algorithm. Students reflect upon the process with the question, “How do you know that you will add the groups together?” Students are thus developing a conceptual understanding of number relationships and strategies for addition fact fluency.
In Module 16, during a lesson on counting to 100 by tens, students find a mystery number on a hundreds chart. Teachers give them clues, such as, “You say my number when you count by tens.” “I am greater than 60.” “I am less than 80.” “What number am I?” Teachers receive the following prompts and sample responses to help guide their students to fluently count by tens: “What numbers do you say when you count by tens?” (10, 20, 30, 40, 50, 60, 70, 80, 90, 100.) “Where are those numbers on the hundred chart?” (In the last column.) “What do you notice about all of these numbers?” (They all end in zero.) “Circle those numbers. What is the second clue?” (I am greater than 60.) “Mark an X on 60. What is the last clue?” (I am less than 80.) “Mark X on 80. “What number do you say when you count by tens, that is greater than 60 and less than 80?” (70) “Color that number red. What is the secret number?” (70) The materials then direct: “Have children count aloud from 70 to 100 by tens.”
The materials support students in the development and use of mathematical language. The materials include embedded opportunities to develop and strengthen mathematical vocabulary and allow students to use vocabulary in context. However, there is little evidence of guidance for teachers to scaffold and support students’ vocabulary development and use. The supports are noted to be utilized for English Learners (ELs), and there are many opportunities for teachers to extend or scaffold; however, these are not explicitly stated in the Teacher’s Edition (TE).
Evidence includes but is not limited to:
Throughout all modules, the unit overviews highlight the mathematical vocabulary developed within the unit and the vocabulary revisited from prior modules and prior grades. Every page includes a “Vocabulary Builder” and “Vocabulary Reader” section. Vocabulary Builder includes review words on a yellow stick-on note and “preview words” in the margin of the TE; in the student edition, the vocabulary words are highlighted. Each module within the unit also includes a vocabulary section, which can be accessed through the multimedia “eGlossary” in the “Go Digit” resources. There is also a “Learning Task” section in the TE that guides teachers in facilitating discussions about mathematical vocabulary students will be using in the lesson. Every module begins with a “Lesson Opener,” which is a short video introducing students to the concept and the “Essential Question” of the lesson. The Opener provides students the opportunity to listen to math vocabulary in context. The materials include or encourage classroom routines to support language development and the use of academic vocabulary. The “Texas Math ELL Activity Guide TE Grade K-2,” although designed particularly for ELs, contains guidance and activities to implement for vocabulary development. The resource activities are designed to help children acquire math vocabulary and the language and writing skills necessary to communicate and understand math concepts. The instructional strategies include drawing, describing, identifying relationships, exploring content, defining, rephrasing, and language modeling. Within the guide, the “Vocabulary Chart” is designed to help students understand math terms related to numbers and operations. The terms are organized by grade level, so teachers can find vocabulary that applies to their children. Materials instruct teachers to use kindergarten vocabulary for first grade, and kindergarten and first grade vocabulary for second grade. The guide also provides teacher tips; for example, in the kindergarten section, materials remind teachers that the terms tens and ones as place value can be confusing, and that children can also confuse one and won when these words are spoken.
Throughout all modules, within the lessons, there is no evidence of classroom routines to support language development and use of academic vocabulary; however, the materials do build from student informal language to formal language by making explicit connections. The section “Supporting Mathematical Processes Through Questioning” included in the “Mathematical Process Standards” component of the TE has sample sentence frames and questions that directly correlate with the process standards of the TEKS. Every module includes a “Literacy and Mathematics” section that encourages students to write about math concepts; however, it does not explicitly direct students to include academic vocabulary. The materials provide some repeated opportunities for students to listen, speak, read, and write using mathematical vocabulary within and across lessons. These opportunities are mainly found in the unit introductions; they also can be found in the “ELL Differentiated Instruction” through the modules and lessons. However, there is no specific scaffolding for all learners.
In Modules 1 and 2, materials specifically note vocabulary. In Module 1, for the “Model and Count 1 and 2” lesson, the vocabulary is one, two, and match. In Module 2, “Count Forward and Backward to Five,” the vocabulary is forward and backward. Materials strategically match the vocabulary to the lessons in order to develop students’ mathematical vocabulary.
In Module 6, a lesson instructs teachers to use the EL strategy “Draw” with the instructions to have students demonstrate their understanding by drawing rather than by using language. The next step is to have students explain their picture.
In Module 8, the learning goal addresses the development of the mathematical vocabulary. The Essential Question is, “How can you use objects to show eighteen and nineteen as ten and some more?” The vocabulary is eighteen and nineteen, which directly correspond with the learning goal.
In Module 9, “Compose Numbers 4 and 5,” the vocabulary word is plus. Students read the expression together in the “Explore” section of the lesson. In the “Share and Show” section, the teacher says, “4 plus 1,” and students repeat. Throughout the student edition in this lesson, there is a dashed plus sign with the word plus above it, so the students have opportunities to write and read it. Materials use the vocabulary within the context of the mathematical tasks throughout the lessons and require students to communicate mathematical ideas.
In Module 11, the “Math Reader,” Pancakes for All, focuses on addition as joining; the essential vocabulary words are how many, one, two, three, four, and five. Students have the opportunity to discuss and write their answers to the questions included at the end of each reader.
Early in Module 20, at the beginning of a lesson, materials introduce the vocabulary word graph. The term is revisited in subsequent lessons as part of the “Engage” portion, in the Lesson Opener and in “Making Connections;” teachers ask students to share what they know about graphs. Questions include “What is a graph?” and “What things can a graph show you?” Students proceed to make a graph and interpret graphs to help solidify their understanding.
The materials provide opportunities for students to apply mathematical knowledge and skills to solve problems in new and varied contexts, including those arising in everyday life and society. Resources include options for students to integrate knowledge and skills together to problem solve and use mathematics efficiently in real-world problems; students have opportunities to analyze data through real-world contexts.
Evidence includes but is not limited to:
Throughout all modules, the materials provide opportunities for students to solve real-world problems in a variety of contexts; students apply their knowledge and skills from multiple units and previous grade levels in problem-solving tasks. The materials provide performance tasks that require students to integrate knowledge and skills from multiple focal areas of mathematics to successfully find a solution. The “Explore” section, which begins each student edition lesson, is usually a real-world word problem; the teacher introduces it, and the students listen and act on the information. The materials provide opportunities for students to analyze data using real-world contexts; lessons require students to compare and contrast as well as graph data.
In Module 4, students solve the following problem: “William has six counters. He has two more red counters than yellow counters. How many red counters does William have?” In this problem, students analyze the number 6 and possible ways to make 6 where one number is two more than the other number.
In Module 6, students compare the numbers 6 and 7; first, they compare using pictures, and then they use connecting cubes to analyze which number is more and which is less.
In Module 9, students compose the numbers 4 and 5. To do this, students must understand, for example, how many 1 and 3 are, and that one counter and three more counters would equal four. Because the first unit of kindergarten builds identifying numbers up to 20, students must have base knowledge before moving on to composing numbers in addition skills. Also in this module, students solve the following problem: “Ryan has three counters and one red counter. How many counters does Ryan have in all?” This is something students can connect with; the problem on their student edition page shows three yellow counters and one red counter for students to practice solving their work. These real-world contexts are developmentally appropriate; problems are based on what they are learning in class or what they would be familiar with outside of class.
In Module 11, students see a picture of children painting and receive a blank addition number sentence. The teacher reads the problem to the students: “Two children are painting. Two more children come to paint. How many children are there now?” The teacher provides students with counters and asks questions to guide students through their problem-solving process: “What do you need to find to solve the problem?” “How many children are already painting at the easel?” “How many more children are coming to paint?” “How can you find out how many children there are in all?” “How many children are there in all?” Students write the addition sentence and use their previous knowledge of reading, writing, modeling, and counting numbers to solve the problem.
In Module 13, a group of lessons focus on “Addition Up to 10.” The first lesson is on finding “one more and one less;” subsequent lessons focus on adding up to numbers preceding ten, then adding up to ten, and then applying sums up to ten through solving word problems. Module 13 is preceded by counting, recognizing and writing numbers, comparing and building numbers to ten, composing numbers, the concept of adding (joining) and subtracting (separating), and adding and subtracting numbers to five. The materials consistently incorporate problem-solving strategies and materials to utilize in solving problems in grades K–2 (e.g., manipulatives (counters, connecting cubes, base-ten blocks), ten-frames, MathBoards, part-part-whole mats, drawing strategies, and math models).
In Module 20, there are data analysis lessons and activities. Students sort, make and read real graphs and picture graphs, and collect and analyze data. In one lesson, students graph their favorite fruit and conduct surveys to graph other favorites such as colors, pets, snacks, and/or games. Students use data to create a picture graph and then answer questions about data analysis of the graph results. Finally, students present to the class. Also in this module, students answer questions about the “Favorite Fruit” graph: “How many children like bananas? How many children like apples? How many children like oranges? Which fruit did more children like?”
The materials are supported by research on how students develop mathematical understanding. Materials include cited research throughout the curriculum that supports the design of teacher and student resources; however, materials do not provide research-based guidance for instruction that enriches educators’ understanding of mathematical concepts and the validity of the recommended approach. The research is not cited throughout the materials; it only appears in the introduction or “Professional Development” section of the Teacher Edition (TE). Best practices, as articulated in the research, are implemented within lessons through the lesson design, questions, inclusion of process standards, etc. Cited research is current, academic, and relevant to skill development in mathematics. Cited research is not specific to Texas context or demographics. A list of resources is referenced on the TEKS correlation pages, but there is not a formal bibliography.
Evidence includes but is not limited to:
Throughout the year, every module follows the 5E lesson plan model (“Engage, Explore, Explain, Elaborate, Evaluate”); however, cited research does not mention this lesson plan model or the effectiveness of its use. Cited research does mention other components of the materials, specifically those focusing on the problem-solving standards: “Students engage in these problem-solving activities when they use a structured plan such as the ‘Problem-Solving MathBoard’ to solve problems. This offers a consistent approach to unlocking problems that builds success. This is important because understanding is a result of solving problems and reflecting on the thinking done to solve the problems” (Lambdin, 2003). The “Math Talk” and “Go Deeper” features provide opportunities for students to communicate their mathematical ideas. Research indicates: “Teachers should promote discourse among students and have students make conjectures and explain their work” (Kline 2008). The materials reference seven research studies; this research is only referenced on two pages of the TE (in the front): the “Texas Essential Knowledge and Skills for Mathematics” page and the “Mathematical Process Standards” page. Additionally, the materials do not provide research-based guidance for instruction that enriches an educator’s understanding of the concepts. The materials provide some research-based guidance for instruction that enriches educator understanding of the validity of the publisher’s recommended approach with sufficient references. The Professional Development component of the TE includes research to support the approach to the integration of mathematical process standards. There is a lack of guidance throughout the materials to enrich teacher understanding of the “why,” and the vertical alignment piece is missing.
In Module 3, in a lesson titled “Count and Order to 5,” teachers encourage students’ discourse: “Have children tell a friend what they know about the numbers and the cube trains.” The materials are scripted with questions teachers ask students in order to encourage and support mathematical discourse and problem-solving. Research by the National Council of Teachers of Mathematics (2000), in “Principles and Standards for School Mathematics,” states the importance of teachers promoting mathematical discourse to promote a deeper understanding of content.
In Module 11, the higher-order thinking skills (HOTS) question is, “In Exercise 2, one child is wearing a green shirt. Suppose two more children wearing green shirts come to the table. Now how many children at the table are wearing green shirts?” The TE explains that students will be guided through an interactive solving of this type of HOTS problem in the “Math on the Spot Video Tutor;” the TE also states that, with these videos and the HOTS problems, children will build skills needed in the Texas assessment. The Mathematical Process Standards page also references the “Math on the Spot” videos, which develop and reinforce problem-solving skills and techniques by demonstrating the solution to a HOTS problem for each lesson.
In Module 12, students use MathBoards and connecting cubes to reinforce subtraction. The materials explain how the TEKS calls for a coherent and balanced curriculum that treats mathematical knowledge and skills in a manner that will enable students to develop a deep understanding of the content, integrating process standards with the mathematics content at every grade level. The process standards are depicted in the top right box of the first page of each lesson within each module. The materials list examples of how this is included within the program, such as in understanding counting and cardinality, understanding addition as joining and subtraction as separating, comparing objects by measurable attributes, understanding and applying place value, and solving problems involving addition and subtraction.
