7th Grade - Gateway 2

The materials reviewed for Desmos Math 7 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

In the Curriculum Guide, Courses, Conceptual Understanding, “Lessons develop students’ conceptual understanding by inviting them into familiar or accessible contexts and asking them for their own ideas before presenting more formal mathematics.” The materials include problems and questions that allow for students to develop conceptual understanding throughout the grade level. Examples include:

• Unit 2, Lesson 2, Screen 4, Two Strategies, students analyze proportional relationships in a real world setting to complete a table of values (7.RP.A). “Here are two different strategies for finding the number of balloons for the rubber duck. Discuss how Ariel and Emma would use their strategies to finish their tables.” Two tables are provided, one shows Ariel’s strategy and one shows Emma’s strategy. 

• Unit 5, Lesson 2, Screen 6, Settle a Dispute, students use a vertical number line to apply and extend previous understandings of addition and subtraction to add and subtract rational numbers (7.NS.1). “Marc and Naoki are trying to evaluate 3-(-2). Marc says, ‘This is like adding 2 anchors, so the submarine goes DOWN to 1.’ Naoki claims, ‘This is like removing 2 anchors, so the submarine goes UP to 5.’ Who is correct?” Choices include: Marc (1), Naoki (5), Both, or Neither. An image of a submarine in water with a vertical number line next to it is provided. The submarine is placed at three on the number line. There is a point at five on the number line labeled Naoki and a point at one labeled Marc.

• Unit 8, Lesson 3, Screen 3, Update Your Prediction, students analyze a simulation to predict the contents of a mystery bag (7.SP.6). “The graph shows the results from 200 picks. Use these results to decide how many of the 10 blocks you think are green.”

The materials provide opportunities for students to independently demonstrate conceptual understanding throughout the grade level. Examples include:

• Unit 4, Quiz, Screen 4, Problem 3, students use proportional reasoning to solve multistep ratio and percent problems (7.RP.3). “To make a certain shade of paint, Anya mixed \frac{2}{3} cups of white paint with 2\frac{2}{3} cups of blue paint. How many cups of blue paint should she mix with \frac{3}{4} cups of white paint to make the same shade?” 

• Unit 6, Lesson 2, Screen 9, Which Restaurant?, students use a bar diagram to solve real-world  problems with equations (7.EE.B). On previous screens students selected tape diagrams to determine how much Raven and her three siblings can spend on a meal if they have $44. One restaurant charges a $3 service fee for each meal, and another charges a $6 service fee for their order. “Here are diagrams that represent the situations on the previous screens. Figure out the value of x and y in the diagrams. Enter your values in the table below. Explain to a neighbor what your values say about which restaurant the siblings should choose.” Two tape diagrams are provided. The tape diagram labeled Burrito Express has four equal boxes labeled x and a box labeled six. The entire tape diagram is labeled 44. The tape diagram labeled Salads-R-Us has four equal boxes labeled $$y+3$$. The entire tape diagram is labeled 44.

• Unit 7, Lesson 5, Practice Problems, Screen 3, Problem 2, students construct triangles from three measures of angles or sides and determine the conditions of a unique triangle, more than one triangle, or no triangle, as they determine a possible third length of a triangle given two side lengths (7.G.2). “One side of a triangle is 5.5 inches long. Another is 10.5  inches long. Which of the following could be the length of the third side? Select all that apply.” Answer choices include: 3 inches, 5 inches, 7 inches, 10 inches, 12 inches, and 20 inches.

The materials reviewed for Desmos Math 7 meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

In the Curriculum Guide, Courses, Procedural Fluency, ”In order to transfer skills, students should be able to solve problems with accuracy and flexibility. Several structures in the Desmos Curriculum support procedural fluency: repeated challenges, where students engage in a series of challenges on the same topic, challenge creators, where students challenge themselves and their classmates to a question they create, and paper practice days that use social structures to reinforce skills before assessments.”

