## Math in Focus: Singapore Math

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### Overall Summary

The materials reviewed for Math in Focus: Singapore Math Grade 3 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.

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

### Focus & Coherence

The materials reviewed for Math in Focus: Singapore Math Grade 3 do not meet expectations for focus and coherence. For focus, the materials do not assess grade-level content and do not provide all students extensive work with grade-level problems to meet the full intent of grade-level standards. For coherence, the materials partially meet expectations for coherence and consistency with the CCSSM.

##### Gateway 1
Does Not Meet 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 Grade 3 do not meet expectations for focus as they do not assess grade-level content and do not provide all students extensive work with grade-level problems to meet the full intent of grade-level standards.

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

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

The materials reviewed for Math in Focus 2020 Grade 3 do not 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 2, Section C, Item 11 (Paper) states, “Evan skipped 127 times in the first round of a competition. He skipped 75 more times in the second round. He said that the number of skips for the second round was 192. Explain Evan’s mistake. What number should have been recorded for the second round? Explain how you arrived at your answer.” (3.NBT.2)

• In Chapter Test 4, Section A, Item 12 (Paper) states, “James looks at the multiplication table of 6 and says that the answers to the multiplication equations are all even numbers. Explain whether James’ observation is true. What multiplication tables have equations with answers that are all even numbers?” (3.OA.9)

• In Cumulative Review 3, Section B, Item 18 (Online) states, “Claire wrote that \frac{1}{4}>\frac{1}{3} and explained that it is because 4 is greater than 3. Is she correct? Explain. Write your answer and your work or explanation in the space below.” (3.NF.3d)

• In Chapter Test 10, Assessment Guide, Section A, Item 4 (Paper) states, ”Ruth went to a party for 135 minutes. Which of the following is equal to 135 minutes? A) 1 hour 35 minutes, B) 2 hours 15 minutes, C) 2 hours 75 minutes, D) 13 hours 5 minutes.” (3.MD.1)

• In Chapter Test 12, Section B, Item 7 (Paper) states, “Is the shape a quadrilateral? Write ‘Yes’ or ‘No’ for each shape.  Hexagon:____ Parallelogram: ____ Rhombus: ____.” (3.G.1)

The provided assessments also assess above-grade assessment items that could not be removed or modified without impacting the structure or intent of the materials. Examples include:

• In Chapter Test 2, Section B, Item 6 (Online) states, “6,359 + 2,178 =____ . Write your answer in the answer grid.” This item assesses 4.NBT.4 (Fluently add and subtract multi-digit whole numbers using the standard algorithm).

• In Chapter 2 Test (Paper), seven of the 12 assessment items align to 4.NBT.4 (Fluently add and subtract multi-digit whole numbers). For example, Section B, Item 8 states, “Ms. Carter saves $1,438. She saves$250 less than Ms. Jones. How much do they save in all?”

• In Chapter Test 3 (Paper), nine of the 12 assessment items are aligned to 4.NBT.4 (Fluently add and subtract multi-digit whole numbers using the standard algorithm). For example: Chapter Test 3, Section A, Item 2 states, “What is the difference between 7,794 and 1,704?” A) 6,054 B) 6,090 C) 7,620 D) 9,498.”

• In Chapter Test 5 (Online), 10 of the 12 assessment items are aligned to 4.NBT.5 (Multiply a whole number of up to four digits by a one-digit whole number). For example:

• In Section A, Item 5 states, “There are 176 pennies in each jar. How many pennies are there in 6 jars? A) 626, B) 1026, C) 1056, D) 2456.”

• In Section A, Item 3 states, “Which expression could not be used to find the value of 549 × 3?” A) (500 × 3) + (40 × 3) + (9 × 3), B) (500 × 3) + (50 × 3) - (1 × 3), C) (500 × 3) + (50 × 3) - (2 × 3), D) (500 × 3) + (40 × 3) + (5 × 3) + (4 × 3).

