## Math in Focus: Singapore Math

##### v1.5
###### Usability
Our Review Process

Title ISBN Edition Publisher Year
Teacher Assessment Guide Grade 3 9780358104964
Singapore Math Fact Fluency Grade 3 9780358105169
Student Edition Set Grade 3 9780358116790
Extra Practice and Homework Set Grade 3 9780358116899
CCSS Teacher Edition Set Grade 3 9780358116998
Teacher and Student Activity Cards Grade K 9780358104926
Teacher Assessment Guide Grade K 9780358104933
Singapore Math Fact Fluency Grade K 9780358105138
Student Edition Set Grade K 9780358116769
Extra Practice and Homework Set Grade K 9780358116868
CCSS Teacher Edition Set Grade K 9780358116967
Teacher Assessment Guide Grade 4 9780358104971
Singapore Math Fact Fluency Grade 4 9780358105176
Student Edition Set Grade 4 9780358116806
Extra Practice and Homework Set Grade 4 9780358116905
CCSS Teacher Edition Set Grade 4 9780358117001
Teacher Assessment Guide Grade 7 9780358105008
Student Edition Set Grade 7 9780358116837
Extra Practice and Homework Set Grade 7 9780358116936
CCSS Teacher Edition Set Grade 7 9780358117032
Teacher Assessment Guide Grade 8 9780358105015
Student Edition Set Grade 8 9780358116844
Extra Practice and Homework Set Grade 8 9780358116943
CCSS Teacher Edition Set Grade 8 9780358117049
Transition Guide Courses 1-3 9780358216643
Teacher Assessment Guide Grade 5 9780358104988
Singapore Math Fact Fluency Grade 5 9780358105183
Student Edition Set Grade 5 9780358116813
Extra Practice and Homework Set Grade 5 9780358116912
CCSS Teacher Edition Set Grade 5 9780358117018
Teacher Assessment Guide Grade 1 9780358104940
Singapore Math Fact Fluency Grade 1 9780358105145
Student Edition Set Grade 1 9780358116776
Extra Practice and Homework Set Grade 1 9780358116875
CCSS Teacher Edition Set Grade 1 9780358116974
Teacher Assessment Guide Grade 6 9780358104995
Singapore Math Fact Fluency Grade 6 9780358105190
Student Edition Set Grade 6 9780358116820
Extra Practice and Homework Set Grade 6 9780358116929
CCSS Teacher Edition Set Grade 6 9780358117025
Teacher Assessment Guide Grade 2 9780358104957
Singapore Math Fact Fluency Grade 2 9780358105152
Student Edition Set Grade 2 9780358116783
Extra Practice and Homework Set Grade 2 9780358116882
CCSS Teacher Edition Set Grade 2 9780358116981
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### Overall Summary

The materials reviewed for Math in Focus: Singapore Math Course 2 partially meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. However, in Gateway 2, the materials do not meet expectations for rigor and practice-content connections.

###### Alignment
Partially Meets Expectations
Not Rated

### Focus & Coherence

The materials reviewed for Math in Focus: Singapore Math Course 2 meet expectations for focus and coherence. For focus, the materials assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards. For coherence, the materials are coherent and consistent with the CCSSM.

##### Gateway 1
Meets Expectations

#### Criterion 1.1: Focus

Materials assess grade-level content and give all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials reviewed for Math in Focus: Singapore Math Course 2 meet expectations for focus as they assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards.

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Materials assess the grade-level content and, if applicable, content from earlier grades.

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)

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Materials give all students extensive work with grade-level problems to meet the full intent of grade-level standards.

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).

#### Criterion 1.2: Coherence

Each grade’s materials are coherent and consistent with the Standards.

The materials reviewed for Math in Focus: Singapore Math Course 2 meet expectations for coherence. The majority of the materials, when implemented as designed, address the major clusters of the grade, and the materials have supporting content that enhances focus and coherence simultaneously by engaging students in the major work of the grade. The materials also include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade. The materials partially have content from future grades that is identified and related to grade-level work and relate grade-level concepts explicitly to prior knowledge from earlier grades.

##### Indicator {{'1c' | indicatorName}}

When implemented as designed, the majority of the materials address the major clusters of each grade.

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.

##### Indicator {{'1d' | indicatorName}}

Supporting content enhances focus and coherence simultaneously by engaging students in the 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.”

##### Indicator {{'1e' | indicatorName}}

Materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.

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.”

##### Indicator {{'1f' | indicatorName}}

Content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

The materials reviewed for Math in Focus: Singapore Math Course 2 partially meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

Materials relate grade-level concepts to prior knowledge from earlier grades. Recall Prior Knowledge highlights the concepts and skills students need before beginning a new chapter. What have students learned? states the learning objectives and prior knowledge relevant to each chapter. The Scope and Sequence shows the progressions of standards from Course 1 through Course 3. The online materials do not include the standard notation. Examples include:

• In Chapter 2, Learning Continuum, What have students learned? states, “In Course 1 Chapter 7, students have learned: Using letters to represent numbers. (6.EE.2, 6.EE.2a, 6.EE,2b, 6.EE.6) Evaluating algebraic expressions. (6.EE.2, 6.EE.2c) Simplifying algebraic expressions. (6.EE.3, 6.EE.4), Expanding and factoring algebraic expressions. (6.EE.2, 6.EE.3, 6.EE.4)”

• In Chapter 4, Learning Continuum, What have students learned? states, “In course 1 Chapters 4, 5, 6, and 9, students have learned: Comparing two quantities. (6.RP.1, 6.RP.3d), Equivalent ratios. (6.RP.3a), Rates and unit rates. (6.RP.2, 6.RP.3), Real-world problems: speed and average speed. (6.RP.3, 6.RP.3b), Real world problems: percent. (6.RP.3c), Points on the coordinate plane. (6.NS.6, 6.NS.6b, 6.NS.6c, 6.NS.8, 6.G.3)”

• In Chapter 5, Chapter Overview, Math Background, states, “In grade 4, students learned to classify angles as acute, obtuse, right or straight. They also developed knowledge of parallel and perpendicular lines. In Grade 5, students learned to classify triangles according to their lengths of sides and angle measures.”

• In Chapter 6, Recall Prior Knowledge, states, “In previous grades, students learned to identify a ray that extends in one direction and to use geometric notation to write rays and angles in degrees. They also learned to measure angles in degrees using protractors.”

• In Chapter 8, Recall Prior Knowledge, states, “In Course 1, students learned to identify measures of variation. They divided a data set into quartiles and identified the interquartile range. Students drew and interpreted box-and-whisker plots. they interpreted data and decided what was ‘typical’ or most likely.”

Materials provide grade-level standards of upcoming learning to future grades with no explanation of the relationship to grade-level content. What will students learn next? states the learning objectives from the following chapters of future courses to show the connection between the current chapter and what students will learn next. The Scope and Sequence shows the progressions of standards from Course 1 through Course 3. Examples include:

• In Chapter 3, Learning Continuum, What will students learn next? states, “In Course 3 Chapter 4 students will learn: Solving linear equations with one variable. (8.EE.7b), Identifying the number of solutions to a linear equation. (8.EE.7a), Solving for a variable in a two-varaible equation. (8.EE.7b), Solving linear inequalities with one variable.”