Materials develop procedural skills and fluency throughout the grade level. Examples include:

• Unit 3, Lesson 3, Screen 6, From Radius to Circumference, students develop procedural skill and fluency using the formula for circumference of a circle to solve problems (7.G.4). “The radius of this circle is 7 centimeters. What is its approximate circumference?” A picture of a circle with radius of 7 cm labeled.

• Unit 5, Lesson 6, Screen 12, Cool-Down, students develop fluency in multiplying rational numbers (7.NS.2). “Determine the value of each expression.” Choices include: (-5)\sdot4, 6\sdot(-2), (-3)\sdot(-7). 

• Unit 6, Lesson 13, Screen 9, Write an Inequality, students construct a simple inequality by reasoning about the quantities (7.EE.4). “Write an inequality that represents this graph.” Students are given a number line with an open circle on 19 with a line heading to the right.

The materials provide opportunities for students to independently demonstrate procedural skills and fluency throughout the grade level. Examples include:

• Unit 1, Lesson 2, Practice Problems, Screen 3, Problem 1.2, students solve problems involving scale drawings of geometric figures (7.G.1). “For each scaled copy, write the scale factor from triangle T to that triangle. If the triangle is not a scaled copy, leave it blank.” The screen contains a triangle T with side lengths 3, 4, and 5. There are 6 other triangles labeled A through F with their side lengths labeled. There is a table with two columns, Triangle and Scale Factor, for the student to enter work. 

• Unit 4, Quiz, Screen 2,  Problem 1, students use proportional relationships to solve multi step percent problems (7.RP.3). “The value of a car decreases over time. This year, Faaria’s car is worth $22,000. If the value of Faaria’s car decreases by 8%, what will her car be worth next year?” Students are given choices ranging from $4,400 to $23,760.

• Unit 8, Lesson 7, Screen 5-6, 3-Day Vacay and Make a Simulation, students design and use a simulation to generate frequencies for compound events (7.SP.8). Students are given a display which shows the percent chance for rain over the period of three days. Screen 5, “Ivan is planning a 3-day vacation. Here is the forecast at his destination. What do you think is the probability that it will rain at least once during these 3 days? Drag the slider to show your guess.” The slider ranges from 0% to 100%. Screen 6, “Ivan wants to design a simulation to estimate the probability of rain during his vacation. Add blocks to each bag to match the probability of rain on each day.”  An interactive is provided with Fri 25%, Sat 25% and Sun 40%.  Under each forecast is a bag and blocks representing rain and sunshine.

The materials reviewed for Desmos Math 7 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of mathematics. 

In the Curriculum Guide, Courses, Application, students “have opportunities to apply what they have learned to new mathematical or real-world contexts. Concepts are often introduced in context and most units end by inviting students to apply their learning…” Materials include multiple routine and non-routine applications of mathematics throughout the grade level. Examples include:

• Unit 2, Lesson 9, Screen 6, Better Mileage, students explain what point (x, y) on the graph of a proportional relationship means in terms of the situation (7.RP.2d). “Kaya wants to buy a new vehicle that gets better gas mileage than her truck. Which vehicle should she pick?” A graph is provided with Maximum Distance (miles) on the y-axis and Gas (gallons) on the x-axis. There is a line labeled “Truck,”and a point labeled “Vehicle A”, and a point labeled “Vehicle B”, on the graph. Students click on either Vehicle A or B and explain their thinking on why they would buy that vehicle.

• Unit 5, Lesson 10, Screen 2, Greater than Zero, students use their knowledge of rational numbers to make the given inequality true (7.NS.1). “Make a true inequality by dragging the cards. Then press Check My Work.” Students are given the inequality [  ]([  ][  ] + [  ]) > 0 and the card choices are: -1, 2, 3, -4, -5, 6, 7, -8.  

