Report for 5th Grade
Overall Summary
The materials reviewed for Math in Focus: Singapore Math Grade 5 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.
5th Grade
Alignment
Usability
Overview of Gateway 1
Focus & Coherence
The materials reviewed for Math in Focus: Singapore Math Grade 5 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
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 5 do not meet expectations for focus as they do not assess grade-level content and partially 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 Grade 5 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 1, Section B, Item 9 (Paper) states, “What is the value of 23 - 5 × (7 - 3)?” Show your work and write your answer in the space below.” (5.OA.1)
In Chapter Test 2, Section B, Item 8 (Online) states, “Share 5 fruit tarts equally among 8 children. What fraction of a fruit tart will each child receive? Show your work and write your answer in the space below.” (5.NF.3)
In Cumulative Review 2, Section C, Item 22 (Paper) states, “Three boys recorded their long jump distances. Eric jumped 6 centimeters further than Daniel. Eddie jumped 0.12 meters further than Eric. The three boys jumped a total of 5.19 meters. How far did Eddie jump?” (5.MD.1)
In the Mid-Year Benchmark Assessment, Section B, Item 22 (Online) states, “Divide 7,001 by 57. Show your work and write your answer in the space below.” (5.NBT.6)
In Chapter Test 8, Section A, Item 3 (Paper) states, “Which statements about the shape are correct? Choose the two correct answers. [A picture of a kite is shown.] A) It is a kite. B) It is a rhombus. C) It has two pairs of parallel sides. D) It has two pairs of equal sides. E) Its opposite sides are equal.” (5.G.3)
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 9 (Online), all assessment items are aligned to 6.RP.1 (Understand the concept of ratio and use ratio language to describe a ratio relationship between two quantities). For example, Section A, Item 2 states, “What is the missing number? 3:7 = 12: ___ A) 16, B) 21, C) 28, D) 40.”
In Chapter Test 10 (Online), all assessment items are aligned to 6.RP.3c (Find a percent of a quantity as a rate per 100 [e.g., 30% of a quantity means 30/100 times the quantity]; solve problems involving finding the whole, given a part and the percent). For example, Section A, Item 5 states, “There are 100 red and blue beads in a box. 30 of the beads are blue. What percent of the beads are red beads?”
In Cumulative Review 4, Section A, Item 8 (Online) states, “There are 800 people at a carnival. 64% of them are adults. How many people are adults? A) 512, B) 486, C) 482, D) 480.” This item assesses 6.RP.3c (Find a percent of a quantity as a rate per 100 [e.g., 30% of a quantity means 30/100 times the quantity]; solve problems involving finding the whole, given a part and the percent).
In the End of Year Benchmark Assessment (Online), 11 of the 40 assessment items align to above-grade-level standards. For example, Section B, Item 20 states, “Express \frac{140}{700} as a percent.” (6.RP.3c)
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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 Grade 5 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 Engage, Learn, Think, Try, Hands-on 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 1.4, Multiplying and Dividing by 2-Digit Numbers Fluently, students multiply multi-digit whole numbers. In the Engage activity on page 45, students begin by using place value chips to multiply. The problem states, “What is 56 × 3? What is 56 × 20? How do you use your answers to find 56 × 23? Explain your reasoning. Can you use the same method to find 549 × 28? What is another way to find the answer? Explain your thinking to your partner.” In Learn, Problem 1, page 45, students multiply using the standard algorithm. The problem states, “Multiply 63 by 28.” Try, Problem 1, page 47, students practice multiplying by a 2-digit number, “97 × 53.” In Independent Practice, Problem 5, page 59, students multiply and estimate to check that each answer is reasonable. The problem states, “235 × 21 = ____.” Students engage with extensive work to meet the full intent of 5.NBT.5 (Fluently multiply multi-digit whole numbers using the standard algorithm).
