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Report Overview
Summary of Alignment & Usability: Singapore Math: Primary Mathematics Common Core Edition | Math
Math K-2
The instructional materials for Earlybird Kindergarten Mathematics Common Core Edition and Primary Mathematics Common Core Edition Grades 1-2 do not meet expectations for alignment to the CCSSM. In Gateway 1, the instructional materials for Kindergarten meet the expectations for focus as they assess grade-level standards and devote at least 65% of instructional time to the major work of the grade, but the instructional materials for Grades 1-2 do not meet the expectations for focus. For coherence, the instructional materials for Grades 1-2 are partially coherent and consistent with the Standards. The instructional materials for Grades 1-2 have an amount of content designated for one grade level that is viable for one school year, but the materials partially meet expectations for the remainder of the indicators within coherence. The instructional materials for Kindergarten are not coherent and consistent with the Standards. The materials for Kindergarten were reviewed for rigor and the mathematical practices in Gateway 2, but the Kindergarten materials do not meet expectations for either of those criteria. Since the materials do not meet expectations for alignment to the CCSSM, they were not reviewed for usability in Gateway 3.
1st Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
2nd Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
Math 3-5
The instructional materials for Primary Mathematics Common Core Edition Grades 3-5 do not meet expectations for alignment to the CCSSM. In Gateway 1, the instructional materials do not meet the expectations for focus as they assess above-grade-level standards and devote less than 65% of instructional time to the major work of the grade. For coherence, the instructional materials are partially coherent and consistent with the Standards. The instructional materials have an amount of content designated for one grade level that is viable for one school year, but the materials partially meet expectations for the remainder of the indicators within coherence. Since the materials do not meet the expectations for focus and coherence in Gateway 1, they were not reviewed for rigor and the mathematical practices in Gateway 2 or usability in Gateway 3.
3rd Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
4th Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
5th Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
Report for 2nd Grade
Alignment Summary
The instructional materials for Primary Mathematics Common Core Edition Grade 2 do not meet expectations for alignment to the CCSSM. In Gateway 1, the instructional materials do not meet the expectations for focus as they assess above-grade-level standards and devote less than 65% of instructional time to the major work of the grade. For coherence, the instructional materials are partially coherent and consistent with the Standards. The instructional materials have an amount of content designated for one grade level that is viable for one school year, but the materials partially meet expectations for the remainder of the indicators within coherence. Since the materials do not meet the expectations for focus and coherence in Gateway 1, they were not reviewed for rigor and the mathematical practices in Gateway 2 or usability in Gateway 3.
2nd Grade
Alignment (Gateway 1 & 2)
Usability (Gateway 3)
Overview of Gateway 1
Focus & Coherence
The instructional materials for Primary Mathematics Common Core Edition Grade 2 do not meet expectations for focus and coherence in Gateway 1. For focus, the instructional materials do not meet the expectations for assessing grade-level standards, and the amount of time devoted to the major work of the grade is less than 65 percent. For coherence, the instructional materials are partially coherent and consistent with the Standards. The instructional materials have an amount of content designated for one grade level that is viable for one school year, but the materials partially meet expectations for the remainder of the indicators within coherence.
Gateway 1
v1.0
Criterion 1.1: Focus
The instructional materials reviewed for Primary Mathematics Common Core Edition Grade 2 do not meet expectations for not assessing topics before the grade level in which the topic should be introduced. The instructional materials include assessment items that align to standards above this grade level.
Indicator 1A
The instructional materials for Primary Mathematics Common Core Edition Grade 2 do not meet expectations for assessing grade-level content. There are many assessment items that align to standards above grade level, and the omission of the items and adaptations of the materials would affect the underlying structure of the materials.
According to the publisher, “Each level offers differentiated tests (Tests A & B) to suit individual needs. Tests consist of multiple-choice questions that assess comprehension of key concepts and free response questions that demonstrate problem-solving skills. Three continual assessments cover topics from earlier units, and a year-end assessment covers the entire curriculum.” Per Test Booklet page 3, the focus of Test A is key concepts and problem solving skills. The focus of Test B is the application of analytical skills, thinking skills, and heuristics.
Three of the twelve Grade 2 units assess multiplication and division, which aligns to 3.OA. Unit 8 addresses money and includes decimal notation, which aligns to 4.NF.C. Unit 9 addresses fractions and assesses students on comparing and ordering fractions, which aligns to 3.NF.3d. For example:
- Unit 4, Tests A and B assess multiplication, which aligns to 3.OA.
- Test A, Question 5, “What is the correct multiplication equation for the picture below?”
- Test A, Question 12, “Write 2 multiplication equations for the picture below.”