• Unit 7, Lesson 13, Screen 8, Are You Ready for More, students solve real-world problems involving volume, and surface area of right prisms (7.G.6).  “On paper, complete the following tasks: 1. Sketch a container that can hold 120 cubic units of popcorn while using as little paper as possible. 2. Label your container's dimensions. Then calculate the amount of paper it uses.” A graphic is provided of a popcorn container in a right prism with height  (h) , width (w), and length (l).  Students have the option of unfolding the container. 

Materials provide opportunities for students to independently demonstrate multiple routine and non-routine applications of mathematics throughout the grade level. Examples include:

• Unit 4, Lesson 3, Screen 6, Sheets of Stickers, students compute unit rates with ratios of fractions (7.RP.1).  “Cho is considering buying stickers by the sheet. Four sheets cost 14. How much would $$11\frac{1}{2}$$ sheets cost?” 

• Unit 5, Lesson 8, Practice Problems, Screen 5, Problem 3.2, students apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers (7.NS.2). “A machine that drills holes for wells drilled to a depth of -72 feet in one day (24 hours). If the machine drilled at a constant rate, what was the depth after 15 hours?”

• Unit 6, Lesson 3, Screen 11, Lesson Synthesis, students use variables to represent quantities in a real-world or mathematical problem (7.EE.4). “Explain how the number 9 is important in each representation. In the story… In the equation… In the tape diagram…” Students are given the following three cards:  Story - Jaylin buys 3 bags of bagels. The store gives her 5 bagels for free, making it 32 bagels total. Equation -3x+5=32. Tape Diagram - Students are given a tape diagram divided into four pieces, the three pieces labeled x are of equal size the last piece is labeled 5. All pieces together must equal 32. 

• Unit 8, Lesson 11, Screen 7, Write a Headline, students use the data from a sampling method to make generalizations about a population in the form of a headline (7.SP.1). “Pick a sampling method below and use the sample to write a headline about how much time Americans spend with their friends per day.” Students are given the following sampling methods to choose from: “Ask 10 students in one high school classroom”, “Ask 10 random people at a nursing home”, and “Dial 10 random phone numbers and ask whoever answers.” Clicking on each sampling method generates a different Mean and dot plot.

The materials reviewed for Desmos Math 7 meet expectations in that the three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade.

All three aspects of rigor are present independently throughout Grade 7. Examples where instructional materials attend to conceptual understanding, procedural skill and fluency, or application include:

• Unit 2, Lesson 5, Screen 9, Lesson Synthesis, students demonstrate conceptual understanding as they explain what they know about proportional relationships by creating their own situation given an equation (7.RP.2). “Make up a situation that could be represented by the equation r=10p.  Be sure to explain what r, 10, and p represent in your situation.” 

• Unit 5, Quiz 1, Screen 4, Problem 3.1, students develop procedural skill and fluency while understanding subtraction of rational numbers as the additive inverse (7.NS.1c).  “Determine the value of the variable that makes the equation true. 15-a=17.”

• Unit 8, Lesson 5, Screen 8, 100 Rolls, students approximate the probability of a chance event be running the simulation and collecting data (7.SP.6). “Roll the number cube as many times as you want. What do you think is the probability that Player 1 wins?” Students are able to roll a number cube 100 times by pressing the “Roll 100 Times” button, the results are recorded in a chart. Player 1 wins if an even number is rolled, and Player 2 wins if an odd number is rolled.

Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single unit of study throughout the materials. Examples include:

• Unit 3, Practice Day 2, Student Workspace Sheet, Problems 1-5, engage students in conceptual understanding, procedural skill and fluency, and application as they use the formulas for the area and circumference of a circle to solve real-world problems (7.G.4 & 7.G.6). Students solve a real-world problem (application) related to circumference and area of circles. Students must demonstrate conceptual understanding by determining which questions refer to circumference and area and then sort the questions from smallest measurement to largest. At the end of the activity students must calculate the circumference and area of a circle using their estimates. Problems 1-5 tasks students with the following: “1. Sort the cards into two groups based on whether you would use the circumference or the area of a circle to answer the question. Record your answers below. 2. Sort the cards in each group from smallest measurement to largest. Record your answers below. 3. Select one circumference card and one area card to examine more closely. What information do you need? Estimates for this information: 4. Use your estimates to calculate an answer to your circumference question. 5. Use your estimates to calculate the answer to your area question.” 

