7th Grade - Gateway 3

The materials reviewed for Math Nation Grade 7 meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students to guide their mathematical development.

Examples of where and how the materials provide comprehensive guidance that will assist teachers in presenting the student and ancillary materials include:

• Course Overview: A Course Overview (Unit 0) is found at the beginning of each course.  Within each Course Overview there is a Course Narrative, which contains a summary of the mathematical content contained in each course, and a Course Guide. The Course Guide contains the following sections: Introduction, About These Materials, How to Use These Materials, Assessment Overview, Scope and Sequence, Required Resources, Corrections, and Cool-Down Guidance. Each of these sections contains specific guidance for teachers on implementing lesson instruction. For example, in the About These Materials section, teachers can find an outline of and detailed information about the components of a typical lesson, including Warm-Up, Classroom Activities, Lesson Synthesis, and Cool-Down. The How to Use These Materials section contains guidance about the three phases of classroom activities (Launch-Work-Synthesize) and utilizing instructional routines. In the Scope and Sequence section, teachers will find a Pacing Guide which contains time estimates for coverage of each of the units.

• Teacher Edition: There is a Teacher Edition section for each unit that contains a unit introduction, unit assessments, and unit-level downloads. The Unit Introduction contains a summary of the mathematical content to be found in the unit. The Assessment component contains downloads for multiple types of assessments (Check Your Readiness, Mid-Unit, and End-of-Unit Assessment). Unit Level Downloads include: Student Task Statements Cool-downs, Practice Problems, Blackline Masters, and My Reflections all of which provide support for teacher planning. Each lesson has a Teacher Edition component that contains guidance for Lesson Preparation, Cool-down Guidance, and a Lesson Narrative. The Lesson Preparation component includes a Teacher Prep Video, Learning Goal(s), Required Material(s), and Full Lesson Plan downloads. Cool-down Guidance provides teachers with guidance on what to look for or emphasize over the next several lessons to support students in advancing their current understanding. The Lesson Narrative provides specific guidance about how students can work with the lesson activities.

• Full Lesson Plan: Within each Teacher Edition lesson component, teachers can find a Full Lesson Plan that contains lesson learning goals and targets, a lesson narrative, and specific guidance for implementing each of the lesson activities. The Lesson Narrative contains the purpose of the lesson, standards and mathematical practices alignments, specific instructional routines, and required materials related to the lesson. Teachers are given guidance for implementing these routines as a way of introducing students to the learning targets. There is also teacher guidance for launching lesson activities, such as suggestions for grouping students, working with a partner, or whole group discussion. The planning section identifies possible student errors and misconceptions that could occur. There is also guidance on how to support English Language Learners and Students with Disabilities.

Materials include sufficient and useful annotations and suggestions that are presented within the context of specific learning objectives. Preparation and lesson narratives within the Course Guide, Lesson Plans, Lesson Narratives, Overviews, and Warm-up provide useful annotations. Examples include:

• Course Guide, Assessments Overview, “Pre-Unit Diagnostic Assessments At the start of each unit is a pre-unit diagnostic assessment. These assessments vary in length. Most of the problems in the pre-unit diagnostic assessment address prerequisite concepts and skills for the unit. Teachers can use these problems to identify students with particular below-grade needs, or topics to carefully address during the unit. Teachers are encouraged to address below-grade skills while continuing to work through the on-grade tasks and concepts of each unit, instead of abandoning the current work in favor of material that only addresses below-grade skills…What if a large number of students can’t do the same pre-unit assessment problem? Look for opportunities within the upcoming unit where the target skill could be addressed in context…What if all students do really well on the pre-unit diagnostic assessment? Great! That means they are ready for the work ahead, and special attention likely doesn’t need to be paid to below-grade skills.”

• Unit 1, Lesson 2, Full Lesson Plan, 1.2.3 Exploration Activity, “Anticipated Misconceptions Students may think that Triangle F is a scaled copy because just like the 3-4-5 triangle, the slides are also three consecutive whole numbers. Point out that corresponding angles are not equal.”