In Section 2.1, Fractions, Mixed Numbers, and Division Expressions, students solve problems involving equal shares resulting in fractional answers. Engage, page 113, states, “Divide two square pieces of paper into three equal parts each. Put the pieces into equal groups. How many ways can you do it? How can you name each group? Now do the same in another way.” In Try, Problem 2a, page 116, students divide bars into equal pieces and write the fraction. The problem states, “Share 2 granola bars equally among 3 children. What fraction of a granola bar does each child receive? 2 ÷ 3 = ____. Each child receives ____ of a granola bar.” In Learn, Problem 1, page 117, students rewrite division expressions as mixed numbers. The problem states, “Mr. Davis made 5 pancakes. The pancakes were divided equally among his 4 children. How many pancakes did each child receive?” There are four colored pies (representing pancakes) divided into four equal parts included in the problem. Two colored rectangles are included in the problem. In Independent Practice, Problem 4, page 121, students “Express each division expression as a fraction in simplest form. Rewrite the fraction as a mixed number if necessary, 18÷ 8 = ___.” Students engage with extensive work to meet the full intent of 5.NF.3 (Interpret a fraction as division of the numerator by the denominator $$(\frac{a}{b}=a÷b)$$. Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem).
In Section 7.1, Making and Interpreting Line Plots, students make and interpret line plots with fractional data, and solve problems involving fractions. In Engage, page 73, students measure lengths and create a data display of the measurements. The materials state, “Measure each piece of ribbon in inches. Now, record the length of each piece of ribbon in feet. Then create a data display. Share with your partner how you did it.” Ten pieces of ribbon with different lengths are provided with the problem. In Try, Problem 1, page 75, students make and interpret line plots. The problem states, “The tally chart (provided) shows the weights of the raisins in 12 bags of trail mix. Use the data to fill in the table and make a line plot.” In Independent Practice, Problem 2, page 77, states, “The table (provided) shows the weights of 10 wedges of cheese. Use the Line plot in 1 to answer 2 and 3. What is the total weight of the 10 wedges of cheese?” Students engage with extensive work to meet the full intent of 5.MD.2 (Make a line plot to display a data set of measurements in fractions of a unit $$(\frac{1}{2}, \frac{1}{4}, \frac{1}{8})$$. Use operations on fractions for this grade to solve problems involving information presented in line plots).
In Section 7.3, Number Patterns and Graphs, students identify and extend number patterns and the relationship between two sets of numbers. In Engage, Problem 1, page 91, students find a rule in a number pattern. The problem states, “Look at each number pattern. a) 2, 4, 8, 16, …, b) 2, 3, 5, 8, 13, … Discuss with your partner how you can find the rules of the patterns.” In Learn, Problem 1, page 94, students generate patterns from a table and draw graphs. The problem states, “Two water bottles A and B are being filled at two different taps. Bottle A is filling at a rate of 50 milliliters of water every second. Bottle B is filling at a rate of 25 milliliters of water every second. The tables show the total amount of water in the two water bottles during the first 5 seconds. How much water is in each bottle after 4 seconds?” In Try, Problem 1, page 98, students generate patterns and draw graphs. The problem states, “Complete the number pattern. Then, plot each point on a coordinate plane and make a line graph. Car A consumes 1 gallon of gas for every 35 miles it travels. Car B consumes 2 gallons of gas for every 60 miles it travels.” Two tables and a graph are shown for cars A and B showing the gas each car consumed (gal) and distance traveled (mL). In Independent Practice, Problem 2 on page 101, students identify the rule in each pattern. A table showing the pattern is given “Pattern: 26, 52, 104, 208, 416, … Rule: _______.” Students engage with extensive work to meet the full intent of 5.OA.3 (Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane).
In Section 8.2, Classifying Polygons, students classify polygons using a hierarchy based on properties. In Engage, page 131, students draw and describe four sided shapes. The materials state, “Draw 2 different shapes with four equal sides. How are they the same? How are they different?” In Learn, Problem 1, page 131, students classify polygons. The problem states, “When all sides of a polygon are equal and all the angles within the polygon are equal, the polygon is called a regular polygon.” In Try, Problem 5, page 134, states, “Write trapezoid, parallelogram, rectangle, rhombus, kite, or square.” In Independent Practice, Problem 3, page 135, states, “Name each polygon. Identify whether each is a regular polygon. Name ______ Is this a regular polygon? ______. “ A picture of an octagon is provided. Students engage with extensive work to meet the full intent of 5.G.4 (Classify two-dimensional figures in a hierarchy based on properties).