• In Chapter 4, Learning Continuum, What will students learn next? states, “In Course 3 Chapter 5, students will learn: Finding and interpreting slopes of lines. (8.EE.6), Understanding slope-intercept form. (8.EE.6), Writing linear equations. (8.EE.6), Real-world problems: linear equations. (8.EE.5)”

• In Chapter 6, Learning Continuum, What will students learn next? states, “In Course 3 Chatpers 9 and 10, students will learn: Dilations. (8.G.3), Understanding and applying congruent figures. Understanding and applying similar figures. (8.G.5)”

• In Chapter 8, Statistics and Probability, Learning Continuum, What will students learn next? states, “In Course 2 Chapter 9, students will learn: Probability of compound events. (7.SP.8), Independent events. (7.SP.8), Dependent events. (7.SP.8), In Course 3 Chapter 12, students will learn: Two-way tables. (8.SP.4)”

• In Chapter 9, Learning Continuum, What will students learn next? states, “In Course 3 Chapter 12, students will learn: Two-way tables. (8.SP.4) In High School, students will learn: Conditional probability and the rules of probability. (S-CP), Using probability to make decisions (S-MD).”

##### Indicator {{'1g' | indicatorName}}

In order to foster coherence between grades, materials can be completed within a regular school year with little to no modification.

The materials reviewed for Math in Focus: Singapore Math Course 2 can be completed within a regular school year with little to no modification to foster coherence between grades.

Recommended pacing information is found in the Teacher’s Edition, Chapter Planning Guide and online under Discover, Planning, Common Core Pathway and Pacing Course 2. Each section consists of one or more Engage-Learn-Try focus cycles followed by Independent Practice. As designed, the instructional materials can be completed in 147 days.

• There are 9 instructional chapters divided into sections of 120 instructional days.

• There is one day for each chapter’s instructional beginning consisting of Chapter Opener and Recall Prior Knowledge, for a total of 9 additional days.

• There is one day for each chapter’s closure consisting of Chapter Wrap-Up, Chapter Review, Performance Task, and Project work, for a total of 9 additional days.

• There is one day for each chapter’s Assessment, for a total of 9 additional days.

The online Common Core Pathway and Pacing Course 2 states the instructional materials can be completed in 146 days, one instructional day added to Section 2.1 in the printed Teacher’s Edition. For the purpose of this review the Chapter Planning Guide provided by the publisher in the Teacher’s Edition was used.

### Rigor & the Mathematical Practices

The materials reviewed for Math in Focus: Singapore Math Course 2 do not meet expectations for rigor and balance and practice-content connections. The materials reflect the balances in the Standards and help students develop conceptual understanding, procedural skill and fluency, and application. However, the materials do not make meaningful connections between the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

##### Gateway 2
Does Not Meet Expectations

#### Criterion 2.1: Rigor and Balance

Materials reflect the balances in the Standards and help students meet the Standards’ rigorous expectations, by giving appropriate attention to: developing students’ conceptual understanding; procedural skill and fluency; and engaging applications.

The materials reviewed for Math in Focus: Singapore Math Course 2 meet expectations for rigor. The materials give attention throughout the year to procedural skill and fluency, spend sufficient time working with engaging applications of mathematics, and do not always treat the three aspects of rigor together or separately. The materials partially develop conceptual understanding of key mathematical concepts.

##### Indicator {{'2a' | indicatorName}}

Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

The materials reviewed for Math in Focus: Singapore Math Course 2 partially meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

Students have opportunities to develop conceptual understanding of mathematical concepts during the Engage and Learn portions of the lessons. Examples include:

• In Section 1.3, Adding Integers, Learn, Problem 1, page 38, students use counters to model addition. The problem states, “Suppose the temperature was -8°F at 7 a.m. Five hours later, the temperature has risen 10°F. Find the new temperature.” Students develop conceptual understanding of 7.NS.1 (Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram).

• In Section 2.4, Expanding Algebraic Expressions, Engage, page 153, students use algebra tiles to expand expressions. The materials state, “Use (green tile shown) to represent +x and (orange tile shown ) to represent +1. Show how you expand 2(2x + 6) and $$\frac{1}{2}$$(2x + 6). Share your method.” Students develop conceptual understanding of 7.EE.1 (Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients).

• In Section 5.4, Interior and Exterior Angles, Activity, page 47, students work in pairs to discover the property of interior angles of a triangle. The materials state, “1) Draw and cut out a triangle. Label the three interior angles of the triangle as 1, 2, and 3. 2) Cut out the three angles. Then, arrange them on a straight line. What do you notice about the sum of the measures of the three interior angles?” Students develop conceptual understanding 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).

• In Section 8.1, Random Sampling Methods, Learn, Problem 3c, page 215, students use a random number table to determine a random sample. The problem states, “Suppose you want to pick a random sample of 30 people from a town that has 500 residents. You can first assign a unique 3-digit number from 001 to 500 to each resident. Then, use a random number table like the one shown below to select the members of the sample.” Students develop conceptual understanding of 7.SP.1 (Understand that statistics can be used to gain information about a population by examining a sample of the population).

• In Section 8.4, Finding the Probability of Events, Engage, page 245, students use pictures of cards to determine the probability of an event occurring. The materials state, “Suppose you randomly pick two of the cards below. What is the probability of picking two cards with the same letter? Explain your answer.” Four pink cards labeled A-D and four purple cards labeled A-D are shown. Students develop conceptual understanding of 7.SP.5 (Summarize numerical data sets in relation to their context).

Students have opportunities to demonstrate conceptual understanding through Try activities, which are guided practice opportunities to reinforce new learning. The Independent Practice provides limited opportunities for students to continue the development of conceptual understanding. Examples include:

• In Section 5.4, Interior and Exterior Angles, Independent Practice, Problem 2, page 55, students use the angle sum of a triangle to find unknown angle measures. The problem states, “The diagrams may not be drawn to scale. Find the value of y. In the diagrams for 4 to 6, ACis a straight line.” Students are shown a triangle with interior angles labeled 18° and 26°. Students independently practice conceptual understanding 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).

• In Section 8.1, Random Sampling Methods, Independent Practice, Problem 7, page 220, students describe how to implement each of the three sampling methods for a given situation. The problem states, “2,000 runners participated in a marathon. You want to randomly choose 60 of the runners to find out how long it took each one to run the race. Describe how you would select the 60 runners if you use a a) random sampling method. b) systematic sampling method. c) stratified sampling method.” Students independently practice conceptual understanding of 7.SP.1 (Understand that statistics can be used to gain information about a population by examining a sample of the population, generalizations about a population from a sample are valid only if the sample is representative of that population).

##### Indicator {{'2b' | indicatorName}}

Materials give attention throughout the year to individual standards that set an expectation for procedural skill and fluency.

The materials reviewed for Math in Focus: Singapore Math Course 2 meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

Students have opportunities to develop procedural skill and fluency during the Engage and Learn portions of the lessons. Examples include:

• In Section 1.2, Writing Rational Numbers as Decimals, Learn, Problem 1, page 23, students write rational numbers as repeating decimals using long division. The problem states, “Since $$\frac{1}{3}$$ means 1 divided by 3, you can write $$\frac{1}{3}$$ as a decimal using long division. When you divide 1 by 3, the division process will not terminate with a remainder of 0. The digit 3 keeps repeating infinitely. A decimal, such as 0.333…, is called a repeating decimal. For the repeating decimal 0.333…, the digit 3 repeats itself. you can write 0.333… as $$0.\bar{3}$$, with a bar above the repeating digit 3. So, 0.333… = $$0.\bar{3}$$.” Students develop procedural skill and fluency of 7.NS.2d (Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats).