• Unit 2, Lesson 7, Cool-down Guidance, “If students struggle with variable placement in the cool-down, plan to focus on how to use the equation y = kx when opportunities arise over the next several lessons. For example, in activity 1 of Lesson 9, have students share their thinking about using the equation to show a proportional relationship.”

The materials reviewed for Math Nation Grade 7 meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series.

The Course Guide, About These Materials sections, states the following note about standards alignment, “There are three kinds of alignments to standards in these materials: building on, addressing, and building towards. Oftentimes a particular standard requires weeks, months, or years to achieve, in many cases building on work in prior grade-levels. When an activity reflects the work of prior grades but is being used to bridge to a grade-level standard, alignments are indicated as ‘building on.’ When an activity is laying the foundation for a grade-level standard but has not yet reached the level of the standard, the alignment is indicated as ‘building towards.’ When a task is focused on the grade-level work, the alignment is indicated as ‘addressing.’” All lessons in the materials have this correlation information. An example:

• Unit 7, Lesson 1, Full Lesson Plan, Lesson Standards Alignment, Building on 4.MD.6, 4.MD.7; Addressing 7.G.A, 7.G.B; Building Towards 7.G.B, 7.G.5.

Explanations of the role of the specific grade-level mathematics in the context of the series can be found throughout the materials including but not limited to the Course Guide, Scope and Sequence section, the Course Overview, Unit Introduction, Lesson Narrative, and Full Lesson Plan. Examples include:

• Course Guide, Scope and Sequence, Unit 1: Scale Drawing, “Work with scale drawings in grade 7 draws on earlier work with geometry and geometric measurement. Students began to learn about two- and three-dimensional shapes in kindergarten, and continued this work in grades 1 and 2, composing, decomposing, and identifying shapes. Students' work with geometric measurement began with length and continued with area. Students learned to "structure two-dimensional space," that is, to see a rectangle with whole-number side lengths as an array of unit squares, or rows or columns of unit squares…This provides geometric preparation for grade 7 work on proportional relationships as well as grade 8 work on dilations and similarity. Students begin by looking at copies of a picture, some of which are to scale, and some of which are not. They use their own words to describe what differentiates scaled and non-scaled copies of a picture…In grade 8, students will extend their knowledge of scaled copies when they study translations, rotations, reflections, and dilations.”

• Course Guide, Scope and Sequence, Unit 2: Introducing Proportional Relationships, “In this unit, students develop the idea of a proportional relationship out of the grade 6 idea of equivalent ratios. Proportional relationships prepare the way for the study of linear functions in grade 8…In grades 6-8, students write rates without abbreviated units, for example as ‘3 miles per hour’ or ‘3 miles in every 1 hour.’ Use of notation for derived units such as mi/hr waits for high school-except for the special cases of area and volume. Students have worked with area since grade 3 and volume since grade 5...”

The materials reviewed for Math Nation Grade 7 meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies. Instructional approaches of the program and identification of the research-based strategies can be found throughout the materials, but particularly in the Course Guide, About These Materials, and How to Use These Materials sections. 

The About These Materials section states the following about the instructional approach of the program, “What is a Problem Based Curriculum? In a problem-based curriculum, students work on carefully crafted and sequenced mathematics problems during most of the instructional time. Teachers help students understand the problems and guide discussions to ensure the mathematical takeaways are clear to all. Some concepts and procedures follow from definitions and prior knowledge so students can, with appropriately constructed problems, see this for themselves. In the process, they explain their ideas and reasoning and learn to communicate mathematical ideas. The goal is to give students just enough background and tools to solve initial problems successfully, and then set them to increasingly sophisticated problems as their expertise increases. However, not all mathematical knowledge can be discovered, so direct instruction is sometimes appropriate. A problem-based approach may require a significant realignment of the way math class is understood by all stakeholders in a student's education. Families, students, teachers, and administrators may need support making this shift. The materials are designed with these supports in mind. Family materials are included for each unit and assist with the big mathematical ideas within the unit. Lesson and activity narratives, Anticipated Misconceptions, and instructional supports provide professional learning opportunities for teachers and leaders. The value of a problem-based approach is that students spend most of their time in math class doing mathematics: making sense of problems, estimating, trying different approaches, selecting and using appropriate tools, evaluating the reasonableness of their answers, interpreting the significance of their answers, noticing patterns and making generalizations, explaining their reasoning verbally and in writing, listening to the reasoning of others, and building their understanding. Mathematics is not a spectator sport.”