• Unit 4, Lesson 6, Student Worksheet, Activity 2: Sea Green Turtle, students build conceptual understanding and application as they use proportional relationships to solve multi step percent problems (7.RP.3). “Some beaches where green sea turtles come ashore to lay eggs have been made protected sanctuaries so the eggs will not be disturbed. This year, there were 234 nesting turtles at a sanctuary. That number is a 10% decrease compared to last year. Create each representation to show how many nesting turtles were at the sanctuary last year. How many nesting turtles were at the sanctuary last year?” Students are asked to create a double number line, a table, and an equation.

• Unit 5, Practice Day 1, Task Cards, Task 2: Cafeteria Food Debt, Problems 1 and 2, students engage in procedural skill and fluency alongside application as they solve a real-world problem involving addition and subtraction of rational numbers (7.NS.1d).  “At the beginning of the month, Emika had $24 in her school cafeteria account. The table below shows how her account balance changed over the course of three weeks. 1. Complete the table for weeks 2-3. 2. How much would Emika have to deposit into the account during week 4 so that the final balance is positive?” A table is included with the columns: Week, Beginning Balance ($), Final Balance ($), Expression for Difference Between Final and Beginning, and Change ($). The row labeled Week 1 is complete. In row 2, students are given the beginning and final balances and must write the expression and calculate the change. In row 3, students are given the beginning balance and the change, and must write the expression and final balance. 

• Unit 6, Lesson 17, Student Worksheet, Activity 1: Orange Juice and Donuts, Problems 1-3 engage students in conceptual understanding, procedural skill and fluency, and application as they solve word problems leading to inequalities of the form px+q>r or px+q, where p, q, and r are specific rational numbers and interpret the solution in the context of the problem (7.EE.4b). “Kiandra wants to surprise some friends before school with orange juice and donuts. At the store, an orange juice costs $2.15 and a donut costs $0.75 . There is no sales tax. The store has a $10 purchase minimum for credit cards. Kiandra used her credit card to pay. How many friends might she have bought treats for? 1. Write an inequality that describes Kiandra’s situation. 2. Solve the inequality you wrote. 3. What does the solution to your inequality mean in this situation?”

The materials reviewed for Desmos Math 7 meet expectations for supporting the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

The MPs are explicitly identified for teachers in the Math 7 Lessons and Standards section found in the Math 7 Overview. MP1 is identified and connected to grade-level content, and intentionally developed to meet its full intent. Students make sense of problems and persevere in solving them as they work with support of the teacher and independently throughout the units. Examples include:

• Unit 1, Lesson 10, Student Worksheet, Activity 1: Measure Your Classroom, students plan a solution pathway to solve a problem involving scale drawings. “With your team, on blank paper: 1. Write a plan for how you will gather, record, and check your measurements. 2. Sketch the outline of your classroom and any permanent objects. Include all measurements.” Activity Facilitation, “Display Sheet 2 of the Teacher Projection Sheets to the class and review the image as an example of what they will produce as a team in Activity 1. Consider reading each question for teams to consider aloud and discussing any questions that might be unclear. Next, invite students to work together to make a plan for creating their rough sketch and gathering the measurements they need (MP1). Follow with a brief whole-class discussion to hear strategies groups have incorporated into their plans.” Students make sense of the problem as they work together to make a plan for creating the group rough sketches, and gathering measurements.

• Unit 5, Lesson 5, Screen 2, Puzzle #1, students use perseverance and creativity to solve a puzzle involving adding and subtracting signed numbers (MP1). “Make a true equation by dragging and flipping the cards. Try to use as few flips as possible. Then press ‘Check my Work.’” Students are provided an equation tool with the equation, an unknown plus an unknown is equal to an unknown subtracted from an unknown. The original card choices are: 1, 2, 3, 4, -5, -6, -7 and -8. All cards can be flipped from positive to negative and vice versa. 