Materials do not provide students the opportunity to engage with the full intent of some grade-level standards. Examples include:
Students are not provided the opportunity to engage with the full intent of 5.NBT.1 (Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and $$\frac{1}{10}$$ of what it represents in the place to its left). For example, in Section 1.1, Numbers to 10,000,000, Try, Problem 9, page 15, students read and write numbers to 10,000,000 in expanded form, standard form, and word form. The problem states, “Complete each expanded form. 2,300,598 = 2,000,000 + _____ + 500 + 90 + 8.” In Independent Practice, Problem 7, page 17, students read numbers in standard form and write them in word form. The problem states, "Write each number in word form: 1,215,905 _________.” According to the CCSS Correlations Chart in the Teacher Manual, page T71, this standard is addressed in Chapter 4 on nearly every page, but no evidence of this standard is present in the student work. Additionally, students do not have extensive work with problems involving an explanation of how digits are $$\frac{1}{10}$$ of what they represent to their place to its left. Students read and write numbers up to 10,000,000 in standard, expanded, and word form. Therefore, students do not have the opportunity to engage with the full intent of 5.NBT.1.
Students are not provided the opportunity to engage with the full intent of 5.MD.1 (Convert among different-sized standard measurement units within a given measurement system and use these conversions in solving multi-step, real world problems). Students only work with metric unit conversions. There is no evidence of conversions with customary units of measurements, intervals of time, money; or solving real-world problems using these conversions. For example, Section 5.8, Converting Metric Units, Engage, Problem 1, page 416, states, “What is 1 centimeter in meters? What is 8 centimeters in meters? What are two ways to find the answer?” In Learn, Problem 3, page 417, states, “Convert 2,500 grams to kilograms.” According to the CCSS Correlations Chart, Teacher Manual on page T7, this standard is also addressed on pages 27-42, 57, 55-62, and 63j-64 of the Student and Teacher Editions. However, there is no evidence that students work with customary units on these pages. Therefore, students are not given the opportunity to engage with the full intent of 5.MD.1.
Materials do not provide extensive work with all standards. Example include:
The materials do not provide extensive work with 5.NBT.3a (Read and write decimals to thousandths using base-ten numerals, number names and expanded form). Section 4.1, Understanding Thousandths, contains limited opportunities for students to write decimals to thousandths using expanded form. Additionally, students do not have the opportunity to write decimals in expanded form using fractions. In Try, Problem 10, page 298, students practice expressing thousandths as decimals. The problem states, “Fill in each blank 5 + 0.3 + 0.07 + 0.004 =_____.” Students have limited opportunities to read or write decimals with number names, write decimals to thousandths using expanded form, and write decimals in expanded form using fractions. Therefore, students do not have the opportunity to engage with extensive work of 5.NBT.3a.
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 5 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.
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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 5 do not meet expectations that, when implemented as designed, the majority of the materials address the major cluster of each grade.
There are 10 instructional chapters, of which 5.5 address major work of the grade, or supporting work connected to major work of the grade, approximately 55%.
There are 83 sections (lessons), of which 48 address major work of the grade, or supporting work connected to major work of the grade, approximately, 58%.
There are 156 days of instruction, of which 99 days address major work of the grade, or supporting work connected to the major work of the grade, approximately 63%.
A day-level analysis is most representative of the instructional materials because the days include all instructional learning components. As a result, approximately 63% of the instructional materials focus on major work of the grade.
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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: Singapore Math Grade 5 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. Examples include:
Section 1.5, Order of Operations, connects supporting work of 5.OA.1 (Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols) to the major work of 5.NBT.5 (Fluently multiply multi-digit whole numbers using standard algorithm), and 5.NBT.6 (Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division, illustrate and explain the calculation by using equations, rectangular arrears, and/or area models). In Independent Practice, Problem 7, page 74, states, “Find the value of each expression. Then, use a scientific calculator to check each answer. 35 × (560 ÷ 70) =_____.”
Section 1.6, Real World Problems: Four Operations of Whole Numbers, connects the supporting work of 5.OA.A (Write and interpret numerical expressions) to the major work of 5.NBT.B (Perform operations with multi-digit whole numbers and with decimals to hundredths as students interpret story problems and use operations to solve). In Try, Problem 5, page 81, states, “The table shows the wages of workers in a plumbing company. Ms. Clark works Tuesday through Sunday. How much does Ms. Clark earn in six days?” A table with the weekdays and weekend days are provided.
