Program Information
- Copyright Type
- Proprietary
Math
Grade 6 | 2015 Series includes:The quality review is the result of extensive evidence gathering and analysis by Texas educators of how well instructional materials satisfy the criteria for quality in the subject-specific rubric. Follow the links below to view the scores and read the evidence used to determine quality.
Section 1. Texas Essential Knowledge and Skills (TEKS) and English Language Proficiency Standards (ELPS) Alignment
Grade |
TEKS Student % |
TEKS Teacher % |
ELPS Student % |
ELPS Teacher % |
Grade 6 |
100% |
100% |
100% |
100% |
Grade 7 |
100% |
100% |
100% |
100% |
Grade 8 |
100% |
100% |
100% |
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 % |
---|---|---|---|---|
Grade 6 | 100% | 100% | 100% | 100% |
The materials spend the majority of concept development of the primary focal areas in sixth grade, as outlined in the TEKS. The materials strategically and systematically develop students’ content knowledge as appropriate for the concept and grade-level as outlined in the TEKS. The materials provide practice opportunities for students to master the content.
Evidence includes but is not limited to:
All 5 of the modules cover one or more of the following: number and operations; proportionality; expressions, equations, and relationships; and measurement and data.
Module 1 includes three main topics and seven out of 12 lessons correlate directly with the focal point, “Using operations with integers and positive rational numbers to solve problems.”
Module 2 includes three main topics, and 12 lessons correlate directly with the focal point, “Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships.”
Module 3 of the materials includes three main topics, and 13 lessons correlate directly with the focal point, “Using expressions and equations to represent relationships in various contexts.”
Modules 4 and 5 of the materials include four main topics, and 13 out of 13 lessons directly correlate with the focal point, “Understanding Data Representations.”
The design of the materials follows a cycle in each of the modules. Each module includes “Connections to Prior Learning,” which is a review of key concepts found in the Teacher's Implementation Guide, and a “Content and Alignment” section of the instructional materials. Each module includes an overview section outlining for the teacher all the learning that will take place within that module. The cycle then continues with a topic overview to detail the specific learning that develops within the module. Finally, a set of lessons and activities are included to develop focused learning in each topic.
In addition, these key focal areas are spiraled among all modules. The materials showcase the focal concepts throughout by providing standard descriptions and essential ideas at the beginning of each module. The lessons include suggestions and materials to practice and reinforce the primary focal area skills in a variety of settings that include performance tasks, MATHia, a technology component, pre-tests, and post-tests. Questions and tasks within and across units build in academic rigor to meet the full intent of the primary focal areas. Problem sets across lessons scaffold from lower-level tasks (e.g., define, identify, or describe) to higher-level question types (e.g., evaluate, analyze, or create).
Lessons contain several activities, as well as the “Talk the Talk” for each lesson before getting to the actual assignment. The activities allow students to have several opportunities to master the content. MATHia is available for each lesson. This provides the students with additional practice to master the content. Students have a skills practice book to allow for more practice on each skill.
Module 2 guides teaching and learning math concepts through a variety of question types and tasks, such as “How are all of the different representations related?” or “Why is estimation important?” Activity 2.2 provides scaffolding questions to help students struggling with content: “What type of ratios are in the recipe?” and “How many parts are in the recipe?” After these scaffolds, students write a ratio that compares the parts in the ratio. In Topic 6.2, students choose a strategy to solve ratio problems. In Topic 6.3, students compare ratios with a double number line, which leads to the mastery of ratios and proportional relationships.
Module 3 shows a progression of rigor to meet the full intent of primary focal areas. Topic 1 introduces students to expressions, Topic 2 adds equations, and Topic 3 culminates with graphing quantitative relationships.
The materials include a variety of types of concrete models and manipulatives, pictorial representations, and abstract representations, as appropriate for the content and grade level. The materials guide teachers to help students move through the CRA continuum; however, there is limited evidence that the materials support teachers in understanding students’ progression along the CRA continuum.
Evidence includes but is not limited to:
The materials use models, manipulatives, and representations for concept exploration and attainment for the primary focal areas: number and operations; proportionality; expressions, equations, and relationships; and measurement and data. Students work with models, manipulatives, and representations used for content exploration and attainment or have previous experience with the instructional materials through teacher guidance and instructions on activity sheets in the students’ Skills Practice Workbook. Every topic in the materials has an overview section to support the teacher before teaching each lesson.
In Module 1, students work with models, manipulatives, and representations used for content exploration and attainment, and students are likely to have previous experience with the materials. In Topic 2.2, students use area models and strip diagrams to multiply and divide fractions. The teacher is given notes in the topic overview on guiding students to use these pictorial models. The materials include a variety of types of concrete models and manipulatives in only some of the lessons. It is more evident that pictorial and abstract representations are present throughout the materials.
In Module 2, students use complete number lines that model integer addition and subtraction. Next, students create a number line to match the expression provided. Then, students are given verbal descriptions without number lines and asked to solve them. In Topic 1.1, students are given a sample half-time score and asked to predict the score at the end of the game (concrete model/pictorial representation). Students collect data in Topic 1.3 and create their own ratio from the data (abstract representation). These representations are used for concept exploration in the sixth-grade focal area of ratios and rates. Students are explicitly taught how to use the models and representations in these lessons through strategic questioning strategies from both the teacher and the student activity sheets for these topics.
Module 3, Activity 3.3 begins with cutting out nets found at the end of the previous lesson and progresses to a writing assignment where students identify the type of figure from a description. This demonstrates the variety of materials moving from concrete to abstract. A differentiation strategy used to extend the activity is to use manipulatives to demonstrate the correct reasoning, thus increasing the rigor.
An activity in Module 4, Topic 1.1 suggests creating a human number line (concrete); suggestions are given on how to create a human number line using masking tape on the floor. In Topic 1.4, students are asked to draw a vertical number line (representation); suggestions are given on how to create vertical number lines for recording temperature as students move through the CRA continuum. Then in Topic 1.5, students are asked to compare two numbers with or without the use of a number line (abstract). In Activity 2.3, students play a game and create specific polygons, with specific areas, across a specified number of quadrants on a coordinate plane. Students may use tangrams, pattern blocks, or other polygon manipulatives to allow investigation locations before drawing on the paper. The next two activities require students to move to pictorial representations of polygons on the coordinate plane then to abstract reasoning through developing an expression for the length of a line segment. Module 4 provides teachers with concrete and visual representations used in conjunction with positive and negative rational numbers as well as a number classification bullseye. Teachers are given background knowledge about students’ understanding of the coordinate plane from the current and previous grades, based on what the students should understand; however, no guidance is provided for teachers to identify where a student's actual understanding is along the CRA continuum. The lesson continues with a concrete representation of a human coordinate plane and several pictorial representations. The materials do not have further teacher support for students to progress if they are not yet working at an abstract level.
The materials support coherence and connections between and within content at the grade-level and across grade levels. The materials include support for students to build their vertical content knowledge by accessing prior knowledge and understanding concept progression. The materials include tasks and problems that intentionally connect two or more concepts as appropriate for the grade-level. The materials provide opportunities for students to explore relationships and patterns within and across concepts. The materials support teachers in understanding the horizontal and vertical alignment guiding the development of concepts.
Evidence includes but is not limited to:
At the beginning of the Teacher's Implementation Guide, a chart entitled “Middle School Math Solution Content at a Glance” explains how concepts are built during the current year and across multiple years. The materials provide a detailed “Introduction” at the beginning of each module and each topic. This section gives teachers a summary of what students should already know in the section called “What is the entry point for students?” This section supports teachers in knowing what the students already know and what they need to learn to build on the next concept. The materials include teacher supports and guiding documents that help teachers understand how concepts build over time. Teachers have access to extensive professional learning with a mobile and web-based app, LONG + LIVE + MATH, an online community, and a “Central Hub” with access to all products and resources included, in addition to the books and software. Additionally, the materials include guiding documents for teachers, which include content and alignment documents for each module and a Teacher's Implementation Guide.
In Module 1, Lesson 1, students access prior knowledge about three-dimensional figures and how to operate with positive rational numbers to answer the question “How can you use what you know to calculate measurements of any rectangular prism, even one with fractional edge lengths?” In Module 1, students use bar models to represent quotients with fractions; this is covered again in Module 3 as a tool to solve one-step addition equations. In Topic 1, students develop a strategy and use it to determine the area of a triangle embedded in a square. In Topic 3, students determine how to measure exactly 4 gallons of water using just two containers: one with 3 gallons and one with 5 gallons. Students come up with their own way of measuring exactly 4 gallons.
The materials explain an increase in depth, breadth, and complexity to prepare students for next year’s work in this area. In Module 2, the content has students consider the different ways in which quantities can be related to each other, such as part-to-part or part-to-whole. Students use strategies and reasoning developed in ratios to solve conversion problems and unit rate problems, including unit pricing and constant speed problems. In Lesson 1.4, before the lesson, teachers remind students that part-to-part ratios are not fractions. Teachers discourage students from using the fractional form to display their part-to-part ratios unless they are using proportions. Later in Lesson 1.4, students determine each ingredient’s amount in a recipe to make four different lollipop batches. Students apply mathematics to create equivalent ratios and input their findings in a table. In Topic 3, students use strategies from previous topics such as tables, tape diagrams, and double number lines to develop ratios and introduce unit rates and proportional relationships. Strategies taught during this lesson will continue to be used in seventh and eighth grade.
In Module 2, Lesson 6.1, students use tables and graphs to determine the ticket cost to an amusement park. The materials suggest that the teacher ask the students specific questions to connect the mathematical idea of ratios to rates: “What do the numbers in the table represent, with respect to the problem situation?” Then, “What do the points on the graph represent, with respect to the problem situation?” and “What does the steepness of the line mean with respect to the problem situation?” Finally, materials support interconnections with the question, “Why can these ratios also be called rates?” In Topic 3, the overview states why unit rate and conversions are important in grade 6 and describes the impact this topic will have in grades 7 and 8. Unit rates and conversions provide a foundation for a prominent topic in algebra: slope. In grade 7, students use their understanding of unit rate to represent proportional relationships between quantities and write equations and graph proportional relationships, developing an informal understanding of slope. In grade 8, students formally define the unit rate as the slope of a proportional relationship graph.
In Module 3, Topic 1, the materials outline how expressions are organized and highlight how students use algebra tiles and properties of arithmetic and algebra to form equivalent expressions, just as they did in Module 1 with numeric expressions. The materials provide opportunities for students to examine relationships and patterns within concepts and across concepts. For instance, Activity 3.1 asks students to relate bar models used to solve addition equations to multiplication equation bar models. The materials mention that during elementary school, students started to write numerical expressions; then, the materials show how the lessons in this topic will develop students’ prior knowledge of writing algebraic expressions. In the “Why is Expressions important?” section, teachers can read about how the expressions lesson will build directly into the future work of algebraic inequalities and their representations. The section describes how this lesson will develop for students as eighth graders, where they will write more complex expressions. In Topic 3.2, students use graphs to solve one-step equations, which they learned how to solve using inverse properties in Module 3, Topic 2. In Topic 4, the Talk the Talk culminating activity for students uses an example of triathlon training to use and look for patterns with the distance formula.