• In Section A, Item 4 (Online) states, students are shown a vertical version of the multiplication problem 1? 8 × 2 = 296. Students answer, “What is the missing digit? A) 1, B) 2, C) 3, D) 4.”

• In Cumulative Review 1, Section C, Item 23 (Online) states, “Alan has $20. He wants to buy some stationery from a store. Alan buys a few different items. He wants only one of each item. The 5 items are listed in a table, ‘Cost of Stationary,’ ranging in cost from$5.25 to \$11.59. Which items should he buy so that he has the least change left? Explain how you arrived at your answer.” This item assesses 5.NBT.7 (Add, subtract, multiply, and divide decimals to hundredths, using strategies based on the relationship between addition and subtraction, relate the strategy to a written method and explain the reasoning used).

• In Chapter Test 7, Section C, Item 10 (Online) states, “There were 24 people at a party. \frac{3}{4} of the people at the party were children and the rest were adults. \frac{1}{2} of the children wore party hats. How many children did not wear party hats? Show your work and write your answer in the space below.” This item assesses 4.NF.4c (Solve word problems involving multiplication of a fraction by a whole number).

• In Chapter 8 Test (Online), 11 of the 12 assessment items align to 4.MD.1 (Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit…). For example, Item 7 states, “A tank contains 7 liters 550 milliliters of water. How many milliliters of water does the tank contain? Show your work and write your answer in the space below.”

• In Chapter 12 Test (Paper), five of the 11 assessment items are aligned to 4.G.2 (Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size…). For example, Item 6 states, “Use a number to complete the sentence. Write the answer in the blank. A rectangle has ___ pairs of parallel sides.”

• In the End-Of Year Benchmark Assessment, Section B, Item 37 (Paper) states, “Which angles are less than a right angle? Write your answers in the space below.” Included is an irregular hexagon with acute and obtuse angles; Angles A, B, C, D, E, and F are noted on the hexagon. This item assesses 4.G.1 (Identifying angles [right, acute, and obtuse]).

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

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 2020 Grade 3 do not meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The 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 an inquiry task that encourages 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 students extensive work with grade-level problems to meet the full intent of some grade-level standards. Examples include:

• In Section 1.5, Rounding Numbers to the Nearest Hundred, students use number lines and place value to round numbers to the nearest hundred. In Engage, Problem A, page 47, students estimate or round numbers to the nearest hundred. The problem states, “Draw a number line starting at 300 and ending at 400, with intervals of 10. Choose 2 points that are nearer to 400. Compare your points with your partner. How are your points different from your partner’s?” In Hands-on Activity, Problem 3, page 49, students work with a partner to practice rounding numbers to the nearest hundred. The problem states, “Work in pairs. Round each number to the nearest hundred. ____ is ____ when rounded to the nearest hundred.” In Try, Problem 4, page 50, students mark numbers on a number line to help them round to the nearest hundred. The problem states, “Mark (x) each number on the number line. Then round each number to the nearest hundred. a) 350 is ____ when rounded to the nearest hundred, b) 460 is ____ when rounded to the nearest hundred, 510 is ____ when rounded to the nearest hundred.” A number line is shown with 300, 400, 500, 600 marked. In Independent Practice, Problem 6, page 54, students round to the nearest hundred without visual aids. The problem states, “Round each number to the nearest hundred. 450 ____.” Students engage with extensive work to meet the full intent of 3.NBT.1 (Use place value understanding to round whole numbers to the nearest 10 or 1000).