Section 5.8, Converting Metric Units, connects the supporting work of 5.MD.1 (Convert among different-sized standard measurement units within a given measurement system [e.g., convert 5cm to 0.05 ml], and use these conversions in solving multi-step real world problems) with the major work of 5.NBT.2 (Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimals multiplied or divided by a power of 10. Use whole -number exponents to denote powers of 10). In Independent Practice, Problem 1, page 419, students solve, “16.02 m = ___ x __ = ___ cm.”
Section 7.1, Making and Interpreting Line Plots, connects the supporting work of 5.MD.2 (Make a line plot to display a data set of measurements in fractions of a unit $$(\frac{1}{2}, \frac{1}{4}, \frac{1}{8})$$. Use operations on fractions for this grade to solve problems involving information presented in the line plots) to major work of 5.NF.4 (Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction). In Learn, Problem 1, page 74, students make and interpret line plots. The problem states, “Emma carried out a science experiment. She measured the volumes of colored water in 10 identical bottles and recorded her data in a table.” A table showing the volume (qt) and number of bottles is provided. A line plot showing the results of Emma's experience is shown where each x represents 1 bottle. Students solve, “a) What is the total volume of colored water in the 10 bottles? b) The total volume of the colored water in the 10 bottles is redistributed equally into each bottle. What is the volume of colored water in each bottle now?”
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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: Singapore Math Grade 5 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 1.2, Multiplying by Tens, Hundreds, Thousands, and Powers of Ten, connects the major work of 5.NBT.A (Understand the place value system) to the major work of 5.NBT.B (Perform operations with multi-digit whole numbers and with decimals to hundredths, as students use place value to multiply by powers of 10). In Try, Problem 4, page 30, states, “$$88 ×10^3$$.”
Section 3.3, Real-World Problems: Multiplying Proper Fractions, connects the major work of 5.NF.A (Use equivalent fractions as a strategy to add and subtract fractions) to the major work of 5.NF.B (Apply and extend previous understandings of multiplication and division, as students solve word problems involving subtraction and multiplication of fractions). In Independent Practice, Problem 3, page 210, states, “Molly has a piece of string $$\frac{5}{6}$$ yard long. She uses $$\frac{3}{5}$$ of the string to tie a present. What is the length of string left?”
Section 6.3, Real-World Problems: Volume of Rectangular Prisms, connects the major work of 5.MD.C (Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition) to the major work of 5.NBT.B (Perform operations with multi-digit whole numbers and with decimals to hundredths, as students calculate the volume of rectangular prisms to solve multi-step real world problems involving decimals). In Try, Problem 1, page 35, states, “There are 1.75 liters of water in the rectangular container shown. How much more water is needed to fill the container completely? Give your answer in liters (1L = 1000 $$cm^3$$). Capacity of the rectangular container = __ × __ × __ = __ $$cm^3$$ = __ L. Volume of water in container = L. Volume of water needed to fill the container = __ ◯ __ = L. __ liter of water is needed to fill the container completely.”
Section 7.3 Number Patterns and Graphs, connects the supporting work of 5.OA.B (Analyze patterns and relationships) to the supporting work of 5.G.B (Classify two-dimensional figures into categories based on their properties). In Independent Practice, Problem 3, page 101, students complete number patterns in a table and graph the points on a coordinate grid. The problem states, “Catalina is drawing a map of her neighborhood. She uses 1 inch to represent 25 miles on her map. The distance on the map and actual distance written as ordered pairs are _____.” A coordinate grid is provided for students to graph the points.
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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 5 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 identifies the key learning objectives and provides an overview of how prior work connects with grade level work. Examples include:
In Teacher Edition, Chapter 1, Whole Numbers and the Four Operations, Recall Prior Knowledge, page 2, connects previous work of 4.NBT.2 (Read and write multi-digit whole numbers) with grade level work of 5.NBT.5 (Fluently multiply multi-digit whole numbers) and 5.NBT.6 (Find whole-number quotients). It states, “Students learned to read and write 6-digit numbers in Grade 4 Chapter 1, multiply and divide up to 4-digit numbers by 1-digit numbers in Grade 4 Chapter 2, and use models to solve multi-step real-world problems in Grade 4 Chapter 2.”