The materials develop students’ ability to use and apply a problem-solving model. Materials guide students in developing and practicing the use of a model that is transferable across problem types and grounded in the TEKS, excluding the justification and evaluation pieces; the materials prompt students to apply the model and provide guidance to prompt students to reflect on their approach to problem solving. The materials provide teacher guidance to support student reflection on the approach to problem solving; this is done only through questioning techniques, which is age-appropriate.
Evidence includes but is not limited to:
Throughout all modules, students have the opportunity to solve problems in an age-appropriate manner. Each module throughout the kindergarten units contains at least one lesson geared at problem-solving; typically, this is the culminating lesson. “Problem Solving” lessons throughout all the kindergarten modules follow the same process: “Make Connections,” “Unlock the Problem,” “Try Another Problem,” “Share and Show,” and “Evaluation;” except Modules 8, 13, and 16 omit the Unlock the Problem step in the “Explore” portion. The materials help students engage with the TEKS; they begin with context-based situations and build to more abstract problems. Students use models, manipulatives, quick pictures, and symbols to build mathematical understandings. There is not a written problem-solving model for students or teachers, but graphic organizers that support a model are available; based on expected kindergarten-level exposure to justifying, evaluating, and reflecting on thinking, this is age-appropriate. Through components of the lesson, including embedded in the problem-solving lessons, “Math on the Go” think-aloud lessons, and the “Essential Questions” materials expose students to “thinking about their thinking.” The scripted lessons provided in Math on the Go contain “Why” and “How” question stems, which allow students to begin to engage in math talk; the teacher presents the problem-solving model verbally. Materials give teachers questions to guide the students in the use of the problem-solving model; students identify what information is provided or that they know, identify what they can do to solve the problem, and then go through the steps to find the answer using the plan. The same or very similar model of questioning is found throughout the modules in the problem-solving sections.
The “Mathematical Process Standards” page at the front of the Teacher Edition (TE) includes prompts for teachers to use to guide students to reflect on their approach to problem solving. Some of these prompts include, “What can you do if you don’t know how to solve a problem? Have you solved a problem similar to this one? How do you know your answer makes sense? Why did you decide to use ...? How do you know your answer is reasonable? Will that method always work? How do you know? What do you think will happen if ...?”
These types of questions are also included in the TE itself. For example, in Module 8, teachers ask, “How can you solve problems using the strategy ‘make a model?’” In Module 11, teachers ask, “How can you solve problems using the strategy ‘act it out?’” In Module 18, materials direct: “Have children analyze the given information and have children justify their solution.” Teachers ask, “How do you know your answer is correct?” This helps students grow in their reflective practices.
In Module 1, students make connections early. They “unlock” the problem (analyze given information); they “try another problem” (formulate a plan or strategy ); they “share and show” (determine and justify a solution); and they are evaluated on the problem to determine reasonableness. For example, a lesson begins with students brainstorming things that come in sets of one to four. The teacher models the digital lesson to the whole group; the lesson shows different types of models to use in determining the number in a set. Teachers then direct students back to the “Learning Task,” where they identify given information and tell a way to show/solve the problem. Teachers guide students to explain how they used counters to model the number of ducks in the pond; they ask, “What was in the pond?” “How many more ducks come in?” “How many ducks are in the pond now?” Students then try another problem using counters; teachers encourage them to use an iTool to model how to solve it. Students then share their process with their peers. Teachers are to remind students to read the problem twice to ensure understanding. Finally, students are evaluated in the problem-solving process, and they answer the Essential Question: “How can you solve problems using the strategy ‘make a model?’”
In Module 2, a lesson presents the following problem: “There are two horses in the pen. Then the two horses leave the pen and go to the field. How many horses are in the pen now?” Materials ask questions that are specific to this problem, but they can be made general. For example, the questions, “What was in the pen?” “Where are the horses now?” “How many are in the pen now?” lead students to analyze what information they know from the problem; this is later taught as the “Read” section found in the problem-solving graphic organizer. The TE has the teacher guide students to formulate a plan (“Plan” section), and the students solve the problem using the plan they created. This same problem-solving model is used throughout the modules, including with money, measurement, and geometry.
In Module 9, in “Model and Draw,” within the “Explain” section, the TE states, “Ask children to point to Exercise 1. Have children place counters in the five-frame as shown.” It displays the five-frame and colored counters to be used as a tool in the student edition, where students can follow along and solve their work. The student edition also prompts students to use the specific problem-solving tools they receive in their lessons. For example, in the homework section of the lesson, the whole section has five-frames and counters.
The materials provide opportunities for students to select appropriate tools for the task, concept development, and grade. They provide opportunities for students to select real objects, manipulatives, representations, and algorithms as appropriate for the stage of concept development, grade, and task. Students have the opportunity to select and use grade-appropriate technology. Materials provide teacher guidance on tools that are appropriate and efficient for designated tasks. However, the materials do not provide a “ tutorial” or “how-to” in teaching students how to use “iTools.”
Evidence includes but is not limited to:
Throughout the materials, materials introduce students to a variety of tools and strategies that are age-appropriate; children have opportunities to choose and explore these tools. In kindergarten, students may have limited experience with manipulatives in a learning environment; therefore, many of the lessons focus on specific manipulatives and their unique use. At the beginning of every unit, a “Materials” section informs teachers about the tool students will use in each lesson. The “Professional Development” portion of the Teacher Edition (TE) states that students need to use tools to be effective problem solvers, as addressed by the third Process Standard (C), which states that students must “select tools, including real objects, manipulatives, paper and pencil, technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.” The program also encourages drawing throughout. The materials state that teachers should be sure tools are available during problem-solving activities. Students need to participate in discussions about the tools they use and how they use them (Jacobs & Kusiak, 2006). This should include talking to each other about how the tools are similar and different; when students engage in these discussions, they learn to select tools that lead to more efficient problem-solving. On the resource page, materials provide “Live Links,” which make connections between TEKS and correlating lesson examples within the modules. The “Interactive Student Edition” (ISE) guides students through number concepts and skills that directly correlate with the lessons in each module. In these interactive lessons, students manipulate iTools through a guided video scenario. The videos, called “Math on the Spot,” help solve more difficult problems online for every lesson. The iTools do have a quick tutorial in the “Help” section for each virtual manipulative. Math on the Spot and ISE videos are easy to follow, but students will require teacher or parent guidance and assistance to use them.
Throughout the modules, kindergarten lessons are focused mostly on the concrete level of the “Concrete, Pictorial, Abstract” (CPA) continuum; therefore, the majority of lessons use hands-on manipulatives and pictures for exploring and solving problems. The materials also teach the use of the five-frame and the ten-frame; these are used to teach numbers up to and beyond 10 as well as adding and subtracting. The program encourages drawing throughout. Students use two-color red and yellow counters and connecting cubes throughout a majority of the modules. Except for the modules involving money and shapes, which allow students to use play coins and attribute blocks (Modules 15, 17, 18), the majority of the 21 modules only have students using two-color counters and/or connecting cubes. As skills are spiraled in and built upon, students use these manipulatives in more complex ways. For example, in Module 5, students use the counters to represent numbers in a ten-frame. In Module 8, they build numbers with counting cubes and then write numbers. Modules 11–14 spiral the ten-frame back in as students begin to explore addition and subtraction and represent equations with the connecting cubes.
The materials also include a “MathBoard;” one side has a section for students to work out story problems using manipulatives or drawings; the other side has a number grid counting by ones up to 100, with every other group of ten colored in, and two blank ten-frames.
In Module 1, in the first lesson, the materials introduce a MathBoard and color counters. As students explore greater quantities, they continue to use color counters and the MathBoard, but, as they progress through the lessons in the units, they may also use other manipulatives, such as connecting cubes, real or play coins, and attribute blocks, before transitioning to drawing numbers, money amounts, and shapes. Students have opportunities to use iTools such as counters, base-ten blocks, and number charts to help them understand number concepts.
In Module 1, materials guide teachers on using counters and a ten-frame with the students. Materials state: “Review counting objects and counting to 8 with children. What numbers do you say when you count to 8? (1, 2, 3, 4, 5, 6, 7, 8) Would you use counters and a five-frame to count 8? (no) Why not? (A five-frame only has 5 squares for each counter.) 8 is greater than 5. You would use a ten-frame.” These steps guide teachers on the tools they will use in the materials.
In Module 2, a lesson plan in the TE states: “You can use the digital lesson opener as a whole-class activity. You can pause at any point to have a discussion. How will children use cubes to model the numbers shown in the problem? Discuss the models with the children. How do they compare? Children will have the opportunity to return to the opening scenario and answer the question in the Daily Assessment Task.”
In Module 6, students must represent a problem where they have 2 leaves plus 2 more leaves. Materials direct teachers: “Remind students to use simple drawings like shapes or dots.” In this same module, the “Common Errors” section provides teacher guidance for student errors. One common error noted is that students might not know how many counters there are to begin with. The “Springboard to Learning” section provides a scaffolding suggestion: Reread the problem to students. Point out the number that was given in the problem. Explain that this is the number to start with. Then children can add or take away counters depending on what the problem is asking.
The materials include opportunities for students to select appropriate strategies for the work, concept development, and grade. Materials prompt students to select a technique; they provide opportunities for students to solve problems using multiple strategies. The resources support teachers in understanding the strategies that could be applied and guide students to utilize more efficient choices.
Evidence includes but is not limited to:
Throughout all modules, the materials include prompts that require students to select a technique for solving a task; a majority of the strategies taught in kindergarten are the use of manipulatives, acting out, and drawing. “Share and Show” in the “Explain” portion of lessons also gives students opportunities to select their method of problem solving with teacher guidance and support appropriate to the grade level. The prerequisite skills that students need to know before learning each particular lesson are available in each unit’s “Vocabulary Ready” section. By understanding these prerequisite skills, teachers can understand which strategies are appropriate for solving a task. In the Teacher Edition (TE), many prompts throughout the lessons guide teachers to distribute information. These prompts also help explain to teachers why a strategy might be more useful than another. Each lesson within each kindergarten module has sample “acceptable” student responses to questions and directions embedded throughout the lesson cycle; these help the teacher understand appropriate strategies. Although the materials provide scripted lessons and suggested activities, the materials do not provide detailed or specific explanations to help teachers guide students to use more efficient strategies.
On the “Mathematical Process Standards” page, at the front of the TE, there are teacher prompts to guide students to reflect on their strategies. Some prompts include, “What can you do if you don’t know how to solve a problem? Have you solved a problem similar to this one? How do you know your answer makes sense? Why did you decide to use…? How do you know your answer is reasonable? Will that method always work? How do you know? What do you think will happen if…?” These types of questions are also included further in the TE; for example, in Module 1, teachers ask, “Is there more than one correct way to show a number? Explain your thinking. Are there more ways to show some numbers than other numbers? Why?” In kindergarten, teachers can use these question stems; however, there is no “formal” math talk designated in the lessons as in the upper grades.
In Module 8, students select a method (make a model or draw) and select a tool (cubes or an “iTool”) to solve problems involving adding, subtracting, and comparing numbers. Students have had experiences with these methods and tools in previous lessons. The teacher explains that there are two ways to compare the cube trains: matching the cubes and counting the cubes. Students decide which strategy they will use and draw a picture illustrating their technique. Students practice this skill again in the next portion of the lesson: They either use cubes or select an iTool to model apples and compare cubes. The teacher provides students with access to iTools and other forms of technology to select as a tool to solve the problem. Students draw the cube and write the numbers to determine how many there are in each set; they also compare numbers and sets to determine which is larger/greater. Students continue comparing using cubes or an iTool to model sets of numbers. Students reflect on the process by answering questions such as “How can you find out which set has fewer cubes?” and “How can you solve problems using the strategy ‘Make a Model?’” Student answers may vary since students have choices in their materials and techniques.
In Module 9, some prompts explain why a certain strategy could be used when adding numbers: “What can we do to solve this problem? Possible answer: We can use two-color counters to show Jake’s counters. How many counters does Jake have? Place 5 yellow counters in the five-frame and write the number on the first line. The problem says that two of Jake’s counters are red. Turn over the two last counters in the five-frame so that they are red. Draw and color the counters. How many counters are red? 2. Write 2 on the second line. Now, how many yellow counters are there? 3. How many yellow counters does Jake have? 3. Write 3 on the last line and trace the symbol. Have children find other ways to take apart 5.” In this example, students use number sense to identify how many counters there are. They also place the manipulatives on the picture as a strategy.
In Module 10, students learn to compose and decompose numbers up to 10 using a ten-frame and two-sided counters. Students write addition sentences and use connecting cubes to model decomposing numbers up to 10 with subtraction sentences. At the end of this module, students solve addition and subtraction problems using strategies of their choice, such as modeling, mental math, or counting.