Examples of materials including and referencing research-based strategies include:

• “The Five Practices Selected activities are structured using Five Practices for Orchestrating Productive Mathematical Discussions (Smith & Stein, 2011), also described in Principles to Actions: Ensuring Mathematical Success for All (NCTM, 2014), and Intentional Talk: How to Structure and Lead Productive Mathematical Discussions (Kazemi & Hintz, 2014). These activities include a presentation of a task or problem (may be print or other media) where student approaches are anticipated ahead of time. Students first engage in independent think-time followed by partner or small-group work on the problem…”

• “Supporting English Language Learners This curriculum builds on foundational principles for supporting language development for all students. This section aims to provide guidance to help teachers recognize and support students' language development in the context of mathematical sense-making. Embedded within the curriculum are instructional supports and practices to help teachers address the specialized academic language demands in math when planning and delivering lessons, including the demands of reading, writing, speaking, listening, conversing, and representing in math (Aguirre & Bunch, 2012).”

• “Instructional Routines … Some of the instructional routines, known as Mathematical Language Routines (MLR), were developed by the Stanford University UL/SCALE team…”

Within the Course Guide, How to Use These Materials, a Reference section is included.

The materials reviewed for Math Nation Grade 7 meet expectations for providing a comprehensive list of supplies needed to support instructional activities. Comprehensive lists of supplies needed to support the instructional activities can be found in Course Guides (Required Resources), Teacher Editions, for each lesson, under Lesson Preparation (Required Material(s)), and in Teacher Guides for specific lessons. Examples include:

• Unit 1, Lesson 7, Lesson Preparation, Required Materials: “Blackline master for Activity 7.2, Cool-down, copies of blackline master, geometry toolkits (tracing paper, graph paper, colored pencils, scissors, and an index card)”

• Unit 3, Lesson 3, Lesson Preparation, Required Materials: “Cool-down, cylindrical household items, empty toilet paper roll, measuring tapes”

• Unit 8, Lesson 6, Lesson Preparation, Required Materials: “Blackline master for Activity 6.2, Cool-down, number cubes, paper bags, paper clips, pre-printed slips, cut from copies of the blackline master”

The materials reviewed for Math Nation Grade 7 meet expectations for including an assessment system that provides multiple opportunities throughout the grade, course, and/or series to determine students’ learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

Student sample responses are provided for all assessments. Rubrics are provided for scoring restricted constructed response and extended response questions on the Mid-Unit Assessments and End-of-Unit Assessments. Mid-Unit Assessments and End-of-Unit Assessments include notes that provide guidance for teachers to interpret student understanding and make sense of students’ correct/incorrect responses. 

Suggestions to teachers for following up with students are provided throughout the materials via the Mid-Unit, and End-of-Unit Teacher Guides, and each lesson provides a Cool-down Guidance that details how to support student learning.

Examples of the assessment system providing multiple opportunities to determine students' learning and sufficient guidance to teachers for interpreting student performance include:

• Course Guide, Assessments Overview states the following: “Rubrics for Evaluating Students Answers Restricted constructed response and extended response items have rubrics that can be used to evaluate the level of student responses. 

  • Restricted Constructed Response

    • Tier 1 response: Work is complete and correct.

    • Tier 2 response: Work shows General conceptual understanding and mastery, with some errors.

    • Tier 3 response: Significant errors in work demonstrate lack of conceptual understanding or mastery. Two or more error types from Tier 2 response can be given as the reason for a Tier 3 response instead of listing combinations.

  • Extended Response

    • Tier 1 response: Work is complete and correct, with complete explanation or justification. 

    • Tier 2 response: Work shows good conceptual understanding and mastery, with either minor errors or correct work with insufficient explanation or justification. 

