## Math in Focus: Singapore Math

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### Overall Summary

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

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

### Focus & Coherence

The materials reviewed for Math in Focus: Singapore Math Grade 2 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, each grade’s 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 2 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: Singapore Math Grade 2 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 and Cumulative Reviews 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, page 7, Problem 4 states, ”Find the value of 267 + 348. Show your work and write your answer in the blank below. 267 + 348 = ____.”  (2.NBT.7)

• In Chapter Test 5, page 32, Problem 2 states, ”How many inches long is the yarn? a) 0 inch; b) 2 inches; c) 5 inches; d) 7 inches.” A picture with a ruler and yarn spanning from the two inch mark to the seven inch mark is given. (2.MD.1)

• In Chapter Test 7, page 54, Problem 2 states, “The bar graph shows the favorite fruit of some children. How many children like apples or pears?” (2.MD.10)

• In Chapter Test 11, page 86, Problem 4 states, “Draw lines to divide each rectangle into thirds. Show two different ways. For each way, color one third of the rectangle.” Two rectangles are provided. (2.G.3)

• In Cumulative Review 1, page 43, Problem 1 states, “There are 95 students at a book fair. 34 of them are first graders. The rest are second graders. How many second graders are at the book fair?” A bar diagram is given, and students fill in the circle for the correct answer of: 31, 61, 62, or 129. (2.OA.1)

The provided assessments also assess above-grade assessment items that could not be omitted or modified or are not mathematically reasonable. Examples include:

• In Chapter Test 4, page 28, Problems 2, 4, 5, 6, and 7, assess 3.OA.8 (Solve two-step word problems using the four operations). Problem 5 states, ”A farmer has 365 apples and pears in all. He has 149 pears. How many more apples than pears does he have?” A blank bar model and blank equation are given. This problem is aligned to 2.OA.1 (Use addition and subtraction within 100 to solve one and two-step word problems). However, these numbers exceed grade level expectations because they contain numbers greater than 100.

• In Chapter Test 8, page 63, Problem 4 states, “Alyssa has 12 stickers. She gives an equal number of stickers to 3 friends. How many stickers does each friend get?” This problem aligns to 3.OA.2 (Interpret whole-number quotients of whole numbers).

• In Chapter Test 10, page 79, Problem 2 states, “The clock shows the time Kiara reaches school in the morning. (7:15) She takes 15 minutes to travel from home to school. What time does Kiara leave home for school?” This problem aligns to 3.MD.1 (Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes).

Additionally, the entire Chapter 6 and Chapter 9 assessments assess Grade 3 standards. In Chapter 6, Assessment Guide Teacher Edition, all problems (1 - 7) assess 3.MD.2: Measure and estimate liquid volumes and masses of objects using standard units grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one step word problems involving masses or volumes that are given in the same units. Examples include:

• Problem 1, page 37, states, “What is the mass of the ball?” A ball on a spring scale is pictured with the line pointing to 300g.

• Problem 5, page 40, states, “A gardener has 27 kilograms of soil. She uses 11 kilograms. How many kilograms of soil does she have left? Draw a bar model to help you solve the problem. Show your work and write your answer on the blank below. The gardener has ___ kilograms of soil left.”

• Problem 7, page 42, states, “The mass of a watch and two identical balls is 900 grams. The mass of the same watch and one of the balls is 650 grams. Find the mass of a ball. Find the mass of the watch. Show your work.”

##### 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: Singapore Math Grade 2 do not 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 the Engage, Learn, Try, and Practice portions of the Section (lesson). Engage activities present an inquiry task that encourages mathematical connections. Learn activities are teacher-facilitated inquiry problems that explore new concepts. Try activities include guided practice opportunities to reinforce new learning. Practice problems help students consolidate their learning, and provide teachers with information to form small differentiated learning groups.

Students engage with extensive work to meet the full intent of 2.NBT.7 (Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds). Examples include:

• In Section 2.2, Add within 1,000 without Regrouping, Learn, Problem 4, page 69, students solve, “There are 871 adults and 27 children at a concert. How many people are at the concert? Add 871 and 27 to find out.”

• In Section 2.3, Adding with Regrouping in Ones, Try, Problem 2, page 79, students add, “136 + 27.”

• In Section 3.5, Subtracting with Regrouping in Hundreds, Tens, and Ones, Try, Problem 1, page 159, students subtract, “241 - 163.”

• In Section 3.6, Subtracting Across Zeros, Problem 11, page 170, students “Subtract. Show your work. 300 - 195 = ____.”