In Modules 11–14, the addition and subtraction modules, students solve problems using multiple appropriate strategies, such as modeling problems with counters or two-color tiles, using ten-frames to represent and solve problems, and/or drawing pictures to represent and solve the problems. Students also make connections across concepts. For example, in Module 14, teachers help students see the connection between addition and subtraction and how they can use their knowledge of addition to help them solve subtraction problems. Teachers write the number sentence 7 + 2 = 9 on the board. They ask, “How does knowing this addition fact help you solve 9 - 2 = ...? How are the number sentences alike? How are the number sentences different?”
In a Module 11 word problem, two children are playing, and three more join. Students must find how many children are now playing. Students follow teacher prompts to use manipulatives, write numbers down (number sense), and finally solve the equation. By seeing the written algorithm, students are learning to understand mental math and abstraction. This problem provides teacher prompts and anticipated student responses.
In Module 14, the teacher asks, “How can you find the number of white bunnies?” A provided possible answer is, “subtract; count.” Also in this lesson, the teacher asks, “How are the number sentences different?” A potential reply is, “The numbers are in a different order, and one number sentence has a plus sign, the other has a minus sign.” The culminating question in this lesson is, “How can you solve subtraction word problems and complete the subtraction sentence?” Possible student answers are, “I can use the pictures to help me subtract and solve the take away and take apart problems. I can use the numbers in the problem to complete the subtraction sentence.” By listing potential student responses, materials help the teacher understand appropriate strategies.
In Module 18, materials direct: “Have children analyze the given information and have children justify their solution and strategy.” Teachers ask, “How do you know your answer is correct?” and “Is there another way you could have solved this problem?”
The materials develop students’ self-efficacy and mathematical identity by providing opportunities to share strategies and approaches to tasks. Materials support students to see themselves and mathematical thinkers who can learn from solving problems, making sense of mathematics, and productively struggling. Resources support students in understanding that there can be multiple ways to solve problems and complete tasks. The materials support and guide teachers in facilitating the sharing of students’ approaches to problem solving.
Evidence includes but is not limited to:
Throughout all modules, the materials present mathematics as a field of study focused on developing efficient and generalizable ways for solving problems, not as a set of procedures to memorize; students are at the center of problem-solving. The “Professional Development” portion of the Teacher Edition (TE) maintains that to engage in problem-solving, students must be provided with problems for which a pathway toward a solution is not immediately evident. When students need to find a pathway, they may refer back to the context of the problem to make sense of how to solve it. Through the lesson structure in each lesson, teachers are able to guide students through higher-order thinking processes. When students get questions wrong, the TE prompts the teacher to ask additional questions or provide additional support in a different way to help students engage and grow by making sense of mathematics. The “Essential Questions” posed in each lesson foster a community of thinkers and support the engagement of mathematical thinking as many of the questions are open-ended. The materials scaffold learning from simple- to higher-rigor problems as the lesson progresses, allowing students to feel success as they develop their critical thinking skills. The materials provide supports for all learners to participate and engage as mathematical thinkers; there are supports for English Learners in each module and in the “ELL Activity Guide;” supports for below-level learners in the “RTI Tier 1, 2, and 3 Guides;” and supports for above-level learners in the “Enrich” section of each module as well as in the “Enrich Guide.” There is also a “Common Errors” section in every lesson, which helps the teacher guide students who may be struggling, get them back on track, and help them solve problems. Materials provide tasks that allow for multiple pathways to a solution. Students are able to see these pathways through whole group and small group discussion as prompted in the TE.
In Module 3, teachers ask, “Did you use matching to compare the sets? (Yes). Explain how you know your answer is correct.”
In Modules 3 and 5, the “Math-on-the-Spot” videos show characters of both genders who are successful in mathematics. In Module 3, Mrs. Sandoval teaches Jeannie how to count and order numbers to 5. In Module 5, Prof. Berger teaches Jeannie to count and write to 9.
In Module 4, an Enrich partner section directs: “Have one child draw from one to six objects on the top part of a sheet of paper. On the bottom part of the same paper, have the other child draw a number of objects that is two greater than the first set. Have partners write how many are in each set. Children switch roles, and the first child draws from three to eight objects. The other child draws a number of objects that is two less. Partners write the numbers for each set.” As they discuss their problems and solutions, students are able to see multiple pathways to a general problem since they each approach the problem in different ways.
In Module 8, a Common Error is that children may not be able to identify the greater number. Materials then direct teachers to “Springboard to Learning” by modeling 18 and 16 with counters and then helping children see that there are two counters without a match, so 18 is greater than 16.
In Module 12, students use cubes to act out a subtraction problem. Students then share how they formulated their problem-solving plan with their peers. In the “Go Deeper” component of this lesson, the teacher alters the problem, and the class discusses how the outcome is different.
In Module 16, students use what they know about finding one more or one less, ordering numbers, and comparing numbers and number patterns in order to count from any number in solving problems. Students count aloud from 34 to 50 and then evaluate the problem-solving process. Students may count, use the clues, and use the hundred chart to find the secret number by applying the concepts of comparing and number patterns. Students also have to be astute to the clues in determining what clue is essential in selecting the correct answer.
The materials include prompts for students to effectively communicate mathematical ideas, reasoning, and their implications using multiple representations. The opportunities are task-appropriate for students. Materials guide teachers in prompting students to communicate in multiple modalities, including writing and using mathematical vocabulary.
Evidence includes but is not limited to:
The “Professional Development” component of the Teacher Edition (TE) states that, throughout all modules, students need to engage in productive discussions about representations of problems and to present problems and their solutions. In the TE, the “Supporting Mathematical Processes Through Questioning” section provides question stems that directly correlate with Process Standards: “What operation did you use to represent the situation? Why does that operation represent the situation? What properties did you use to find the answer? How do you know your answer is reasonable?” These embedded questions cue the teacher to help students communicate mathematical ideas. Throughout lessons, prompts and guidance help teachers facilitate discourse in age-appropriate ways. Teachers model and reinforce mathematical language within the lessons; materials also encourage language modeling at home and through the homework assignments. Students can demonstrate their understanding in multiple ways, such as through visual, physical, contextual, verbal, and symbolic representations and within the “5E” lesson model. The unit overviews highlight the mathematical vocabulary developed within the unit and which vocabulary is revisited from prior units and prior grades. Every unit page includes a “Vocabulary Builder” section and a “Vocabulary Reader” section. Vocabulary Builder includes review words on a yellow sticky note and “preview words” in the margin of the TE.
In Module 5, “Model, Count, and Write 10,” students use their knowledge of representing numbers using counters in a ten-frame. Students again connect their knowledge of numbers in the middle of the year, in Module 10, when they compose and decompose numbers to ten. At the end of the year, in Modules 11–14, they once again connect their sense of numbers to addition and subtraction, using counters and ten-frames in more complex ways throughout these modules. Students solve problems using multiple appropriate representations, such as modeling problems with counters or two-color tiles, using ten-frames to represent and solve problems, and/or drawing pictures to represent and solve the problems. Students also have opportunities to make connections across concepts.
In Module 7, a lesson’s “Go Deeper” section provides the following suggestion to encourage math discourse among the students: “Have children explain how they know that 14 is one greater than 13. Explanations should include that there are more counters below a ten-frame for 14 than there are below a ten-frame for 13 and that 14 is said after 13 when counting in a number sequence.”
In Module 8, students use paper clips, counters, pictorial representations, ten-frames, numeral cards, verbal explanations, their fingers, and various virtual “Go Digital Resources” to answer the Essential Question, “How can you use objects to show 18 and 19 as ten and some more?” Students can thus use a variety of mathematical representations to show how they found their answer. This lesson, focusing on 18 and 19, also utilizes mental math strategies, which is another way students can communicate mathematical ideas. Students must have automaticity with numbers up to 17. For example, the Student Edition asks students: “Hold up both of your hands. How many fingers do you count? (10) Put down one of your fingers. How many fingers are you holding up now? (9) What does that number look like when you write it? (Children will write a 9 on their papers.)” The homework listed at the end of this lesson does not instruct students to use manipulatives, assuming that students have mastered the idea of 18 and 19 and have been released to do independent work on their own. In the homework listed at the end of each lesson, each student uses pencil-and-paper pictorial representations of counters to show that they understand what they have learned.
In Module 17, students examine various shapes in multiple formats (tangible blocks, pictures, and visual representations) to identify squares and determine what distinguishes a square from a “non-square.” Students trace a square using their finger, then trace it with a pencil or crayon, and then physically point to vertices. Students share observations throughout the process. Students are guided to understand that, like a rectangle, a square also has four straight sides and four vertices, but the sides are all of equal length. Students use a sorting mat to distinguish squares from other shapes/figures that are not squares and justify their selections by explaining what constitutes a square. Teachers remind students that squares are regular shapes; the class discusses how the shapes in the “not squares” category are irregular. Students then discuss whether using different numbers of blocks to build a square changes the number of sides and vertices the square has. The square is then manipulated and presented in a different format (turned so that the vertices are pointing north, south, east, and west). Students use counters to help justify that this shape is still a square even though it is turned. Students then use grid paper to draw squares of varying sizes. The teacher asks children to think about things that are shaped like squares. Students brainstorm and create a list.
In Module 21, in a “Share and Show” section of the lesson, materials guide teachers: “Tell children that today they are going to look at some different pictures of children. Some pictures will show children playing. Other pictures will show children doing a chore to earn money or income. Explain that people need to earn income to be able to buy or pay for things that they need.” The materials then provide teacher prompts, such as “Which picture shows a child working to earn money? Draw a circle. Which picture shows a child playing? Draw an X on the picture.” Students use diagrams to help communicate their understanding of the content.
The materials provide opportunities to discuss mathematical ideas to develop and strengthen content knowledge and skills. Students have opportunities to engage in mathematical discourse in a variety of settings; the materials integrate discussions throughout to support students’ development as appropriate for concept and grade level. The resources guide teachers in structuring and facilitating discussions as appropriate for the concept and grade level.
Evidence includes but is not limited to:
Throughout all modules, some lessons encourage mathematical discussions within the whole group, small group, partners, and individual instructional settings. This is fostered throughout the “5E” lesson format as well as in center activities, STEM activities, vocabulary activities, English Learner (EL) activities, and “Enrich” activities. The groupings vary in the lessons depending upon the nature of the skill, concept, and activity. The materials offer little to no guidance for teachers on how to structure discussion that is appropriate for the grade level, but the lessons are scripted and contain questions with answers and/or possible student responses. “Lesson Openers” and the “Share and Show” sections embed small group discussions that can be used for remediation and challenge to help struggling students clarify misconceptions, and also to deepen and extend thinking for students who are ready to extend the skills and concepts. Every lesson provides “Differentiated Instruction” in a small group setting, allowing for small group discourse. Every lesson provides “Grab-and-Go” activities for partners or small groups.
The “ELL Activity Guide” for all grade levels provides the following guidance for teachers in working with EL students: “Teachers can provide comprehensible input through the use of gestures, appropriate speech rate, dramatization, visuals, realia, and hands-on activities using manipulatives, charts, repetition, and rephrasing.” Teachers are also guided to encourage student interaction because of the social nature of language learning. Materials state that students need continual opportunities for interaction, both child-to-child and teacher-to-child. Materials instruct teachers to provide ELs with frequent opportunities to interact with native English speakers.
In Modules 1–5, students discuss how to model, count, and identify the numbers 1 through 10. In Module 6, students discuss how to compare numbers to 10. In Modules 7–8, students discuss how to read, write, and model numbers through 20 and answer the following “Essential Question:” “How can you count forward to 20 from a given number?”
In Module 5, in a whole group discussion, students review counting to 9 and discuss how to count to 10. Materials instruct: “Guide the children to count more than 9. What does Scout need to count? (the buckets) What will counting tell you? (how many there are) Why is Scout having trouble counting? (He hasn’t counted this many before.) How high can Scout count? (to 9) How many more buckets do you see? (1 more).”
In Module 9, at the beginning of the lesson, in the “Making Connections” section, students have a whole group discussion: “Invite children to tell you what they know about modeling numbers. What number is one more than 1? (2) What number is one more than 2? (3)” In the EL “Language Support” section, students have a small group discussion: “Children can practice their comprehension by describing in words what they have seen. Have children make a green two-cube train. Have children add one orange cube to the train and describe the train. The cube train has two green cubes and one orange cube. You can also say that the cube train has three cubes. Have children repeat this phrase.” In the “Share and Show” section that follows, students have a whole group discussion: “How many counters are in the five-frame in all? (2) How can you tell? I can count all the counters.” In the “Enrich” section, students work with partners: “Give partners a paper bag and five cubes. Ask one partner to take out no more than four cubes; then, the other partner takes out the remaining cubes. Ask partners to make two sets of cubes and to write the numbers that represent their sets of cubes. Have them write how many cubes there are now. Have partners take turns being the first to take out some cubes.”
