7th Grade - Gateway 1

The materials reviewed for Math in Focus: Singapore Math Course 2 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

Summative assessments provided by the materials include Chapter Tests, Cumulative Reviews, and Benchmark Assessments and are available in print and digitally. According to the Preface of the Math in Focus: Assessment Guide, "Assessments are flexible, teachers are free to decide how to use them with their students. ... Recommended scoring rubrics are also provided for some short answer and all constructed response items to aid teachers in their marking." The following evidence is based upon the provided assessments and acknowledges the flexibility teachers have in administering them in order to understand their students' learning.

The provided assessments, found in the Assessment Guide Teacher Edition, assess grade-level standards. Examples include:

• In Chapter Test 1, Section B, Item 9 states, “At 6 p.m., the temperature was 2.5°F. By midnight, it had dropped by 6.8°F. By 6 a.m. the next day, it had risen by 3.4°F. What was the final temperature in °F?” (7.NS.3)

• In Chapter Test 4, Section C, Item 11 states, “The price of a computer was marked up by 50% and then marked down by 50%. James said that there was no change in the price of the computer in the end. Explain why James’ reasoning is incorrect. Calculate the percent change in the price of the computer. Explain how you found your answer.” (7.RP.3) 

• In Cumulative Review 1, Section B, Item 11 states, “Evaluate -20 + 45 ÷ (-3) × (-2).” (7.EE.1)

• In Chapter 6 Test, Section C, Item 12 states, “This question has two parts. Part A: Construct triangle ABC where AB = 4cm, BC = 5.3cm, and AC = 6.6cm. State the type of triangle you constructed. Show your drawing and answer in the space below. Part B: Triangle ABC is enlarged to produce another triangle XYZ by a scale factor of 1.4. What is the area of triangle XYZ? Write your answer and your work or explanation in the space below.” (7.G.1)

• In the End-of-Year Benchmark Assessment, Section B, Item 34 states, “This question has two parts. A population consists of the heights in centimeters of 100 students. A random sample of 10 heights is collected. 170, 175, 180, 176, 175, 174, 173, 178, 176, 177 Part A: Calculate the sample mean height of the students. Estimate the population mean height. Write your answers in the space below. Part B: Draw a plot for the heights and the mean height in the space below.” (7.SP.2)

The materials reviewed for Math in Focus: Singapore Math Course 2 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

Materials provide opportunities for students to engage in grade-level problems during Engage, Learn, Think, Try, Activity, and Independent Practice portions of the lesson. Engage activities present inquiry tasks that encourage mathematical connections. Learn activities are teacher-facilitated inquiry problems that explore new concepts. Think activities provide problems that stimulate critical thinking and creative solutions. Try activities are guided practice opportunities to reinforce new learning. Activity problems reinforce learning concepts while students work with a partner or small group. Independent Practice problems help students consolidate their learning and provide teachers information to form small group differentiation learning groups.

The materials provide one or more Focus Cycles of Engage, Learn, Try activities and opportunities for Independent Practice which provide students extensive work with grade-level problems to meet the full intent of grade-level standards. Examples include:

• In Section 1.6, Order of Operations with Integers, students engage with solving real-world and mathematical problems involving the four operations with rational numbers. In the Engage activity on page 75, students write algebraic expressions for real-world situations. The activity states, “A game show awards 30 points for each correct answer and deducts 50 points for each incorrect answer. A contestant answers 2 questions incorrectly and 3 questions correctly. How do you write an expression to find the contestants’ final score? Discuss.” In the Learn activity, Problem 3, page 74, students apply the order of operations with integers. The problem states, “Evaluate -5 + (8 - 12) (-4).” In the Try activity, Problem 4, page 75, students practice applying the order of operations with integers. The problem states, “48 ÷ (-8 + 6) + 2 ⋅ 28.” In Independent Practice, Problem 17, students practice translating real-world situations into expressions and solve. The problem states, “Sarah took three turns in a video game. She scores -120 points during her first turn, 320 points during her second turn, and -80 points during her third turn. What was her average score for the three turns?” Students engage with extensive work and full intent of 7.NS.3 (Solve real-world and mathematical problems involving the four operations with rational numbers).