    • Tier 3 response: Work shows a developing but incomplete conceptual understanding, with significant errors. 

    • Tier 4 response: Work includes major errors or omissions that demonstrate a lack of conceptual understanding and mastery.”

• Unit 6, Mid-Unit Assessment (A), Question 6, “A food pantry is making packages. Each package weighs 64 pounds. Here are two situations. For each situation, write an equation to represent the situation. If you get stuck, consider drawing a diagram. 1. Each package contains 4 boxes. Each box contains a 7-pound bag of beans and a bag of rice. The bags of rice are all identical. 2. Each package contains 4 identical bags of rice and a 7-pound bag of beans. Solution Sample response: 1. 4(x +7) = 64 (diagram shows 4 equal parts of x+7 with a total of 64) 2. 4x+7 = 64 (diagram shows 4 equal boxes labeled x and one box labeled 7, with a total of 64) Minimal Tier 1 response: Work is complete and correct. Sample: 1. 4(x +7) = 64 (diagram shows 4 equal parts of x+7 with a total of 64) 2. 4x+7 = 64 (diagram shows 4 equal boxes labeled x and one box labeled 7, with a total of 64) Tier 2 response: Work shows general conceptual understanding and mastery, with some errors. Sample errors: one of the equations has been written correctly with errors in the other, diagram for one situation is drawn correctly but the other has errors. Tier 3 response: Significant errors in work demonstrate lack of conceptual understanding or mastery. Sample errors: both equations have been written incorrectly or both diagrams have been drawn incorrectly, both responses are flawed in some way.”

Examples of the assessment system providing multiple opportunities to determine students' learning and suggestions to teachers for following up with students include:

• Course Guide, Cool-Down Guidance states the following: “Each cool-down is placed into one of three support levels: 1. More chances. This is often associated with lessons that are exploring or playing with a new concept. Unfinished learning for these cool-downs is expected and no modifications need to be made for upcoming lessons. 2. Points to emphasize. For cool-downs on this level of support, no major accommodations should be made, but it will help to emphasize related content in upcoming lessons. Monitor the student who have unfinished learning throughout the next few lessons and work with them to become more familiar with parts of the lesson associated with this cool-down. Perhaps add a few minutes to the following class to address related practice problems, directly discuss the cool-down in the launch or synthesis of the warm-up of the next lesson, or strategically select students to share their thinking about related topics in the upcoming lessons. 3. Press pause. This advises a small pause before continuing movement through the curriculum to make sure the base is strong. Often, upcoming lessons rely on student understanding of the ideas from this cool-down, so some time should be used to address any unfinished learning before moving on to the next lesson.”

• Unit 3, Lesson 6, Cool-down Guidance, “Support Level 2. Points to emphasize. Notes If students struggle with estimating the area of irregular shapes in the cool-down, plan to focus on this skill when opportunities arise over the next several lessons. For example, in Activity 1 of Lesson 7, make sure to invite multiple students to share their thinking about how they estimated the areas of the shapes.”

• Unit 7, End-of-Unit Assessment (B), Question 1, “Students failing to select A, or students selecting E, may need more work on approximate angle measures and calculating their sums. Students failing to select C, or students selecting B, need a review of the triangle inequality: 6, 12, and 13 is fine, but 11 cm is too long to be the third side of a triangle containing side lengths of 3 cm and 7 cm. Students failing to select D may have said so because they aren’t given the specific locations of the sides and angles, but this is a reason for more than one triangle to exist with the given conditions.”

The materials reviewed for Math Nation Grade 7 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of the course-level standards and practices across the series.

All assessments regularly demonstrate the full intent of grade-level content and practice standards through a variety of item types such as multiple choice, short answer, extended response prompts, graphing, mistake analysis, and constructed response items. Assessments are to be downloaded as Word documents or PDFs and designed to be printed and administered in-classroom. Examples Include:

• Unit 2, Lesson 2, Cool-down, demonstrates the full intent of 7RP.2 and MP2. “When you mix two colors of paint in equivalent ratios, the resulting color is always the same. Complete the table as you answer the questions. (Table is provided) 1. How many cups of yellow paint should you mix with 1 cup of blue paint to make the same shade of green? Explain or show your reasoning. 2. Make up a new pair of numbers that would make the same shade of green. Explain how you know they would make the same shade of green. 3. What is the proportional relationship represented by this table? 4. What is the constant of proportionality? What does it represent?” 