• In Section 4.1, Multiplying by 6, students use skip counting and properties of operations to multiply by 6. Engage, page 226, students use an known fact to help determine an unknown fact. It states, “What is 5 × 6? Draw a picture to show how you found the answer. How does knowing 5 × 6 help you find 7 × 6? Explain your thinking.” In Learn, Problem 1, page 226, students use known multiplication facts to find other multiplication facts. The problem states, “Use known multiplication facts to find other multiplication facts. 7 × 6 = ? You can use array models to show multiplication facts. Start with 5 groups of 6.” Students are shown how to use the distributive property to find 7 x 6. In Try, Problem 2, page 229, students practice multiplying by 6 using array models and known multiplication facts, “7 × 6 = ?, 5 × 6 = ___,  2 × 6 = ___, 7 × 6 = (5 × 6) + (2 × 6) = ___ + ___ = ___ .” In Independent Practice, Problem 3, page 232, states, “Find 5 groups of 6. 5 × 6 = ___.” Five pictures with six strawberries in baskets are shown. Students engage in extensive work to meet the full intent of 3.OA.1 (Interpret products of whole numbers).

• In Section 9.1, Area, students use square units to find the area of plane figures made of squares and half-squares. They then compare the area of plane figures and make plane figures of the same area. In Engage, page 119, students use square units to design shapes. The problem states, “Use 5 (squares) to create as many different figures as you can. Sketch each figure. How many figures did you create? Share your figures with your partner.” In Hands-on Activity, Problem 1, page 120, students work in pairs using square units to find the area. The problem states, “Use 4 square tiles to make as many different figures. Draw them below.” Try, Problem 1, page 121, students count square tiles to determine a figure’s corresponding area. The problem states, “Look at each figure and answer each question. How many square tiles make each figure? a) Figure A is made up of ___ square tiles, b) Figure B is made up of ___ square tiles, c) Figure C is made up of ___ square tiles.” In Independent Practice, Problem 5, page 127, students compare the area of figures. The problem states, “Look at each set of figures. Circle the figures that have the same area.” Students engage in extensive work to meet the full intent of 3.MD.5 (Recognize area as an attribute of plane figures and understand concepts of area measurement).

Materials do not provide students the opportunity to engage with the full intent of some grade-level standards. For example:

• Students are not provided the opportunity to engage with the full intent of 3.G.2 (Partition shapes into parts with equal areas and express the area of each part as a unit fraction of the whole). For example, Section 7.3, Fractions as Part of a Set, Think, page 25, students work in pairs to read, write, and identify fractions of a set and find the number of items in a fraction of a set, “$$\frac{3}{8}$$ of the pupils in a class wear glasses. 9 pupils in the class wear glasses. How many pupils are there in the class?” In Learn, Problem 1, page 27, students use bar models to show fractions as part of a set. The problem states, “Ms. White had 12 oranges. She gave $$\frac{3}{4}$$ of the oranges to Cooper. How many oranges did she give to Cooper?” In Try, Problem 4, page 30, students use bar models to show fractions as part of a set. The problem states, “Find the value of each of the following. Draw a bar model to help you. $$\frac{7}{8}$$ of 16.” Students engage in solving problems involving multiplication of a fraction by a whole number, which are the expectations of fourth grade standard 4.NF.4c (Solve word problems involving multiplication of a fraction by a whole number). By engaging in the work of 4.NF.4c, students do not have the opportunity to engage with the full intent of 3.G.2.

Materials do not provide extensive work with some grade-level standards. Examples include:

• The materials do not provide extensive work with 3.OA.7 (Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations). Chapter 4 contains sections: Multiplying by 6, Multiplying by 7, Multiplying by 8, Multiplying by 9, Multiplying by 11, and Multiplying by 12. There is no evidence of students using strategies or properties to understand multiplication facts for 0, 1, 2, 3, 4, 5, or 10, except for within the context of facts of 6, 7, 8, 9, 11, and 12. In the Teacher’s Manual, page 217C states, “What have students learned? In Grade 2 Chapter 8, students have learned: How to multiply (2.OA.4), How to divide. In Grade 2, Chapter 9, students have learned: Multiplying in any order (3.OA.5).” Students work with 3.OA.7 in Grade 2. In the Teacher's Manual, page 217 A, Math Background states, “Students have learned the basic meanings of equal groups of multiplication and division in Grade 2, where they were taught about multiplication as the addition of equal groups, and division as sharing equally. They have also learned the multiplication facts for 2, 3, 4, 5, and 10.”