In Module 4, Topic 1, students use familiar number lines to learn the concept of signed numbers, which builds from ordering positive rational numbers in a previous module. In the overview, teachers learn that ordering signed numbers is preparing students to perform mathematical operations with signed numbers in seventh grade and work with irrational numbers in eighth grade and beyond. In Topic 2, students solve the following word problem: “The gravitational pull of the Moon is not as great as Earth’s. In fact, if a person checks his weight on the Moon, it will be only 16 of his weight on Earth. If a person weighs 186 pounds on Earth, how much will he weigh on the Moon? How many pounds different from his actual weight is that?” One student might divide 186 pounds by 6 to determine the weight on the Moon. Another student might use a proportion to calculate the unknown weight for the Moon. A third student may create an equation to calculate their weight on the Moon.
The materials include quality tasks that address content at the appropriate level of rigor and complexity. Some tasks are designed to engage students in the appropriate level of rigor (conceptual understanding, procedural fluency, or application) as identified in the TEKS and as appropriate for the development of the content and skill. The materials clearly outline for the teacher the mathematical concepts and goals behind each task. The materials integrate contextualized problems throughout, providing students the opportunity to apply math knowledge and skills to new, but not varied, situations. The materials provide some teacher guidance on anticipating student responses and strategies. Lastly, the materials provide some teacher guidance on preparing for and facilitating strong student discourse grounded in the quality tasks and concepts.
Evidence includes but is not limited to:
The Teacher's Implementation Guide provides teachers guidance in each topic’s overview, including how students demonstrate understanding and how each topic’s tasks promote student expertise. The materials provide “Learning Together,” which is a subsection of the topic overview. It shows the progression of each lesson and the standards addressed, both target and spiral. The materials explain how each task builds student efficacy towards the goal of demonstrating mastery. For example, in the “Facilitation Notes” guide for each topic, the materials provide summaries of each activity and what students should demonstrate after completion. This section provides the teacher with a list of indicators to look for that constitute a student’s understanding of the topic’s standards. For example, the materials suggest that the teacher looks for students’ identification of parts in a numerical expression using terms such as sum, factor, product, and coefficient to understand the distributive property.
The materials include meaningful tasks for students set in real-world contexts and allows them to demonstrate mastery of math concepts. For example, in introducing unit rates, the materials offer several real-world activities such as finding the best buy for various sizes of popcorn, calculating the unit price for a number of fair tickets, determining the miles per gallon for different cars, and deciding on the better buy between two kinds of cereal. The materials do not guide the teacher on how to appropriately revise content to be relevant to their specific students, backgrounds, and interests. The materials provide teachers with possible student strategies to practice questions and tasks. For example, the materials include a problem-type called “Thumbs Up/Thumbs Down” to analyze problem solving in examples provided. When an incorrect response is presented, students look for errors in calculation and correctly solve it.
The materials’ online component, MATHia, provides students with multi-level hints to help them solve problems. No evidence was found that the materials provide teacher guidance throughout the topic or lesson overview on anticipated student strategies. The facilitation notes section in every lesson provides several open-ended questions to ask students and support discourse. The materials provide teacher responses to possible students’ responses, including how to direct students’ misunderstandings or misconceptions. The misconception section is included in most lessons, as are differentiation strategies to help students who may struggle. For students having difficulty finding the percent of a number, the materials suggest that the teacher uses diagrams and models and explains that a percent is part of a whole and can be any size. The materials do not provide rubrics or keys with which teachers can evaluate and provide feedback to students while engaging in discourse. The materials partially support the teacher with setting up and reinforcing strong practices for student discourse. Although every topic in the materials provides an overview as a guide for the teacher to use guided questions to support students through the topic’s learning, little to no detail is given to the setup and reinforcement of these practices.
Module 2 begins with the first topic, ratios, to increase the rigor in the second topic, percents, and ends with unit rates and conversions as the third topic. These three topics have sub lessons that also increase in rigor by breaking down the lessons and gradually moving into multiple representations of relating quantities. In Topic 1, the lesson structure builds in complexity from “Getting Started” to “Talk the Talk.” Students begin using estimation skills, move to determining the cost of tickets to an amusement park, compare double number lines, differentiate between additive and multiplicative relationships, and finish with selecting a strategy to explain scaling up and down. In Lesson 5.3, students use a ratio to generate values in a table and then use the table to create a graph. These representations are used to answer questions in the scenario. The materials provide teachers with common misconceptions on student responses and strategies and how to combat those misconceptions for some of the lessons.
In Module 3, Topic 1, students first evaluate numeric expressions, then add variables to learn algebraic expressions. Next, students learn equivalent expressions and how to verify equivalent expressions. Finally, students use algebraic expressions to analyze and solve problems. Activities 1.1 and 1.2 include a misconception section in the teacher’s facilitation notes. Other than the misconceptions section, there is no evidence of material providing teachers with possible student responses or guidance on which anticipated strategies are appropriate. In Lesson 1, students work through examples and move into questions that contain real-world concepts; however, there was no evidence of guidance for the teacher on how to revise content to be relevant to backgrounds and interests. Throughout the materials, the facilitation notes for each lesson include an extensive list of questions to support student discourse. For example, the following questions are included for teachers to use to promote discourse: “How did you use the rate to write an equation?” “What is the independent variable, and what does it represent in this situation?” “How can you use the graph to determine unknown values?”
In Module 4, Topic 1, students make a human number line; they then create a number line model to learn more about opposite numbers and their location on the number line. Finally, they analyze given number lines with a number other than zero as the benchmark for comparison. In Module 4, students practice interpreting the coordinates of graphs in the first quadrant to prepare students to interpret coordinates in all four quadrants. Topic 1.2 states, “Opposite numbers are reflections of each other across 0 on the number line. The opposite of a positive number is a negative number, and the opposite of a negative number is a positive number.” The materials explain how each task builds student efficacy towards the goal of demonstrating mastery. For example, the first section of the facilitation notes for each lesson contains a statement of how the lesson will lead to student understanding. In Topic 1.3, the facilitation notes start with, “In this activity, students analyze two number line representations of a real-life scenario, one with $0 as the benchmark for comparison and one with the movie price as a benchmark for comparison.”
The materials integrate fluency over the course of the year and include some teacher guidance and support for conducting fluency practice as appropriate for the concept development and grade; however, the materials do not include an explicit year-long plan for building fluency as appropriate for the concept development and grade. The materials integrate fluency at appropriate times and with purpose as students progress in conceptual understanding; however, the integration is not explicit and is not found throughout the materials. The materials include some scaffolds and supports for teachers to differentiate fluency development for all learners.
Evidence includes but is not limited to:
The Teacher's Implementation Guide provides detailed descriptions in the “Module and Topic Overview” that explain the plan for that module to build concept development and fluency and how it will address the targeted student expectation. This is consistently done throughout the materials for every module and topic; however, guidance is limited throughout the lessons and activities. The materials provide lessons and pacing structure that includes directions on helping students move through multiple fluency practice activities within a single lesson. Each assignment contains a review section that provides a spaced practice of concepts from the previous lesson and topic and the fluency skills important for the course. The materials include some opportunities within the facilitation notes of each activity for students to discuss their conceptual understanding behind the fluency practice by using questions listed for the teachers to guide the students through this process. The materials provide a “Stretch” section for every lesson for students to extend fluency when they have already met the fluency expectations. The materials provide a section in the facilitation notes titled, “As students work, look for.” This section lists for teachers certain key things that help the teacher determine if students need differentiated supports.
The online component, MATHia, provides individual practice for students to build their fluency throughout the school year and track their progress within each module and targeted skill. The table of contents in the materials shows each module’s alignment, topic, lesson, and activity with the student expectation and the MATHia workspace. However, there is no guidance on how and when to use resources in the scope and sequence or individual lessons. The materials include the “Skills Practice Workbook” with activities that focus on building student fluency.
In Module 1, the Teacher's Implementation Guide states the connections to future learning by introducing the fluency standards at the beginning of the course, allowing practice opportunities throughout the year. However, throughout the lesson, minimal guidance is provided. In Topic 2, the materials provide the students with several fluency activities and several choices for the strategy they can use to multiply and divide fractions. The first activity teaches students to use the area model for multiplying fractions and mixed numbers. Students work on physical and number line models to represent dividing a fraction by another fraction and dividing a whole number by a fraction in the next activity. In the third activity, students use strip diagrams to continue their exploration of dividing fractions. These activities allow students to develop their own rules and conceptual understanding for calculating the products and quotients of two fractions. Activity 3.1 requires students to solve rectangular prism volume problems and provides students with an opportunity to gain fluency in multiplying decimals. The activity includes a recommended extension of providing students with models of prisms other than those with rectangular bases and calculating the volume of other 3-D shapes. Conversely, if a student is struggling with the same activity, the text recommends offering the student a stack of paper to demonstrate the formula V=Bh or to use a milk crate to help students visualize a cubic foot.
The Module 2 overview in the Teacher's Implementation Guide explains how fluency in ratios and ratio reasoning helps students in the concept development of percents, unit rates, and conversions. In Lesson 1.1, students solve four warm-up problems where they write a fraction to represent each of the four problem situations. This warm-up activity helps develop the conceptual understanding of ratio and ratio reasoning. In Activity 1.3, students play the “Percentage Match Game,” which reviews equivalent forms of fractions, decimals, and percents. Students who struggle with fluency use a hint sheet to support their learning while they play the game with peers who may be more fluent with these benchmark values. In Topic 2, the review section requires students to practice the standard algorithm to determine each quotient problem.
In the facilitation notes of Module 4, Lesson 1.3, the materials guide the teacher to prompt students with questions about the classification of whole numbers, integers, percents, and fractions. The teacher provides discourse opportunities by asking the students if there are numbers written as percentages that can also be classified as rational numbers. Because a percent can be converted into a decimal and a fraction, it can be classified as a rational number and a whole number and an integer (depending on what the percentage is). The teacher-guided questions promote students’ strategic discourse to develop a deeper understanding of the rational number system.
Module 5, Lesson 1.2 guides the teacher through a two-day lesson that includes four fluency activities on analyzing numerical data displays. The materials tell the teachers when to guide students, when they should be applying their knowledge, and when they should demonstrate what they have learned. The directions explain when students should read aloud, what questions the teacher should ask, and when they should work in groups or pairs.
The materials integrate fluency at appropriate times and with purpose as students progress in conceptual understanding; however, the integration is not explicit and is not found throughout the materials. The materials include some scaffolds and supports for teachers to differentiate fluency development for all learners.
The materials include some embedded opportunities to develop and strengthen mathematical vocabulary. The materials include some guidance for teachers to scaffold and support students’ development and use of academic mathematical vocabulary in context.