• In Section 3.3, Real-World Problems: Algebraic Equations, Learn, Problem 4, page 235, students translate descriptions into algebraic equations. The problem states, “Ivan has 12 more comic books than Hana. If they have 28 comic books altogether, how many comic books does Ivan have? Let the number of comic books that Hana has be x. Then, the number of comic books that Ivan has is x + 12. Because they have 28 books altogether, x + (x + 12) = 28. Number of books that Ivan has: x + 12 = 8 + 12 = 20. Ivan has 20 comic books.” Students develop procedural skill and fluency of 7.EE.B.4a (Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently).

• In Section 4.3, Real-World Problems: Direct Proportion, Independent Practice, Problem 10, page 315, students write a proportion to find an unknown quantity given one of the quantities. The problem states, “It costs $180 to rent a car for 3 days. Find the cost of renting a car for 1 week.” Students independently engage in routine application of 7.RP.2 (Recognize and represent proportional relationships between quantities). • In Section 7.6, Real-World Problems: Surface Area and Volume, Independent Practice, Problem 3, page 188, students find the volume and surface area of a composite solid made up of a triangular prism and a rectangular prism. The problem states, “Mr. Turner builds a shed to store his tools. The shed has a roof that is in the shape of a triangular prism. a. Find the amount of space the shed occupies. b. Find the surface area of the shed, including its floor.” A diagram with dimensions is provided. Students independently engage in routine application of 7.G.6 (Solve real-world and mathematical problems involving area, volume and surface area of two-and three- dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms). Students have opportunities throughout the materials to engage in non-routine application of mathematics. Examples include: • In Section 1.5, Multiplying and Dividing Integers, Engage, page 63, students represent a multiplication situation using counters. The materials state, “Show 2 × 4 using (picture of yellow and orange counter shown). How do you show 2 × (-4)? Create a real-world problem to model each situation. Share your real-world problems.” Students engage in non-routine application of 7.NS.2 (Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers). • In Section 1.7, Operations with Fractions and Mixed Numbers, Engage, page 91, students apply operations with rational numbers in a real-world context. The materials state, “A clock’s battery is running low. Every 6 hours, the clock slows down by $$\frac{1}{2}$$ hour. How do you find out how much time the clock slows down by in 1 hour? Share your method.” Students engage in non-routine application of 7.NS.3 (Solve real-world and mathematical problems involving the four operations with rational numbers). • In Section 2.7, Real-World Problems: Algebraic Reasoning, Enage, page 192. students work in pairs to solve a percent problem involving algebraic expressions. The materials state, “Ms. Evans bought a total of 60 pens and pencils. There was an equal number of pens and pencils. She gave x percent of the pens and y percent of the pencils to her students. Use algebraic reasoning to write an algebraic expression for the number of pens and pencils that she gave her students. Share your reasoning.” Students engage in non-routine application of 7.EE.3 (Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form). • In Chapter 8, Performance Task, Problem 2, page 293, students find the probability of winning if they draw two number cards and the difference is 3 or more. The problem states, “In a game, you and your friend are asked to each select a card from a deck of ten cards with the numbers 1 to 10. Your friend selects a card from the deck. Then, you select a card from the ones remaining in the deck. You do not know your friend’s number. You win if the difference between your number and your friend’s number is at least 3. a) For which of your friend’s numbers do you have the greatest chance of winning? b) For which of your friend’s numbers do you have the least chance of winning? c) What is the probability that you will win?” Students independently engage in non-routine application of 7.SP.8 (Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation). ##### Indicator {{'2d' | indicatorName}} 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. The materials reviewed for Math in Focus: Singapore Math Course 2 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 the materials. For example: • In Section 1.7, Operations with Fractions and Mixed Numbers, Learn, Problem 2, page 86, students multiply rational numbers. The problem states, “Evaluate $$-\frac{3}{7} ⋅ \frac{8}{15}$$.”Students engage in procedural skill and fluency of 7.NS.2c (Apply properties of operations as strategies to multiply and divide rational numbers). • In Section 3.5, Real-World Problems: Algebraic Inequalities, Independent Practice, Problem 10, page 266, students write and solve inequalities. The problem states, “A cab company charges$0.80 per mile plus $2 for tolls. Rachel has at most$16 to spend on her cab fare. Write and solve an inequality for the maximum distance she can travel. Can she afford to take a cab from her home to an airport that is 25 miles away?” Students engage in application of 7.EE.4b (Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem).

• In Section 8.3, Defining Outcomes, Events and Sample Space, Try, Problem 1, page 237, students practice identifying outcomes, samples spaces, and events. The problem states, “Jake spun the spinner on the right and recorded the numbers where the spinner lands. a) List all the possible outcomes. b) State the number of outcomes in the sample space.” Students engage in conceptual understanding of 7.SP.7a (Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events).

Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials. For example:

• In Section 1.4, Subtracting Integers, Try, Problem 3, page 53, students use the additive inverse property to subtract integers. The problem states, “A fishing boat drags its net 35 feet below the ocean’s surface. Then, it lowers the net by an additional 12 feet. Find the fishing net’s new position relative to the ocean’s surface.” Students develop procedural skill and fluency and apply the mathematics of 7.NS.1c (Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q)).

• In Section 2.1, Adding Algebraic Terms, Learn, Problem 1, page 132, students simplify algebraic expressions with decimal or fractional coefficients by adding like terms. The problem states, “Simplify the expressions 0.9p + 0.7p. Represent the term 0.9p with nine 0.1p sections and the term 0.7p with seven 0.1p sections. From the bar model, 0.9p + 0.7p = 1.6p. The sum is the total number of colored sections in the bar model.” Students develop conceptual understanding and build procedural skill and fluency of 7.EE.1 (Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients).

• In Section 7.3, Real-World Problems: Circles, Try, Problem 1, page 156, students use the formula for area of a circle to solve real-world problems. The problem states, “Alex recycled some old fabric to make a rug. He cut out a quadrant and two semicircles to make the rug. Find the area of the rug. Use $$\frac{22}{7}$$ as an approximation for $$\pi$$.” A diagram of the rug with dimensions is provided. Students develop procedural skill and fluency and apply the mathematics of 7.G.4 (Know the formulas for the area and circumference of a circle and use them to solve problems).

#### Criterion 2.2: Math Practices

Materials meaningfully connect the Standards for Mathematical Content and Standards for Mathematical Practice (MPs).

The materials reviewed for Math in Focus: Singapore Math Course 2 do not meet expectations for practice-content connections. The materials support the intentional development of MP3 and partially support the intentional development of MP6. The materials do not support the intentional development of MPs 1, 2, 4, 5, 7, and 8.

##### Indicator {{'2e' | indicatorName}}

Materials support 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 materials reviewed for Math in Focus: Singapore Math Course 2 do not 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.