In Module 11, in a “Share and Show” lesson, teachers read the problem aloud and prompt the class discussion: “There are three children eating lunch. One more child joins them. How many children are having lunch now? (4) Place one counter on each child having lunch. Write the number. How many children are joining the group? (1) Place one counter on the child joining the group. Write the number. What will you have to do to find how many children there are now?” The TE suggests small groups, whole groups, and partner groups throughout the lessons for discussion guidance. Also in this module, a “Making Connections” lesson section states: “Invite children to tell you what they know about joining objects or numbers together” as a whole group. In the same lesson, the “Differentiated Instruction” section suggests using small groups.
In Module 15, a lesson on money starts with a Lesson Opener to activate prior knowledge of numbers and discuss what a penny looks like. Prompts include “What is Scout trying to learn about pennies?” The next section, “Share and Show,” includes more prompts to scaffold students’ learning through discourse: “This coin is called a penny. What color is it?” The lesson ends with a Higher-Order Thinking (HOT) problem; the prompt is: “Josh has 8 pennies. He needs some pencils for school. Pencils with sparkles cost 5 pennies. Plain pencils cost 3 pennies. Josh decides to buy plain pencils. How many pencils can he buy? Explain your answer.”
In Module 21, students name workers and describe what they might do at work. After reading/listening to clues about various workers, students brainstorm other skills each of the workers might need in order to do his or her job well. Students then work in small groups to create riddles about jobs and analyze clues to determine potential answers. The discussion goes a bit deeper as students predict the tools needed by certain workers. Finally, students answer the Essential Question, “How do you identify what skills are needed for a job?” and support their responses.
The materials provide opportunities for students to justify mathematical ideas using mathematical representations and precise language. Students are able to construct and present arguments that justify mathematical ideas using multiple representations; teachers assist in facilitating the construction of arguments using grade-level-appropriate ideas and mathematical language. There are no formal “Math Talks” in kindergarten, but the teacher provides ample opportunities for students to justify their work and answers.
Evidence includes but is not limited to:
Throughout all modules, there is a write-in Student Edition (SE) for every grade. Students record, represent, solve, and explain as they discover and build new understandings. The Teacher Edition (TE) includes routines and structures that teachers can use to facilitate students’ construction of arguments. The “Mathematical Process Standards” at the front of every grade-level TE provide the following question prompts for teachers: “Will that method always work? How do you know? What do you think about what she said? What do you think will happen if …? When would that not be true? Why do you agree/disagree with what he said? What do you want to ask her about that method? Why did you decide to use …?”
In Module 2, students use counting cubes to create towers representing a number from 1 to 5. Teachers ask, “What do you notice about the cube towers when you are counting forward?” Each tower is one cube taller than the previous tower, which concretely displays number progression. Later in this lesson, students count backward from 5 using their fingers on one hand, which enables them to justify mathematical representation in a concrete, visual way. The TE provides teacher guidance for the lesson; for example: “Guide children to understand that as they count forward, each cube tower (or number) represents a set of cubes that contains one more cube than the previous cube tower (or number).”
In Module 4, materials guide teachers: “By having children explain what they know, you are providing them with opportunities to use mathematical language as well as deepening their understanding of mathematical ideas and directing students to think about how they made a set of seven counters.” Throughout this module, teachers ask questions to help students justify their thinking, such as “How are seven counters different than six counters?” “Would seven buckets of popcorn be enough for our class, or would we need more or fewer buckets?” Materials instruct teachers to accept all reasonable answers; however, they do not provide examples of reasonable answers. There is a possible answer provided for the “Essential Question:” “How can you show and count seven objects? (I can make sets with seven counters. I can draw a set of seven counters.”
In Module 5, in the “Go Digital” section, the TE prompts teachers: “Use counters to help the children model the number of apples.” In the “Literacy and Mathematics” section, students think of words that rhyme with “nine” and write a story. Both of these representations help students justify mathematical ideas. In the “Explore” section, students use counters to solve problems. In the “Share and Show” section, students use pictorial representations of counters and also write numbers — another representation. In the “Enrich” section, students use connecting cubes of two different colors to create “cube trains” of nine cubes; they record their work by drawing what they created. In the “Explore” section, the teacher asks, “When you are counting, is a number always greater than or less than the one before it? (Greater than).” This open-ended question creates a platform for discussion and facilitates student construction of arguments. The same can be said of the question in the Share and Show section: “Look at the model for nine that you made; what number or counters put with five make nine? How did you find the answer?”
In Modules 11–14, the addition and subtraction modules, students are given the opportunity to solve problems and justify their mathematical ideas using multiple appropriate representations, such as modeling problems with counters or two-color tiles, using ten-frames to represent and solve problems, and/or drawing pictures to represent and solve the problems. Students also make connections across concepts. For example, in Module 14, teachers help students see the connection between addition and subtraction and how they can use their knowledge of addition to help them solve subtraction problems using picture representations.
In Module 13, in the TE, the “Differentiated Instruction” section gives the following guidance: “Restating key vocabulary helps children understand math problems.” The English Learner strategy “Restate,” for use individually or in small groups, states: “Help students see the correspondence between ‘is equal to’ and ‘is the same as’ and between ‘plus’ and ‘add.’”
In Module 15, the teacher helps students make connections to one-to-one correspondence and realize the value of a penny. The teacher asks, “How is counting a penny like counting a counter?” In the “Go Deeper” portion of this lesson, students use coins and pencils or drawings to determine that the character in the problem will only be able to buy two pencils for six pennies. The TE advises the teacher that student explanations should include that he will have two pennies left, which isn’t enough for another pencil. The materials prompt the teacher to discuss why Josh may have decided to buy plain pencils. Some children may find he could buy one sparkle pencil with 8 pennies. These questions and prompting support and guide students through their justification process and proving reasonableness.
In Module 20, an Essential Question functions as an Exit Ticket: “How can you collect data and use that data to create a graph?” A possible answer is, “I can ask my classmates a question. Then I can record their answers by drawing circles in a graph.”
The materials include developmentally appropriate diagnostic tools and guidance for teachers and students to monitor progress. Materials include various tools such as anecdotal and formal tools and provide teachers with guidance to ensure consistent and accurate administration of the tools. However, there is little evidence of students monitoring their own progress and growth. Diagnostic tools measure all content and process skills as outlined in the TEKS and Mathematical Process Standards.
Evidence includes but is not limited to:
Materials state: “The Prerequisite Skills Inventory in the Assessment Guide should be given at the beginning of the school year or when a new child arrives. The multiple-choice test assesses children’s understanding of prerequisite skills. Test results provide information about the review or intervention that children may need in order to be successful in learning the mathematics related to the TEKS for the grade level. The IRF for the Prerequisite Skills Inventory provides suggestions for intervention based on the child's performance.” Every module across grade levels begins with an “Are You Ready?” pre-assessment that can be found in the “Assessment Guide” for each grade level. The Assessment Guide also includes a “Prerequisite Skills Inventory,” a “Beginning-of-Year Test,” a “Middle-of-Year Test,” an “End-of-Year Test,” and Module and Unit Tests. These Module and Unit Tests are also found in the Teacher Edition (TE) and Student Edition (SE) across grade levels. The materials include an “Online Assessment System,” which offers flexibility to individualize assessment for each child. Teachers can assign entire tests from the Assessment Guide or build customized tests from a bank of items. For customized tests, teachers can select specific TEKS to test. Multiple-choice and fill-in-the-blank items are automatically scored by the Online Assessment System; this provides immediate feedback. Tests may also be printed and administered as paper-and-pencil tests. The same intervention resources are available in the Online Assessment System, as in the Assessment Guide for each grade level.
In all modules, assessments and activities allow students to demonstrate understanding in a variety of ways and settings. Every module and unit assessment across grade levels indicates the TEKS that each question assesses. The materials provide suggestions for tracking progress in the Assessment Guide, which includes “Individual Record Forms” (IRF) for all tests. The IRF for each test also provides correlations to the TEKS. The Prerequisite Skills Inventory includes correlations to the TEKS from prior grade levels to assist teachers in developing plans for additional support. There are routine and systematic progress monitoring opportunities through the “RTI Quick Check,” “Problem Solving,” “HOT problems,” and “Daily Assessment Task” sections found in the TE of every lesson. The materials include recommendations for assessing students with formal progress monitoring measures at least three times during the school year: at the beginning of the year, in the middle of the year, and at the end of the year. This frequency allows teachers to identify who is and is not demonstrating progress.
In the Middle-of-the-Year Assessment, if a student misses item number six, the materials indicate that the student most likely missed this item because he/she does not understand the concept of “greater.” The teacher is directed to “Soar to Success Activity 1.03,” which correlates with Lesson 4.6 in Module 4 and Process Standard 4.2E. The materials are scripted, so teachers have support in what to say and what to ask when administering assessments. Materials provide direct guidance following assessments; teachers have clear guidance as to where to go to find support lessons/activities and enrichment activities depending upon if the student needs intervention or extension. The script helps ensure fidelity and consistency in testing administration.
In Module 1, materials provide questions to assess student understanding, such as “How did you use cubes to show the sets of toys?” In the same lesson, the RTI Quick Check guides teachers on how to act on the results of a diagnostic tool (e.g., if the student misses questions three and four, differentiate instruction with RTI Tier 1 Lesson 4).
In Modules 1–14, students use two-color counters and/or connecting cubes to represent and solve problems using concrete models. As materials spiral and build upon skills, students use these manipulatives in more complex ways. In Module 5, students use the counters to represent numbers in a ten-frame. In Module 8, students build numbers with counting cubes and then write numbers. In Modules 11–14, the use of the ten-frame is spiraled back in as students begin exploring addition and subtraction and represent equations with the connecting cubes. Students are assessed throughout the lesson via their representations and their verbal responses to questions such as “How can you show a number with counters?”
In Module 5, in the “Access Prior Knowledge” section, the TE prompts: “Use the ‘Are You Ready?’ 14.1 in the Assessment Guide to assess children’s understanding of the prerequisite skills for this lesson.” 14.1 in the Assessment Guide covers how many make up the numbers six and seven. This is appropriate for grade and content level because the lesson’s question is, “How can you show differences within 7?”
In Module 6, the RTI Quick Check states: “If a child misses the checked exercise(s), then Differentiate Instruction with RTI Tier 1 Lesson 41. If a student got the assigned questions correct, they can move on to higher-level thinking problems.” This Quick Check after “Share and Show” is strategically placed to allow students the opportunity to understand the lesson whole group and practice whole group, usually with manipulatives and always with pencil and paper, in the SE. Lessons also include a Daily Assessment Task section. “Common Errors” sections serve as an informal assessment. In this lesson, Common Errors states: “Children may have difficulty making number comparisons and using comparative language. Springboard to Learning: Help children to connect greater with more and less with fewer. Review that when you count, the number that comes after another number is greater. Have children tell which is greater, 1 or 2. (2).”
In Module 8, in “Model and Count 18 and 19,” materials recommend teachers use Are You Ready? to assess prior knowledge and to assess the prerequisite skills for this lesson. The RTI Quick Check states: “If a child misses the checked exercise, then Differentiate Instruction with RTI Tier 1 Lesson 26.” Common Errors guides teachers on possible misconceptions students may have as they attempt to master the lesson’s concept; for example, “Children may not draw the correct number of counters. Springboard to Learning: Have children count the drawings by placing a dot on each to see if there are 18. If there are not, ask children to tell how many more counters are needed to complete the drawing.” The Daily Assessment Task asks if students can use objects to show 18 and 19 as ten and some more. If no, it directs teachers to use “Soar to Success Math Warm-Up 1.08.” If yes, teachers use “Enrich 37, Homework and Practice Lesson 8.3.”
In Module 11, the beginning activity is an Are You Ready? assessing the prerequisite skill of using addition strategies to solve word problem situations. This lesson contains differentiation/leveled activities for English Learners, an RTI Quick Check with supports to use should a student experience difficulty, and HOT problems and “Go Deeper” exercises for students who are mastering the skill/concept. Should students be ready to perform the Go Deeper task, the “Math on the Spot Video Tutor” provides a mediation piece to guide students through the addition processes. The RTI Daily Assessment Task in this lesson asks students to solve problems using the “act it out” strategy. If successful, students move onto the “Enrich” and “Homework and Practice” portions. If students need more support, the materials direct teachers to specific Soar to Success activities. In the “Evaluate” portion of this lesson, students individually solve addition story problems as part of a culminating independent assessment. Since this lesson is the final one in Module 11, there is a summative assessment to culminate the module and assess student learning and progress.