Evidence includes but is not limited to:
The Teacher's Implementation Guide and the Consumable Student Edition include key terms listed and defined in the “Module and Topic Overviews.” When appropriate, in the margins of the Consumable Student Edition, characters called “The Crew” use speech bubbles to highlight and define academic vocabulary. At the beginning of each lesson, the materials list the learning goals and key terms on the same page; however, the development of mathematical vocabulary is not addressed. Key terms are bolded in each activity’s text and accompanied by the formal definition, which is used within the lesson context. At the end of each topic, a summary is included for the students and teachers to review key terms learned throughout the series of lessons within that topic. The lessons embed the introduction and use of vocabulary within the context of mathematical tasks requiring students to communicate mathematical ideas. For example, the Student Edition embeds academic vocabulary within each lesson.
The materials provide repeated opportunities for students to listen, speak, read, and write using mathematical vocabulary within and across lessons. At the end of each lesson, students complete three sections: “Write,” “Remember,” and “Practice.” Students make connections to the previous activities in the lesson and also reiterate the formal language of mathematics. The materials do not explicitly build from students’ informal language to the formal language of mathematics by making explicit connections throughout the materials. The materials provide a section for differentiation in most lesson activities; however, vocabulary development is not one of the strategies provided. The Teacher's Implementation Guide prompts teachers to create a word wall of key vocabulary terms used through the materials.
In Module 1, Lesson 1, the facilitation notes provide the vocabulary words introduced in the first activity and reused later in the lesson. In Lesson 4, students pre-read the lesson before being introduced to the lesson to skim through the materials and find the key terms and the definitions. Students then rewrite the definitions in their own words.
Module 3, Lesson 2 has students read formal expression definitions and write the correct term in the corresponding blank. Furthermore, students are encouraged to use proper academic vocabulary when speaking with a partner or group. In Topic 2, the facilitation notes provide a differentiation strategy for struggling students, guiding the teacher to discuss the common definition of isolate and how it relates to the mathematical phrase isolate the variable. Additionally, the strategy suggests making the connection between inverse and reverse explicit. In Lesson 2.2, the key terms are listed as bar models and a one-step equation. One of the learning goals states that students will use bar models to represent one-step addition equations. Therefore, understanding the listed vocabulary is required to meet the learning goals.
Module 4, Lesson 1.1 prompts students to work in a group to complete questions about negative numbers and then share responses as a class. These activities are repeatedly used throughout the materials to promote reading the math questions, listening to a group conversation, and speaking about their thinking process and response. In Module 4, Lesson 1.1, students demonstrate their learning by explaining the relationship between opposites and negative numbers. In Module 4, Lesson 2.1, the materials suggest that the teacher listen to the students discuss the coordinate plane and listen for specific vocabulary in their explanations such as ordered pairs, origin, units, and grid lines. In Module 4, Topic 2, students are asked to explain ordered pairs by using specific terms like axis, quadrants, and coordinates. Students are given a reminder about the key vocabulary they learned in the lesson that can guide them in their writing assignments. Finally, students are asked to read and solve five practice problems that only include formal mathematics language.
In Module 5, Lesson 1.1, the materials suggest that teachers guide students to take notes to keep track of the vocabulary in the lesson on statistics, highlight and circle vocabulary words, and continue this process throughout the lesson.
The materials provide opportunities for students to apply mathematical knowledge and skills to solve problems in new and varied contexts, including problems arising in everyday life, society, and the workplace. The materials include opportunities for students to successfully integrate knowledge and skills to problem solve and use mathematics efficiently in real-world problems. Materials provide students opportunities to analyze data through real-world contexts.
Evidence includes but is not limited to:
The program requires students to integrate knowledge and skills together to make sense of a context and develop an efficient and successful solution strategy. For example, each topic includes an open-ended performance task that allows students to be creative in demonstrating what they learned. The task presents a scenario that includes student directions for acceptable work and a detailed rubric, teacher notes, and a sample answer. The materials include opportunities for students to solve real-world problems from a variety of contexts. For example, each lesson contains real-world problems such as buying back-to-school supplies, taking a bike ride home from school, and making brownies for the class.
In Module 1, Topic 1, “Factors and Area,” students view a diagram showing dimensions of a lawn with information about the amount of lawn fertilizer needed per square foot and the fertilizer’s cost. Students determine the cost of fertilizer for the lawn diagram provided. In Lesson 1.1, students design the floor plan of a gymnasium for different after-school activities. Students use the distributive property to represent their model and identify how the gym’s width and area are reflected in their equation. In Lesson 1.5, students use the information given about a girl with three bags of beads, each containing different numbers of beads, to determine how many smaller bags of beads she can make for each of her friends, with each bag having the same quantity of beads. In Activity 2.1, students determine the fractional amounts of ingredients needed to make Hawaiian trail mix.
Module 2 requires students to evaluate percent, fraction, and decimal equivalence by demonstrating how percents are everywhere. For example, students create a statement to explain the meaning of discounts, the chance of snow, and test scores. In Lesson 2.1, students analyze the data from a survey that asked one hundred students which historical site they would like to visit on a class field trip. Students complete a table where they convert the ratio to a fraction, then a decimal, and finally a percent. In Activity 3.3, students analyze the results of a quiz to determine rates and proportionality. In Lesson 5, students are given a double number line of data and a coordinate plane for a local sports team’s website views per hour.
Module 3 provides a variety of real-world problems for students when using equations to solve problems like tripling a brownie recipe, determining how many non-spam emails a person may receive, and calculating how many times taller an ostrich is than a hummingbird. In Topic 1, students create algebraic expressions from problems, including costs of t-shirts, numbers of pages in folders, and discounts at restaurants. In Lesson 2.4, students solve problems about a middle school hosting a picnic for 125 students. Students interpret remainders in solution when calculating the number of sandwiches, drinks, and desserts to buy for the picnic. In Lesson 3.4, students analyze and solve problems about competing in triathlons to investigate the relationship between distance, rate, and time. Students create, use, and analyze graphs, equations, and tables. Finally, students summarize the relationship between distance, rate, and time by generating and using the equation d=rt. In Activity 4.1, students use a grade-appropriate graph of swimming distances and times to determine Deazia’s swim rate.
In Module 4, Lesson 2.3, students apply their knowledge of plotting rational numbers on a coordinate plane, creating tables of values, and writing and solving equations to solve various problems situated on the coordinate plane. Then, students carry out their chosen strategy using the table and graph representations to answer questions for specific real-life problems. In Lesson 3, students use positive and negative numbers to model and analyze Julio’s weight throughout the summer. Students plot Julio’s data in Quadrant I, transform the data, and plot the transformed data in Quadrants I and IV. The data is developmentally and thematically appropriate for grade-level students. In Activity 4.3, students analyze the information gathered in previous activities concerning statistics from a triathlon to determine the formulas for distance and rate expressed in ratios.
The materials do not show how they are supported by research on how students develop mathematical understandings. The materials do not include cited research throughout the curriculum that supports the design of teacher and student resources. The materials provide limited research-based guidance for instruction that enriches educators’ understanding of mathematical concepts and the recommended approach’s validity. Cited research that is current, academic, and relevant to skill development in mathematics, and applicable to Texas-specific contexts and demographics is not evident in the materials. A bibliography is not present.
Evidence includes but is not limited to:
At the beginning of the Teacher's Implementation Guide, there is a section titled “Our Research” where research is mentioned. Still, no actual research or synopsis of research is cited or included in the materials. Although the materials speak of their research, known in the materials as “The Carnegie Learning Way” founded by Carnegie Mellon University, teachers’ guidance does not include the physical research behind Carnegie Mellon’s research; the actual research is not cited.
On their home page, the materials briefly describe that educators from Pittsburg Public Schools teamed up with Carnegie Mellon University to create these materials. However, the materials have no evidence that their research is current, academic, and relevant to skill development in mathematics. The program does not describe the students’ context and demographics in the research used to design the program. It is not applicable to the Texas-specific context and demographics.
The instructional materials do not have a bibliography present but do include an acknowledgment page.
The materials provide guidance to prompt students to reflect on their approach to problem solving. The materials also provide guidance for teachers to support student reflection of approach to problem solving. The materials do not prompt or guide students in developing and practicing the use of a problem-solving model that is transferable across problem types and grounded in the TEKS.
Evidence includes but is not limited to:
At the beginning of the Consumable Student Edition, students are introduced to a section called “Habits of Mind.” This section explains mathematical practices divided into five sections, four of which have an associated icon that can be found through the activities. Each section includes an overall approach to problem solving and lists 3–4 questions a student should ask themselves when they see the related icon. However, this is not a problem-solving model because it is not grounded in the TEKS mathematical process standards. It does not include analyzing given information, formulating a plan or strategy, determining a solution, justifying the answer, and evaluating the problem-solving process and the reasonableness of the solution in an organized format.
Although the Teacher’s Implementation Guide mentions problem solving several times as an important mathematical practice, the materials do not develop or practice a consistent and specific problem-solving model. The materials include activities grounded in the TEKS mathematical process standards where students analyze information, formulate a strategy, determine and justify a solution, and evaluate the problem-solving process and the solution, but a specific problem-solving model is not included. There are several guiding questions to help students problem solve through each activity in the materials, but no specific model for them to use while problem solving.
In Module 2, Topic 3, students are shown how coordinate planes can help visualize unit rates at the beginning of the lesson. At the end of the lesson, students are reminded that they can use models, i.e., coordinate plane, ratio reasoning, and unit analysis, to convert units using conversion rates.
In Module 3, Lesson 1.4, the materials provide an activity where students compare two expressions and determine if they are equivalent or nonequivalent. Students use tables, graphs, and the commutative and associative properties to prove that the two expressions are equivalent. The materials guide the teacher with questions to ask about what methods (properties, table, or graph) were most efficient in helping them determine equivalency within the facilitation notes. The questions guide teachers to ask about the advantages of the methods used. These questions help teachers guide students in reflecting on their problem-solving approach and the efficiency that different approaches provide in determining equivalence.
In Module 3, Activity 3.1, students identify structure and regularity in their reasoning. The lesson structure design is grounded in the mathematical process, where students “Engage,” “Develop,” and “Demonstrate” their reasoning about multiplication equations. Module 3, Activities 3.3 and 3.4 guide students to develop and practice problem solving in various problem types such as solving multiplication equations with and without models. The lesson prompts the student to reflect on how they know when to compose or decompose a bar graph model for solving equations.
In Module 4, Activity 3.6, the teacher guide provides questions to support students on the real-world situation of hours worked and money earned in a hardware store in an equation, table, and graph form.
The materials provide students with opportunities to select and use real objects, manipulatives, representations, and algorithms as appropriate for the stage of concept development, grade, and task. The materials provide opportunities for students to select and use technology (e.g., calculator, graphing program, virtual tools) as appropriate for the concept development and grade. The materials provide some teacher guidance on tools that are appropriate and efficient for the task.