• Unit 3, End-of-Unit Assessment (A), Question 5, demonstrates the full intent of 7.G.4 and MP1.  “For each quantity, decide whether circumference or area would be needed to calculate it. Explain or show your reasoning. 1. The distance around a circular track. 2. The total number of equally-sized tiles on a circular floor. 3. The amount of oil it takes to cover the bottom of a frying pan. 4. The distance your car will go with one turn of the wheels” 

• Unit 4, End-of-Unit Assessment (B), Question 7, demonstrates the full intent of 7.RP.3 and 7.EE.3. “Jada’s sister works in a furniture store. 1. Jada’s sister earns $15 per hour. The store offers her a raise—a 9% increase per hour. After the raise, how much will Jada’s sister make per hour? 2. The store bought a table for $200, and sold it for $350. What percentage was the markup? 3. Jada’s sister earns a commission. She makes 3.5% of the amount she sells. Last week, she sold $7,000 worth of furniture. How much was her commission?”

The materials reviewed for Math Nation Grade 7 meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level mathematics.

Course Guide, How to Use These Materials, Supporting Students with Disabilities sections states the following: “The philosophical stance that guided the creation of these materials is the belief that with proper structures, accommodations, and supports, all children can learn mathematics. Lessons are designed to maximize access for all students, and include additional suggested supports to meet the varying needs of individual students. While the suggested supports are designed for students with disabilities, they are also appropriate for many children who struggle to access rigorous, grade-level content. Teachers should use their professional judgment about which supports to use and when, based on their knowledge of the individual needs of students in their classroom.” Suggested supports are identified for teachers in the Full Lesson Plan to support learners of all levels. Lesson and activity-level supports, identified as “Support for Students with Disabilities,” are aligned to an area of cognitive functioning and are paired with a suggested strategy aimed to increase access and eliminate barriers. Supports are classified under the following categories: eliminate barriers, processing time, peer tutors, assistive technology, visual aids, graphic organizers, and brain breaks. Examples include:

• Assistive Technology: “Assistive technology can be a vital tool for students with learning disabilities, visual spatial needs, sensory integration, and students with autism. Assistive technology supports suggested in the materials are designed to either enhance or support learning, or to bypass unnecessary barriers. Physical manipulatives help students make connections between concrete ideas and abstract representations. Often, students with disabilities benefit from hands-on activities, which allow them to make sense of the problem at hand and communicate their own mathematical ideas and solutions.” Unit 1, Lesson 9, Full Lesson Plan, 1.9.2 Exploration Activity, “Support for Students with Disabilities…Fine Motor Skills: Assistive Technology. Provide access to the digital version of this activity…”

• Eliminate Barriers: “Eliminate any barriers that students may encounter that prevent them from engaging with the important mathematical work of a lesson. This requires flexibility and attention to areas such as the physical environment of the classroom, access to tools, organization of lesson activities, and means of communication.” Unit 4, Lesson 13, Full Lesson Plan, 4.13.2 Exploration Activity, “Support for Students with Disabilities…Conceptual Processing: Eliminate Barriers. Allow students to use calculators to ensure inclusive participation in the activity”.

• Processing Time: “Increased time engaged in thinking and learning leads to mastery of grade level content for all students, including students with disabilities. Frequent switching between topics creates confusion and does not allow for content to deeply embed in the mind of the learner. Mathematical ideas and representations are carefully introduced in the materials in a gradual, purposeful way to establish a base of conceptual understanding. Some students may need additional time, which should be provided as required.” Unit 2, Lesson 7, Full Lesson Plan, 2.7.3 Exploration Activity, “Support for Students with Disabilities Conceptual Processing: Processing Time. Check in with individual students, as needed, to assess for comprehension of the concept of ‘constant pace.’”