Students have limited opportunities to make sense of problems and persevere in solving them in connection to grade-level content, identified as mathematical habits in the materials. Student materials do not provide guidance, teacher guidance is repetitive, not specific, and activities are scaffolded preventing intentional development of the full intent of MP1. Examples include:

• In Chapter 3, Algebraic Equations and Inequalities, Put On Your Thinking Cap! Problem 1, page 268, students solve real-world problems using algebraic equations. The problem states, “Jamar is five times as old as Kylie. Larissa is five times as old as Jamar. Mitchell is twice as old as Larissa. The sum of their ages is the age of Nora. Nora just turned 81. How old is Jamar?” Teacher guidance states, “You may want to guide students on applying the various heuristics using the problem-solving heuristics poster. Refer students to the corresponding teacher resources for prompts and worked out solutions.” Teacher guidance gives a generic reference to have students use the heuristics poster which is repeated throughout the materials.

• In Chapter 4, Proportion and Percent of Change, Put On Your Thinking Cap! Problem 1, page 358, students solve real-world problems using proportional relationships. The problem states, “Ms. Davis plans to drive from Town P to Town Q, a distance of 350 miles. She hopes to use only 12 gallons of gasoline. After traveling 150 miles, she checks her gauge and estimates that she has used 5 gallons of gasoline. At this rate, will Ms. Davis arrive at Town Q before stopping for gasoline? Justify your answer.” Teacher guidance states, “You may want to guide students on applying the various heuristics using the problem-solving heuristics poster. Refer students to the corresponding teacher resources for prompts and worked out solutions.” Teacher guidance gives a generic reference to have students use the heuristics poster which is repeated throughout the materials.

• In Chapter 7, Put on Your Thinking Cap!, Problem 2, page 190, students solve a real-world problem using their understanding of circumference of circles and quadrants to find the distance of a shaded part. The problem states, “A cushion cover design is created from a circle of radius 7 inches and 4 quadrants. Find the total area of the shared parts of the design. Use $$\frac{22}{7}$$ as an approximation for $$\pi$$.” Teacher guidance states, “Go through the problem using the four-step problem-solving model. Students may need some help getting started after they have understood the problem. Suggest to students that they start by studying the figure and determining what shapes are involved. They can then make a plan as to which formula to use and in what order.” Teacher guidance gives a generic reference to have students use the four-step problem-solving method which is repeated throughout the materials.

• In Chapter 9, Probability of Compound Events, Put on Your Thinking Cap! Problem 1, page 364, students solve real-world problems using their understanding of dependent events to find the probability of an event, without replacement. The problem states, “If there are 12 green and 6 red apples, find the probability of randomly choosing three apples of the same color in a row, without replacement. Show your work.” Teacher guidance states, “You may want to guide students on applying the various heuristics using the problem-solving heuristics poster. Refer students to the corresponding teacher resources for prompts and worked out solutions.” Teacher guidance gives a generic reference to have students use the heuristics poster which is repeated throughout the materials.

Materials identify focus Mathematical Habits for MP1 in the Chapter Planning Guide and in the Section objectives. However, these Mathematical Habits are not intentionally addressed in the activities and problems. Examples include:

• Section 2.7, Real-World Problems: Algebraic Reasoning, is noted as addressing MP1 on pages 187-196 in the Standards for Mathematical Practice Chart, Chapter Planning Guide, and Section Objectives. However, no identified opportunities for students to make sense of problems and persevere in solving them are provided.

• Section 6.4, Real-World Problems: Percent Increase and Decrease, is noted as addressing MP1 on pages 345-356 in the Standards for Mathematical Practice Chart, Chapter Planning Guide, and Section Objectives. However, no identified opportunities for students to make sense of problems and persevere in solving them are provided.

Students have limited opportunities to reason abstractly and quantitatively in connection to grade-level content, identified as mathematical habits in the materials. Student guidance is not provided in the materials, teacher guidance is repetitive, not specific, and activities are scaffolded preventing intentional development of the full intent of MP2. Examples include:

• In Section 2.2, Subtracting Algebraic Terms, Independent Practice, Problem 21, page 144, students write algebraic expressions for finding the area of rectangles, and then simplify the expression with rational coefficients by subtracting like terms. The problem states, “Luke simplified the algebraic expression $$\frac{3}{2}x - \frac{1}{3}x$$ as shown below: $$\frac{3}{2}x$$ - $$\frac{1}{3}x$$ = $$\frac{18}{12}x$$ - $$\frac{4}{12}x$$ = $$\frac{14}{12}x$$ Is Luke’s simplification correct? Why or why not?” Teacher guidance states, “Assesses students’ ability to simplify an algebraic expression with unlike fractional coefficients. They are required to recognize that the given solution is correct but is not in simplest form.” The materials misidentify MP2, as students do not consider units involved in a problem, attend to the meaning of quantities, nor understand the relationships between problem scenarios and mathematical representations.

• In Section 6.1, Constructing Triangles, Independent Practice, Problem 10, page 90, students recognize that many triangles can be created given the sum of measures of three angles. The problem states, “Suppose you are given three angle measures with a sum of 180. Can you construct a triangle given this information? Can you construct other different triangles? Explain.” Teacher guidance states, “Assesses students’ ability to recognize that many triangles can be created given the sum of measures of three angles. Changing the side lengths of this kind of triangle will make many similar triangles.” Teacher guidance gives a generic reference to assess students’ abilities which is repeated throughout the materials.

• In Section 8.6, Developing Probability Models, Activity, Problem 6, page 283, students compare the theoretical and experimental probability of randomly selecting a number from 0 to 9. The problem states, “Compare each of the experimental probability models you made with the theoretical probability model at the beginning of this activity. What effect does increasing the number of selected digits have on the experimental probabilities? Which experimental probability model resembles the theoretical probability model more closely? Explain.” Teacher guidance states, “In 6, students compare the two experiments with the theoretical model and graph. Pose the following question to students and prompt them for their reasoning. Does the second experiment more closely resemble the theoretical probability? Why? You may want to conclude the activity by having students share their responses with the class.” The materials misidentify MP2 in this problem, students do not consider units involved in a problem, attend to the meaning of quantities, nor understand the relationships between problem scenarios and mathematical representations.

• In Section 9.1, Compound Events, Independent Practice, Problem 13c, page 326, students recognize outcomes and realize that two simple events can be switched and the number of outcomes still remains the same. The problem states, “For a game, Jesse first rolls a fair four-sided number die labeled 1 to 4. The result recorded is the number facing down. Then, he randomly draws a ball from a box containing two different colored balls. If Jesse first draws a colored ball and then rolls the four-sided number die, will the number of possible outcomes be the same? Explain your reasoning.” Teacher guidance states, “Assess students’ ability to draw a tree diagram, recognize the outcomes, and realize that the two simple events can be switched and the number of outcomes still remains the same.” Teacher guidance gives a generic reference to assess students’ abilities which is repeated throughout the materials.

Materials identify focus Mathematical Habits for MP2 in the Chapter Planning Guide and in the Section objectives. However, these Mathematical Habits are not intentionally addressed in the activities and problems. Examples include:

• Section 1.8, Operations with Decimals, is noted as addressing MP2 on pages 97-110 in the Standards for Mathematical Practice Chart, Chapter Planning Guide, and Section Objectives. However, no identified opportunities for students to reason abstractly and quantitatively are provided.