Evidence includes but is not limited to:
The materials provide activities where students have to select from various tools, including a graphing calculator, an interactive whiteboard, and the online software MATHia for solving a problem. MATHia is an online, 1-on-1 adaptive math coaching software students can use throughout the course. MATHia includes various electronic tools, including virtual manipulatives, an expression editor, and a calculator that students can use. As students progress through MATHia, they choose the tools most appropriate for them to use on their current tasks. Students explore tools, use animations, categorize answers, and select problem-solving tools within MATHia.
MATHia allows students to use virtual representations for each of the topics in the materials that include grade-appropriate concepts such as area, circumference, proportions, graphing, integers, the order of operations, probability, angle measures, volume, and surface area. Within each module, the MATHia software provides students virtual manipulatives and embedded tutorial hints for lessons.
Module 1, Topic 1 includes a section on misconceptions when using the area model to learn the Distributive Property. The materials guide that “it is much more efficient to use rectangles” to learn the distributive property. In Topic 2, the Teacher's Implementation Guide explains, in detail, the tools that are introduced to students in the topic of positive rational numbers. The materials give the teacher the background knowledge needed to teach students how to use bar models, shaded grids, and number lines before guiding them in learning about ordering rational numbers and multiplying and dividing fractions. Students use the MATHia software to express fraction, multiplication, and division relationships represented in bar models and then use these models to solve real-world and mathematical problems. In Lesson 2.3, students use strip models, number lines, area models, and rulers as helpful tools to multiply and divide fractions. The materials start by showing students how to use these tools to represent the math problem by providing the model for the students and having them write the expression that matches the model. The lesson then guides students to start drawing their models to find the product and quotient to given problems. Students choose what model they will draw to determine the quotient to division problems involving fractions and whole numbers.
In Module 3, Topic 1, the overview states that as students grow as mathematical thinkers, their toolbox and strategies must also grow. Students use various tools, including algebra tiles, tables, graphs, and properties, to create or recognize equivalent expressions. In Lesson 3, students use algebra tiles when rewriting algebraic expressions. In Lesson 3.2, the materials provide an activity where students use graphs to solve one-step equations. Students start by using colored pencils to draw the horizontal lines that represent two given equations. They use a ruler or a straight edge for precision and then see where the two graphed lines intersect. The materials then offer graphing calculators to represent the same problem and determine the point of intersection.
In Module 4, Lesson 3, students use any mathematical tool they like to determine when the water in a pool reaches 3 inches above the desired fill level. In Module 5, Lesson 1.3, the materials guide the teacher to provide students with technology or graph paper to create bar graphs instead of drawing them freehand. Using these tools allows the students to spend less time creating an accurate bar graph so they can analyze the data within the graph and discuss their observations.
The materials prompt students to select a technique (mental math, estimation, number sense, generalization, or abstraction) as appropriate for the grade-level and the given task. The materials support teachers in understanding the appropriate strategies that could be applied and how to guide students to more efficient strategies. The materials provide opportunities for students to solve problems using multiple appropriate strategies.
Evidence includes but is not limited to:
The “Habits of Mind” are tips used throughout the materials to guide teachers and students towards the appropriate strategies for problem solving. The Habits of Mind are introduced and explained at the beginning of the Teacher's Implementation Guide for teachers to refer to all year long.
Module 1, Lesson 1 provides two techniques for ordering rational numbers. The first technique is using benchmark numbers, and the second is using equivalent fractions. Activity 1.4 requires students to use both techniques to order the rational numbers least to greatest. However, students are free to select any technique to order the next set of rational numbers. Module 1, Activity 1.1 provides teachers with facilitation notes that outline how area models connect to the Distributive Property and why this strategy is used to develop this procedure. In Topic 2, the students select between mental strategies, estimation, and the algorithms for multiplying and dividing fractions. In Lesson 2.3, students learn multiple division strategies, estimation, and mental strategies to solve fractions problems.
In Module 2, Topic 1, the Teacher's Implementation Guide explains how students develop different strategies for understanding ratios and the advantages and limitations of each. In Topic 3, on relating quantities, students learn to apply conversion rates to convert units of measure by using various strategies, such as double number line, ratio table, scaling up and down, and unit analysis, to solve a variety of unit rate problems.
Module 3 provides teachers a detailed module overview with information about the importance of beginning the module with algebra tiles and introducing expressions, then moving into solving equations for an unknown value, and finally using a graph to represent the relationship on a coordinate plane. The module overview section gives teachers background knowledge and guidance in understanding which strategies are appropriate for solving problems within that module for students to determine unknown quantities. In Topic 2, students learn several strategies to solve equation problems. For instance, students use number sense, bar models, Division Property of Equality, and Multiplication Property of Equality to write equivalent expressions. These strategies for solving an equation are based on the form of the equation. In Lesson 3.4, students select between a graph, table, or given rate to analyze the rate for a specific triathlon segment. By guiding the students through different activities, the materials then introduce the equation d=rt for any distance or rate problem.
In Module 5, Lesson 2.1, the materials provide teachers facilitation notes on how to guide students through different strategies when analyzing data using center measures. Students practice analyzing data within dot plots, stem-and-leaf plots, and histograms. The teacher is prompted to ask questions about the strategy that would be most efficient, depending on the representation presented.
The materials support students to see themselves as mathematical thinkers who can learn from solving problems, make sense of mathematics, and productively struggle. The materials 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:
The materials include tasks designed to support students in productive struggle as they make sense of the problem and solve it. “Habits of Mind” encourages experimentation, creativity, and false starts to help students tackle difficult problems and persevere when they struggle. For instance, the materials provide students with worked examples throughout that have a thumbs up and thumbs down icon next to it. At times, students determine if the thumb should be up or down based on the example. If the solution is correct, students identify connections between the steps. If the example is incorrect, students indicate a thumbs-down icon, identify the error made, and then correct it.
The materials challenge beliefs and biases that conflict with all students seeing themselves as mathematical thinkers. For example, a section called “Myth” at the beginning of each topic debunks common misconceptions about math. The following are examples of math myths busted that demonstrate all students are mathematical thinkers: “I don’t have the math gene,” “Asking questions means you don’t understand,” “There is one right way to do math problems,” “I’m not smart,” and “Faster = smarter.” Each module also includes a family guide. One topic of the family guide focuses on debunking common myths that students might believe about being a poor mathematician and replacing the myth with positive and encouraging statements about being a successful mathematician.
The materials provide suggestions for sequencing the discussion of student strategies for solving the problem. For example, each activity includes facilitation notes in the Teacher's Implementation Guide, a detailed set of guidelines that walk teachers through implementing the “Getting Started,” “Activities,” and “Talk the Talk” portions of the lesson. Each lesson includes an activity overview, grouping strategies, guiding questions, possible student misconceptions, differentiation strategies, student look fors, and an activity summary. The materials provide instructional supports for facilitating the sharing of students’ approaches. The materials provide teachers with “listen fors,” so teachers can be prepared for how to respond to students’ thinking while solving problems. Each activity contains an extensive list of sequential questions for teachers to ask students to work through learning tasks individually, in small groups, or in large groups.
The materials provide instructional supports for facilitating the sharing of students’ approaches. For instance, alternative grouping strategies, such as whole class participation and the jigsaw method, are sometimes recommended for specific activities under differentiation strategies in the Teacher's Implementation Guide. Additionally, grouping suggestions appear to help chunk each activity into manageable pieces and establish the lesson’s cadence.
In Module 1, Lesson 1.4, the teacher’s guide explains the introductory activity to common factors and multiples. The guide starts with a whole group activity where students answer guiding questions provided by the teacher. The guide then offers suggestions for struggling students, showing them the factoring tree strategy to solve problems. It also extends the activity by suggesting that the teacher provide students three numbers or more to find common factors and multiples instead of only two numbers.
In Module 2, Lesson 1.6, students use tables, double number lines, and graphs to compare ratios. Students are given plenty of practice through four activities within the topic to practice each of the pathways to compare ratios.
In Module 3, students solve puzzles as an introduction to expressions. Students learn several strategies for working with expression, some structured and others open-ended, through discussion and working with partners and small groups. In Activity 1.1, the Teacher's Implementation Guide supports teachers with monitoring students as they work on substitution to understand equality problems to ensure they are not using inverse operations when determining missing numbers. In Lesson 1.3, students explore equivalent expressions by first using algebra tiles, combining like terms, and then using rules and properties to check for equivalency. These three methods are used throughout the lesson through four different activities and allow students to choose between the hands-on manipulatives, the algebraic representations, or the understanding of memorized rules. The materials provide a section in the module called “Myth: Just give me the rule. If I know the rule, then I understand math.” This section gives students information about this myth. It explains that rules without meaning will not be remembered nor learned. In Lesson 2.2, students create and share numeric expressions that are equal to zero. Within the materials’ facilitation notes, teachers are guided in the section titled, “As students work, look for.” The materials suggest that teachers look for commonalities between the ways students write these equations and observe what operation was used to write them. The materials ask teachers to look for the use of grouping symbols and fractions, decimals, or mixed numbers. In Lesson 3, Planes, Trains, and Paychecks, students use multiple representations (table, graph, word problem, algebraic equation) for solving equation problems. In Activity 3.3, the Teacher's Implementation Guide explains how multiple approaches to solving one-step multiplication equations is a process that begins with having students analyze the structure of an equation before applying solution strategies to determine unknown values.
In Module 4, Activity 1.3, students pair up with someone who completed a different number line to compare and share findings of real-world movie price comparisons. In Activity 3.8, Talk the Talk, students create a situation modeled by the given graph and write at least three sentences for their presentation.
In Module 5, Lesson 2.3, students change a data set into numerical data to determine the mean absolute deviation. The facilitation notes guide teachers in asking students to share one way they can change this data set, and then ask students to share another way to do this. The materials frequently show this type of question throughout the modules so that students can share their solving process and listen to their classmates and their approaches. In Lesson 3, Getting Started, students create two different bar graphs using the same set of state park categorical data displayed in a table. The goal of the activity is for students to begin the process of contrasting bar graphs and histograms. Students work with a partner or group to create frequency tables and histograms with continuous data at different intervals. Students display their work on posters and share with the class.
The materials allow students to communicate mathematical ideas and solve problems using multiple representations, as appropriate for the task. The materials guide teachers in prompting students to communicate mathematical ideas and reasoning in multiple representations, including writing and the use of mathematical vocabulary, as appropriate for the task.
Evidence includes but is not limited to:
The materials include multiple opportunities within every module, topic, and lesson to communicate mathematical ideas. Students are able to solve problems and communicate their thinking process with small groups, partners, and the whole class. At the end of each lesson, the materials provide a “Talk the Talk” and a “Write” section where students are usually asked to communicate their ideas in written format. Throughout the materials, teachers engage students with higher-level questions during the teaching process. The questions happen in small groups and in large groups. Students communicate their learning within those groups in a variety of ways.