There are several accessibility options (accessed via the wrench icon in the lower left-hand corner of the screen) available to help students navigate the materials. Examples include:

• Tools Menu allow students to change the language, and access a Demos Scientific and Graphing Calculator.

• Accessibility Menu allows students to change the language, page zoom, font style, background and font color, and enable/disable the following features: text highlighter, notes, screen reader support. 

• UserWay, allows students to adjust the following: Change contrast (4 settings), Highlight links, Enlarge text (5 settings), Adjust text spacing (4 settings), Hide images, Dyslexia Friendly, Enlarge the cursor, show a reading mask, show a reading line, Adjust line height (4 settings), Text align (5 settings), Saturation (4 settings). 

Additionally, differentiated videos explaining course content - varying from review to in-depth levels of explanation - are resources available for each lesson to support students.

The materials reviewed for Math Nation Grade 7 meet expectations for providing extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity.

Course Guide, How to Use These Materials, Are You Ready For More? section states the following: “Select classroom activities include an opportunity for differentiation for students ready for more of a challenge. Every extension problem is made available to all students with the heading ‘Are You Ready for More?’ These problems go deeper into grade-level mathematics and often make connections between the topic at hand and other concepts at grade level or that are outside of the standard K-12 curriculum. They are not routine or procedural, and intended to be used on an opt-in basis by students if they finish the main class activity early or want to do more mathematics on their own. It is not expected that an entire class engages in Are You Ready for More? problems and it is not expected that any student works on all of them. Are You Ready for More? problems may also be good fodder for a Problem of the Week or similar structure.” If individual students would complete these optional activities, then they might be doing more assignments than their classmates.

Examples of opportunities for advanced students to investigate grade-level mathematics content at a higher level of complexity include:

• Unit 3, Lesson 8, 3.8.5 Exploration Extension: Are you Ready for More?, “A box contains 20 square tiles that are 2 inches on each side. How many boxes of tiles will Elena need to tile the table?” This is a direct extension of the 3.8.4 Exploration Activity in which students calculate the area of a circular table with a given diameter. 

• Unit 5, Lesson 12, 5.12.4 Exploration Extension: Are you Ready for More?, “During which part of either trip was a Piccard changing vertical position the fastest? Explain your reasoning. 1. Jacques's descent; 2. Jacques’s ascent; 3. Auguste’s descent; 4. Auguste’s ascent“ This is a direct extension of the 5.12.3 Exploration Activity in which students use different operations with signed numbers to represent real-world situations.

• Unit 7, Lesson 10, 7.10.4 Exploration Extension: Are you Ready for More?, “Using only a compass and the edge of a blank index card, draw a perfectly equilateral triangle. (Note! The tools are part of the challenge! You may not use a protractor! You may not use a ruler!)”

The materials reviewed for Math Nation Grade 7 meet expectations for providing strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.

The Course Guide, How to Use These Materials section states the following: “The framework for supporting English language learners (ELLs) in this curriculum includes four design principles for promoting mathematical language use and development in curriculum and instruction. The design principles and related routines work to make language development an integral part of planning and delivering instruction while guiding teachers to amplify the most important language that students are expected to bring to bear on the central mathematical ideas of each unit.” The four design principles are, support sense-making, optimize output, cultivate conversation, and maximize meta-awareness. Each design principle has an explanation that goes into more detail about how teachers can use it to support students. The routines are the Mathematical Language Routines (MLRs), the materials state, “The mathematical language routines (MLRs) were selected because they are effective and practical for simultaneously learning mathematical practices, content, and language. A mathematical language routine is a structured but adaptable format for amplifying, assessing, and developing students' language. The routines emphasize uses of language that is meaningful and purposeful, rather than about just getting answers. These routines can be adapted and incorporated across lessons in each unit to fit the mathematical work wherever there are productive opportunities to support students in using and improving their English and disciplinary language use. Each MLR facilitates attention to student language in ways that support in-the-moment teacher-, peer-, and self-assessment for all learners. The feedback enabled by these routines will help students revise and refine not only the way they organize and communicate their own ideas, but also ask questions to clarify their understandings of others' ideas.” These design principles and routines are referenced under Instructional Routines, in the Full Lesson Plan for lesson, to assist teachers with lesson planning. The “Supports for English Language Learners” section within the Full Lesson Plan contains explanations of how to implement the MLRs. 