In Teacher Edition, Chapter 2, Fractions and Mixed Numbers, Chapter Overview, Math Background, page 107A, connects prior work 4.NF.3 (Adding and subtracting like fractions) to grade level work 5.NF.1 (Adding and subtracting fractions with unlike denominators). It states, “In addition, students will expand their knowledge of adding and subtracting fractions with like denominators to adding and subtracting fractions with unlike denominators.”
In Teacher Edition, Chapter 5, Four Operations of Decimals, Recall Prior Knowledge, page 332, connects prior learning 3.OA.C.7 (Fluently multiply and divide within 100) to grade level learning 5.NBT.7 (Add, subtract, multiply, and divide decimals to hundredths). It states, “Students have learned to read and regroup decimals to hundredths in Grade 4 Chapter 4, and to thousandths in Grade 5, Chapter 4. They have learned to add, subtract, multiply, and divide whole numbers in previous chapters and grades.”
In Teacher Edition, Chapter 7, Line Plots and the Coordinate Plane, Chapter Overview, Math Background, page 67A, connects prior learning 3.MD.3 (Draw scaled picture and bar graphs) to current learning 5.MD.2 (Make line plots). It states, “In previous grades, students learned to make and interpret picture graphs and bar graphs and read line graphs. They learned that bar graphs are useful for comparing data especially when the numbers are large, while picture graphs are better for comparing data where the numbers are small or are multiples of each other. Line plots are used to show how data changes over time.”
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? states 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 4, Decimals, Learning Continuum, What will students learn next?, page 287D, states, “In Chapter 5, students will learn: Adding decimals (5.NBT.7), Subtracting decimals (5.NBT.7), Multiplying decimals (5.NBT.7), Dividing decimals (5.NBT.7), Dividing by tens, hundreds and thousands, (5.NBT.2, 5.NBT.7), Estimating decimals (5.NBT.7), Real- world problems decimals (5.NBT.7).”
In Teacher Edition, Chapter 5, Four Operations of Decimals, Learning Continuum, What will students learn next?, page 331G, contains a list of future standards. It states, “In Course 2, Chapter 1, students will learn: Writing Rational Numbers as Decimals (7.NS.2d), Operations with Decimals (7.NS.1d, 7.NS.2c).”
In Teacher Edition, Chapter 6, Volume, Learning Continuum, What will students learn next?, page 1E, states, “In Course 1 Chapter 11, students will learn: Prisms and Pyramids (6.G.4), Surface Area of Solids (6.G.4, 6.EE.2c), Volume of Rectangular Prisms (6.G.2, 6.EE.2c), Real-World Problems: Surface Area and Volume (6.G.4, 6.EE.2c).”
In Teacher Edition, Chapter 7, Line Plots and the Coordinate Plane, Learning Continuum, What will students learn next?,page 67E, contains a list of future standards. It states, “In Grade 6, Chapter 12, students will learn: Collecting and Tabulating Data (6.SP.1, 6.SP.5a, 6.SP.5b), Dot Plots (6.SP.2, 6.SP.4), Histograms (6.SP.4).”
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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 5 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 156 days.
There are 10 instructional chapters divided into sections. The pacing for each section ranges between one to three days, consisting of 108 instructional days.
For each Chapter, one day consists of a Chapter Opener and Recall Prior Knowledge, totaling 10 days.
For each Chapter, one day is spent on the Math Journal and Put On Your Thinking Cap, totaling 10 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 20 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.
Overview of Gateway 2
Rigor & the Mathematical Practices
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.
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Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
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Materials give attention throughout the year to individual standards that set an expectation for procedural skill and fluency.
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Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.
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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).
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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.
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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.
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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.
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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.
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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.
Overview of Gateway 3
Usability
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.
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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.
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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.
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Materials include standards correlation information that explains the role of the standards in the context of the overall series.
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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.
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Materials provide explanations of the instructional approaches of the program and identification of the research-based strategies.
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Materials provide a comprehensive list of supplies needed to support instructional activities.
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This is not an assessed indicator in Mathematics.
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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.
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Assessment information is included in the materials to indicate which standards are assessed.
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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.
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Assessments include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.
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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
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Usability
1st Grade
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Usability
2nd Grade
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Usability
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.
3rd Grade
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Usability
4th Grade
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Usability
5th Grade
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Usability
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.