• In Section 2.6 Writing Algebraic Expressions, students translate verbal descriptions into algebraic expressions with one or more variables involving the distributive property. In the Engage activity on page 171, students work in pairs to use bar models to model a situation with one variable. The activity states, “A wooden plank is x feet long. Draw a bar model and write an expression to represent the total length of two such planks. Now, use the bar model to represent the length of $$\frac{1}{3}$$ of the total length of the two planks. How do you write an expression to show it? Explain your reasoning.” In the Learn activity, Problem 1, page 176, students translate verbal descriptions into algebraic expressions with more than one variable. The problem states, “Some situations may require you to use more than one variable. Adam has m coins. Rachel has $$\frac{1}{2}r$$ coins. Assuming Adam has more coins than Rachel, how many more does Adam have?” In the Try activity, page 177, students practice translating verbal descriptions into algebraic expressions with more than one variable. The activity states, “The price of a bag is p dollars and the price of a pair of shoes is 5q dollars. Ms. Scott bought both items and paid a sales tax of 20%. Write an algebraic expression for the amount of sales tax she paid.” In Independent Practice, Problem 11, students practice translating more complex verbal problems into algebraic expressions. The problem states, “The length of $$\frac{2}{3}$$ of a rope is (4u - 5) inches. Express the total length of the rope in terms of u.” These activities provide extensive grade-level work with 7.EE.2 (Understand that rewriting an expression in different form in a problem context can shed light on the problem and how the quantities in it are related). 

• In Section 4.5, Percent Increase and Decrease, students find a quantity given a percent increase or decrease and find percent increases and decreases. In the Engage activity on page 335, students work in pairs to represent percent changes by drawing bar models. The activity states, “A: A cake cost $20. Its price increased by $5. Express this increase as a percent of the original price. What can you say about the percent increase of the price of the cake? B: Using your answer in (a), what do you think is the percent decrease in price if the cake originally cost $25 and had its price reduced by $5?” In the Learn activity on page 335, students find a quantity given a percent increase or decrease. The activity states, “The price of a pair of running shoes increased by 15% since last year. If the price of the running shoes cost $60 last year, how much does it cost now?” Method 1 shows the original price multiplied by the discounted percent and Method 2 starts with the discounted percent multiplied by the original price. In the Try activity, Problem 2, page 340, students practice finding percent increase or decrease. The problem states, “Alex deposited $1,200 into a savings account. At the end of the first year, the amount of money in the account increased to $1,260. What was the percent interest?” In Independent Practice, Problem 4, students practice finding the new quantity given the original quantity and percent increase or decrease. The problem states, “The price of a pound of grapes was $3.20 last year. This year, the price of grapes fell by 15% due to a better harvest. Find the price of a pound of grapes this year.” Students engage with extensive work and full intent of 7.RP.3 (Use proportional relationships to solve multistep ratio and percent problems).

• In Section 7.2, Area of a Circle, students use formulas to find the area of circles, semicircles, and quadrants. In the Engage activity on page 143, students find different ways to approximate the area of a circle. The activity states, “On a piece of paper, draw a circle with a diameter of 4 centimeters and a square of sides 4 centimeters. a. How can you find the area of the circle? Discuss the steps you would take to find the area of the circle. b. What is the area of the square? What can you observe about the area of the circle and the area of the square? Discuss.” In the Learn activity on page 143, students find the area of a circle. The activity states, “1. The figure on the right shows a circle of radius r in a square. Find the area of the square in terms of r. 2. Draw a square in the circle as shown. Then, find the area of the square in terms of r. 3. Estimate the area of the circle using the areas found in 1. and 2. the area of a circle is less than ____ square units but is more than ____ square units. The area of the circle is about ____ square units.” In the Try activity, Problem 1, page 146, students practice finding the area of a circle. The problem states, “Find the area of a circle that has a radius of 18 centimeters.” In Independent Practice, Problem 9, students practice finding the area of a circle when given the radius or diameter and using $$\frac{22}{7}$$ for $$\pi$$. The problem states, “A circular pendant has a diameter of 7 centimeters. Find its area. Use $$\frac{22}{7}$$ as an approximation for $$\pi$$.” Students engage with extensive work and full intent of 7.G.4 (Know the formulas for the area and circumference of a circle and use them to solve problems). 