Throughout the materials, in every module, topic, and activity, the materials provide a series of questions for teachers to ask students. Sometimes students answer those questions in writing in their Consumable Student Edition, and other times they answer the questions orally in their small groups. Both oral and written responses are included multiple times during each topic. The materials provide students a Write section at the end of every lesson throughout every module. Every topic within each module starts by giving the teacher an overview of the topic’s focus and includes essential vocabulary. Within every topic, the lessons begin with vocabulary development. To review each topic, the materials include a section where the vocabulary is summarized for students.
In Module 1, Activity 1.1, students answer questions 3 and 4 about positive rational numbers with a partner. When pairs finish, they share their answers, and the teacher pays attention to how students explain their reasoning. Two of the questions asked are, “How can you prove that all of Vivian’s cards have the same value?” and “Do you prefer the use of fractions or decimals to show that those representations are equal?” In Lesson 2, teachers ask questions such as “What mathematical terms did you use to describe the sides and the angles?” In Lesson 4, the Teacher's Implementation Guide notes an EL tip due to heavy vocabulary in the section and suggests that students use a pre-reading guide for the chapter before introducing the lesson.
In Module 2, students use a graphic organizer to demonstrate their understanding of ratios by generating a definition, writing characteristics, and creating an example and non-example. In Module 2, Activity 1.1, the teacher guide provides questions to ask students as they work on predicting the final score of a basketball game using either multiplicative or additive reasoning. In Activity 1.4, students answer questions about the process of converting units and the reasonableness of their results with a partner or group. In Activity 2.3, students write ratios from the given graphic, convert those ratios to unit rates, and then use their work to identify the best buy. In Module 2, the facilitation notes in the teacher’s guide prompt the teacher with several questions to ask students throughout the whole topic of unit rates and conversions to elicit communication of mathematical ideas. This is done several times as a whole class, in partners, in small groups, and also when students work individually. This is evident throughout the materials in every lesson, topic, and module. In Lesson 3.3, the materials provide a lesson on multiple representations of unit rates. Students solve problems using double number lines, tables, equivalent ratios, tape diagrams, and equations to develop their understanding of unit rates. For example, students use a double number line to compare miles per hour and kilometers per hour; students then answer questions and share responses as a class. In the “Demonstrate” activity, students read a graph and write a corresponding story problem with unit rates. After they write their story problem, students also write their own questions and answers that can be solved using the graph given.
In Module 3, Activity 2.1, students work in partners and use bar models to develop rational thinking and mathematical reasoning to answer questions on decomposing addition equations. In Activity 3.1, students use bar models and algorithms to solve equations. In Activity 3.3, teachers ask questions that prompt students to give answers in different forms when analyzing equations from different scenarios. In Lesson 4, “Triathlon Training,” students solve one-step real-world and mathematical problems to analyze relationships between two quantities using graphs, equations, and proportional approaches. Students summarize the relationship between distance (d), rate (r), and time (t) using multiple representations like verbal statements, graphs, tables, and equations.
In Module 5, Activity 1.3, students use a graphic organizer to show their understanding of each component of the statistical process. In Activity 2.4, students share results with the class after writing a summary of the data analysis results. In Activity 3.3, the Teacher's Implementation Guide prompts teachers to have students use vocabulary when comparing Mean Absolute Deviation (MAD) and Interquartile Range (IQR) and completing fill-in-the-blank definitions.
The materials provide opportunities for students to engage in mathematical discourse in a variety of settings (e.g., whole group, small group, peer-to-peer). The materials integrate discussion throughout to support students’ development of content knowledge and skills appropriate for the concept and grade-level. The materials guide teachers in structuring and facilitating discussions as appropriate for the concept and grade-level.
Evidence includes but is not limited to:
Throughout the materials, in every activity, there is at least one opportunity for students to engage in mathematical discussions with a partner, a small group, or the whole class. Most activities include multiple opportunities for these discussions. Every activity includes at least one opportunity for discussion in various groups, including the beginning, middle, and end of concept and skill development. The Teacher's Implementation Guide provides teachers with a series of questions to ask students to prompt discussions in every activity throughout the materials. Sometimes those discussions are guided by the teacher, and other times the discussions are guided by the students.
Each lesson is designed to have students work with a partner or in groups to answer specific lesson questions and then share responses with the class. Each lesson is designed to have an active discussion engagement. Materials are designed to move from student discussion to classroom discussion with teacher guidance. Each lesson guides differentiated grouping strategies, such as whole group or jigsaw, in the “Differentiated Strategies” section of the teacher guide. The materials offer teachers guidance on how to structure discussion that is appropriate for the grade level and choose a grouping structure for discussion that will support students in developing content knowledge and skills.
In Module 3, the materials include four lessons and 16 separate activities within those lessons for the concept development of expressions. As students work out each of these 16 activities with the teacher’s guidance, the concept moves from introducing numerical expressions to determining equivalent expressions to analyzing and solving problems using algebraic expressions. Every one of the 16 activities includes opportunities for students to discuss in whole group, small groups, and partners at each phase of the concept development (beginning, middle, and end). In Lesson 1.1, the teacher moves students into small groups or partners in certain sections of the lesson delivery to evaluate numerical expressions. In the introductory lesson, students build expressions for three numerical puzzles with a partner or a small group to compare answers. The teacher prompts students to reach a consensus and discuss differences in each member’s numerical expressions. By the last activity in the lesson, the teacher asks students to answer questions independently first, then regroup and discuss the process used in writing certain expressions and go over answers as a class. This type of example is evident throughout the materials in every lesson. Lesson 1.3 is about equivalent expressions; the facilitation notes guide the teacher to question students in the whole group about the unit squares they are using as manipulatives to represent the x tiles and y tiles. Then the teacher moves students into partners or groups to answer questions in the student workbook. After they have finished, students come back to the whole group and share responses as a class.
In Module 3, Lesson 2, the teacher asks, “What comes to mind when you see the number 0?” to the whole class for discussion. In the next activity, students continue to discuss relevant questions with a partner or group and then share with the whole group. In the conclusion of the lesson, students respond to questions individually, with a partner, and as a whole class when writing about solving one-step equations. In Activity 3.2, students create a model of each expression using algebra tiles with a partner or a group and then share responses as a class.
In Module 4, Activity 2.2, students engage with a partner to discuss the interpretation of absolute value statements and progress to a discussion on absolute value statements in everyday life.
The materials provide opportunities for students to construct and present arguments that justify mathematical ideas using multiple representations. The materials assist teachers in facilitating students to construct arguments using grade-level appropriate mathematical ideas.
Evidence includes but is not limited to:
The materials follow the same structure for all topics and lessons. This structure includes introducing a concept in a whole-class setting, then moving students into partners or small groups to answer questions. Within these group settings, teachers use the materials’ facilitation notes, which provide prompts for the teacher to assist students when constructing arguments. Each module of the Teacher's Implementation Guide includes “Questions to Ask” that structure the facilitation of constructing arguments. Students consistently have to reflect and ask themselves, “How can I justify my answer to others,” indicating that whenever students explain their reasoning, they need to be able to justify their answer.
The materials provide a “Thumbs Up/Thumbs Down” section throughout the lessons that give students a problem that has been worked out by a fictional student. Sometimes the problem shown is worked out correctly, and sometimes it is incorrect. The student analyzes the method used to solve the problem shown and either gives it a thumbs up or a thumbs down. Students write if they agree with the method and the solution or not and explain their reasoning behind their answer. Based on the student's answer, teachers help students redirect their misconceptions or confirm their understanding of a concept.
In Module 1, students sort a variety of rational numbers and models of rational numbers into categories with a partner. The group then attaches their cards to a poster and shares it with the class. The teacher facilitates a discussion and asks whether students would change any of their groups based on what their classmates did. Students explain their reasoning, and the teacher clarifies any misconceptions students may have had.
In Module 2, the teacher uses several examples to help students identify the most appropriate measurement. Students then decide the most appropriate measurement for four objects on their own, constructing arguments to justify their selection.
In Module 3, the Teacher's Implementation Guide’s facilitation notes guide what to look for as students work and provide questions for the teacher to ask while observing student work. In Lesson 3, students move through lessons on multiple representations of equations and share findings with the class at the end of each lesson using verbal descriptions, tables, equations, and graphs.
In Module 4, the materials provide three activities to introduce and help students understand negative numbers and compare values. Students use multiple representations, such as physically creating a human number line, visually drawing horizontal and vertical number lines, and symbolically learning the notation for the opposite of a number. Students answer questions about how they know one negative number is greater or less than another negative number. Students justify their answers using one of the representations they have learned. The materials also ask students to create a statement that would work to compare any two rational numbers and then test and justify their statements with specific criteria (e.g., comparing a zero to a negative number or comparing a positive and a negative number.)
In Module 5, students are given a Thumbs Up/Thumbs Down question about the mean and median in a data set shown on a dot plot. Before students can agree or disagree and construct an argument for their statement, they have to calculate the mean and median themselves and use those calculations to prove their argument. The side note on the activity gives the teacher the correct answer. This allows the teacher to assist students when it is observed that they do not fully understand the concept.
The materials include a variety of diagnostic tools that are developmentally appropriate (e.g., observational, anecdotal, formal). The materials do not guide teachers to ensure consistent and accurate administration of diagnostic tools. The materials include some tools for students to track their own progress and growth; however, some of those tools were not accessible for review. The materials include diagnostic tools to measure all content and process skills for the grade level, as outlined in the TEKS and Mathematical Process Standards.
Evidence includes but is not limited to:
Based on the Texas Education Agency’s definition of diagnostic tools, “systematic assessments and instruments to gather information to monitor progress and identify learning gains,” the materials reviewed include diagnostic tools. The homepage of the material’s website has a brief description of two assessments used to check student progress. One of them is “MATHia,” which is a computer-based component of the materials. MATHia includes a formative assessment for each skill. There is an indication that MATHia may provide the opportunity for students to track their own progress and growth throughout. The second is a partnership with “Edulastic,” described as a separate addition to the materials that includes summative assessments addressing K-12 standards. The MATHia component was available for review in a limited demo. Edulastic was not available for review.
Formative assessments are provided throughout each lesson and workspace, providing the teacher with ongoing student performance feedback. A variety of topic-level summative assessments are provided to measure student performance, a designated set of standards. Before, during, and after each topic, the materials offer opportunities to assess students’ learning appropriately. This is done throughout the materials in the Teacher's Implementation Guide through suggested questions for the teacher to check for understanding during the activities within each lesson. The materials also provide pre- and post-assessments by topic.
The materials are designed to allow students to demonstrate understanding in a variety of ways. For example, in the “Demonstrate” portion of each lesson, students solve questions in multiple ways. In Module 1, students determine the shaded triangle area inside a square, explain the strategy used, and create a solution strategy presentation. In Module 3, Topic 3, students describe similarities and differences between pairs of equations, among graphs, and how to use a graph to solve one-step equations. The materials advise students to use these activities to reflect on the lesson’s main ideas.
For each module, students learn the lesson goals and set their own goals. Students reflect on the lesson’s main idea, ask questions to clarify their learning, and revisit questions posed at the lesson’s opening. There is no explicit student tracker for data; it is suggested that students track progress independently. Diagnostic tools are not included to measure all content and process skills, as outlined in the grade-level TEKS. Still, various topic-level summative assessments are provided to measure student performance on a designated set of standards.