Students engage with extensive work to meet the full intent of 2.MD.1 (Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes). Examples include:

• In Section 5.1, Measuring in Meters, Hands-on Activity, Problem 3, page 261, students “Use the meter stick to measure the lengths of the objects.” Students record measurements in a table with the following headers: “The height of your classroom door, The width of your classroom door, The length of your desk, The length of your teacher’s desk.”

• In Section 5.2, Measuring in Centimeters, Independent Practice, Problems 4 and 5, page 275, students measure lines in centimeters.

• In Section 5.5, Measuring in Feet, Hands-on Activity, Problem 2, page 305, students “Use a foot ruler to measure the length of each object.” Students record the lengths in feet of seven predetermined items on a table.

• In Section 5.6, Measuring in Inches, Independent Practice, Problems 1-2, page 315, students “Measure each line. Use an inch ruler.” Problems 1 and 2 contain pictures of lines that students measure in inches.

Within Chapter 7, Graphs and Line Plots, students engage with the full intent of 2.MD.10 (Draw a picture graph and a bar graph and solve simple problems using information given in a bar graph). Examples include:

• In Section 7.1, Picture Graphs, Hands-on Activity, Problem 1-4, page 10, students, “Make a list of four possible snacks. Conduct a survey to find out what your classmates’ favorite snacks are. Then, record your data in the tally chart. Use the tally chart in 2 to complete the picture graph. Write a question from the picture graph. Get your partner to answer the question.”

• In Section 7.2, Bar Graphs, Hands-on Activity, Problems, 1-4, pages 19-20, students, “Make a list of four possible places to go. Have your classmates choose a favorite place. Then, record your data in the tally chart. Use the tally chart in 2 to draw a bar graph. Write a question from the bar graph. Get your partner to answer the question.”

• In Section 7.2, Bar Graphs, Try, Problem 7, page 22, students use the bar graph titled, “Number of Books Read,” to solve, “The children read ___ books in all.”

Students do not have the opportunity to engage in extensive work with 2.OA.3 (Determine whether a group of objects [up to 20] has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends). Examples include:

• In Section 8.4, Odd and Even Numbers, Hands on Activity, Problem 1, page 94, states, “Take 7 (cubes). Group them in this way. (given model). Do you have an even or odd number of cubes? Why?” On page 95, Try, Problem 1 states, “Circle to make groups of 2. Then, answer each question.” Students are presented with a picture of 16 triangles in two rows of eight. They solve, “Is 16 an even or odd number?” In Independent Practice, page 97, Problem 1 states, “Circle to make groups of 2. Answer each question. Then, fill in each blank with odd or even.” Eleven dolphin erasers are given in a picture. Students solve, “Are there any (dolphins) left? How many left? 11 is an ___ number.”

Students do not have the opportunity to engage in extensive work with 2.NBT.1a (100 can be thought of as a bundle of ten tens — called a "hundred"). Examples include:

• In Section 1.1, Counting to 1,000, Learn, Problem 1, page 7, students, “Put ten (ten blocks) together to make (hundred block).” A picture of 10 ten blocks is given pointing to a hundred block and the caption, “100 one hundred.”

Materials present limited opportunities for all students to engage with extensive work to meet the full intent of 2.NBT.3 (Read and write numbers to 1,000 using base-ten numerals, number names, and expanded form). Examples include:

• Standard 2.NBT.3 is addressed in Chapter 1, Numbers to 1,000. Students have limited opportunities to write numerals, write the number name, and write the expanded form of a three-digit number.

Students do not have the opportunity to engage in extensive work with 2.NBT.6 (Add up to four two-digit numbers using strategies based on place value and properties of operations). Examples include:

• In Section 2.6, Adding Four 2-Digit Numbers, Independent Practice, Problems 15 and 16, page 104, students add and show their work. Problem 15 states, “38 + 13 + 14 + 41 = _.” Problem 16 states, “53 + 24 + 25 + 32 = _.”

Students do not have the opportunity to engage with extensive work with 2.MD.2 (Measure the length of an object twice, using length units of different lengths of the two measurements; describe how the two measurements relate to the size of the unit chosen). Examples include:

• In Section 5.7, Comparing and Ordering Customary Lengths, Independent Practice, Problem 5, page 326, students “measure the height of a table using inches. Then, measure the height using feet. Did it take more inches or more feet to measure the height? Explain.”

Students do not have the opportunity to engage in extensive work with 2.MD.7 (Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.). Examples include:

• In Section 10.1, Reading and Writing Time, Independent Practice, Problems 9-14, page 212, students write the time on each clock. Problem 9 displays a clock with the time 9:15. Problem 10 displays a clock with the time 7:50. Problem 11 displays a clock with the time 12:30.