• Unit 6, Lesson 12, Student Worksheet, Activity 1: Three Reads, students solve multi-step equations. “Kyrie is making ___ invitations to their school’s Community Day. They have already made ___ invitations, and they want to finish the rest of them within a week. Kyrie plans to spread out the remaining work so that they can make the same number of invitations each day.” Students answer: “1. With a partner, discuss what this situation is about. 2. Draw a tape or hanger diagram to represent this situation. 3. Given these values, adjust your diagram. Then use your diagram to figure out how many invitations Kyrie should make each day.” Students make sense of the verbal descriptions of situations.

• Unit 8, Lesson 10, Screen 7, See Some Samples, students use a slider to examine the relationship between the sample mean and population mean. “1. Drag the point to collect crabs and see the mean width for the sample. 2. Discuss the advantages and disadvantages of using a large sample.” Students make sense of the relationship between the sample mean and the population mean as they think about the advantages and disadvantages of using a large sample, as well as the role of randomness in sampling.

MP2 is identified and connected to grade-level content, and intentionally developed to meet its full intent. Students reason abstractly and quantitatively as they work with support of the teacher and independently throughout the units. Examples include:

• Unit 1, Lesson 7, Student Worksheet, Activity 1, Will it Fit?, students use the measurements of a scale drawing to calculate the actual dimensions of a figure. “Here is the scale drawing that Karima presented to her neighborhood park’s board of directors. 1. The scale for Karima’s drawing is 2 cm to 5 m. Explain what this means in your own words. 2. Will Karima’s court fit in the 20-by-20-meter square area the park directors designated for the court? Use your measuring tools and the table below to help you with your thinking. Round each measurement to the nearest tenth of a centimeter. Explain how you know whether or not the court will fit.” Students find the scale and actual measurements of the Length of the Court, the Width of the Court, the Hoop to 3-pt Line, and the 3-pt. Line to the Side Line. Students reason abstractly and quantitatively as they find the measurement of the scale drawing and convert to the dimensions of the actual court. 

• Unit 2, Lesson 5, Screen 4, Cake Calculations, students represent a proportional relationship symbolically with an equation. “A cake recipe says to use 3 cups of flour for every 2 cakes. Write a proportional equation to calculate the amount of flour needed, f, for any number of cakes, c.”

• Unit 5, Lesson 7, Screen 6, What It Means, students connect the concepts of rate, time, and position. Students are given a picture of a turtle on a number line and scaled by 10s with the interval -30 ft to 30 ft and -3.2 minutes in a white box. “One student wrote the following equation to determine Tam's position on the previous screen: (-5)(-3.2)=16. Explain what each number represents in the scenario. -5 represents…, -3.2 represents…, 16 represents…” Teacher Moves, “The purpose of this discussion is to connect rate, time, and position with numerical expressions and equations, and to explain why the product of two negative values is positive (MP2).”

• Unit 8, Lesson 5, Screen 4, Keeping Track of Heads, students read and interpret graphs of probabilities. Students are shown a video in which a coin is flipped, then the “Fraction of Heads (So Far)” is graphed along with the “Number of Flips.” Students answer: “1. What does the point (10, \frac{1}{2}) mean? 2. How might a graph help you determine if a coin is fair?”