• Chapter 6, Geometric Construction, Performance Task, is noted as addressing MP2 on pages 119-120 in the Standards for Mathematical Practice Chart, Chapter Planning Guide, and Section Objectives. However, no identified opportunities for students to reason abstractly and quantitatively are provided.

##### Indicator {{'2f' | indicatorName}}

Materials support 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 materials reviewed for Math in Focus: Singapore Math Course 2 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.

Students have the opportunity to construct viable arguments in connection to grade-level content leading to the intentional development of MP3, identified as mathematical habits in the materials. However, the teacher guidance is often repetitive, not specific, and often distracts from the intentional development of MP3. Examples include:

• In Section 1.1, Representing Rational Numbers on the Number Line, Activity, Problem 3, page 15, students construct viable arguments when locating rational numbers on a number line. “What is another way to locate the rational numbers on the number line? Explain your answer.” Teacher guidance states, “Display the task and give students time to work on it in pairs. Invite students to share their completed number line. Prompt them to share explanations and emphasize: how to convert fractions to decimals and vice versa. How to determine additional segments needed to accurately place the rational numbers. The correct placement of positive and negative numbers. Reasonable approximations, such as 3.6 is a little more than 3.5, so 3.6 is a little more than halfway between 3 and 4. Identify positions of opposites, for instance, -3.6 needs to be the same distance from 0 as 3.6 is from 0.”

• In Section 4.3, Real-World Problems: Direct Proportion, Independent Practice, Problem 20, page 316, students construct viable arguments. The problem states, “Laila wants to buy some blackberries. Three stores sell blackberries at different prices. Which store has the best deal? Explain.” Three bowls of blackberries with different prices per pound are shown. Teacher guidance states, “assesses students’ ability to compare unit rates to determine the best deal, They may need to be reminded that there are 16 ounces in a pound.” While this teacher guidance does not intentionally develop MP3, students do have the opportunity to construct a viable argument.

Students have the opportunity to critique the reasoning of others in connection to grade-level content leading to the intentional development of MP3, identified as mathematical habits in the materials. However, the teacher guidance is often repetitive, not specific, and distracts from the intentional development of MP3. Examples include:

• In Section 3.1, Identifying Equivalent Equations, Independent Practice, Problem 12, page 220, students critique the reasoning of others when finding equivalent equations. The problem states, “Chris was asked to write an equation equivalent to $$\frac{2}{3}$$x = 3 - x. He wrote the following: $$\frac{2}{3}$$x = 3 - x, $$\frac{2}{3}$$x ⋅ 3= 3 ⋅ 3 - x, 2x = 9 - 3x. Chris concluded that $$\frac{2}{3}$$x = 3 - x and 2x = 9 - x are equivalent equations. Do you agree with his conclusion? Give a reason for your answer.” Teacher guidance states, “assesses students’ ability to identify a mistake in the expansion on the right side of the equation. This is a good opportunity to point out the importance of using parentheses when distributing.” While this teacher guidance does not intentionally develop MP3, students do have the opportunity to critique the reasoning of others.

• In Section 4.5, Percent Increase and Decrease, Math Sharing, page 342, students critique the arguments of others when solving direct proportion problems involving percent. The materials state, “Caleb has 40 magnets. Zara has 50 magnets. Zara says that she has 25% more magnets than Caleb, hence, Caleb has 25% fewer magnets than her. Do you agree with Zara? Discuss.” Teacher guidance states, “Pose the problem to students. Have students express the number of Zara’s magnets as a percent of the number of Caleb’s magnets, $$\frac{50}{40}$$ ⋅ 100% = 125%. Lead them to see that Zara has 25% more magnets than Caleb. Prompt them to explain why they have to use 40 as a base when calculating the percent. Then, have students express the number of Caleb’s magnets as a percent of the number of Zara’s magnets, $$\frac{40}{50}$$ ⋅ 100% = 80%. Lead them to see that Caleb has 20% fewer magnets than Zara. Prompt them to explain why they have to use 50 as a base when calculating the percent in this instance. Reiterate the importance of using the correct base when calculating a percent of one quantity over another.”

Math Journal Activities provide opportunities for students to engage in the intentional development of MP3. However, the teacher guidance is often repetitive, not specific, and distracts from the intentional development of MP3. Examples include:

• In Chapter 2, Algebraic Expressions, Math Journal, page 197, students construct viable arguments and critique the reasoning of others when simplifying expressions. The materials state, “Brielle expanded and simplified the expression 6(x+3) - 2(x+1) + 5 as follows: 6(x + 3) − 2(x + 1) + 5 = 6x + 3 − 2x + 1 + 5 = 6x − 2x + 3 + 1 + 5 = 4x + 9. Explain to Briella her mistakes and show the correct solution.” Teacher guidance states, “Review with students the various strategies learned in this chapter. Encourage students to work independently. Error analysis is a useful activity because it leads to fewer mistakes in the future.” While this teacher guidance does not intentionally develop MP3, students do have the opportunity to construct a viable argument and critique the reasoning of others.

• In Chapter 4, Proportion and Percent of Change, Math Journal, page 357, students construct viable arguments and critique the reasoning of others. The materials state, “Ameila has a box of 150 beads that are either red, purple, or yellow. 20% of the beads are read and $$\frac{2}{5}$$ of the remaining beads are yellow. Ameila worked out the number of yellow beads as follows: 100% - 20% = 80%, $$\frac{2}{5}$$ ⋅ 150 = 60, There were 60 yellow beads. Explain to Ameila her mistake and show her the correct solution.” Teacher guidance states, “Review with students the various strategies learned in this chapter. Encourage students to write and explain their steps clearly to avoid such mistakes.” While this teacher guidance does not intentionally develop MP3, students do have the opportunity to construct a viable argument and critique the reasoning of others.

Materials identify focus Mathematical Habits in the Standards for Mathematical Practice Chart, Chapter Planning Guide, and in the Section Objectives. However, these mathematical habits are not intentionally addressed in the activities and problems. Examples include:

• Section 5.4, Interior and Exterior Angles, is noted as addressing MP3 on pages 47-58  in the Standards for Mathematical Practice Chart, Chapter Planning Guide, and Section Objectives. However, no opportunities for students to construct arguments or critique the reasoning of others is provided in the lesson.

• Section 7.1, Radius, Diameter, and Circumference of a Circle, is noted as addressing MP3 on pages 127-142  in the Standards for Mathematical Practice Chart, Chapter Planning Guide, and Section Objectives. However, no opportunities for students to construct arguments or critique the reasoning of others is provided in the lesson.

##### Indicator {{'2g' | indicatorName}}

Materials support 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 materials reviewed for Math in Focus: Singapore Math Course 2 do not 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.