• The materials do not provide extensive work with 3.NBT.2 (Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction). In Section 2.3, Adding Fluently Within 1,000, Independent Practice, Problems 1-16, students have the opportunity to add within 1,000. For example, Problem 9 states, “82 + 257 = ___.” Problem 10 states, “382 + 536 = ___.” Problem 11 states, “475 + 363 = ___.” In Section 3.2, Subtracting Fluently Within 1,000, Independent Practice, Problems 1-16, students have the opportunity to subtract within 1,000. For example, Problem 5 states, “461 - 355 = ___.” Problem 6 states, “367 - 184 = ___.” Problem 7 states, “809 - 433 = ___.” Per the Math in Focus 2020 Comprehensive Alignment to CCSS: Grade 3, these are the two lessons that address 3.NBT.2. Therefore, students do not have the opportunity to engage in extensive work with 3.NBT.2.

• The materials do not provide extensive work with 3.NBT.3 (Multiply one-digit whole numbers by multiples of 10 in the range 10-90 using strategies based on place values and properties of operations). For example, Section 5.2,  Multiplying Without Regrouping, Try, Problem 1, page 329, students practice multiplying 3-digit numbers without regrouping, “210 × 4 = (200 × 4) + (10 × 4) + (0 × 4) = ___ + ___ + ___ = ___.” A number bond for 210 with 200, 10, and 0 is shown. In Independent Practice, Problem 8, page 332, students multiply 2-digit and 3-digit numbers by a 1-digit number, without regrouping using the vertical form, multiply, and then, fill in each corresponding letter to find the answer. The problem states, “The Williams family went for a vacation. Where did they go? (T) 23 x 2 = ___, (E) 31 × 3  = ___, (C) 124 × 2 + ___, (O) 112 × 2 = ___, (N) 212 × 4 = ___, (Y) 204 × 2 = ___, (R) 303 × 3 = ___, (K) 122 × 4 = ___, (W) 432 × 2 = ___. The Williams went to: ___, ___, ___, ___, ___, ___, ___.” Each blank space correlates to the solution for each of the letters to spell out where the family went on vacation. In Section 5.3, Multiplying with Regrouping, Engage, Problem 1, page 333, students multiply 3-digit numbers with regrouping. The problem states, “Mia uses (counters) to show 3 groups of 15. How many (counters) does she have? She then places the (counters) on the ones column of a place-value chart. Regroup them in two ways. Explain your thinking.” In Recall Prior Knowledge, Problem 1a, page 362, students multiply by a 1-digit number without regrouping, “21 × 4 = ?” In these sections, students multiply a whole number of up to four digits by a one-digit whole number (4.NBT.5). Due to the amount of off grade level work, there is not extensive work with 3.NBT.3.

• The materials do not provide extensive work with 3.MD.2 (Measure and estimate liquid volumes and masses of objects using standard units of grams, kilograms, and liters and add, subtract, multiply or divide to solve one step word problems involving masses or volumes that are given in the same units). For example, in Section 8.1, Mass: Kilograms and Grams, Hands-on Activity, Problems 1-3, page 71, students measure mass in kilograms and grams. The problems state, (1) “Hold a 1-kilogram weight in one hand,“ (2) “Hold a completely filled 1-litre water bottle in the other hand. Compare its mass with the 1-kilogram weight. Fill in the blank with more or less. The completely filled 1-litre water bottle is ___ than 1 kilogram,” and (3) “Find its actual mass using a weighing scale. The actual mass of the filled 1-litre water bottle is ___ kilogram ___ grams.” In Section 8.2, Liquid Volume: Liters and Milliliters, Try, Problem 1, page 80, students practice measuring volume in liters and milliliters. The problem states, “Circle each correct unit of measure. A glass of juice: 200 liters/milliliters.” A picture of a glass of juice is shown. In Section 8.3 Real World Problems: One-Step Problems, Try, Problem 4, page 93, students practice solving one-step real-world problems involving measurement. The problem states, “A chef poured 9 cups of water into a pot. Each cup of water contained 240 milliliters of water. How much water did the chef put into the pot? Give your answer in liters and milliliters.” In all three sections students engage with 4.MD.1 (Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit). By engaging in the work of 4.MD.1, students do not have the opportunity to engage in extensive work with 3.MD.2. Per the Math in Focus 2020 Comprehensive Alignment to CCSS: Grade 3, these are the two lessons that address 3.MD.2.