The provided materials include guidance for teachers and administrators to analyze and respond to data from diagnostic tools. There are supports, guidance, and directions for teachers to respond to individual students’ needs in all areas of mathematics based on the measures. Tools yield meaningful information for teachers to use for planning instruction and differentiation, and materials guide teachers on how to leverage different activities to respond to the data. However, there is no guidance for administrators to support teachers in analyzing or responding to data.
Evidence includes but is not limited to:
Throughout the curriculum, every module across grade levels includes one or two problems for teachers to use as a “Quick Check” to monitor and assess students’ needs. If a student misses the Quick Check problems, teachers provide them with differentiated instruction using lessons from the “RTI Guide.” There is also a “Data-Driven Decision Making” section in every grade level’s Teacher Edition (TE); module and unit assessments guide teachers on next steps for individual and whole-class instruction. The lessons within the modules include various opportunities for differentiating instruction in the “RTI Quick Check,” “Problem Solving,” “HOT Problems,” and “Daily Assessment Task” sections. An “Assessment Guide” resource outlines the purpose of the diagnostic assessments, thus supporting understanding. The Assessment Guide includes “Individual Record Forms” (IRF) for all tests. On these forms, each test item is correlated to the TEKS it assesses; there are intervention resources correlated to each item. “Common Errors” explain why a child may have missed the item. These forms can be used to follow progress throughout the year, identify strengths and weaknesses, and make assignments based on the intervention options provided. Although administrators can use the data included in the materials to identify specific areas of need for program improvement or to provide support for teachers to improve instruction, this is not explicitly stated or evidenced in the materials.
In Unit 2 (which covers multiple modules), in the TE, the “Summative Assessment” contains a Data-Driven Decision-Making section, which, similarly to the “Module Assessments,” provides guidance and suggested responses to those needing additional practice in order to master the concept(s). It states if children struggle with numbers 4–5 (Lessons 11.3, 13.3), teachers should use RTI Lessons 59 and 63 as well as “Soar to Success Math 10.09.” A listed Common Error is that the student may not understand how an addition sentence or expression relates to a model.
In Unit 3 (which covers multiple modules), the “Assessing Prior Knowledge” component has students complete “Show What You Know” on their own. Tested items are the prerequisite skills of this unit. The “Diagnostic Interview Task” evaluates understanding of each Show What You Know skill. There is a diagnostic chart used for intervention on prerequisite skills. Students place 18 two-color counters in ten-frames; they must count the number of counters and write the number. The teacher displays the number 17 and asks, “What is the number?” (17) The teacher counts out 17 connecting cubes and then fills two ten-frames with 20 connecting cubes or counters. Students count the number of cubes or counters and write the number. The teacher refers to a chart to determine the next course of action. The chart directs the teacher on supports (tiered activities) to provide if students were unsuccessful in the task; it also directs the teacher on independent activities for students who were successful with the task.
In Module 6, the RTI Quick Check states: “If a child misses the checked exercise(s), then Differentiate Instruction with RTI Tier 1 Lesson 41.” If a student got the assigned questions correct, they can move on to HOT problems. This Quick Check after “Share and Show” is strategically placed to allow students the opportunity to understand the lesson whole group and practice whole group, usually with manipulatives and always with pencil and paper, in the Student Edition. Lessons also include a Daily Assessment Task section. Common Errors sections serve as an informal assessment. In this lesson, Common Errors states: “Children may have difficulty making number comparisons and using comparative language. Springboard to Learning: Help children to connect greater with more and less with fewer. Review that when you count, the number that comes after another number is greater. Have children tell which is greater, 1 or 2. (2).”
In Module 8, a Common Error is that students may not be able to identify the greater number. Materials direct teachers to “Springboard to Learning” by modeling 18 and 16 with counters and then helping children see that there are two counters without a match, so 18 is greater than 16.
In Module 7, in the “Model and Count 13 and 14” lesson, the RTI Quick Check formative assessment in the TE states: “If a child misses the checked exercises, then Differentiate Instruction with RTI Tier 1 Lesson 21.” At the end of the lesson, students complete a Daily Assessment Task. The TE provides guidance on how to respond to students who are not successful.
In Module 9, if students can solve problems using the “Make a Model” strategy, teachers give them Exercise 43 from the “Enrich Guide.” The Daily Assessment Task section guides students who are unsuccessful to complete the Soar to Success activity “Warm-up 10.03 a and 11.03.”
In Module 13, teachers perform an RTI Quick Check with an “If …, then …” course of action. If a student misses a checked item within the Share and Show lesson activity, the teacher differentiates instruction by using RTI Lesson 64. Common Errors states that if students write the wrong numbers for addends, they should count to check the number of objects in each picture and count the number in each set twice before writing the addition sentence. Students who master the assigned tasks can complete HOT problems, and the “Go Deeper” and “Enrich” activities. These are scripted and correlate to respective lesson objectives. The “Evaluate” lesson portions contain the Daily Assessment Task, which also provides recommendations in responding to student needs. In one lesson in this module, students show and write addition sentences for sums to 10. If students are unsuccessful, they complete the Soar to Success Math Warm-Up 10.09. If the students are successful, they complete Enrich 58 and the “Homework and Practice” Lesson 13.4, which provide more practice on the concepts and skills of this lesson.
The provided materials include frequent, integrated formative assessment opportunities. There are routine and systematic progress monitoring opportunities that measure and track progress. The frequency of progress monitoring is appropriate for the age and content skill.
Evidence includes but is not limited to:
Throughout all modules, there are routine and systematic progress monitoring opportunities through the “RTI Quick Check,” “Problem Solving,” “HOT problems,” “Common Errors” sections, and “Daily Assessment Task” sections found in the Teacher Edition (TE) of every lesson. These sections consistently and accurately measure and track student progress. A “Prerequisite Skills Inventory” in the “Assessment Guide” is given at the beginning of the school year or when a new child arrives. This multiple-choice test assesses children’s understanding of prerequisite skills. The “Assessment Guide” for each grade level also includes “Individual Record Forms” (IRF) for all tests. On these forms, each test item is correlated to the TEKS it assesses. There are intervention resources correlated to each item as well. At the end of every lesson, the last “E” of the “5E” model is “Evaluate.”
Module tests evaluate if students have mastered the content of that module; unit tests check if students have mastered all of the modules in the unit; the “Beginning of the Year Test” sets the baseline; the “Middle of the Year Tests” allows teachers and administrators to see if and how much students have grown; the “End of the Year Test” monitors if they have mastered the content for the year and show a year’s worth of growth. Modules also provide options on how students demonstrate the skill for progress monitoring. Every unit begins with a “Show What You Know” assessment that assesses students’ prerequisite skills for the unit. A “Diagnostic Assessment” graphic/chart is included on each unit page for teachers to use to determine if children need intervention for the unit’s prerequisite skills. This graphic includes sections with Tier 2 and Tier 3 skills, number of questions missed, intervention, online intervention, and independent activities. If students are unsuccessful with Show What You Know, teachers intervene with the lessons listed on the chart from the RTI Tier 2 or 3 Guide or the online “Soar to Success Math” lessons.
In Module 5, in the TE, the Access Prior Knowledge section prompts teachers: “Use the Are You Ready? 14.1 in the Assessment Guide to assess children’s understanding of the prerequisite skills for this lesson.” The suggested lesson covers how many make up the numbers 6 and 7. This is appropriate for grade and content level because the lesson’s question is, “How can you show differences within 7?”
In Module 6, the RTI Quick Check states: “If a child misses the checked exercise(s), then Differentiate Instruction with RTI Tier 1 Lesson 41. If a student got the assigned questions correct, they can move on to higher-level thinking problems.” This Quick Check after “Share and Show” is strategically placed to allow students the opportunity to understand the lesson whole group and practice whole group. Common Errors sections serve as an informal assessment. In this lesson, Common Errors state: “Children may have difficulty making number comparisons and using comparative language. Springboard to Learning: Help children to connect greater with more and less with fewer. Review that when you count, the number that comes after another number is greater. Have children tell which is greater, 1 or 2. (2).” The Daily Assessment Task section in this lesson states: “Can children solve problems using the strategy ‘Make a Model?’” If no, materials guide teachers to Soar to Success Math small group activities.
In Module 9, if students cannot solve problems using the strategy “Make a Model,” teachers give them a Soar to Success Math activity to complete.
In Module 10, students compose the numbers 6 and 7. In the “Explain” portion of the lesson, the teacher performs the RTI Quick Check. For any student who missed the checked exercise, the teacher differentiates instruction using an RTI Tier 1 lesson, in which students compose numbers to 6 and 7 with concrete objects, pictures, and ten-frames. The Daily Assessment Task challenges students to put together numbers to make 6 and 7. If students are unsuccessful, they complete Warm-Ups 10.03 and 10.09 in Soar to Success Math to help reinforce and remediate this skill.
In Module 11, the first lesson, on using addition strategies to solve word problem situations, begins with an “Are You Ready?” that assesses students’ prior knowledge of the prerequisite skills for the lesson. This lesson contains differentiation/leveled activities for English Learners and an RTI Quick Check, which directs the teacher on supports to use should a student experience difficulty and provides HOT problems and “Go Deeper” activities for students who are mastering the skill/concept. Should students experience challenges with the Go Deeper task experience, a mediation piece through the “Math on the Spot Video Tutor” guides students through the addition processes. The RTI Daily Assessment Task in this lesson has students solve problems using the strategy “act it out.” If successful, students move on to the “Enrich” and “Homework and Practice” portions. If students need more support, the materials direct teachers to specific Soar to Success Math activities. In the Evaluate portion of this lesson, students individually solve addition story problems as part of a culminating independent assessment.
In Module 13, in a lesson on addition, teachers use Are You Ready? 13.4 to assess children’s understanding of prerequisite skills. The RTI Quick Check states: “If a child misses the checked exercises, then Differentiate Instruction with RTI Tier 1 Lesson 64.” Every lesson incorporates a “Daily Assessment Task” in which students are assessed on their ability to show and write addition sentences for sums to 10.
The provided materials include guidance, scaffolds, supports, and extensions that maximize student learning potential. The materials provide recommended targeted instruction and activities for students who struggle to master content; they provide enrichment activities for all levels of learners.
Evidence includes but is not limited to:
In all modules, the Teacher Edition (TE) provides an outline of how and where to find activities to provide targeted instruction for students who may require additional support; the TE also provides prompts for differentiation in each module. Assessment guides titled “Are You Ready?” assess children’s understanding of the prerequisite skills for the lessons within the module. There are suggested scripts and activities for each content area as well as enrichment activities; these are embedded in the module and in resources such as the “Response to Intervention” (RTI) Tiers 1–3 support and the assessment guides. Further scaffolds are given in the “Math on the Spot” video tutor and in the online resources. Each lesson includes graphic organizers, visual aids, and opportunities to use hands-on manipulatives. In each lesson, there is a differentiation component that equips the teacher with a strategy to assist English Learners (ELs) — content language support within a small group setting. Every lesson includes leveled activities for each TELPAS level: Beginning, Intermediate, Advanced, and Advanced High. Enrichment activities are available, which include visual and kinesthetic activities in individual, partner, and small group settings. 17 out of the 21 modules contain hands-on lessons; all modules include hands-on center activities. Module lessons also include two higher-order thinking skills (HOTS) questions that require students to use HOTS and, typically, multiple steps to solve. Throughout all modules during the year, materials use the 5E lesson model: “Engage, Explore, Explain, Elaborate, and Evaluate” to build students’ mathematical learning and understanding.
In Module 5, lessons provide RTI checks to understand how students respond to practice questions and exercises. If the student misses the checked questions, materials recommend teachers incorporate differentiated instruction with RTI Tier 1 lessons.
In Module 17, the lessons’ “Lesson Opener” helps students make connections to prior knowledge; it asks, for example, “Name some shapes that you know. What are some things that are round? What are some things that are not round?” In addition to the Lesson Opener, the TE provides the “Are You Ready?” pre-assessment to check for previous knowledge and to help scaffold the lesson. Each lesson provides a differentiated center in the “Grab-and-Go” section; for this module, activities include games such as “Follow the Figures.”
In all modules, the Elaborate part of each lesson gives further guidance for students who are ready to move on to the next steps and HOTS questions. Materials only guide the teacher to this part in the lesson once students complete the first few assignments correctly. The teacher can then guide students to these problems, which require using HOTS skills or multiple steps to solve. If a student needs additional help with these problems, they can use Math on the Spot, the video tutor. To extend thinking, teachers can then guide students to the “Go Deeper” sections. Materials provide teacher guidance for walking through each lesson, covering Lesson Openers, “Making Connections,” how to use the digital lesson, and what specifically to discuss with each lesson.