• In Section 8.2, Making Inferences About Populations, students make inferences about a population using statistics from a sample, estimate a population mean, and make comparative inferences about two populations using two sets of sample statistics. In the Engage activity on page 221, students discover the connection between sample data and population data, based on experimental results, and make an inference about the population. The activity states, “Susan has a bag of marbles. She chooses a marble and then replaces it. Of her ten trials, she picks a red marble 8 times. What is reasonable to conclude about the bag of marbles? Explain.” In the Learn activity, Problem 1b, page 226, students make comparative inferences about two populations. The problem states, “The weights of the players on two football teams are summarized in the box plots (Team A and B box plots shown). Express the difference in median weight in terms of the interquartile range.” Students are shown how to divide the difference in median weight by the interquartile range. In the Try activity, Problem 2, page 225, students practice using an inference to estimate a population mean. The problem states, “A random sample of ages {15, 5, 8, 7, 18, 6, 15, 17, 6, 15} of 10 children was collected from a population of 100 children. a. Calculate the sample mean age of the children and use it to estimate the population mean age. b. Calculate the MAD of the sample. c. Calculate the MAD to mean ratio d. Draw a dot plot for the ages and the mean age. e. Using the MAD to mean ratio and the dot plot, describe informally how carried the population ages are.” In Independent Practice, Problem 2, students infer about populations from a sample, given the mean and the MAD. The problem states, “You interviewed a random sample of 25 marathon runners and compiled the following statistics. Mean time to complete the race = 220 minutes MAD = 50 minutes What can you infer about the time to complete the race among the population of runners represented by your sample?” Students engage with extensive work and full intent of 7.SP.2 (Use data from a random sample to draw inferences about a population with an unknown characteristic of interest).

The materials reviewed for Math in Focus: Singapore Math Course 2 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade.

• There are 9 chapters, of which 5.5 address major work of the grade, or supporting work connected to major work of the grade, approximately 61%.

• There are 49 sections (lessons), of which 29.5 address major work of the grade, or supporting work connected to major work of the grade, approximately 60%.

• There are 147 days of instruction, of which 98 days address major work of the grade, or supporting work connected to the major work of the grade, approximately 67%.

A day-level analysis is most representative of the instructional materials because the days include all instructional learning components. As a result, approximately 67% of the instructional materials focus on major work of the grade.

The materials reviewed for Math in Focus: Singapore Math Course 2 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Digital materials provide “Math in Focus 2020 Comprehensive Alignment to CCSS: Course 2” located under Discover, Planning. This document identifies the standards taught in each chapter’s section allowing connections between supporting and major work to be seen. Examples include: 

• In Section 5.1, Complementary, Supplementary, and Adjacent Angles, Try, Problem 2, page 12, students find angle measures involving adjacent angles which connects the supporting work of 7.G.5 (Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure) with the major work 7.EE.4 (Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities). Students solve, “In the diagram below, ∠AOC, ∠COD and ∠DOB are adjacent angles on a straight line, $$\bar{AB}$$.” A diagram shows ∠AOC measures 126$$\degree$$, ∠COD measures x°, and ∠DOB measures 2x$$\degree$$, and students find the value of x.

• In Section 6.2, Scale Drawings and Lengths, Try, Problem 1, page 97, students calculate lengths and distances from scale drawings which connects the supporting work of 7.G.1 (Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale) with the major work of 7.RP.A (Analyze proportional relationships and use them to solve real-world and mathematical problems). Students solve, “The scale of a map is 1 inch: 15 miles. If the distance on the map between Matthew’s home and his school is 0.6 inch, find the actual distance in miles.”

• In Section 7.1 Radius, Diameter, and Circumference of a Circle, Independent Practice, Problem 18, page 141, students write an equation to find the distance around one quadrant of a circle which connects the supporting work of 7.G.4 (Know the formulas for the area and circumference of a circle and use them to solve problems) with the major work of 7.EE.4 (Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities). Students solve, “Find the distance around each quadrant. Use $$\frac{22}{7}$$ as an approximation for $$\pi$$.” A quadrant of a circle with a radius of 3.5 in. is shown. 