#### 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 2 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: Singapore Math Grade 2 do not meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade.

When implemented as designed, the materials for Grade 2 Math In Focus 2020 devote less than 65% of class time to major work of the grade and/or supporting work connected to the major work of the grade.

• The approximate number of chapters devoted to major work of the grade (including assessments and supporting work connected to the major work) is 5 out of 11, approximately 45%.

• The approximate number of sections (lessons) devoted to major work of the grade (including assessments and supporting work connected to the major work) is 41 out of 87, approximately 47%.

• The approximate number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 86 out of 160, approximately 54%.

A day-level analysis is most representative of the instructional materials as the days include major work, supporting work connected to major work, and the assessments embedded within each chapter. As a result, approximately 54% 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 Grade 2 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Materials are designed so that supporting standards/clusters are connected to the major standards/ clusters of the grade. Examples include:

• In Section 7.1, Picture Graphs, Independent Practice, page 13, Problems 3, 4, 9, and 10 connect the supporting work of 2.MD.10 (Draw a picture graph and a bar graph [with single-unit scale] to represent a data set with up to four categories...) to the major work of 2.OA.1 (Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions...). Problem 3 states, “How many fewer lilies than sunflowers are there?” Problem 4, “How many more roses than lilies and daisies are there?” Problem 9 states, “Bear has __ more apples than Hedgehog.” Problem 10 states, “Fox and Hedgehog have __ more apples than Racoon and Bear.”

• In Section 7.3, Line Plots, pages 28 and 29, Hands on Activity connects the supporting work of 2.MD.9 (Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object...) to the major work of 2.MD.1 (Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes). Students collect measurements in inches of classroom objects, record the measurements in a table, and then display the data on a line plot. Students “Work in groups. 1. Find four possible objects less than 4 inches on your desk or in your classroom. 2. Measure the length of each object to the nearest inch. Then, record your data in the table. 3. Collect the measurements from two other classmates. Then, record all of your data in the tally chart. 4. Use the tally chart in 3 to draw a line plot.”

• In Chapter 7, Graph and Line Plots, Performance Task, page 47, Problems 1 and 2 connect the supporting work of 2.MD.10 (Draw a picture graph and a bar graph [with single-unit scale] to represent a data set with up to four categories) to the major work of 2.OA.2 (Fluently add and subtract within 20 using mental strategies). Problem 1 states, “The animals shown below are found near a pond. Draw a picture graph. Use (triangles) to stand for 1 animal.” Problem 2 states, How many animals are there in all?”

• In Section 10.5, Real-World Problems, Money, Try, page 251, Problem 1 connects the supporting work of 2.MD.8 (Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $and ¢ symbols appropriately) to the major work of 2.OA.1 (Represent and solve problems involving addition and subtraction). Students “Solve. Use the bar model to help you. A toy train costs$42. A toy car costs $38 more. A toy airplane costs$99. How much does the toy car cost? How much more does the toy airplane cost than the toy car?”

##### 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 Grade 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. The instructional materials contain connections between major work and major work, and connections between supporting work and supporting work. Examples include:

• In Section 2.5, Adding with Regrouping in Ones and Tens, Try, page 94, Problem 1 connects the major work of 2.NBT.B (Use place value understanding and properties of operations to add and subtract) to the major work of 2.NBT.A (Understand place value as students connect regrouping ones and tens to their understanding that 100 can be thought of as a bundle of ten tens). Students “Practice adding within 1,000 with regrouping in ones and tens. 1) 288 + 23 = ? First, add the ones. Regroup the ones into tens and ones. Next, add the tens. Regroup the tens into hundreds and tens. Then, add the hundreds.” Pictures of place value blocks showing 288 and 23 are given.

• In Section 3.1, Subtracting Fluently within 100, page 123, Hands-on Activity connects the major work of 2.OA.A (Represent and solve problems involving addition and subtraction) to the major work of 2.OA.B (Add and subtract within 20). Students “Pick one item from the bag. Think of a story using the item that you pick. Use the name of two friends and numbers smaller than 20. Show the story with an addition or a subtraction sentence.”

• In Section 4.1, Using Part-Whole in Addition and Subtraction, Try, page 191, Problem 1 connects the major work of 2.OA.A (Represent and solve problems involving addition and subtraction) to the major work of 2.NBT.B (Use place value understanding and properties of operations to add and subtract). Students solve, “A restaurant bought 72 bags of potatoes last week. The same restaurant bought 28 bags of potatoes this week. How many bags of potatoes did the restaurant buy in all?”