In a lesson in Module 5, students find unknowns to solve a problem. The Math on the Spot video tutor guides students through an interactive problem solution related to the lesson objective. Grab-and-Go activities provide independent practice in an engaging, project-based exploration format. The Lesson Opener allows students to make connections to the lesson and determine the purpose; it also helps the teacher determine students’ prior knowledge about the topic.
In all modules, the lessons follow a consistent format, beginning with scaffolding prior knowledge through Lesson Openers and ending with the HOTS problems at the end of the “Problem Solving Practice.” In addition, the lessons provide recommended extension and enrichment activities through the “Enrich Small Group Activities.” In Module 6, materials guide students to create representations of doubles plus one, then represent doubles minus one, and then create a number sentence to share with their peers. This allows students to move from representational to abstract while discussing the process.
In Module 11, materials direct teachers to ask guiding questions throughout the module, in the Lesson Opener, as well as in each component of the 5E lesson model. In the Elaborate section, teachers ask students the following HOTS question: “Two children are sitting on a rug. One more child joins them. How many children are sitting on the rug now?” Teachers then ask students how they would solve that problem. Materials include possible responses and suggestions. There are further scaffolds in Math on the Spot and in the online resources. Throughout this lesson, there are graphic organizers, visual aids, and opportunities to use hands-on manipulatives.
In Module 10, in the “Enrich” section, there is an activity for visual and kinesthetic learners to be used in small groups. This activity uses colored cubes, distributed to each group of two or three children. Students are told to make two groups of cubes; they add or take away cubes so that there are six in all. Once they figure out how many are in each group, they start over. This time, after making two groups of cubes, students add or take away cubes so that there are seven in all. This activity enriches the main activity, “Composing 6 and 7;” students have to think “backwards” to get the addends for the sum in each group. The Enrich section also prompts teachers to go to thinkcentral.com for additional enrichment activities (in the “Enrich Activity Guide”).
In kindergarten STEM sections, a lesson extends the skills of sorting and graphing. The lesson provides “Differentiation” with two options for leveled activities: “Extra Support” or “Enrichment.” Extra Support entails naming the season from sorted cards and suggesting words and phrases associated with the season pictured. Enrichment has students take a walk to observe signs of the current season, pointing out trees and other plants that show seasonal changes. Students discuss smells and sounds associated with the current season and contribute words, phrases, and sentences to an experience story about their walk. STEM activities include a drama activity, in which students act out the seasons; a math activity, in which students make a picture graph depicting favorite seasons; a language arts activity, in which students write a poem to describe seasonal changes; a social studies activity, in which students write a postcard to children who live in another place to learn how the seasons change there; and a “Take It Home” activity, in which students create a display of family birthdays and seasons.
The materials include a variety of instructional methods that appeal to a variety of learning interests and needs. Materials include a variety of instructional approaches to engage students in the mastery of the content. They support developmentally appropriate strategies, flexible grouping, and multiple types of practice. Materials provide guidance and structures to achieve effective implementation.
Evidence includes but is not limited to:
Throughout all modules, students cycle through the systematic “Engage, Explore, Explain, Elaborate, and Evaluate” (5E) format. Materials include hands-on, concrete practice with manipulatives and work with visual representations in both the digital and workbook (paper-and-pencil) format. Hands-on, concrete practice with manipulatives appears in the Engage, Explore, and Elaborate portions of lessons as well as in the “Grab-and-Go” differentiated centers. Each lesson provides opportunities for various instruction techniques; these include, but are not limited to, learning types, such as visual or kinesthetic learners; and instructional settings, such as individual, partners, or small groups. Materials provide scripts for large and small group instruction throughout each lesson. Each lesson suggests pre-assessment tools in the “Are You Ready?” resource. Whole group instruction contains directed “Lesson Openers.” The 5E lesson format begins with an interactive video and an “Essential Question” that helps students make a relevant connection. The implementation of manipulatives and models is consistent throughout the modules. Manipulatives are also available in the “Problem Solving” portion of each module; manipulatives, visual representations, and symbolic abstractions are also recommended in the “Differentiated Instruction” portion. The materials state that Tier 3 intervention support is included “for children who need one-on-one instruction to build foundational skills for the unit.” Later activities, such as in the “ELL” (English Learner [EL]) and “Enrich” sections, suggest individual, partner, or small group instruction. However, there is no direction for whole group transitions to working with other peers if students do not fall in the EL or Enrich categories, and there is no guidance for teachers to support small groups that are on-level.
In Module 3, if a student misses the “Quick Check” exercise, which is denoted by a checkmark, the student receives additional practice in the “Response to Intervention” (RTI) book; there, the student uses connecting cubes in squares to determine which number is greater. If the student gets the Quick Check question correct, the student goes on to the problem-solving page or engages in an enrichment activity.
In Module 4, the Engage portion of a lesson has students use counters to review counting and represent numbers learned in previous lessons. The Explore portion continues with the manipulative component; students utilize counters to demonstrate numerical representation and the early stages of addition. The Elaborate section has students use counters to show different ways to compose the number 7.
In Module 7, the materials recommend Practice Problem #2 for a Quick Check. If the students struggle to solve this problem correctly, the materials suggest using an RTI Tier 1 lesson. The Teacher Edition (TE) also lists “Common Errors” and strategies to assist students; for example, students may not be able to count past 10. The recommendation is to model in small groups or one on one. The teacher counts to 11 using cubes or counters, and the students count along with the teacher; this is followed by counting to 12.
In Module 8, materials guide teachers through Lesson Opener introductions on the concept of “one more and one less.” In the next section, teachers read a story problem while the students listen. Students use counters to show how to set up the problem with manipulatives. Teachers say, “The number of flowers Juan has is one less than what Melissa has. How can you show that number in the ten-frame?” (Take one counter away). The TE provides further teacher prompts and possible answers. The teacher checks for understanding by seeing if the students’ responses match the possible answer in the scripted lesson. If they do, and students are able to master the correlating assignments in the student edition, the teacher moves them to a higher level of mastery of the concept.
In Module 14, the TE recommends an activity to extend the students’ thinking; this is found in the “Go Deeper” section at the end of the lesson. Students “begin by drawing objects to represent the number they start with.” Students count four objects to show how many are left and cross out the rest. Students count them to show how many are taken away; finally, they complete the 7 - 3 = 4 number sentence. Students explain what they knew to do, what they needed to find out, and how they found the answer. Teachers are to remind students that they know how many there are in all, they know one part of the whole group, and they need to find the other part.
In Module 15, students investigate money. The TE states, “Some children from other countries may be unfamiliar with U.S. coins.” The teacher reviews the name of each coin; the teacher shows each coin and says its name aloud for the children to repeat. The teacher gives each group coins and writes a number of coins on the board. The teacher says them aloud (e.g., “One dime and four pennies”) and then has groups find the coins to make the set and repeat with different values. Teachers receive additional support for their English Learners through the digital “ELL Activity Guide.”
In Module 20, students use connecting cubes to create a pictograph. Later, students apply that concrete model to an abstract model. The materials include instructional routines designed to support students in engaging with the content and skills present in the lesson.
The materials include supports for English Learners (ELs) to meet grade-level expectations. The materials include communicated, sequenced, and scaffolded linguistic accommodations commensurate with various levels of English language proficiency. However, there is not much evidence of students using their first language as a means to develop skills in English.
Evidence includes but is not limited to:
Throughout all modules, every lesson contains leveled activities for each type of EL (Beginning, Intermediate, Advanced, and Advanced High); they correspond with the appropriate English Language Proficiency Standards (ELPS). The materials are structured to provide a variety of effective strategies for teachers to support students at different English language proficiency levels. The modules include an “English Language Learners” box in the margin of the Teacher Edition (TE); it provides teachers with leveled activities in the “ELL Activity Guide” for students at each proficiency level across grades K–2. The guide encompasses effective instructional strategies such as drawing, describing, identifying relationships, exploring content, defining, rephrasing, and modeling language. Each module also includes an “ELL Language Support” section for teachers to use to support ELs. Each module focuses on a different ELP strategy; strategies are referenced on the unit planning page at the beginning of every unit (units include multiple modules). The materials provide opportunities for repetition in a fun and engaging way, such as in the “Grab-and-Go” sections found at the end of every lesson, the “Interactive Math Videos,” and the “Soar to Success” activities.
The “Bilingual MathBoards” resource has graphic organizers in Spanish to support Spanish-speaking ELs when problem-solving; however, this does not benefit ELs whose primary language is not Spanish. The materials also provide “Vocabulary Cards” in English and Spanish, which have pictures to represent the math term; these cards do not fully benefit ELs whose primary language is not Spanish. The materials do not include a list of resources for teachers to access to learn more about ELs. They also do not contain examples of how to use students’ first language as the foundation for developing skills in English; the short overview in the ELL Activity Guide does indicate that doing so is important.
For all modules, the ELL Guide, included for grades K–2, provides scaffolds and language development strategies. It includes a list of effective instructional strategies and a list of mathematical vocabulary words and their definitions for every grade level (K–2). The guide also provides teachers with tips to help students develop and use academic vocabulary. One tip is, “Many numbers and number concepts are best demonstrated with physical objects or visualized with drawings. Provide drawings and demonstrations whenever possible to help children gain an understanding of the definitions.” Another tip is, “The use of the terms tens and ones as place value can be confusing. Children may also confuse one and won when these words are spoken.”
In Module 2, students are learning about “which object doesn’t belong,” and materials provide leveled activities for ELs. Beginning ELs complete Activity 18; Intermediate ELs complete Activity 22; Advanced ELs complete Activity 41; and Advanced High ELs complete Activity 16. Activity 18, “Which Picture Doesn’t Belong?” uses the strategy of identifying relationships; it is geared toward a partner setting and should last for 10 minutes. There is a “Speaking Objective” for the activity: “Make connections among pictured vocabulary words to identify relationships.” It prompts teachers: “Provide children with four to six pictures that illustrate grade-level vocabulary. All of the pictures should be related in some way except for one. Children choose a picture that doesn’t belong. Encourage children to discuss how the other pictures are related to reinforce their decision. If they don’t know the name for one of the pictures, name it for them and have them repeat the word.” Activity 18 also has a leveling option for Intermediate ELs: Teachers “select pictures that are more closely related; for example, a nickel, a dime, a penny, and a dollar; or three clocks that show time to the hour and one that shows time to the half-hour. Have children complete the following sentence frames to help them discuss their choice: ... does not belong. The other pictures are ….”
In a Module 7 lesson, students are counting and writing 13 and 14. The ELL Activity Guide prescribes corresponding leveled lessons. Beginning ELs use speaking skills to make connections among pictured vocabulary words and identify relationships using pictures. Intermediate ELs use speaking and reading skills to practice vocabulary and make connections between new words and prior knowledge using vocabulary charts. Advanced ELs use listening, speaking, and writing skills to identify numbers with base-ten blocks or connecting cubes. Advanced High ELs use reading and writing skills to unscramble words and make math words, using vocabulary charts as needed.
In Module 13, the ELL Support section provides scaffolds and tells the teacher, “Restating key vocabulary helps children understand math problems.” Teachers write 8 = 5 + 3 on the board and tell children that this addition sentence says 8 is equal to 5 plus 3. The teacher then states it another way: “8 is the same as 5 and 3.” Materials instruct teachers to help students see the correspondence between “is equal to” and “is the same as” and between “plus” and “and.”
In Module 13, a “Grab-and-Go” lesson consists of “Games: Spin to Add,” in which children use connecting cubes to model addition problems; “Literature: Flowers for Flossie,” where students read the book and count and add flowers of different colors; and “Activities: All Together Now!” where children use two-color counters in combinations that add up to 9.
In Module 15, the TE states, “Some children from other countries may be unfamiliar with U.S. coins.” Materials direct the teacher to review the names of each coin, show each coin, and say its name aloud for the children to repeat. The teacher then gives coins to each group, writes several coins on the board, and names them aloud (e.g., one dime and four pennies). Groups find the coins to make the set, and the teacher repeats with different values.
The materials include a year-long plan with practice and review opportunities that support instruction. They include a cohesive plan to build students’ mathematical literacy skills; however, there is little evidence to consider how to vertically align instruction that builds year to year to future grades. These materials provide review and practice of foundational skills throughout the curriculum.