Students have limited opportunities to model with mathematics in connection to grade-level content, identified as mathematical habits in the materials. Additionally, MP4 is referred to as “use mathematical models” in the student and teacher materials. Students are told which models to use and teacher guidance is often repetitive, not specific, and activities are scaffolded preventing intentional development of the full intent of MP4. Examples include:

• In Chapter 2, Algebraic Expressions, Put On Your Thinking Cap, Problem 2, page 199, students convert degrees Fahrenheit to degrees Celsius. The problem states, “Steven and his father are from Singapore, where the temperature is measured in degrees Celsius. While visiting downtown Los Angeles, Steven saw a temperature sign that read 72°F. He asked his father what the equivalent temperature was in °C. His father could not recall the Fahrenheit-to-Celsius conversion formula. C = $$\frac{5}{9}$$(F - 32) However, he remembered that water freezes at 0$$\degree$$C or 32$$\degree$$F and boils at 100$$\degree$$C or 212$$\degree$$F. Using these two pieces of information, would you be able to help Steven figure out the above conversion formula? Explain.” Teacher guidance states, “Requires students to solve a problem using algebraic reasoning. Go through the problem using the four-step problem-solving model. Students may need some help getting started after they have understood the problem. If students seem stuck, tell them that a diagram with the given information might help. Encourage them to think of the two scales a double number line, in which 0$$\degree$$C equals 32$$\degree$$F and 100$$\degree$$C to 212$$\degree$$F. So a change in 180 degrees in Fahrenheit correspond to 100 degrees in Celsius. 1 unit in Celsius = $$\frac{180}{100}$$ or $$\frac{9}{5}$$ units in Fahrenheit, and 1 unit in Fahrenheit equals $$\frac{100}{180}$$ or $$\frac{5}{9}$$ units in Celsius. Remind students that scales start at different places. 0$$\degree$$C equals 32$$\degree$$F. If they continue to have trouble, help them think through the expression F = $$\frac{9}{5}$$C + 32 or C = $$\frac{5}{9}$$(F - 32).” Students are told what type of model to use (double number line), and teacher guidance gives a generic reference to have students use the four-step problem-solving method which is repeated throughout the materials.

• In Chapter 3, Algebraic Equations and Inequalities, Put On Your Thinking Cap!, Problem 2, page 269, states, “Sara can buy 40 pens with a sum of money. She can buy 5 more pens if each pen costs $0.05 less. a. How much does each pen cost? b. If Sara wants to buy at least 10 more pens with the same amount of money how much can each pen cost at most?” Teacher guidance states “requires students to solve a real-world problem using algebraic reasoning. The challenge is in writing an equation and inequality to represent the situation. Go through the problem using the four-step problem-solving model. Have students work in pairs or small groups. Encourage them to discuss and share strategies.” Teacher guidance gives a generic reference to have students use the four-step problem-solving method which is repeated throughout the materials. • In Chapter 9, Probability of Compound Events, Put On Your Thinking Cap!, Problem 3, page 365, students find the probability of dependent events. The problem states, “Diego plans to visit Australia for a vacation, either alone or with a friend. Whether he goes alone or with a friend is equally like. If he travels with a friend, there is a 40% chance of him joining a guided tour. If he travels alone, there is an 80% chance of him joining a guided tour. a) What is the probability of Diego traveling with a companion and not joining a guided tour? b) What is the probability of Diego joining a guided tour?” Teacher guidance states, “requires students to recognize that the first event is whether Diego goes alone or with someone, and the second event is dependent on the occurrence of the first event. Students need to use the concept of complementary events to find the probability. Go through the problem using the four-step problem-solving model. Students may need some help getting started after they have understood the problem. Suggest to students that they start by drawing a tree diagram.” Teacher guidance gives a generic reference to have students use the four-step problem-solving method which is repeated throughout the materials. Additionally, students are encouraged to use a tree diagram. Materials identify focus Mathematical Habits for MP4 in the Chapter Planning Guide and in the Section objectives. However, these Mathematical Habits are never intentionally addressed in the activities and problems. Examples include: • Section 1.3, Adding Integers, is noted as addressing MP4 on pages 35-40 in the Standards for Mathematical Practice Chart, Chapter Planning Guide, and Section Objectives. However, no identified opportunities for students to model mathematics are provided. • Section 7.3, Real-World Problems: Circles, is noted as addressing MP4 on pages 151-158 in the Standards for Mathematical Practice Chart, Chapter Planning Guide, and Section Objectives. However, no identified opportunities for students to model mathematics are provided. Students have limited opportunities to use appropriate tools strategically in connection to grade-level content, identified as mathematical habits in the materials. Teacher guidance is repetitive, not specific, and activities are scaffolded preventing intentional development of the full intent of MP5. Examples include: • In Chapter 6, Geometric Construction, Put On Your Thinking Cap!, Problem 1, page 112, students find the area of an enlarged triangle. The problem states, “Construct triangle ABC, where AB = AC, BC = 8cm and m∠ABC= 37$$\degree$$. Triangle ABC is enlarged to produce triangle DEF by a scale factor of 2.5. Find the area of triangle DEF.” Teacher guidance states, “You may want to guide students on applying the various heuristics using the problem-solving heuristics poster. Refer students to the corresponding teacher resources for prompts and worked out solutions. Requires students to find the area of an enlarged triangle. What are we required to do? What strategies can we use to find the area of triangle DEF? Alert students that the height is measured 4 centimeters. Encourage students to work with a partner to determine the area of the constructed triangle and then multiply it by the scale factor squared.” Teacher guidance gives a generic reference to have students use the heuristics poster which is repeated throughout the materials. • In Section 9.3, Probability of Compound Events, Independent Practice Problem 11, page 351, students solve probability problems. The problem states, “Hunter tosses a fair six-sided die twice. What is the probability of tossing an even number on the first toss and a prime number on the second toss?” Teacher guidance states, “Assesses students’ ability to find the probability of a compound event that consists of tossing an even number followed by a prime number when a six-sided number die is tossed twice.” Teacher guidance gives a generic reference to assess students’ abilities which is repeated throughout the materials. Students do not have the opportunity to use appropriate tools strategically. Materials identify focus Mathematical Habits for MP5 in the Chapter Planning Guide and in the Section objectives. However, these Mathematical Habits are never intentionally addressed in the activities and problems. Examples include: • Chapter 6, Recall Prior Knowledge, is noted as addressing MP5 on pages 76-77 in the Standards for Mathematical Practice Chart, Chapter Planning Guide, and Section Objectives. However, no identified opportunities for students to use tools strategically are provided. • Section 7.1, Radius, Diameter, and Circumference of a Circle, is noted as addressing MP5 on pages 131-133 in the Standards for Mathematical Practice Chart, Chapter Planning Guide, and Section Objectives. However, no identified opportunities for students to use tools strategically are provided. ##### Indicator {{'2h' | indicatorName}} Materials attend to 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 materials reviewed for Math in Focus: Singapore Math Course 2 partially 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. Students have some opportunities to attend to precision and the specialized language of mathematics in connection to grade-level content, identified as mathematical habits in the materials. However, little to no student guidance is provided. Examples include: • In Section 6.2, Scale Drawings and Lengths, For Language Development, TE page 92, teacher guidance includes, “Make sure that students understand the meaning of ‘scale’. You may want to share some examples of scale drawings. Show maps and architectural drawings, pointing out the scales, and explaining that the region or building is ‘scaled down’ in the scale drawing.” • In Section 9.2, Probability of Compound Events, For Language Development, TE page 328, teacher guidance includes,“Be sure students understand the words and the concept of ‘favorable outcomes’. Favorable does not mean ‘good’ or ‘bad’. It refers to the elements of which we are trying to find the probability.” • In Chapter 9, Probability of Compound Events, Math Journal, Problem 1, page 363, students have the opportunity to use the specialized language of mathematics to explain outcomes. The problem states, “Use an example to explain the difference between possible outcomes and different outcomes.” Teacher guidance states, “Requires students to explain the difference between possible outcomes and different outcomes. Encourage them to give examples such as tossing a coin twice, which has four outcomes. Are all the outcomes different? If order does not matter, then the outcome (H, T) is identical to the outcome (T, H). If we draw one piece of fruit from a bag of apples and oranges, we have two mutually exclusive outcomes (apple and orange) and the two outcomes are different. Review with students the various strategies to explain the difference between the probability terms. Encourage students to work independently. You may want to pose the following question to students who are struggling with using precise mathematical language. What strategy would you use to explain the difference between probability terms?” Students have some opportunities to attend to precision and the specialized language of mathematics in connection to grade-level content, identified as mathematical habits in the materials. However, there is no student guidance and teacher guidance is repetitive and not specific, preventing intentional development of the full intent of MP6. Examples include: • In Section 1.4, Subtracting Integers, Independent Practice, Problem 21, page 60, Problem 21, students have the opportunity to attend to the specialized language of mathematics as they subtract integers. The problem states, “Ms. Davis has only$420 in her bank account. Describe how to find the amount in her account after she writes a check for \$590.” Teacher guidance states, “Assess students’ ability to explain the steps involved in subtracting a negative integer from a positive one.” Neither teacher guidance nor student directions prompt students to use specific mathematical terms to explain their thinking or communicate their ideas.