#### Criterion 1.2: Coherence

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

The materials reviewed for Math in Focus: Singapore Math Grade 3 partially meet expectations for coherence. The materials have supporting content that enhances focus and coherence simultaneously by engaging students in the major work of the grade and 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. The majority of the materials do not, when implemented as designed, address the major clusters of each grade.

##### 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 Grade 3 do not meet expectations that, when implemented as designed, the majority of the materials address the major cluster of each grade.

• There are 12 instructional chapters, of which 5 address major work of the grade, or supporting work connected to major work of the grade, approximately 42%.

• There are 95 sections (lessons), of which 44 address major work of the grade, or supporting work connected to major work of the grade, approximately 46%.

• There are 158 days of instruction, of which 67.5 days address major work of the grade, or supporting work connected to the major work of the grade, approximately 43%.

A day-level analysis is most representative of the instructional materials because the days include all instructional learning components. As a result, approximately 43% 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 instructional materials reviewed for Math in Focus 2020 Grade 3 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. Examples include:

• Section 2.1, Addition Patterns, connects the supporting work of 3.NBT.2 (Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction) to the major work of 3.OA.9 (identify arithmetic patterns [including patterns in the addition table], and explain them using properties of operations). In the Hands-on Activity, Problem 1, page 82, students "Look at the pattern in the diagonal boxes in yellow. Color another diagonal that shows the same pattern yellow. Complete the sentence below: When an odd number and an even number are added, the result is an ____number.”

• Section 7.1, Understanding Unit Fractions, connects the supporting work of 3.G.2 (Partition shapes into parts with equal areas…) to the major work of 3.NF.1 (Understand a fraction1/b as the quantity formed by 1 part when a whole is partitioned into be equal parts understand a fraction a/b as the quantity formed by a parts of size 1/b). In the Hands-on Activity, Problem 1, page 8, students “Work in pairs using fractions to describe equal parts of a whole. [Your teacher will provide you with five rectangular strips of paper] Fold a rectangular strip of paper into 2 equal parts.”

• Section 9.5, More Perimeter, Independent Practice, connects the supporting work of 3.MD.8 (Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters) to the major work of 3.OA.D, as students solve problems involving the four operations and identify and explain patterns in arithmetic. Problem 15, page 188, states, “The length of a rectangular hall is 3 times its width. The perimeter of the hall is 32 meters. Find the length and the width of the hall.”

• Section 11.2, Making Bar Graphs with Scales, connects the supporting work of 3.MD.3 (Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs) to the major work of 3.OA.3 (Use multiplication and division within 100 to solve word problems situations involving equal groups, arrays, and measurement quantities…). In Learn, Problem 1, page 284, students make bar graphs from picture graphs. The problem states, “Four friends went for a nature walk. The picture graph on the next page shows the number of butterflies each friend saw. a) How many butterflies does each __stand for? Each __ stands for 2 butterflies. b) Who saw the most number of butterflies?” Two graphs showing the number of butterflies seen are provided.

##### 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 instructional materials for Math in Focus 2020 Grade 3 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.