• In Section 5.3, Comparing and Ordering Metric Lengths, Try, page 283, Problem 3 connects the major work of 2.OA.B (Add and subtract within 20) to the major work of 2.MD.A (Measure and estimate lengths in standard units), as students subtract lengths to determine which object is longer. Students solve, “How much longer is the pencil than the crayon? __ - __ = __   The pencil is __ centimeters longer than the crayon.” Pictures of a crayon, pencil, and ruler are given with measurements.

No connections between supporting work and supporting work were found; however, there was only one missed connection determined to be mathematically reasonable:

• No connections were found for 2.OA.C (Work with equal groups of objects to gain foundations for multiplication) and 2.G.A (Reason with shapes and their attributes). Connections between arrays with groups of objects and arrays created by partitioning rectangles were not present in the materials.

##### 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 Grade 2 partially meet the expectations that content from future grades is identified and related to grade-level work and relating grade-level concepts explicitly to prior knowledge from earlier grades.

The materials include connections to prior knowledge from earlier grades. Connections can be found in the Math Background or Learning Continuum; however, the standards are not cited in the explanations.  Examples include:

• In Chapter 1, Numbers to 1,000, Chapter Overview, Math Background, page 1A states, “In Grade 1, children have learned to count numbers to 120. They have also learned to read and write the numbers. They have extended the knowledge of counting numbers to separating the numbers into tens and ones and then, expressing them using the place values. Students have practiced strategies that will be revisited, such as, comparing and ordering numbers. In this chapter, students will extend their concept of numbers and learn how to read, write, count, and compare numbers up to 1,000.”

• In Chapter 3, Subtraction Within 1,000, Chapter Overview, Math Background, page 117A states, “In Grade 1, students have learned the concepts of number bonds and place value. They have applied these concepts to subtract within 100 using subtraction algorithm. Students have practiced strategies that will be revisited, such as counting back, using place-value charts and number bonds, and subtracting mentally.” Page 117C states, “In Grade 1 Chapter 11, students learned: Subtraction without regrouping (1.NBT.6) Subtraction with regrouping. In Grade 2, What are students learning? Subtract numbers within 20 mentally using different strategies. (2.OA.2) Use subtraction strategies and algorithm to subtract numbers within 100. (2.NBT.5, 2.NBT.8).”

• In Chapter 4, Using Bar Models: Addition and Subtraction, Chapter Overview, Learning Continuum, page 181C states, “In Grade 1 Chapter 5, students have learned: Real-world problems: addition and subtraction facts. (1.OA.1) In Grade 1 Chapter 8, students have learned: Real- world problems: addition and subtraction. (1.OA.2).” In Key Learning Objectives, page 181A states, “In Section 1, students will learn to interpret the part-whole concept in the addition and subtraction problems by representing them using bar models. In Section 2, students will extend the use of concrete manipulatives to add on or to take away sets to subtract. In Section 3, students will learn to interpret and represent the concept of comparing in addition and subtraction problems pictorially.”

• In Chapter 7, Graphs and Line Plots, Chapter Overview, Math Background, page 1A states, “In Grade 1, students have learned how to analyze simple picture graphs and use them to answer questions. They have also learned to collect and organize data in tally charts and bar graphs. Reading and interpreting picture graphs involved only counting the number of symbols in each category. Students have also learned to use appropriate vocabulary to compare the set of data. In Grade 2, students will learn how to analyze more complex picture graphs, bar graphs, and line plots. Students will learn that the same set of data can be represented in different ways.”

• In Chapter 11, Shapes, Chapter Overview, Math Background, page 279A states, “In Grade 1, students have learned to identify some flat shapes and some solid shapes. They have also been introduced to the concepts of sides and corners of flat shapes. In Grade 2, students will learn about more flat shapes and understand the difference between lines and curves. They will learn to make different figures using lines and curves. They will review attributes like sides, corners, and angles for each shape, as well as, identify the shapes in real-life objects.”

Chapters 1, 2, 3, 4, 5, 7, 10, and 11 include connections to future learning. Within these chapters, connections can be found in the Math Background or Learning Continuum. The connections do not clearly identify how the content is connected, as the future grade-level work is a bulleted list of lesson titles from the Grade 3 textbook. Chapters 6, 8, and 9 could not be included in the analysis as they represent above-grade-level content. Examples include:

• In Chapter 1, Numbers to 1,000, Chapter Overview, Learning Continuum, pages 1C and 1E states, “What have students learned? In Grade 1 Chapter 10, students have learned: Counting to 120. (1.NBT.1), Place Value (1.NBT.2), Comparing, ordering, and patterns. (1.NBT.3) What will students learn next? In Grade 3 Chapter 1, students will learn: Counting to 10,000, Place value, Comparing and ordering numbers, Round numbers to the nearest ten. (3.NBT.1), Round numbers to the nearest hundred. (3.NBT.1).”