The materials include diagnostic tools; however, some of the tools were not accessible to review. The materials support teachers with some guidance and direction to respond to individual students’ needs in all mathematics areas, based on measures of student progress appropriate to the developmental level. Diagnostic tools yield meaningful information for teachers to use when planning instruction and differentiation. Materials provide some resources and teacher guidance on how to leverage different activities to respond to student data. The materials do not provide guidance for administrators to support teachers in analyzing and responding to data.
Evidence includes but is not limited to:
Materials include “LiveLab” data monitoring tools to analyze student usage of MATHia. The tool provides teachers with a monitoring section where students are listed in order from those struggling the most to the students that have mastered the concept. When a teacher clicks on a specific struggling student, LiveLab provides an at-risk predictive warning at the top of the page with remediation suggestions on skills or concepts needing to be re-taught or reviewed to be successful in that specific topic. LiveLab provides teachers with a tour video to explain how to understand the diagnostic tools’ results. Although limited access was provided to the Texas Resource Review to evaluate the videos, it is clear that more videos similar to the tour video exist for teachers to access. The MATHia software component includes a reporting platform where data can be analyzed for each student, class, and the whole school. This platform’s reports are the Adaptive Personalized Learning Score (APLSE) report, session report, standard report, and detailed student report.
In the “Edulastic Assessment Suite,” reports are color-coded to help identify areas for improvement and strengths. The materials provide various suggestions and activities for teachers to use to address the results of student assessments. For example, in MATHia, access, facilitation, and follow-up suggestions after a formative assessment are available via the CL Online Resource Center. The Edulastic Assessment Suite allows teachers to view assessment summaries, sub-group performance, question analyses, response frequency, performance by standards, and students’ performance. Furthermore, teachers can view individual student assessment profiles and mastery profiles.
Based on the limited access to MATHia, Livelab, and the Edulastic Assessment Suite, it is not evident that the materials meet the indicator.
The materials include routine and systematic progress monitoring opportunities that accurately measure and track student progress. The frequency of progress monitoring is appropriate for age and content skills.
Evidence includes but is not limited to:
Formative assessments are provided throughout each lesson and workspace, providing the teacher with ongoing feedback on student performance. A variety of topic-level summative assessments are provided to measure student performance over a designated set of standards. For example, before, during, and after each topic, the materials offer multiple opportunities to assess students’ learning appropriately. This is done throughout the Teacher's Implementation Guide through suggested questions for the teacher to check for understanding during the activities within each lesson. The materials provide pre- and post-assessments by topic. The materials also provide progress monitoring through MATHia and the Edulastic Assessment Suite; however, these were not accessible to review.
Each lesson includes a “Demonstrate” section known as “Talk the Talk.” This section is essentially an ongoing formative assessment that helps the teacher make decisions about helpful connections that need to be made in future lessons. Each topic includes specific aligned assessments: pre-test, post-test, end-of-topic test, standardized test practice, and performance task. In the Teacher's Implementation Guide, each lesson includes “As students work, look for” sections that note specific language, strategies, and errors to look and listen for as the teacher circulates and monitors students working in pairs or groups. Each lesson embeds “Questions to Ask” and “Misconceptions to Look For” that help teachers monitor progress.
In Module 3, there are various options for progress monitoring, including the use of writing riddles, correcting mistakes, the MATHia software, and paper/pencil assessment. In Lesson 1, in the “Talk the Talk” activity, students examine several problems that have already been worked out to look for mistakes and correct them. In Lesson 2, students create and share numeric expressions that are equivalent to 0 using a variety of number types and operations. The “As students work, look for” section notes to look for common ways students wrote each numeric expression and grouping symbols.
The “LiveLab” data monitoring tools in the materials are used to analyze the student’s use of MATHia. The materials provide teachers a tour video to explain how to understand the results of the diagnostic tools. Access to reviewers is limited to just a tour video. Materials also include the Edulastic Assessment Suite; however, the Texas Resource Review did not have complete access to evaluate assessment guide checkpoints, timelines, or teacher tips for tracking progress.
Materials include some guidance, scaffolds, supports, and extensions that maximize student learning potential. Materials provide recommended targeted instruction; however, the materials lack sufficient activities for students who struggle to master content. Materials provide recommended targeted instruction and activities for students who have mastered content. Materials provide some additional enrichment activities for all levels of learners.
Evidence includes but is not limited to:
The materials provide some recommended targeted instruction; however, there is a lack of evidence that the materials include activities for students who struggle to master content. Throughout the materials, the lessons provide differentiation strategies, tasks, and questions for struggling students. The Teacher's Implementation Guide provides a “Facilitation Notes” section embedded at the beginning of each lesson, including “Differentiation Strategies,” such as additional scaffolding or alternative methods to help struggling learners. Materials help teachers identify and provide students with opportunities to develop precursor skills and concepts necessary to the content and aligned to the “Where Have We Been?” section of each lesson. There is limited evidence of additional lessons or activities for targeted instruction that include differentiated instructional approaches. The materials include limited instructional strategies that address various accessibility needs such as vision or hearing impairment; for example, the materials’ digital component (MATHia) includes audio narratives.
In Module 1, students read the definition of numeric expression and write numeric expressions; the materials include the following guidance: “For students who may struggle to generate even one numerical expression, provide students with 1–2 examples to start or suggest a specific operation to use.” In Topic 3.1, the teacher uses 3-D models of the figures when students are having trouble conceptualizing the drawn figures.
In Module 3, students rewrite expressions using the Order of Operations and properties, write and evaluate algebraic expressions with variables, and create and identify equivalent expressions. For students who struggle with algebra tiles and combining like terms, Activity 3.1 guides teachers to provide more practice with the x, x2, and one tile before introducing students to the y and y2 tiles.
Module 5, Lesson 1.3, prompts students to create two bar graphs with different data and answer questions related to the graphs. The materials suggest students who struggle creating the graphs could be given graph paper or technology such as a graphing calculator to help them focus on analyzing the graphs rather than creating the graphs.
The materials provide recommended targeted instruction and activities throughout for students who have mastered content. Each lesson includes differentiation strategies that include additional challenges for students ready to advance beyond the scope of the activities within the lesson. The materials include a “Stretch” section in each lesson for advanced learners who have already mastered the lesson’s concepts. Furthermore, the materials include recommendations for upward scaffolds or extensions to deepen grade-appropriate learning by providing “Questions to Ask” in the material’s facilitation notes.
Module 1 provides students examples and non-examples, such as an oblique, rectangular prism, a triangular prism, a cylinder, and a cone. As an extension activity, students determine why they do or do not fit the definitions addressed in the lesson. In Activity 1.1, teachers extend the activity by introducing the distributive property, which goes beyond the scope of the student expectations as identified in the TEKS.
In Module 5, Lesson 1.2, the Stretch activity challenges students who have mastered the lesson on analyzing data from stem-and-leaf plots. The activity consists of a side-by-side stem-and-leaf plot and asks students to describe the distribution of each of the two data sets shown and use the key to list each numerical data value. Because this activity has two stem-and-leaf plots instead of just one, students extend their understanding of analyzing data from this graphical representation.
The materials include some additional enrichment activities for all levels of learners. The materials provide students opportunities to explore and apply new learning in various ways by including activities that allow students to analyze and internalize target instruction. Each topic includes a performance task, or an open-ended question where students can be creative in showing how they can demonstrate their learning.
In Module 2, Lesson 2, students use their knowledge of ratios to decide which player on a soccer team should take a penalty based on previous performance. Students then take their answers, place them on a hundredths grid, and change answers to percentages.
Module 3 provides an enrichment activity to discuss compound inequalities and provide an example of a compound inequality that has no solution, e.g., x<5 and x>6; and in contrast, provide an example of a compound inequality that has a solution of all numbers, e.g., x<5 or x>3. Students have only worked with simple inequalities, so introducing compound inequalities allows students to explore new learning.
The materials include a variety of instructional approaches to engage students in the mastery of the content. The materials support developmentally appropriate instructional strategies. The materials support some flexible student grouping. Although the materials provide routines and activities across all modules, the routines and activities are primarily designed for large and small group instruction. The materials lack teacher guidance for students who need one-on-one attention for a particular skill or concept acquisition. The materials support multiple types of practices and provide some guidance and structures to achieve effective implementation.
Evidence includes but is not limited to:
The materials include hands-on, concrete practice with manipulatives, visual representations, and symbolic abstractions throughout all modules. Students use models to solve problems and then solve problems without the use of models. “Think-Pair-Share,” hands-on activities, and discovery-based learning are examples of the different instructional approaches used to engage students in the mastery of the content across all instructional materials’ modules.
The materials provide an online component called MATHia, where students work on self-paced instruction incorporated for individual exploration. MATHia provides unit overviews, step-by-step instructions, hints, and a glossary. The materials offer learning experiences included for individual exploration.
The Teacher's Implementation Guide provides suggestions for teaching strategies but includes limited support on when to use a specific strategy. Throughout the materials, there are examples of several different teaching strategies that include but are not limited to teaching with multiple representations, accessing prior knowledge, creating and using models, and students participating in authentic mathematical discourse. Common misconceptions are provided for the teacher to address throughout the lesson, but there is a lack of activities to meet all individual students’ needs. Differentiation strategies in each lesson are geared primarily for students who struggle; however, these strategies generally suggest a grouping rearrangement and offer limited indicators to help teachers understand when a student needs these interventions.
In Module 1, Lesson 1.2, the materials suggest using the jigsaw strategy and provide the teacher with a description of how this grouping activity should work.
In Module 2, Activity 1.1, the materials provide questions to ask in each chunk of the activity and scaffolds based on student responses. Teachers are encouraged to work problems together as a class and allow students to work in small groups during the teaching process. In Lesson 2.1, the materials suggest that students work with a partner or in groups to complete questions and share responses with the whole group. While the materials suggest students work in pairs or groups to solve a given problem, there is a lack of evidence that the materials for sixth grade support students who need one-on-one interventions for skill or concept acquisition.
In Module 3, Lesson 1.2, the materials prompt the teacher to have students work with a partner if they struggle to generate a numerical expression. Students work with a partner to write equations and ask their partners to solve their equations. In Activity 2.3, students work in groups to answer a question about addition equations. As the groups finish answering their problem, they share responses and present their reasoning to the whole class. The materials are designed mostly for large group instruction. In some lessons, the materials suggest small group work; however, small group instruction is not evident.
In Module 5, Activity 1.1, students complete questions 1 and 2 with a partner or in a group and then share their responses with the whole class. The materials provide learning experiences incorporated for individual exploration. For instance, in Activity 1.4, students compare and contrast three different measures of center individually. The materials do not provide activities to support students who need more one-on-one attention for a particular skill or concept acquisition.