The materials reviewed for Desmos Math 7 meet expectations for supporting the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

The MPs are explicitly identified for teachers in the Math 7 Lessons and Standards section found in the Math 7 Overview. Students engage with MP3 in connection to grade-level content, as they work with support of the teacher and independently throughout the units. Examples include:

• Unit 1, Lesson 2, Screen 6, Anushka's Robot, students explain the relationship between lengths in a figure and corresponding lengths in a scaled copy. “Anushka built a robot and made a copy that is not a scaled copy. Explain Anushka's strategy. What advice would you give Anushka to help her make her new robot a scaled copy?”  Students are given an image with two robots, one with dimensions labeled 3, 4, 1 and the other labeled with dimensions 9, 10, 1. Teacher Moves, “Consider asking students how they know the two figures are not scaled copies. If it does not come up naturally, consider mentioning that the angles of the two figures are different. Give students 2–3 minutes to inspect Anushka’s robot and record their responses. Encourage students to read others’ responses and/or discuss their response with a partner and decide if others' strategies were similar to or different from their own. If time permits, consider using the snapshots tool or dashboard's teacher view to display several student suggestions for different ways to make a scaled copy. Routine (optional): Consider using the routine Critique, Correct, Clarify to help students communicate about errors and ambiguities in math ideas and language.” Students engage with MP3 as they explain/justify their strategies and thinking orally or in writing using concrete models, drawings, actions, or numbers.

• Unit 2, Lesson 12, Student Worksheet, Cool-Down, students use proportional relationships to analyze a problem about water usage. “Marshall wants to buy a kitchen faucet.  Faucet A fills a 4-gallon water jug in 1 minute. Faucet B fills a 1-gallon water jug in 20 seconds. Which faucet uses less water? Explain your thinking.” Students engage with MP3 as they explain/justify their strategies and thinking orally or in writing using concrete models, drawings, actions, or numbers.

• Unit 4, Lesson 4, Screen 4, It’s All About the Money, students create different strategies to determine 10% less than 15. “In order to make more money, DesWorst Granola bars are now 10% shorter. If the original bar was 15 centimeters long, how long is the new granola bar? Use paper if it helps you with your thinking.” Teacher Move, “While students are working, monitor for different expressions students use and select them using the snapshots tool. When most students have completed this screen, facilitate a whole-class discussion. Ask students to justify their strategy and critique each other’s reasoning (MP3).”

• Unit 6, Lesson 8, Student Worksheet, Activity 2: Step by Step by Step by Step, students critique the reasoning of others as they apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. “Here is an equation and the first steps that Sadia and Amir wrote to solve it.” The worksheet shows two students’ first step in solving the equation 2(x-9)=10. “1. Are each of their first steps correct? Explain your reasoning.” 

The materials reviewed for Desmos Math 7 meet expectations for supporting the intentional development of MP4: Model with mathematics; and MP5: Choose tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

The MPs are explicitly identified for teachers in the Math 7 Lessons and Standards section found in the Math 7 Overview.There is intentional development of MP4 to meet its full intent in connection to grade-level content. Examples include:

• Unit 4, Lesson 9, Student Worksheet, Activity 2: What’s Fair?, Problem 2, students model a real-world situation, involving multistep ratio and percent problems, with an appropriate expression and use it to solve the problem and interpret the results. In Activity 1, students are presented with information about four servers who work in four different restaurants. It tells how many hours they work, how many tables they serve in a typical week, the average bill at the restaurant, and the percentage tip they typically earn. Activity 2: What’s Fair?, Problem 2, “Consider these three approaches to paying servers that we have seen so far: A. Servers get paid $2.13 per hour, plus tips. B. Servers get paid $7.25 per hour, plus tips. C. Servers get paid $15 per hour, with no tips. Invent and describe a system to determine a server’s pay that you think is fairer than the ones above. Calculate what each of the four people would earn under your system.” This activity attends to the full intent of MP4, model with mathematics.

• Unit 6, Lesson 17, Lesson Guide, Warm-Up, provides guidance for teachers to engage students in MP4 as they solve word problems leading to inequalities. Teacher Projection Sheets, Warm-Up, “Jamal volunteers to hand out sandwiches to people who are hungry in his community. He raised $85 and i s trying to figure out how many sandwiches he can purchase for $6.25 each. He writes the inequality 6.25x≤85. Then he solves the inequality and gets x≤13.6. Select all the statements that are true about this situation. A. He can order 13.6 sandwiches. B. He can order 14 sandwiches. C. He can order 12 sandwiches. D. He can order 9.5 sandwiches. E. He can order – 4 sandwiches.”Lesson Guide, “Facilitation: Display Sheet 1 of the Teacher Projection Sheets. Consider reading the story aloud as a class and asking students what connections they make to the story. Ask them what the variable x represents in Jamal’s inequality. Then give students one minute to think quietly and another minute to share their reasoning about which statements are true with a partner.” This activity intentionally develops MP4, model with mathematics.