• In Chapter 1, Numbers to 1,000, Chapter Overview, Learning Continuum, pages 1C-1E states, “What are students learning? Use base-ten blocks to count, read, and write numbers to 1,000. Count on by 1s, 10s, and 100s to 1,000. (2.NBT.1a, 2.NBT.2, 2.NBT.3) Use a place- value chart to read, write, and represent numbers to 1,000. (2.NBT.1, 2.NBT.1b, 2.NBT.2, 2.NBT.3) Read and write numbers to 1,000 in expanded form, standard form, and word form. (2.NBT.1, 2.NBT.3) Use base-ten blocks and place-value charts to compare numbers. (2.NBT.4) Compare numbers using the terms greater than and less than. (2.NBT.4) Compare numbers using symbols < and >. (2.NBT.4) In Grade 3 Chapter 1, students will learn: Counting to 10,000. Place value. Comparing and ordering numbers. Round numbers to the nearest ten. (3.NBT.1) Round numbers to the nearest hundred. (3.NBT.1).”

• In Chapter 2, Addition Within 1,000, Chapter Overview, Learning Continuum, pages 51C-51E, students are learning to “Use addition strategies and algorithm to add up to 3-digit numbers with regrouping in tens and ones (2.NBT.7, 2.NBT.9) Use addition strategies and algorithm to add up to four 2-digit numbers (2.NBT.6, 2.NBT.9) In Grade 3 Chapter 2, students will learn: Adding fluently within 1,000.(3.NBT.2) Adding without regrouping. (3.OA.8) Adding with regrouping. (3.OA.8).”

• In Chapter 3, Subtraction within 1,000, Chapter Overview, Learning Continuum, page 117E states, “What are students learning? Subtract numbers within 20 mentally using different strategies. (2.OA.2) Use subtraction strategies and algorithm to subtract numbers within 100. (2.NBT.5, 2.NBT.8). In Grade 3 Chapter 3, students will learn: Subtracting fluently within 1,000.” (3.NBT.2) Subtracting without regrouping. (3.OA.8) Subtracting with regrouping. (3.OA.8).”

• In Chapter 4, Using Bar Models: Addition and Subtraction, Chapter Overview, Learning Continuum, pages 181C-181E, students are learning to "use bar models to solve two-step addition and subtraction real-world problems (2.OA.1, 2.NBT.7). In Grade 3, students will learn: Real-world problems: addition (3.OA.8, 3.NBT.1) Real-world problems: subtraction (3.OA.8, 3.NBT.1)."

• In Chapter 10, Time and Money, Chapter Overview, Key Learning Objectives, page 197A states, “In Sections 1 and 2, students will learn to show and tell time for every five minutes after the hour. Students will learn to use visual clues in pictures along with the representation of clocks to tell time using A.M. and P.M.” On page 197E, Learning Continuum states, “In Grade 3 Chapter 10, students will learn: Telling time. (3.MD.1) Converting hours and minutes. Measuring elapsed time. (3.MD.1).”

##### 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 Grade 2 fosters coherence between grades and can be completed within a regular school year with little to no modification.

According to the Teacher’s Chapter Planning Guide and the Common Core Pathway and Pacing, the instructional materials can be completed in 160 days. The Common Core Pathway and Pacing identifies 31 days of lessons that are not aligned to standards for this grade level. If these 31 days of instruction are removed, the total days needed to complete the materials is 129.

There are 12 Chapters representing 160 days of instruction. Each Chapter includes:

• Chapter Opener and Recall Prior Knowledge - 1 day

• Sections (lessons) - range from 1 to 4 days

• Math Journal and Put on Your Thinking Cap! - 1 day

• Chapter Review, Performance Task, Project Work, and Chapter Assessment - 2 days

• Cumulative Assessments - 4 days

The Sections (lessons) consist of four components: Engage, Learn, Try, and Independent Practice.

• Engage activities present an inquiry task that encourages mathematical connections.

• Learn activities are teacher-facilitated inquiry problems that explore new concepts.

• Try activities include guided practice opportunities to reinforce new learning.

• Independent Practice problems help students consolidate their learning and provide teachers information to form small group differentiation learning groups.

### 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

## 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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