Evidence includes but is not limited to:
Throughout all modules, the content plan is cohesively designed to build upon students’ current level of understanding with clear connections within and between lessons. There is a year-long plan of content delivery, as seen in the “Unit at a Glance” and “Module at a Glance” found in the introduction of each unit as well as in the Table of Contents, with the expectation that the concepts are taught in this order. The Teacher Edition (TE) for every grade level includes a unit page for each set of modules that allows the teacher to visually see how concepts are spiraled throughout the year. The materials connect learning to previously learned concepts, knowledge, and skills in a variety of ways; there are reviews and practice throughout the curriculum, as seen in the “Grab-and-Go” activities and “Differentiation Lessons” found in each lesson. The units are designed so that skills and concepts move from concrete or context-based situations and then build to the abstract as students encounter more opportunities to practice and apply the objective of study. Along the way, students use models, manipulatives, quick pictures, and symbols to build mathematical understanding.
However, the materials do not include a specific vertical alignment chart that shows how activities align, both directly and indirectly, to concepts and skills outlined for students in subsequent grades. Although the materials do not use preceding and subsequent grades’ TEKS, the skills used in kindergarten are built upon in first grade and then further built upon in second grade. For example, students learn basic numbers and basic addition in kindergarten, which correlates with the kindergarten TEKS. In first grade, students continue to use addition and subtraction and identify many strategies to perform those tasks. In second grade, they are finally introduced to adding and subtracting with two-digit numbers, using the same strategies learned in first grade. At the end of each module across grade levels, spiral review problems allow students to practice major skills and vocabulary learned throughout the modules. There is also a unit assessment at the end of every unit, across grade levels, that provides students an opportunity to practice and review major skills learned throughout the unit.
In Modules 1–8, the Unit 1 introduction states, “Prior Knowledge in Pre-K. Children may: know that numbers and names can be written; know more than, fewer than, and the same; count items in a set of 1–5, saying one number name per item; recognize that the last number said tells the number of objects in the set. This selection reviews some of these prerequisite skills.” Module 1 begins with students modeling, counting, and writing the number 1. The modules progress with this same format through Module 8, where students model, count, and write the number 20. However, the materials do not refer to how the current concept will align with future grade-level concepts, such as in first grade. Modules 1–8, Unit 1, are about “Number and Operations: Represent, Count, Write, and Compare Numbers to 20.” Each of the eight modules progresses through the numbers, typically introducing two new numbers every two or three lessons. Each module in Unit 1 concludes with a “Problem Solving Lesson,” which has students apply the number concept. In Unit 2, students learn about “Number and Operations: Compose and Decompose Numbers, Add and Subtract, Coins.” Throughout Unit 2, students take the basic number foundation as acquired in Unit 1 to compose and decompose these numbers, and now learn this along with addition and subtraction and coin counting, thus showing skill progression. The TE contains a TEKS for “Mathematics Correlations” that lists the “Learning Opportunities” correlated with “Focal Areas” available throughout the year. This shows how the materials structure the foundation for later work, how the skills are spiraled, and where to go within the materials to practice designated TEKS.
In Module 1, in Grab-and-Go, students can read and practice counting five kittens with the story “Pancakes for All;” students can also practice showing multiple sets of three objects with the activity “Number 3.” In the same lesson, there are opportunities for additional practice in the “Differentiated Instruction” section, which uses “RTI” Tier 1 Lesson 5 and “Enrich” 4, as well as on “Homework and Practice” pages in every lesson. Additionally, each module provides “Math on the Spot” videos, the “Interactive Student Edition” (interactive tutorial videos), and “Soar to Success Math” activities.
In Module 5, in a lesson on “Model, Count, and Write 10,” students use their knowledge of representing numbers using counters in a ten-frame. In Module 10, in the middle of the year, students again review their knowledge of numbers when they compose and decompose numbers to 10. At the end of the year, in Modules 11–14, students review and practice their sense of numbers with addition and subtraction.
In Module 8, “Count and Write 18 and 19,” the “Essential Question” is: “How can you count and write 18 and 19 with words and numbers?” Students have already modeled, counted, and written numbers 1 through 17 using counters and ten-frames in a consistent manner. During a “Making Connections” piece of a “Lesson Opener” in this module, students tell the teacher what they know about counting and writing up to 17 as done in prior lessons. As part of the Lesson Opener, students also count the number of legs on an octopus out loud, up to 17, beginning with the number 10, and write number 18 in number form.
In Modules 9–14, lessons cover telling time to the hour, then to the half-hour, then to the hour and half-hour; in the last lesson, students practice telling time to the hour and the half-hour. Both of the “Addition and Subtraction” modules cover increasingly complicated problems, such as adding up to 8, adding up to 9, and then adding up to 10. Each subsequent lesson is more difficult, and students must understand earlier lessons before moving on to larger numbers.
In Modules 17–19, the Unit 4 assessment asks students to review the following Essential Question: “How can you use words, colors, and categories to describe and identify shapes?”
The materials include some implementation support for teachers and administrators. Materials are accompanied by a TEKS-aligned scope and sequence outlining the essential knowledge and skills that are taught in the program, and there is a year’s worth of instruction, including pacing guidance and routines. The program does not provide much guidance to build across grade levels. Materials include support to help teachers implement materials; however, there are neither resources nor guidance to help administrators support teachers.
Evidence includes but is not limited to:
In the curriculum, the materials do not include a formal scope and sequence; however, the lessons within the modules are aligned to the TEKS; these standards are listed at the beginning of each lesson script. The Teacher Edition (TE) introduction states: “The content knowledge and skills in grades K-5 are organized into five mathematical strands: Number and Operations, Algebraic Reasoning, Geometry and Measurement, Data Analysis, and Personal Financial Literacy. In addition, in each grade K-5, TEKS outlines primary focal areas for instructional emphasis. This design permits instruction in each grade to focus on fewer concepts and skills in greater depth, while simultaneously building a foundation for the next grade, establishing an effective learning progression.” “Unit Overviews” list the TEKS and Mathematical Processes taught in each lesson within each module. “Mathematics Correlations” provides a list of learning opportunities for each standard; there are also live links connecting the lessons to each of the TEKS. A teacher may search for a specified TEKS, and the resource generates all the lessons associated with that TEKS. The scope and sequence do not describe how the TEKS build and connect across grade levels, but the lessons do begin with context-based situations and then build to more abstract problems in accordance with the state standards. There are no clear explanations of how the TEKS connect within the materials other than personal internalization. The only guidance the administrators have is the same as is provided to teachers in the introduction of the TE.
The materials include lessons and activities for a full year of instruction in the classroom. Materials are organized in a way that makes sense for ease of implementation, including accessing and storing of materials. All of the TEs come in a cardboard storage box, which includes a booklet for all modules; these TEs can be found and accessed through online resources. The lessons are designed to be implemented within one (or sometimes two) math blocks on an instructional day. Materials do not mention specific time or date parameters, but the units can be reasonably implemented within the timeframe of a school year, with ample time for pre-teaching, re-teaching, intervention, and extensions, as recommended within the lessons. The consistent “5E” format of the lessons helps maintain pacing. The assessment data from formative and summative assessments, as well as information gathered from “RTI Quick Checks” and “Daily Assessment Tasks” help the teacher to effectively group students and provide the needed instructional support. For example, if a student is unsuccessful on a Daily Assessment Task, materials provide guidance on necessary support items. The same is true if a student is successful in the Daily Assessment Tasks. The materials include embedded realistic pacing guidance at the unit and lesson level. Each unit has an overview that helps the teacher review the TEKS and focal areas, identify needed materials, and determine appropriate resources. Students have opportunities to spend sustained time developing content and skills in grade-appropriate areas. The materials spend more time on some focal areas compared to others; 11 out of the 21 modules focus on whole numbers; four modules focus on addition and subtraction; and only one module focuses on two-dimensional shapes and three-dimensional solids.
Modules 1–8 begin with counting, writing, and representing numbers 1 through 4; then, students repeat this with numbers 5 through 10; then, they compare, order, and add numbers to 10; finally, students repeat the same process with numbers 11–20. This continues throughout the unit, giving students multiple opportunities to establish a strong foundation in number representations before moving on to application processes. The unit page for “Number and Operations” states: “In Pre-K, children may: know that numbers and names can be written; know more than, fewer than, and the same; count items in a set of 1–5, saying one number name per item; recognize that the last number said tells the number of objects in the set. Materials further explain how teachers can review these prerequisite skills prior to beginning the lessons within Modules 1–8.
In Module 4, Lesson 1, the top-right corner of the first page has a section labeled “Texas Essential Knowledge and Skills,” which states: Number and Operations — K.2.B, Read, write, and represent whole numbers from 0 to at least 20 with and without objects and pictures; K.2.C, and K.2.I; Mathematical Processes — K.1.a, Apply mathematics to problems; K.1.e, Create and use representations. In the bottom right-hand corner, a “Go Digital Resources” section reminds teachers to access the “Digital Management Center,” which organizes program resources by TEKS.
In Module 5, “Model, Count, and Write 10,” students use their knowledge of representing numbers using counters in a ten-frame. In the middle of the year, in Module 10, students again connect their knowledge of numbers when they compose and decompose numbers to 10. At the end of the year, in Modules 11–14, they once again connect their sense of numbers to addition and subtraction.
In Module 9, the “Lesson at a Glance” provides a detailed breakdown of each lesson within the module; it includes the “Essential Question,” TEKS, Process Skills, vocabulary, materials, print resources, and available “Go Digital” resources. Each lesson is scripted and contains guidance; “Are You Ready?” sections help access prior knowledge; “Lesson Openers” contain guidance on making connections, using the digital lesson, and incorporating literacy. Lessons have scripted questions and possible answers; there are differentiated lessons for English Learners, struggling learners, and those needing enrichment. RTI Quick Checks help teachers guide the lesson; “Common Errors” explain how to help students that misunderstand the concept; the Daily Assessment Task at the end of the lesson provides guidance on the next steps. For example, “If the student can identify, describe and name pennies, then have them work on the Enrich 64 activity or Homework and Practice. If no, then have the student work on Soar to Success Math Warm-up 27.05.”
In Module 13, in its top-right corner, one lesson lists TEKS K.3B Number and Operations: Solve word problems using objects and drawings to find sums up to 10 and differences within 10. Without going back to the Unit Overview, looking in the “TEKS Correlation Guide,” or relying on memory, the teacher does not know if this is the first time this standard is presented or if this is a TEKS for review or practice.
The provided resources partially meet the criteria for implementation guidance to meet variability in programmatic design and scheduling considerations. There is embedded guidance, but there is no specific guidance for implementation that ensures the sequence of content is taught in an order that is consistent with the developmental progression of mathematical concepts and skills. The materials are designed in a way that allows LEAs the ability to incorporate the curriculum into district, campus, and teacher design and considerations. However, the materials do not include guidance that supports teaching focal areas aligned to a classroom context without disrupting the sequence in which the content should be taught.
Evidence includes but is not limited to:
Throughout the curriculum, units, and modules, each unit across grade levels includes a unit overview that lists the TEKS, skills, and objectives in each lesson. The introduction in the Teacher Edition (TE) explains how the TEKS need to be implemented within a coherent and balanced curriculum that treats mathematical knowledge and skills in a manner that will enable students to develop a deep understanding of the content by integrating process standards with the mathematics content. The materials also provide a suggested sequence of units that considers the interconnections between the development of conceptual understanding and procedural fluency. The sequence in these lessons makes sense since the lessons build on each other in order for students to build their base knowledge. This sequence of content is taught in an order consistent with the developmental progression of mathematics; as stated in the Introduction under “Texas from the Ground Up,” the instruction is grouped around each Texas focal area; within each unit, each module is designed around a concept.
The materials do not provide specific support for LEAs to consider how to incorporate the materials into a variety of school designs; however, the units and modules are built as “stand-alone” so that districts, campuses, and teachers can rearrange the materials in a way that adapts to their needs. The materials do not include specific timelines for teaching each TEKS, which allows districts flexibility in scheduling considerations. The “Program Overview” in the introduction of every grade level’s TE states: “‘Texas GO Math!’ helps you with the big jobs of teaching. Our ‘Teacher Digital Management Center’ helps you create lesson plans that support your curriculum, can be sequenced to align with district requirements, and are completely focused on TEKS.” The materials do have online components such as iTools, “Math On the Spot Videos,” and an “Interactive Student Edition,” which correlates with each lesson within each module. Even though there is no direct guidance regarding online schools or blended model schools, the online components do make these school options feasible.
In all modules, all components of the “5E” lesson plan model can be taught in a whole group setting: Engage (“Lesson opener”); Explore (working through a problem together); Explain (“Model and Draw” and “Share and Show”); Elaborate (“Problem Solving”); and Evaluate (“Daily Assessment Task”). The activities designed to be taught in a small group setting are the “ELL Language Support” section, “Enrich” section, “Grab-and-Go” center activities, and “RTI Interventions.”