• In Section 3.2, Solving Algebraic Equations, Independent Practice, Problem 13, page 229, students have the opportunity to attend to precision looking for an error another student made, “Tara was asked to solve the equation -4p + 5 = 7 Her solution is shown. (An index card is shown with Tara’s steps.) Tara concluded that p = $$\frac{1}{2}$$ is the solution of the equation -4p + 5 = 7. Describe and correct the error that Tara made.” Teacher guidance states, “assesses students’ ability to identify a mistake that involves dividing by a negative coefficient.” Neither teacher guidance nor student directions prompt students to attend to precision. Furthermore, this problem lends itself to MP3.

• In Section 4.2, Representing Direct Proportion Graphically, Independent Practice, Problem 6, students have the opportunity to use the specialized language of mathematics to explain a direct proportion. The problem states, “Explain how you can determine whether a line represents a direct proportion.” Teacher guidance states, “Assesses students ability to explain what determines a direct proportion graph.” Neither teacher guidance nor student directions prompt students to use specific mathematical terms to explain their thinking or communicate their ideas.

There are some instances when the materials attend to the specialized language of mathematics; however, these lessons were not identified as aligned to MP6. For example:

• In Section 2.1, Adding Algebraic Terms, For Language Development, TE page 130, states, “Be sure students understand the meaning of like terms. Explain that like terms are terms that have the same variable part. Constant terms are also like terms. Give examples of like terms such as 2, $$\frac{1}{4}$$, 0.3, and -5; a, 3a, $$\frac{1}{2}$$ a, 2.4a, and -7a. List a variety of ten terms (both like terms and unlike terms) on the board and invite volunteers to identify like terms.”

Materials identify focus Mathematical Habits in the Standards for Mathematical Practice Chart, Chapter Planning Guide, and in the Section Objectives. However, this mathematical habit is not intentionally addressed in the activities and problems. Examples include:

• Section 2.6, Writing Algebraic Expressions, is noted as addressing MP6 on pages 171-186  in the Standards for Mathematical Practice Chart, Chapter Planning Guide, and Section Objectives. However, no opportunities for students to attend to precision and attend to the specialized language of mathematics are identified in the lesson.

• Section 5.1, Complementary, Supplementary, and Adjacent Angles, is noted as addressing MP6 on pages 5-18  in the Standards for Mathematical Practice Chart, Chapter Planning Guide, and Section Objectives. However, no opportunities for students to attend to precision and attend to the specialized language of mathematics are identified in the lesson.

##### Indicator {{'2i' | indicatorName}}

Materials support 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 the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for Math in Focus: Singapore Math Course 2 do not 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.

Students have minimal opportunities to look for and make use of structure in connection to grade-level content, identified as mathematical habits in the materials. There is no student guidance, teacher guidance is often repetitive, not specific, and activities are scaffolded preventing intentional development of the full intent of MP7. Examples include:

• In Section 1.4, Subtracting Integers, Learn, Problem 5, page 49, students use counters to subtract integers. The problem states, “Based on your results in 1 to 4, explain how you can subtract integers.” In Question 1, students used counters to evaluate 5 - (+2) compared with 5 + (-2). In Question 4, students used counters to evaluate 7 - (-3) and 7 + 3. Teacher guidance states, “Conclude the activity by asking students to generalize what they have observed about subtraction. You may want to consider each case: a positive minus a positive, a negative minus a positive, a positive minus a negative, a negative minus a negative. Guide students to conclude the task in ENGAGE.” Materials scaffold MP7 in this problem which prevents the opportunity to identify structure. Students are provided the model of using counters for each problem and guided through its development. Therefore students do not independently look for and make use of structure to generalize their understanding of subtraction.

• In Chapter 1, Rational Numbers, Put On Your Thinking Cap!, Problem 1, page 112, students write an equivalent expression using the distributive property. The problem states, “The 4 key on your calculator is not working. Show how you can use the calculator to find 321 × 64.” Teacher guidance states, “Requires students to solve a problem that involves writing an equivalent expression, and evaluating it using the distributive property. Step 1. Understand the problem: What information can we gather from the problem? What are we asked to find? Step 2: Think of a plan: What can we do to help us solve the problem? What number do we have to change in the expression, and how? What is equivalent to 64? Step 3. Carry out the plan: So, what is an equivalent expression of 321 ⋅ 64?  Are all these expressions equivalent? Why? Which expression will be easier to evaluate? Why? Invite volunteers to share their equivalent expressions, and ask students to evaluate each of them. Ensure that students are able to apply the distributive property correctly. For example, 321 ⋅ (65 − 1) = 321 ∙ 65 − 321 ∙ 1. If necessary, suggest that students write the subtraction within the parentheses as adding the opposite to help them keep track of the signs. Prompt students to see that the equivalent expressions all have the same result of 20,544. Step 4. Check the answer.” Teacher guidance gives a generic reference to have students use the four-step problem-solving method which is repeated throughout the materials and does not require students to look for or use structure in solving.

Materials identify focus Mathematical Habits for MP7 in the Chapter Planning Guide and in the Section objectives. However, these Mathematical Habits are not intentionally addressed in the activities and problems. Examples include:

• Chapter 5, Wrap-Up, Chapter Review, Performance Task, is noted as addressing MP7 on pages 270-276 in the Standards for Mathematical Practice Chart, Chapter Planning Guide, and Section Objectives. However, no identified opportunities for students to make use of structure are provided in the lesson.

• Section 8.5, Approximating Probability and Relative Frequency, is noted as addressing MP7 on pages 261-276 in the Standards for Mathematical Practice Chart, Chapter Planning Guide, and Section Objectives. However, no identified opportunities for students to make use of structure are provided in the lesson.