• Unit 8, Lesson 7, Screen 1, Warm-up, students apply what they have learned about probability tools and repeated experiments to simulate multi-step real-world events. “Aniyah saw this forecast for the weekend's weather. What do you think is the probability that it will rain at least once this weekend? 1. Drag the slider to show your guess. 2. Explain your thinking”  Students are given two images depicting weather with one labled SAT (40%) and SUN (60%). This activity attends to MP4, model with mathematics.

There is intentional development of MP5 to meet its full intent in connection to grade-level content. Examples include:

• Unit 4, Lesson 3, Screen 5, Cho’s Logo, Teacher Moves, provides guidance for teachers to engage students in MP5 as they consider the effectiveness of different tools as they determine unknown values in proportional relationships. “Early Finishers: Encourage students who finish Screens 2–5 early to use different tool and to determine which tool is more effective for this problem and why. (MP5).”

• Unit 6, Lesson 3, Screen 2, Baking Cookies, Teacher Moves, provides guidance for teachers to engage students in MP5 by allowing students to consider the available tools when solving a mathematical problem. “Activity 1 Purpose: On Screens 2–5, students use equations and tape diagrams to make sense of a situation. Students answer a question about a situation involving baking cookies using any representation (MP5).”

• Unit 8, Lesson 2, Screen 7, How Many, Teacher Moves, provides guidance for teachers to engage students in MP5 as they show their familiarity with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful. Students experiment with how to organize their thinking about a complex sample space. “Facilitation: …While students are working, monitor for students who use drawings, organized lists, or other tools to help them determine the size of the sample space (MP5).”

The materials reviewed for Desmos Math 7 meet expectations for supporting the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

The MPs are explicitly identified for teachers in the Math 7 Lessons and Standards section found in the Math 7 Overview. Students have many opportunities to attend to precision in connection to grade-level content as they work with support of the teacher and independently throughout the modules. Examples include:

• Unit 1, Lesson 10, Student Worksheet, Activity 3: Creating Your Scaled Drawing, Problem 6, students select a unit of measure and scale to create a drawing. “On graph paper, make an accurate scale drawing using your chosen scale.” Teacher guidance, “Remind students that unlike their sketch, these scale drawings should be drawn with precision to scale.” This problem attends to MP6 as students attend to the precision of mathematics as they create a scaled drawing accurately.

• Unit 8, Lesson 2, Screen 4, Prob-bear-bility, students use a randomizer to understand sample space to determined the probability of an event. “1. Here is a randomizer. Press “Spin” to get a random creature. 2. Drag the point to show how likely you think it is to get a bear on one spin.” Students are given a number line with a range from zero to one, zero being impossible and one being certain. It is also labeled at the \frac{1}{2} mark.  Students attend to precision as they understand that the probability of a chance event is a number between 0 and 1.

Students have frequent opportunities to attend to the specialized language of math in connection to grade-level content as they work with support of the teacher and independently throughout the modules. Examples include:

• Unit 2, Lesson 2, Screen 6, Proportional Relationships, “When two quantities are always in an equivalent ratio, it is called a proportional relationship. Which of these two tables represents the proportional relationship between weight and balloons? Explain your thinking.” The screen contains two tables with the data for weight (oz.) and number of balloons. Students attend to the specialized language of mathematics as they use the term proportional relationship and apply their understanding to recognize proportional relationships between quantities. 