Examples of connections between major work and major work and connections between supporting work and supporting include:

• Section 4.4, Multiply by 9, connects the major work of 3.OA.A (Represent and solve problems involving multiplication and division) to the major work of 3.OA.B (Understand properties of multiplication and the relationship between multiplication and division, as students skip count by 9s and use known multiplication facts to find other multiplication facts to understand the properties of multiplication and solve problems involving multiplication). In Independent Practice, Problem 1, page 263, students “Fill in each blank. Find 3 groups of 9. 3 × 9 =____, Multiply 9 by 3. 9 × 3. 9 × 3  =____  So, 3 × 9 = 9 × 3 =_____.”

• Section 4.8, Dividing Using Multiplication Facts, connects the major work of 3.OA.A (Represent and solve problems involving multiplication and division) to the major work of 3.OA.C (m=Multiply and divide within 100, as students use multiplication facts to find related division facts and write multiplication and division equations). In Try, Problem 1, page 292, students “Find each missing number. Use related multiplication facts to help you. Arrange 48 chairs equally into 6 rows. 48 ÷ 6 = ____. There are ____chairs in each row. 6 × ____ = 48, So, 48 ÷ 6 = ____.”

• Section 6.3 Real-World Problems: Four Operations, connects the major work of 3.OA.C (Multiply and divide with 100) to the major work of 3.OA.D (Solve problems involving the four operations, and identify and explain patterns in arithmetic, as students use multiplication and division to solve multi-step problems). In Try, Problem 3, page 394, states, “A baker has 28 kilograms of flour. He uses 8 kilograms of it to make some pies. He packs the remaining flour equally into 5 bags. How many kilograms of flour does each bag contain?”

• Section 9.4, Perimeter and Area, connects the major work of 3.MD.C (Geometric measurement: understand concepts of area and relate area to multiplication and addition) to the major work of 3.OA.A (Represent and solve problems involving multiplication and division). In Try, Problem 4, page 162, students “Find the area of each rectangle. Each rectangle is not drawn to scale. Area =____.” A rectangle with the length = 12 cm and width = 5cm is shown. Students must use the length and width of the rectangle to find the area of the rectangle by using multiplication and the distributive property of multiplication.

• Section 11.3 Reading and Interpreting Bar Graphs, connects the supporting work of 3.MD.B (Represent and interpret data) to the supporting work of 3.NBT.A (Use place value understanding and properties of operations to perform multi-digit arithmetic, as students use addition and subtraction within 1,000 to answer questions about bar graphs). In Independent Practice, Problem 25, page 307, students are given a bar graph titled, “Flowers Jason Sold” and asked, “How many fewer sunflowers than roses were sold?”

##### 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 2020 Grade 3 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. Prior Knowledge highlights the concepts and skills students need before beginning a new chapter. The section What have students learned? states the learning objectives and prior knowledge relevant to each chapter. The Math Background shows the key learning objectives and provides an overview of how prior work connects with grade level work. Examples include:

• In Teacher Edition, Chapter 7, Fractions, Math Background, page 1A, connects the prior work of 2.G.3 with the grade level work of 3.NF.1. It states, “In Grade 2, students were introduced to the idea of fractions. They learned to partition shapes into two, three, or four equal parts, and describe the parts using halves, thirds, or fourths. Fractions were represented using models that helped students to visualize the relationship between the parts and the whole before moving on to the more abstract symbolic level in Grade 3. In this chapter, students will work with fractions of a whole that are divided into more than four equal parts: sixths and eighths. Students will learn new concepts such as equivalent fractions and identifying a fraction of a set using their understanding of unit fractions. Students will develop an understanding of the different meanings and uses of fractions, such as representing parts of a whole, parts of a set, point or distances on a number line and more than one whole represented as a fraction.”