In Module 1, “Counting, Writing and Representing numbers 1–4,” Lesson 1 is a hands-on lesson about modeling and counting to 1 and 2. Lesson 2 covers counting and writing 1 and 2. Lesson 3 covers modeling, counting, and writing 3 and 4. Lesson 4 is the final lesson in the module and is a problem-solving lesson that covers understanding numbers 1 through 4.
In Module 16, Unit 3, students use their foundational counting skills developed over the modules in Units 1 and 2 to help them count on from any number up to 100. The materials maintain that the curriculum represents a comprehensive system of mathematics instruction that provides teachers the tools and resources needed to support students’ successful mastery of the TEKS.
Modules 17–19, Unit 4, are grouped around the focal area “Compare objects by measurable attributes.” In a Module 17 lesson, “Identifying Rectangles,” students explore and learn about what attributes can make a two-dimensional shape a rectangle. In a Module 18 lesson, “Identify Spheres,” students learn the attributes of three-dimensional shapes that make them a sphere. In another Module 18 lesson, students use the attributes of three-dimensional objects to solve problems where they must identify the shape based on the flat surfaces of the objects. Once students have mastered the concept of identifying two-dimensional and three-dimensional objects based on their attributes, students learn to compare lengths, heights, and weights in Module 19. In a Module 19 lesson, students solve the following problem: “Ling has two pencils. How can she find if one is longer, one is shorter, or if they are about the same length?” Students learn how to measure the length of objects in order to compare them.
In Module 5, the lesson “Model, Count, and Write 10,” at the beginning of the year, asks students to use their knowledge of representing numbers using counters in a ten-frame. Students again connect their knowledge of numbers in Module 10, in the middle of the year, by composing and decomposing numbers to 10. At the end of the year, they once again connect their sense of numbers to addition and subtraction in Modules 11–14. In Module 16, “Model, Count, and Write to 20,” teachers review with children what they know about counting and ordering up to 20 and up to 50.
The provided materials partially meet the criteria for guidance and fostering connections between home and school. The materials do not support the development of strong relationships between teachers and families enough, but there are specific activities for use at home to support students’ learning and development.
Evidence includes but is not limited to:
The curriculum does encourage some building of relationships between teachers and families through the suggested family “Home Activity” in each lesson; there is little to no guidance provided to teachers on how to facilitate and foster these connections. Although these activities do allow the family to take part in the process, they do not necessarily provide opportunities to build a strong relationship between home and school. There is an ”At-Home Learning Support Section” online that includes lessons, “Vocabulary Builder” sections, “Vocabulary Reader” sections, “Write About Math” sections, as well as lessons and homework. “At-Home Learning” is a digital copy of the Student Edition book for both volumes. This resource begins with a letter addressed to students and families, explaining that the resource contains hands-on activities to do and real-world problems to solve. At the beginning of each unit, there is a page with a “Home Note” for families; it states that this will help families gauge where their child is and maybe areas they should improve. There is no evidence of other language support, but At-Home Learning Support could be easily used by families who speak English. The introduction in the “Digital Resources” section states, “Interactive Student Edition: Includes all Student Edition (SE) pages for student access at school or home.” The materials provide tips for parents to practice new skills at home in meaningful, authentic ways. The ideas suggested involve items that are typically available in the home and do not require parents to buy anything or have special training.
Each unit includes a “Take-Home Vocabulary Reader.” This take-home book allows students to review some prerequisite skills as well as learn new mathematical vocabulary needed for the unit. It also lets parents know which skills and TEKS will be reviewed in the book. The materials provide digital resources for the student and parent to access, such as the “eStudent Edition,” “Math on the Spot Videos,” “Math Concept Readers,” “Mega Math,” “Interactive Student Edition,” and “Math iTools.” These materials are available through the student’s login. The eStudent Edition is the digital version of the student math books. Math on the Spot Videos are short tutorials for each lesson. Math Concept Readers are short math books available in three levels (Below Level, On Level, Above Level). Mega Math interactive math games are sorted by the concepts being learned, allowing for students to have additional practice. The Interactive Student Edition is another tutorial video designed for the beginning of a lesson or a review for those struggling with the concept. Math iTools are digital manipulatives students may use or practice using, such as counters, base-ten blocks, and connecting cubes.
In Module 1, a Take-Home Activity directs parents: “Show your child one group of 10 pennies and one group of 8 pennies. Ask your child to tell how many tens and ones there are, and say the number. Repeat with other numbers from 11 to 19.”
In Module 4, a Take-Home Activity suggests: “Ask your child to show a set of seven objects. Have him or her show one more object and tell how many.”
In Module 10, a Take-Home Activity directs: “Have your child use buttons or beans to make groups of five. Then have him or her count by fives to tell how many objects.”
In Modules 9–15, Unit 2, the Take-Home Reader is Flutter by Butterfly; it reinforces modeling, counting, comparing, and writing numbers to 20 and emphasizes the vocabulary terms more and fewer.
In Module 11, a lesson’s Take Home Activity on skip counting states: “Have your child use buttons or beans to make groups of five. Then have him or her count by fives to tell how many objects.” The Homework and Practice pages often contain a “Home Activity,” such as the following in a Module 11 lesson: “Show your child a set of 1 to 5 objects such as pencils or markers. Have your child add one more to the set and count to tell how many in all.”
In Module 12, the Take Home Activity states: “Have your child explain the strategies he or she can use to add the numbers 7, 2, and 3.” Another activity directs parents: “Tell your child a short subtraction word problem. Have him or her use objects to act out the word problem.”
In Module 14, the online resource provides activities that reinforce and have practice opportunities for students to subtract numbers between zero and ten. The students may manipulate the activities in an interactive online format; there are also printable versions of worksheets available. Each activity has instructional supports such as resources and tools and even a note-taking section, allowing students to take notes on their learning.
In Module 15, a Home Activity states: “Show your child a quarter. Have him or her tell you the name of the coin and describe both sides.” This activity builds relationships between the teacher and family by communicating ideas on how the family can participate in the daily lessons at home, allowing the parents to be part of the learning process. Although this activity does allow the family to part of the process, it does not necessarily provide opportunities to build strong relationships.
In Module 18, the Take Home Activity directs parents: “Show your child the time on a clock to the hour or half-hour. Ask him or her to tell you what time is shown.”
In Module 19, a Take-Home Activity directs parents: “Have your child compare the weights of two household objects. Then have him or her use the terms heavier and lighter to describe the weights.”
The visual design of student and teacher materials (whether in print or digital) is neither distracting nor chaotic. Materials include appropriate use of white space and design that does not distract from student learning; pictures and graphics are supportive of learning without being distracting.
Evidence includes but is not limited to:
Throughout all modules, the Teacher Edition (TE) is designed with a few blank spaces within each lesson as well as blank pages at the end of each module to be used for notes. The TEs are designed with clear, designated places for important information. The TEs are designed in a way that teachers can locate important information for lesson planning and implementation. For example, the unit overview pages list vocabulary; tools needed; and ancillary materials that can be used to support differentiated learning, the TEKS, skills, and objectives in each lesson. The introduction pages cite online tools and blackline masters that are used to support implementation. Within the module lessons, subheadings are color-coded, and important features are depicted in varied fonts to help teachers cue into the information. Parts of the “5E” lesson cycle include vignettes for teachers that provide sample questions and student responses to support instruction and discussion, as well as some supportive scripts for teachers to utilize. The materials include vocabulary cards with clear and authentic pictures and drawings to define and support the new words students are learning. There is an interconnection and sequential progression of math concepts across units that also builds on prior knowledge and toward the following grade’s continuation of the concept.
The materials provide easy-to-recognize pictures and graphics that support student learning; as seen in the picture glossary for vocabulary, the images are clear and match the vocabulary term. Each lesson in the Student Edition (SE) has a large white space where children can work. The subsequent pages in a lesson are mostly white with little distraction. Most text is in black, which creates a stark contrast to help students focus on the content. The question numbers are in blue, which also differentiates from the black text to keep students on track. There are little images throughout the SE that may connect with the content displayed. Clear and authentic pictures and drawings support the word problems that the students encounter. The materials include graphics that are easily identifiable to students and support their learning, as seen in the “Math on the Spot Videos” and “Interactive Student Edition” tutorials. Tutorials utilize the same characters and routines for all lessons, making it easy for students to follow. The materials include pictures and graphics that are engaging, as seen in the “Vocabulary Readers” found at the beginning of each unit and the “Math Concept Readers” found in the digital resources. The pictures and graphics for student use adhere to “User Interface Design” guidelines; print, graphics, charts, models, pictures, and components are easily visible, clear, and appropriate for the learning tasks. Users can understand the representations and guidance pieces.
In Module 13, the pictures and graphics are colorful, and there is ample space for students to manipulate counters or draw pictures to solve simple addition problems. The area in which students are to write the number sentence is developmentally appropriate, as kindergarten students are still gaining fine motor control and often need a larger space to write. There are dotted lines to help guide the placement of the numbers and symbols on the page. The numbers that students are instructed to read are in large, dark print and thus clear and easily seen.
In Module 14, there are butterfly graphics depicted in an authentic manner for students to cross out when subtracting. There are other colorful graphics of other animals in this lesson (ducks, ants, bees) that help support the concept of subtraction. In the Unit 3 Vocabulary Reader, the materials include real photographs of various objects (rocks, wind-up toys, dinosaur figures, and seashells) to support the skills of counting, sorting, and adding.
The provided technology and online components are appropriate for grade-level students and provide support for learning. These components align with the curriculum’s scope and sequence and enhance student learning. There could be more guidance for the teachers in relation to assisting students within the components.
Evidence includes but is not limited to:
Throughout the curriculum, all of the Teacher Editions (TEs), as well as other digital resources, are available to help support teachers in implementing the materials: the “eTeacher Edition,” “Teacher Digital Management Center,” “Teacher Resource Book for Assessment,” “Online Assessment System,” “Assessment Guide,” “Student Edition,” “Teacher Edition For Intervention,” “Response to Intervention” (RTI) Tier 1, 2, and 3, “Soar to Success Math For Instruction and Differentiation,” “ELL Activity Guide,” “Math Concept Readers,” “Enrich” activities, “Mega Math,” and “iTools.”
The introduction in the “Digital Resources” section states: “Interactive Student Edition: Includes all Student Edition pages for student access at school or home. Provides audio reinforcement for each lesson. Features point-of-use links to animated math models.” It also states, “Students are engaged and learn with point-of-use animated math models.” “Math on the Spot Videos” are also introduced in this section: “Actively introduces lesson concepts. Helps students solve the H.O.T. problems in the Interactive Student Edition. Builds the skills needed in the TEXAS assessment.” The Interactive Student Edition has large color-coded navigation buttons to help students use the technology appropriately and efficiently. For example, students click on a large orange button with an arrow inside to go to the next section. To go back a section, the arrow in a box points the opposite way; it is smaller, which makes the larger button more intuitive so students don’t get confused about how to go to the next section. There are other student-friendly buttons, like a speaker for sound, a home button to go home, a book with “A Z” on it for the glossary, and a wrench for “tools.” The TE is set up in the exact same way, except there is an additional button that features an apple for teacher resources. Mega Math provides additional lesson practice with engaging activities, which include audio and animation.
The materials provide opportunities for students to select grade-appropriate technology tools for solving tasks. iTools enable students to solve problems with interactive digital manipulatives and model and explore lesson math concepts. Grade K-2 iTools include counters, math mountains, base-ten blocks, number lines, number charts, bar models, number tiles, secret code cards, graphs, fractions, geometry, measurement, probability, algebra, and place value drawings. These tools include a help button that explains to students how to use them. However, this feature does not read the directions to them.
The technology components align with the scope and sequence and “flow” of the materials as they are organized by units, modules, and lessons. During the “Lesson Opener” in every lesson, there is a “Using the Digital Lesson” section with guidance on how the teacher can apply the Interactive Student Edition within the start of the daily lesson. In addition, each lesson refers to the “Math on the Spot Video Tutor” for guidance and support for the lesson’s HOT (higher-order thinking) problems. With these videos and the HOT problems, children will build skills needed in the Texas state assessment. The materials guide teachers to have students use the Soar to Success Math Warm-Ups if they do not show mastery within the “Daily Assessment Task.” The TE refers teachers to resources they can provide for students in centers, as seen in the “Grab-and-Go” sections in every lesson.
There is an “At-Home Learning Support Section” online that includes lessons, “Vocabulary Builder” sections, “Vocabulary Reader” sections, “Write About Math” sections, as well as lessons and homework. At the beginning of each unit, there is a page with a “Home Note.” For example, in Unit 1, it states: “This page checks your child’s understanding of important skills needed for success in Unit 1.” This will help families gauge where their child is and maybe areas they should improve.
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