• In Section 8.4, Finding Probability of Events, Independent Practice, Problem 10, page 259, students calculate the probability of events which connects the supporting work of 7.SP.6 (Approximate the probability of a chance event) with the major work of 7.RP.3 (Use proportional relationships to solve multistep ratio and percent problems). Students solve, “At a middle school, 39% of the students jog and 35% of the students do aerobic exercise. Of the students who do aerobic exercise, 1 out 5 students also jogs. a. What percent of the students do both activities? b. Draw a Venn diagram to represent the information. c. What fraction of the students only jog? d. What is the probability of randomly selecting a student who does neither activity? Give your answer as a decimal.”

• In Section 9.3, Independent Events, Try, Problem 1, page 344, students use the multiplication rule and the addition rule of probability to solve problems involving independent events which connects the supporting work of 7.SP.8 (Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation) with the major work of 7.NS.3 (Solve real-world and mathematical problems involving the four operations with rational numbers). Students solve, “A game is played with a fair coin and a six-sided number die. To win the game, you need to randomly obtain heads on a fair coin and 3 on a fair number die. a. Complete the tree diagram. b. Find the probability of winning the game in one try.”

The materials reviewed for Math in Focus: Singapore Math Course 2 meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.

Digital materials provide “Math in Focus 2020 Comprehensive Alignment to CCSS: Course 2” found under Discover, Planning. This document identifies the standards taught in each chapter’s section showing connections between supporting to supporting work and major to major work. 

There are connections from supporting work to supporting work throughout the grade-level materials, when appropriate. Examples include:

• In Section 6.3, Scale Drawings and Areas, Independent Practice, Problem 1, connects the supporting work of 7.G.A (Draw construct and describe geometrical figures and describe the relationships between them) to the supporting work of 7.G.B (Solve real-life and mathematical problems involving angle measure, area, surface area, and volume). Students solve, “On a map, 1 inch represents an actual distance of 2.5 miles. The actual area of the lake is 12 square miles. Find the area of the lake on the map.”

• In Section 7.5, Volume of Prism, Independent Practice, Problem 12 connects the supporting work of 7.G.B (Solve real-life and mathematical problems involving angle measure, area, surface area, and volume) to the supporting work of 7.G.A (Draw construct and describe geometrical figures and describe the relationships between them). Students solve, “The volume of a triangular prism is 700 cubic centimeters. Two of its dimensions are given in the diagram. Find the height of the triangular base.” The triangular prism diagram shows a base of 10 cm and a width of 14 cm.

• In Section 8.2, Making Inferences About Populations, Independent Practice, Problem 2 connects the supporting work of 7.SP.A (Use random sampling to draw inferences about a population) to the supporting work of 7.SP.B (Draw informal comparative inferences about two populations). Students solve, “You interviewed a random sample of 25 marathon runners and compiled the following statistics. Mean time to complete the race=220 minutes. MAD=50 minutes. What can you infer about the time to complete the race among the population of runners represented by your sample?”

There are connections from major work to major work throughout the grade-level materials, when appropriate. Examples include:

• In Section 1.8, Operations with Decimals, Independent Practice, Problem 19 connects the major work of 7.NS.A (Apply and extend previous understanding of operations with fractions to add, subtract, multiply, and divide rational numbers) to the major work of 7.EE.B (Solve real-life and mathematical problems using numerical and algebraic expressions and equations). Students solve, “Evaluate each expression. 11.3 - 5.1 + 3.1 0.2 - 1.1.”

• In Section 3.3 Real-World Problems: Algebraic Equations, Independent Practice, Problem 7 connects the major work of 7.EE.B (Solve real-life and mathematical problems using numerical and algebraic expressions and equations) to the major work of 7.EE.A (Use properties of operations to generate equivalent expressions). Students solve, “Kevin wrote a riddle. A positive number is 5 less than another positive number. 6 times the lesser number minus 3 times the greater number is 3. Find the two positive numbers.”

• In Section 4.3, Real-World Problems: Direct Proportion, Independent Practice, Problem 1 connects the major work of 7.RP.A (Analyze proportional relationships and use them to solve real-world and mathematical problems) to the major work of 7.NS.A (Apply and extend previous understanding of operations with fractions to add, subtract, multiply, and divide rational numbers). Students solve, “m varies directly as n, and m = 14 when n = 7. a. Write an equation that relates m and n. b. Find m when n = 16. c. Find n when m = 30.”