The materials include some accommodations for linguistics; however, the accommodations are broad for all English Learners, and accommodations commensurate with various English language proficiency levels are limited. The materials do not offer scaffolds for English Learners. The materials provide limited opportunities to encourage the strategic use of students’ first language to develop linguistic, affective, cognitive, and academic skills in English.
Evidence includes but is not limited to:
The sixth-grade course materials include no reviewable evidence of various linguistic accommodations for students learning English, particularly regarding their English language proficiency level. The materials provide mostly general EL tips that are not specific to developmental levels of English language proficiency.
The Teacher's Implementation Guide serves as the resource for teachers to provide extra modifications within the lessons and activities. The materials include EL tips to make these modifications intentional and natural to the specific activity and lesson. For example, the materials provide multiple opportunities for interaction between students while working on problems in small groups or partners. Some of the EL tips guide the teacher in grouping strategies that are appropriate for specific activities. Although there are several suggestions throughout the materials for EL students to be paired or work in a small group that includes native English speakers, these groups’ focus is not to develop language development. The instruction is not sequenced to support students at varying levels and does not allow for playful and interactive repetition.
In Module 1, Lesson 1, an EL tip notes that students may struggle with describing mathematical operations using “plain” language, particularly when asked to do it in multiple ways. This is an opportunity for partner interviews, or perhaps interviews in groups of three. Each student is responsible for one of the three statements, and the interviewer asks probing questions about the vocabulary and the specific meaning of the words.
In Module 2, Topic 1, the Teacher's Implementation Guide suggests arranging ELs into expert and novice pairs to discuss why they think the ratio is called a “just right” ratio and answer the question “Is there a way to tell whether the bread recipe ratio will be dry or runny by looking at the graph?” In Lesson 1, the Teacher's Implementation Guide provides an EL tip that guides the teacher to use an activity where students act like a radio talk show host. In the activity, students use academic language by asking “guests” questions about situations and methods for solving problems, while other EL students “call-in” to ask the host and guest questions. In Lesson 6, the Teacher's Implementation Guide suggests the teacher arrange ELs into expert and novice pairs to discuss ratios using the W.I.T. questioning model to aid in comprehension. In Activity 1.5, the Teacher's Implementation Guide suggests breaking down the word percent into per and cent, which means “per hundred.” Cent is from the Latin word meaning “one hundred.” The use of this is seen in money (dollars and cents), but also in measurements (centimeter). Many EL students will be familiar with the metric system, and pointing out cent in measurements will help connect the term percent to known terms.
In Module 3, Activity 1.5, the Teacher's Implementation Guide suggests beginning ELs write an inequality symbol on one side of a card and an associated English phrase on the other side to develop the basic vocabulary for comparative phrases. Advanced students can help beginning learners sort cards based on structure or spelling patterns. For example, the symbol < may be used with the phrase less than.
In Module 5, Lesson 2, the Teacher's Implementation Guide suggests that new EL students circle unknown terms and look up definitions, then reread the passage and summarize the situation in their own words with a partner. In Activity 4.4, students write a response to describe the distribution. Then, students pair up and use their combined work to create a better description with more detail. Each pair should then find another pair to create a combined response. This provides EL an opportunity to revise and read aloud, which helps improve language skills.
The materials include a cohesive, year-long plan to build students’ mathematical literacy skills and consider how to vertically align instruction year to year. The materials provide review and practice of mathematical skills throughout the span of the curriculum.
Evidence includes but is not limited to:
The instructional materials include a cohesive, year-long plan to build students’ concept development and consider how to align instruction that builds year to year vertically. The materials include a year-long plan of content delivery based on 160 instructional days. The Teacher's Implementation Guide provides a map that shows the sequence of topics and the number of blended instructional days (1 day is 50 minutes). The materials include a content plan that is cohesively designed to build upon students’ current level of understanding with clear connections within and between lessons and grade levels. For instance, each module includes three sections: “Connections to Prior Learning,” “Overview,” and “Connections to Future Learning.” Additionally, the Teacher's Implementation Guide provides a course content map that shows connections between lessons in the modules. The materials include guidance that supports the teacher in understanding the vertical alignment for all focal areas in Math Texas Essential Knowledge and Skills in preceding and subsequent grades. In the Teacher's Implementation Guide, each module overview begins with Connections to Prior Learning and Connections to Future Learning.
Within the Teacher's Implementation Guide, there is a resource map, “Middle School Math Solution Content at a Glance,” that shows the instruction sequence for the year and the number of instructional days allocated for each year. In the Teacher's Implementation Guide, the “Course Standards Overview” document provides a mapping of how standards are targeted and reviewed within each lesson. The material includes the following five overarching modules and their corresponding, focused topics, and lessons that require a complete year-long plan to deliver the content: “Module 1: Composing and Decomposing”—3 subtopics and 12 lessons and multiple activities within each lesson; “Module 2: Relating Quantities”—3 subtopics and 12 lessons and multiple activities within each lesson; “Module 3: Determining Unknown Quantities”—3 subtopics and 13 lessons and multiple activities within each lesson; “Module 4: Moving Beyond Positive Quantities”—2 subtopics and 6 lessons and multiple activities within each lesson; “Module 5: Describing Variability of Quantities”—2 subtopics and 7 lessons and multiple activities within each lesson. These five modules are sequenced to develop students’ understanding by providing a plan that connects modules and lessons. A description of the connections made is provided in the Teacher's Implementation Guide with a table showing each of the five modules and the Connections to Prior Learning, Overview of the module, and the Connections for Future Learning.
The materials include a detailed module and topic overview in the Teacher's Implementation Guide, which teachers can read before lesson delivery to learn the vertical alignment in previous and subsequent grades. These module and topic overviews do not mention specific TEKS, but they do all fall under one of the focal areas that align directly to the TEKS. At the beginning of each module, a section explains how each topic is connected to prior learning. At the beginning of each topic, there is a section entitled “What is the entry point for students?” that clearly states the connections to prior learning. At the beginning of each topic, there is also a section entitled “Why is the topic important?” that clearly explains when students will use the knowledge learned in the topic in subsequent lessons during the current school year and future math courses. At the end of each lesson, there is a section called Talk the Talk, which serves as a cumulative review of all of the lesson’s activities. Each lesson within each topic provides opportunities for practice through teacher questioning, the Consumable Student Edition, the Skills Practice Workbook, and the MATHia software. The practice materials within a topic build upon previously taught content from within that topic. The final section of each assignment is “Review” and includes problems from previous lessons and modules. The Review for the lessons in Module 1 includes questions from material learned in fifth grade.
In Module 1, the materials provide a module overview that makes teachers aware that in the current module, where students will learn to compose and decompose numbers, the previous fifth-grade knowledge of standard algorithms will help in developing fluency to solve problems, which include finding the area of composite figures, common factors, and common multiples.
In Module 4, Topic 1, the materials provide three different focused lessons and 11 activities where students explore and practice how to work with negative numbers, absolute value, and the rational number system. In Lesson 1, the material guides teachers in understanding how building on prior knowledge of positive rational numbers and plotting them on the number line helps them extend their knowledge to the negative. Lesson 1.1 introduces negative numbers. Lesson 1.2 builds on that knowledge and focuses on absolute value. Finally, the third lesson categorizes different numbers and focuses on the rational number, which could not be done without first exposing students to the previous two lessons. In Lesson 1.3, students learn about the rational number system using Venn diagrams, but students still answer three problems at the end of the lesson to review and practice problems previously taught in the materials, such as absolute value, solving equations using a table, and plotting ordered pairs on a coordinate plane.
In Module 5, Topic 1, students practice creating a frequency table and a histogram using scores from a card game, “Clubs and Swords.” Then, students describe the distribution of data and create a second frequency table and histogram to provide a different view of the data distribution.
The materials are not accompanied by a TEKS-aligned scope and sequence outlining the essential knowledge and skills that are taught in the program, the order in which they are presented, and how knowledge and skills build and connect across grade levels. The materials include supports to help teachers implement the materials as intended. The materials do not have resources and guidance to help administrators support teachers in implementing the materials as intended. The materials include a school years’ worth of math instruction, including realistic pacing guidance and routines.
Evidence includes but is not limited to:
The materials include a webpage with a link to the alignment to standards by state. The TEKS alignment to the scope and sequence of the materials can be accessed through this page. The materials include a table that shows the Course 1 materials’ correlations to the 2012 Texas Essential Knowledge and Skills. The table is a 15-page list of all the TEKS included within the materials. The TEKS listed show that they are all content SEs; however, the process standards are not shown on this table. The table shows the textbook number, the module, topic and lesson, and the MATHia software location where the student expectation will be presented. The materials include a standards overview in the Teacher's Implementation Guide and provide a mapping document that identifies where the standard will be targeted and where it will be reviewed within each module, topic, and lesson. This standards overview does not list the standards using TEKS. A Texas teacher would have to reference the correlation table to align the materials’ standards overview to the TEKS. The materials do not include a scope and sequence that describes how the essential knowledge and skills build and connect across the grade levels. However, each module in the materials includes an overview that provides a connection across grade levels described in detail, but this is not listed on the scope and sequence document that aligns with the Texas standards.
The instructional materials for grade 6 include support to help teachers implement the materials as intended. The materials support teachers in understanding how to use the resource as intended. The Teacher's Implementation Guide provides teachers with consistent lesson structure and walks teachers through key features of each lesson: “Learning Goals,” “Connections,” “Getting Started,” “Activities,” “Talk the Talk,” and “Assignments.” The Teacher's Implementation Guide provides facilitation notes by activity, a detailed set of guidelines that walks the teacher through implementing the various components of the lesson. These guidelines include an activity overview, grouping strategies, guiding questions, possible student misconceptions, differentiation strategies, student look fors, and an activity summary. The Teacher's Implementation Guide describes the depth of understanding that students need to develop for each standard and a pathway for all learners to succeed. The facilitation notes provide detailed support for the planning process and are the primary resource for planning, guiding, and facilitating student learning. Materials can be accessed online or in print.
The materials include a digital version of the materials and modules that include a “MyPL” Professional Learning app with videos to give teachers background knowledge for a particular lesson and ideas on how to implement it. MyPL includes custom learning sessions, led by Master Math Practitioners, in an online video library accessible. They also include a PowerPoint presentation for each lesson that could be used by teachers. This is also available in Google Slide format. The materials provide links on their homepage to a “LiveLab Tour” for teachers to learn how to use this assessment tool within the materials. There is also a “Help Center” link on the homepage that supports Teacher's Implementation and provides quick “how-to” guides. The materials are available in print and digital format. Accessing the materials on the materials’ webpage is easy to follow. Each module’s format, topic, and lesson materials follow the same format, making it consistent and organized.
The instructional materials for grade 6 do not include resources and guidance explicitly stated to help administrators support teachers in implementing the materials as intended. The materials also do not provide tools explicitly stated to support the administrator in recognizing best instructional practices and arrangements in a math classroom. However, administrators can use many of the materials mentioned above to support teachers in implementing the materials. For example, the scope and sequence, including the list of math essential knowledge and skills, can be used by administrators to support teachers in their implementation of the materials.