• Unit 3, Lesson 2, Screen 6, Madison’s Circles, “Madison made a drawing using circles. Describe her drawing as precisely as you can so that someone who can't see her drawing could recreate it. Use the sketch tool if it helps you with your thinking.” Students are given an image of four circles inscribed in one another on the coordinate plane. Teacher facilaton suggests, “The purpose of this discussion is to support students in attending to precision in their language when describing circles (MP6). Use the mathematical language routine Critique, Correct, Clarify to support students in attending to precision in their language. If it does not come up naturally, consider introducing the word center.” This activity attends to MP6 as students attend to the specialized language of mathematics as they describe properties of circles. Students begin to use precise terminology to describe the parts of a circle. 

• Unit 7, Lesson 2, Screen 3, Complementary and Supplementary, “The terms complementary and supplementary describe special pairs of angles. Describe what you think these terms mean.” The screen contains pictures of examples of complementary and supplementary angles. Students attend to the specialized language of math and develop an understanding of supplementary and complementary angles.

The materials reviewed for Desmos Math 7 meet expectations for supporting the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to grade-level content standards, as expected by the mathematical practice standards. 

The MPs are explicitly identified for teachers in the Math 7 Lessons and Standards section found in the Math 7 Overview. MP7 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students have many opportunities throughout the modules to look for, describe, and make use of patterns within problem-solving as they work with support of the teacher and independently. Examples include:

• Unit 2, Lesson 7, Screen 3, Are They Proportional?, “Here are the equations from the worksheet. Select all the equations that represent a proportional relationship. Then explain one way to decide if an equation represents a proportional relationship.” The screen contains 4 equations: y=12x, y=500+35x, y=\frac{1}{2}x, y=x^2. Students look for and use structure to generalize types of equations that do and do not represent proportional relationships. 

• Unit 5, Lesson 4, Student Worksheet, Activity 2: Draw Your Own Conclusion, Problem 3, “Select one of these statements. Explain whether it is always, sometimes, or never true. Use examples and number line diagrams to support your explanation.” There are 3 statements: Statement D: x-y is the opposite of y-x, Statement E: x is less than x+y, Statement F: x-y is greater than x+y. Students look for and use structure to reason about whether expressions involving integer operations with variables are always, sometimes, or never true.

• Unit 7, Lesson 11, Screen 10, Lesson Synthesis,“Here are several prisms you’ve seen in this lesson. Describe a general strategy for determining the volume of any prism.” The screen shows images of three different prisms. Students look for patterns or structures to make generalizations about determining the volume of prisms.

MP8 is identified and connected to grade level content, and there is intentional development of the MP to meet its full intent. Students have multiple opportunities throughout the materials, with support of the teacher or during independent practice, to use repeated reasoning in order to make generalizations and build a deeper understanding of grade-level math concepts. Examples include:

• Unit 1, Lesson 5, Screen 5, Scaling Rectangles, “Here is a rectangle and a scaled copy. The area of the original rectangle is 8 square units. What is the area of the scaled copy?” Students use repeated reasoning to explain why it is that when a figure is scaled by a scale factor, the area is not scaled by the same amount.

• Unit 4, Lesson 3, Screen 2, Different Sizes, “Here's a logo that Aditi is making into stickers. Enter the missing values so that the logo looks the same on each sticker. Then describe your strategy.” Students are given an image with four stickers. Two stickers have the length and width labeled. The other stickers have only the length or width labeled, and students must use repeated reasoning to find the other. This activity attends to the full intent of MP8, look for and express regularity in repeated reasoning as students notice repeated calculations to understand algorithms and make generalizations or create shortcuts.

• Unit 8, Lesson 4, Screen 5, Your Turn, “1. Spin Amari and Nathan’s spinner as many times as you want. 2. Discuss what is happening to the fraction of red spins as you add more spins.” Students are given a spinner and a graph to work, while they approximate the probability of how many red spins vs blue spins. This activity attends to the full intent of MP8, use repeated reasoning as students approximate the probability of a chance event by collecting data.