• In Teacher Edition, Chapter 9, Area and Perimeter, Math Background, page 113A, connects the prior work of 2.MD.1 and 2.GA.1 with the grade level work of 3.MD.5. It states, “In earlier grades, students learned to use a ruler to measure in meters and centimeters, and to identify shapes. In Chapter 5, students learned to multiply using an area model. These crucial skills will enable them to find the area of figures efficiently. In this chapter, students first learn to count square units to find the area of plane figures. This concept is then extended to finding the area of a rectangle by multiplying its length by its width.”

Within the Chapter Overview, Learning Continuum, materials relate grade-level concepts to upcoming learning but do not identify content from future grades. The section What will students learn next? identifies the learning objectives from the following chapter (or grade) to show the connection between the current chapter and what students will learn next. However, there is no specific correlation made to how the standards connect. The online materials do not include the standard notation. Examples include:

• In Teacher Edition, Chapter 1, Numbers to 10,000, Learning Continuum, What will students learn next?, page 1E, states, “In Grade 4, Chapter 1, students will learn: Numbers to 100,000 (4.NBT1, 4.NBT.2). Numbers to 1,000,000 (4.NBT.1, 4.NBT.2). Comparing and ordering numbers (4.NBT.2, 4.OA.5). Adding and subtracting multi-digit numbers fluently (4.NBT.4).”

• In Teacher Edition, Chapter 2, Addition Within 10,000, Learning Continuum, What Will Students Learn Next?, page 71E, states, “In Grade 4 Chapter 1, students will learn: Adding and subtracting multi-digit numbers fluently (4.NBT.4).”

• In Teacher Edition, Chapter 5, Multiplication, Learning Continuum, What will students learn next?, page 309E, states, “In Grade 4 Chapter 2, students will learn: Real-world problems: multiplication (4.OA.2, 4.OA.3), Real-world problems: the four operations (4.OA.3).”

• In Teacher Edition, Chapter 6, Using Bar Models: The Four Operations, Learning Continuum, What will students learn next?, page 361D, states, “In Grade 4 Chapter 2, students will learn: Real-world problems: the four operations (4.OA.3).”

• In Teacher Edition, Chapter 10, Time, Learning Continuum, What will students learn next?, page 211D, states, “In Grade 4 Chapter 5, students will learn: Time (4.MD.1, 4.MD.2).”

##### 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 2020 Grade 3 can be completed within a regular school year with little or no modifications to foster coherence between grades.

The recommended pacing information is found in the Teacher’s Edition and Chapter Planning Guide. The Chapter Planning Guide lists the Lesson Resources each section, which include the Student Edition, Extra Practice and Homework, Fact Fluency, as well as Reteach and Enrichment activities. Each section consists of one or more Engage-Learn-Try focus cycles followed by Independent Practice. Instructional pacing is provided in days, not minutes. For the purpose of this review, the Chapter Planning Guide provided by the Publisher in the Teacher's Edition was used. The Instructional Pathway, found in the Teacher Edition shows how each of the on-line and print resources can be used within each chapter. As designed, the instructional materials can be completed in 158 days.

• There are 12 instructional chapters divided into sections. The pacing for each section ranges between one to three days, consisting of 102 instructional days.

• For each chapter, one day consists of a Chapter Opener and Recall Prior Knowledge, totaling 12 days.

• For each chapter, one day is spent on the Math Journal and Put On Your Thinking Cap, totaling 12 days.

• For each chapter, two days are spent on the chapter’s closure, which consists of a Chapter Wrap-up, Chapter Review, Performance Task, and Project work, totaling 24 days.

• The cumulative review and benchmark assessments represent an additional 8 days.

• There are no additional days for each chapter’s reteach, extra practice, enrichment. These activities are included in the sections for each instructional chapter.

### Rigor & the Mathematical Practices

Not Rated

#### 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.

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

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

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

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

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

Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.

##### 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.

#### Criterion 2.2: Math Practices

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

##### 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.

##### 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.

##### 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.

##### 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.

##### 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.

### 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

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### Overall Summary

###### Alignment
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###### Usability
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##### Gateway {{ gateway.number }}
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