The sixth-grade materials include five modules that span for the pacing of 160 days of the standard 180 days of instruction to allow for flexibility for assessments, an extension of lessons, and differentiation for students. The Teacher's Implementation Guide contains “Middle School Math Solution Content” at a glance with pacing outlined by unit and lessons to allow extra days to address assessments, differentiation, and extended opportunities. Each lesson includes pacing suggestions. Additionally, each module overview includes pacing information and a topic overview, which includes more detailed information to help teachers with pacing. The lesson structure and pacing are included for each lesson and are provided for the entire course to be completed in a school year.
The materials provide some guidance for strategic implementation without disrupting the content sequence that must be taught in a specific order following a developmental progression. The materials are not designed in a way that allows LEAs the ability to incorporate the curriculum into district, campus, and teacher programmatic design and scheduling considerations.
Evidence includes but is not limited to:
The instructional materials for grade 6 provide guidance for strategic implementation without disrupting the sequence of content that must be taught in a specific order following a developmental progression. The materials include strategic guidance on implementation that ensures the sequence of content is taught in the order consistent with the developmental progression of mathematics. For instance, the Teacher's Implementation Guide provides a table in the “Content and Alignment” section that demonstrates how the sequence of modules, topics, and lessons are developed to coherently build new understanding onto the foundations developed in prior grades or previous lessons of the course. Additionally, supporting standards are positioned to reinforce the readiness standard of the grade. In grade 6, students are taught equivalent expressions before solving one-step equations. Each course materials’ Table of Contents delineates modules and topics to ensure students learn about precursor concepts first. All courses include all focal areas within the years’ instruction without disrupting the content’s sequence.
However, the materials do not include guidance that supports teaching focal areas aligned to a classroom/school context without disrupting the content’s sequence. While this is the case, at least one of the focal areas for sixth grade (operations with integers and positive rational numbers, ratios and rates including using equivalent ratios to represent proportional relationships, expressions and equations to represent relationships, and data representation) is included in each of the five modules designed for sixth grade. The module and topic overview supports teachers on how that module/topic aligns with focal areas in mathematics; the materials do not guide teachers on how lessons could be taught if the given sequence is disrupted.
The material design offers some variety to allow for easy implementation of school designs. Printed materials and digital materials are available. The teacher’s implementation materials allow for extensions of the lessons, and grouping options are often mentioned. Suggestions for co-teaching, multi-grade classrooms, and varying lengths of times for mathematics instruction are not included in the materials. According to the materials, the materials are designed for daily instruction in a 50-minute class period. There is no guidance on implementing the materials in any other school setting.
In Module 1 of the materials, students compose and decompose numbers, a very concrete concept. It is also the next developmental progression from fifth grade, where students focus on number operations and fluency. Module 2 then progresses into relating quantities, which is more abstract for students. In Module 3, Topic 1, the Overview of Teacher's Implementation Guide material supports teachers in identifying how students build on their existing knowledge of operating with numbers and geometric measurement to develop their understanding of variables and algebraic expressions.
The materials provide some support for the development of strong relationships between teachers and families. The materials specify some activities for use at home to support students’ learning and development. The materials reference literature for parents and at-home support; however, some of the materials referenced were not accessible to the reviewers.
Evidence includes but is not limited to:
The materials provide “Home Connections” in the MyCL portal, including a video detailing basics about the materials and the use of it in class and at home. The MyCL portal includes a “Community Tools” section with helpful study skills and tips and additional math practice exercises. It also includes a parent/caregiver webinar offering strategies for supporting student learning at home. This webinar was not available for a deep evaluation by the Texas Resource Review.
The materials include a “Math Power for Parents Handbook” to help parents understand the course materials by giving them a summary and examples of each math topic. This is offered in both English and Spanish. The example available to the reviewers online was for elementary. It is unclear if this is also offered for middle school students. The online component of the materials, called MATHia, is available to students anytime and anywhere. However, it is unclear if the parents have access to MATHia to view their student’s progress and work or if they just help support them as they work on it at home.
The materials’ website notes “Family Math Nights,” where students can present their work; however, examples of what is included in the materials are not evident. The materials provide a “Family Guide” at the beginning of each topic intended to be sent home to keep parents informed of what their child will be learning in that topic. Family Guides, available in English and Spanish for each topic, overview the mathematics that will be taught, what the student should have previously learned, and how it will be used for future learning. They include real-world examples, standardized test question examples, and some key vocabulary students will learn.
Each topic within each module includes a Family Guide. The Family Guide includes an overview of the topic, “Where Have We Been?” and “Where Are We Going?” sections, examples of problems to be learned in the topic, key terms to be introduced during the topic, talking points, and an explanation of a false myth that many people believe about math. However, there is no guidance or recommendation for teachers to use the Family Guide or develop strong relationships between teachers and families.
In Module 2, Topic 2, the Family Guide states that students will learn about percentages and outlines what students have learned before and where their learning is going. A percent model is using a hundredths grid, and an explanation is included. The Family Guide also includes a debunked myth, key terms, and talking points parents can discuss with their students about the topic. In Module 2, Topic 3, the materials suggest that parents have their child explain whether their answer makes sense when converting a measurement into different units.
In Module 3, Topic 3, the Family Guide suggests parents discuss what graphs they see online, on television, and in print and demonstrate what two quantities they are comparing to support the lesson on quantitative graphing relationships.
The materials include appropriate white space and design that supports and does not distract from student learning. Pictures and graphics are supportive of student learning and engagement without being visually distracting.
Evidence includes but is not limited to:
The Teacher's Implementation Guide follows a clear and consistent design for information. This guide includes a module and a topic overview, facilitation notes, materials needed for the lesson, lesson and activity overviews, standards addressed, essential ideas, lesson structure, pacing, differentiation strategies, and a summary.
The materials include intentional white space in each margin so that teachers can make additional planning notes or reflect on the lesson’s implementation. This appears in every lesson throughout the material next to the facilitation notes section of the activity overviews and the section labeled “Questions to Consider.” The Student Edition is consumable; the pages include an appropriate amount of white space to show work. The graphics are simple, clear, and concise. Visuals are placed with purpose throughout the materials, i.e., tables, graphs, models.
The materials include fonts that are clear and easy to read. Headings are bold and identified through a colorful box for emphasis. Lessons and activities include pictures, tables, and graphs that do not distract from the text on the page or interfere with learning. Numbers within the tables, grids, and graphs are large enough for students to read easily.
The Student Edition includes “The Crew” images that have thought bubbles with reminders about previous content, questions to help students think about different strategies, and fun facts. The teacher aide’s images guide students by making connections and reminding students to think about the details. Models are placed throughout the materials, and “Habits of Mind” icons trigger students to ask themselves reflective questions as they work.
The materials adhere to User Interface Design guidelines. For instance, the materials have a consistent layout and color scheme: green, black, and white; it is not distracting. The overall aesthetic of the materials is visually appealing and includes a minimalist design. Workspace and note sections are provided in the Teacher's Implementation Guide and Student Edition to provide space for reflection or for documentation purposes.
In MATHia, animation offers user control and freedom to rewatch demonstrations of various math concepts. MATHia software contains familiar options such as play, volume, enter full screen, and print icon images and terminology for easy student use. Resources also provide a glossary with definitions and graphic images, such as for x-axis and solid volume.
In Module 2, Lesson 2, students use pictures of battery icons, circles, and squares to estimate the percent of shaded parts. In Activity 5, the student materials include large print graphic organizers that are clear and concise to support student learning ratios.
In Module 3, Lesson 1, the teacher asks, “What aspect of the graph helped you determine the correct match for each scenario?” In Lesson 4, students evaluate the visual model of balancing equations, solve and check an equation, rewrite an equation, and determine units’ conversion.
In Module 4, Lesson 2.1, the students can see the warm-up section as the starting point because the icons are bold and green. The learning goals and key vocabulary terms are to the side in a black font, which indicates that students do not have to write or answer anything in that section. The rest of the lesson follows the same pattern with questions and problems to answer in green and directions in black font. The lesson includes pictures of coordinate planes and enough white space to solve the problems and answer the questions. Side notes help students answer questions or remind them of something important included throughout the lesson. Charts and tables are big enough for students to write in and read clearly. The topic number, title, and page number are included at the bottom of each page for easy access. At the end of each activity, the materials intentionally provide an empty blank page for students to show math work, make notes, or summarize their thinking throughout the activity. The Teacher's Implementation Guide includes facilitation notes with support, such as a detailed description of what is needed to create a human coordinate plane and what questions to ask during the lesson. These sections are labeled with larger bold fonts that allow for easy identification.
In Module 5, Lesson 1.3, the materials include an activity on a histogram and displaying data. The activity pages show pictures of students with quotes, giving students hints to answer the questions and problems provided on that page. The histogram activity and displaying data include several graphs that are large enough for students to read clearly. The titles for the graphs and the titles for the x-axis and y-axes are easily readable, and so are the numbers displayed on the graphs. A frequency table is included in this lesson. The table consists of enough space for the students to write inside and enough space around the graphics to show their mathematical thinking process.
The materials include online components that are grade-level appropriate and provide learning support. The online elements align with the curriculum’s scope and provide support and enhance student learning as appropriate, as opposed to distracting from it, and include teacher guidance.
Evidence includes but is not limited to:
The materials reviewed include a computer-based software called MATHia that can be accessed anytime and anywhere by students and teachers. Each lesson in the materials has a corresponding lesson in MATHia and is included in the pacing guide for each module, topic, and lesson. MATHia is a 1-to-1 adaptive math coaching program that provides a personalized learning path and ongoing formative assessment. MATHia contains a mini video, “Why this Matters,” that students watch to see a real-world connection to learning. MATHia technology supports include videos, immediate feedback in practice problems, interactive tools, and manipulatives. Additional activities and assessments for each topic and lesson are found in MATHia. It creates a personalized learning path for each student with feedback and hints that are embedded within the software. It also provides teachers with reports of class and individual students’ progress by standards.
In the Teacher's Implementation Guide, the materials outline how MATHia can be incorporated into each module and what topics it will cover. Additionally, there are “Learning individually with MATHia” or “Skills Practice'' sections in the “Module Overview” that summarize how MATHia will be used for each topic and standard and how many instructional days are needed using the software. The individual student practice helps support their learning in the classroom when interacting with the materials since the concepts in MATHia overlap and reinforce the targeted learning standards. The MATHia computer-based software in the materials promotes student participation by providing additional practice for each topic. Since MATHia is accessible at any time and any place, students can continue participating and interacting with the materials at home and even on the weekend to enhance their learning. The Teacher's Implementation Guide provides teachers information about MATHia, how it is structured, how it is aligned to each lesson, and the type of problems included within the software that students will work on. The guide also includes a description of the reports and how to access them. The materials provide teachers with a MATHia browser in the MyCL portal to view and experience the software as a student would. This allows teachers to read a report, review, and reteach a student who is not successful in a MATHia module.