Students have minimal opportunities to look for and express regularity in repeated reasoning in connection to grade-level content, identified as mathematical habits in the materials. There is no student guidance, teacher guidance is often repetitive, not specific, and activities are scaffolded preventing intentional development of the full intent of MP8. Examples include:

• In Section 3.4, Solving Algebraic Inequalities, Learn, Problem 1, page 248, Problem 1, students analyze a table of values involving dividing inequalities with positive and negative integers. The problem states, “Fill in the table. Use the symbols > or <. a) What happens to the direction of the inequality symbol when you divide by a positive number? Based on your observation, write a rule for dividing both sides of an inequality by a positive number. b) What happens to the direction of the inequality symbol when you divide by a negative number? Based on your observation, write a rule for dividing both sides of an inequality by a negative number. Teacher guidance states, “Summarize that the inequality symbol remains the same when we multiply or divide by a positive number, and the direction of the symbol is reversed when we multiply or divide by a negative number. Help students to visualize why this occurs. Ask them to consider x > y. In other words, when we multiply by a negative number, we flip the number line, moving to the left.” Students are provided problems with answers (in the table) and are only responsible for comparing the answers. They do not independently look for and make use of structure in generalizing an understanding of inequalities.

• In Section 6.3, Scale Drawings and Areas, Learn, Problem 5, page 104, students explore the relationship between scale factor and corresponding area. The problem states, “Compare the side lengths and the areas for the various scale factors. What pattern do you observe? What relationship between scale factor and area can you deduce?” Teacher guidance states, “In 5, encourage students to look for patterns, in particular the relationship between the scale factor and the area. What is the relationship? Emphasize that this property applies to the areas of other two dimensional figures as well. You may want to conclude the activity by discussing the activity in terms of inductive reasoning, as described in the Best Practice below.” Materials scaffold MP8 in this problem which prevents the opportunity to look for and express regularity in repeated reasoning. Students are provided models to find areas of scaled images and a partially completed table designed to organize results. Students look for and express regularity in repeated reasoning to understand the relationship between scale factors and corresponding areas with teacher assistance, including a heavily scaffolded problem.

Materials identify focus Mathematical Habits for MP8 in the Chapter Planning Guide and in the Section objectives. However, these Mathematical Habits are not intentionally addressed in the activities and problems. For example:

• Section 7.4, Area of Composite Figures, is noted as addressing MP8 on page 164 in the Standards for Mathematical Practice Chart, Chapter Planning Guide, and Section Objectives. However, no identified opportunities for students to look for and express regularity in repeated reasoning are provided in the lesson.

### Usability

Not Rated

#### Criterion 3.1: Teacher Supports

The program includes opportunities for teachers to effectively plan and utilize materials with integrity and to further develop their own understanding of the content.

##### Indicator {{'3a' | indicatorName}}

Materials provide teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.

##### Indicator {{'3b' | indicatorName}}

Materials contain adult-level explanations and examples of the more complex grade-level/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.

##### Indicator {{'3c' | indicatorName}}

Materials include standards correlation information that explains the role of the standards in the context of the overall series.

##### Indicator {{'3d' | indicatorName}}

Materials provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.

##### Indicator {{'3e' | indicatorName}}

Materials provide explanations of the instructional approaches of the program and identification of the research-based strategies.

##### Indicator {{'3f' | indicatorName}}

Materials provide a comprehensive list of supplies needed to support instructional activities.

##### Indicator {{'3g' | indicatorName}}

This is not an assessed indicator in Mathematics.

##### Indicator {{'3h' | indicatorName}}

This is not an assessed indicator in Mathematics.

#### Criterion 3.2: Assessment

The program includes a system of assessments identifying how materials provide tools, guidance, and support for teachers to collect, interpret, and act on data about student progress towards the standards.

##### Indicator {{'3i' | indicatorName}}

Assessment information is included in the materials to indicate which standards are assessed.

##### Indicator {{'3j' | indicatorName}}

Assessment system 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.

##### Indicator {{'3k' | indicatorName}}

Assessments include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.

##### Indicator {{'3l' | indicatorName}}

Assessments offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.

#### Criterion 3.3: Student Supports

The program includes materials designed for each child’s regular and active participation in grade-level/grade-band/series content.

##### Indicator {{'3m' | indicatorName}}

Materials provide strategies and supports for students in special populations to support their regular and active participation in learning grade-level/series mathematics.

##### Indicator {{'3n' | indicatorName}}

Materials provide extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.

##### Indicator {{'3o' | indicatorName}}

Materials provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.

##### Indicator {{'3p' | indicatorName}}

Materials provide opportunities for teachers to use a variety of grouping strategies.

##### Indicator {{'3q' | indicatorName}}

Materials provide 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.

##### Indicator {{'3r' | indicatorName}}

Materials provide a balance of images or information about people, representing various demographic and physical characteristics.

##### Indicator {{'3s' | indicatorName}}

Materials provide guidance to encourage teachers to draw upon student home language to facilitate learning.

##### Indicator {{'3t' | indicatorName}}

Materials provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

##### Indicator {{'3u' | indicatorName}}

Materials provide supports for different reading levels to ensure accessibility for students.

##### Indicator {{'3v' | indicatorName}}

Manipulatives, both virtual and physical, are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

#### Criterion 3.4: Intentional Design

The program includes a visual design that is engaging and references or integrates digital technology, when applicable, with guidance for teachers.

##### Indicator {{'3w' | indicatorName}}

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.

##### Indicator {{'3x' | indicatorName}}

Materials include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

##### Indicator {{'3y' | indicatorName}}

The visual design (whether in print or digital) supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

##### Indicator {{'3z' | indicatorName}}

Materials provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

## Report Overview

### Summary of Alignment & Usability for Math in Focus: Singapore Math | Math

#### Math K-2

The materials reviewed for Math in Focus: Singapore Math Grades K-2 do not meet expectations for Alignment to the CCSSM. In Gateway 1, the materials do not meet expectations for focus and partially meet expectations for coherence.

##### Kindergarten
###### Alignment
Does Not Meet Expectations
Not Rated
###### Alignment
Does Not Meet Expectations
Not Rated
###### Alignment
Does Not Meet Expectations
Not Rated

#### Math 3-5

The materials reviewed for Math in Focus: Singapore Math Grades 3-5 do not meet expectations for Alignment to the CCSSM. For Grade 4, the materials partially meet expectations for focus and coherence in Gateway 1 and do not meet expectations for rigor and practice-content connections in Gateway 2. For Grades 3 and 5, the materials do not meet expectations for focus and coherence in Gateway 1.

###### Alignment
Does Not Meet Expectations
Not Rated
###### Alignment
Does Not Meet Expectations
Not Rated
###### Alignment
Does Not Meet Expectations
Not Rated

#### Math 6-8

The materials reviewed for Math in Focus: Singapore Math Grades 6-8 vary in meeting expectations for Alignment to the CCSSM. For Grades 6 and 7, the materials partially meet expectations for Alignment to the CCSSM as they meet expectations for Gateway 1 and do not meet expectations for Gateway 2. For Grade 8, the materials partially meet expectations for Gateway 1 and do not meet expectations for Gateway 2.

###### Alignment
Partially Meets Expectations
Not Rated
###### Alignment
Partially Meets Expectations
Not Rated
###### Alignment
Does Not Meet Expectations
Not Rated

## Report for {{ report.grade.shortname }}

### Overall Summary

###### Alignment
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###### Usability
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### {{ gateway.title }}

##### Gateway {{ gateway.number }}
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