Examples where the materials provide strategies and supports for students who read, write, and/or speak in a language other than English include:

• Unit 4, Lesson 11, Full Lesson Plan, 4.11.2 Exploration Activity, “Support for English Language Learners Reading, Writing: MLR 6 Three Reads. Use this routine to support reading comprehension of this word problem, without solving it for students. In the first read, students read the problem with the goal of comprehending the situation (e.g., A car dealership bought a car. The dealership wants to make a profit. They need to decide what price the car should be.). If needed, discuss the meaning of unfamiliar terms at this time (e.g., profit, wholesale, retail price, commission, etc.). Use the second read to identify the important quantities by asking students what can be counted or measured (e.g., wholesale price, profit or markup, and retail price). In the third read, ask students to brainstorm possible mathematical solution strategies to complete the task. This will help students connect the language in the word problem and the reasoning needed to solve the problem while keeping the intended level of cognitive demand in the task. Design Principle(s): Support sense-making”

• Unit 6, Lesson 17, Full Lesson Plan, 6.17.3 Exploration Activity, “Support for English Language Learners Conversing: MLR 4 Information Gap. This activity uses MLR 4 Information Gap to give students a purpose for discussing information necessary for solving problems involving inequalities. Design Principle(s): Cultivate conversation”

• Unit 8, Lesson 3, Full Lesson Plan, 8.3.2 Exploration Activity, “Support for English Language Learners Speaking: MLR 1 Stronger and Clearer Each Time. After students decide whether it will be more likely to spin the current day of the week or the pull out the paper with the current month, ask students to write a brief explanation of their reasoning. Invite students to meet with 2–3 other partners in a row for feedback. Encourage students to ask questions such as: ‘How many days are there in a week?’, ‘How many months are there in a year?’, and ‘How did you determine the likelihood of spinning the current day of the week?’ Students can borrow ideas and language from each partner to refine and clarify their original explanation. This will help students revise and refine both their reasoning and their verbal and written output. Design Principle(s): Optimize output (for explanation)”

The materials reviewed for Math Nation Grade 7 meet expectations for providing manipulatives, both virtual and physical, that are representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

Virtual and physical manipulatives support student understanding throughout the materials. Examples include:

• Unit 1, Lesson 3, 1.3.2 Exploration Activity, students use an applet to draw scale copies of selected figures. “1. Draw a scaled copy of either Figure A or B using a scale factor of 3. 2. Draw a scaled copy of either Figure C or D using a scale factor of \frac{1}{2}.” A GeoGebra applet is available for students to increase or decrease the figure depending on the scale factor.

• Unit 5, Lesson 7, 5.7.5 Exploration Activity, students plot points to create a shape and and find the side length of that shape. “Plot these points on the coordinate grid: A = (5,4), B = (5,−2), C = (−3,−2), D = (−3,4) 1. What shape is made if you connect the dots in order? 2. What are the side lengths of figure ABCD? 3. What is the difference between the x-coordinates of B and C? 4. What is the difference between the x-coordinates of C and B? 5. How do the differences of the coordinates relate to the distances between the points?” A GeoGebra applet is available for students to use to plot the points.

• Unit 7, Lesson 6, 7.6.2 Exploration Activity, students learn about what shapes are possible under certain constraints by using an applet to construct various polygons. “1. Use the segments in the applet to build several polygons, including at least one triangle and one quadrilateral. 2. After you finish building several polygons, select one triangle and one quadrilateral that you have made. a. Measure all the angles in the two shapes you selected. Note: select points in order counterclockwise, like a protractor. b. Using these measurements along with the side lengths as marked, draw your triangle and quadrilateral as accurately as possible on separate paper.” A GeoGebra applet is available with several lines of various lengths for students to build polygons with.