- Test B, Question 9, “Write 2 multiplication equations for the picture below.”
- Test B, Question 11, “There are 7 eggs in each basket. How many eggs are there in 3 baskets?”
- Unit 4, Tests A and B assess division, which aligns to 3.OA.
- Test A, Question 2, “Eight blocks are shared equally between 2 children. How many blocks does each child receive?”
- Test A, Question 13, “Circle to make groups of 4. Then write a division equation.”
- Test B, Question 10, “Write 2 multiplication equations and 2 division equations for the picture below.”
- Test B, Question 13, “Fourteen tickets are shared equally among some children. Each child gets 2 tickets. How many children are there?”
- Unit 5, Tests A and B assess multiplication tables of 2 and 3 and division, which align to 3.OA.
- Test A, Question 2, “Multiply 2 by 6. What is the answer?”
- Test A, Question 8, “2 x ___ = 6, 6 divided by 2 = ____”
- Test B, Question 9, “___ x 3 = 9, 9 divided by 3 = ____”
- Test B, Question 12, “Darryl has 18 guppies. He puts them equally into three tanks. How many guppies are there in each tank?”
- Unit 7, Tests A and B assess multiplication and division, which align to 3.OA.
- Test A, Question 1, “Multiply 7 by 4. What is the answer?”
- Test A, Question 3, “Kiran packed 32 apples equally into baskets. Each basket holds 4 apples. How many baskets of apples are there?”
- Test B, Question 2, “Divide 20 stickers equally among 10 children. Which equation shows the number of stickers each child receives?”
- Test B, Question 7, “4 x 7 is ____ more than 4 x 5.”
- Unit 8, Tests A and B assess money including decimal notation, which aligns to 4.NF.C.
- Test A, Question 5, “Subtract. $9.60 - $3.55 = ______.”
- Test A, Question 11, “Add. Fill in the boxes. $3.75 + $6.15 = ______.”
- Test B, Question 4, “$4.55 + $3.85 = ______.”
- Test B, Question 10, “Add. $6.30 + $5.95”
- Unit 9, Tests A and B assess comparing and ordering fractions, which aligns to 3.NF.3d.
- Test A, Question 4, “What is the greatest fraction? 1/8, 1/5, 1/3”
- Test A, Question 9, “Arrange the fractions in order. Begin with the greatest. 3/8, 1/8, 7/8“
- Test B, Question 6, “1/11 is _____ 1/7”
- Test B, Question 9, “Arrange these fractions in order. Begin with the smallest. 1/3, 1/10, 1/2, 1/5”
Criterion 1.2: Coherence
The instructional materials reviewed for Primary Mathematics Common Core Edition Grade 2 do not meet expectations for devoting the large majority of class time to the major work of the grade. The instructional materials spend less than 65% of instructional time on the major work of the grade.
Indicator 1B
The instructional materials reviewed for Primary Mathematics Common Core Edition Grade 2 do not meet expectations for spending a majority of instructional time on major work of the grade.
- The approximate number of units devoted to major work of the grade (including assessments and supporting work connected to the major work) is 6 out of 12, which is approximately 50 percent.
- The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 67 out of 146, which is approximately 46 percent.
- The number of weeks devoted to major work (including assessments and supporting work connected to the major work) is 13 out of 29, which is approximately 45 percent.
A lesson-level analysis is most representative of the instructional materials because it represents the total amount of class time that addresses major work, 46 percent. As a result, approximately 46 percent of the instructional materials focus on major work of the grade.
Criterion 1.3: Coherence
The instructional materials for Primary Mathematics Common Core Edition Grade 2 partially meet expectations for being coherent and consistent with the Standards. The instructional materials have an amount of content designated for one grade level that is viable for one school year. However, the instructional materials partially engage students in the major work of the grade through supporting content, do not identify content from future grades, do not give students extensive grade-level problems, and miss connections between two or more clusters in a domain or two or more domains.
Indicator 1C
The instructional materials reviewed for Primary Mathematics Common Core Edition Grade 2 partially meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.
Sometimes supporting work is used to enhance focus and coherence by engaging students in the major work of the Grade 2.
- A connection is made between the supporting standard 2.MD.7 and the major standard 2.NBT.2. In the Teacher’s Guide page 153, the teacher is directed to, “Ask students to use the clock face to find the number of minutes in an hour. Ask students how they can count the number of minutes in the shortest time possible; they should count by 5s.” In the Student Textbook page 68, the multiples of five are shown adjacent to the numbers on the clock face, and on Workbook page 120, students fill in the missing multiples of five that are displayed adjacent to the numbers on the clock face.
- The supporting standard 2.MD.9 is connected to the major standard 2.MD.1. In Unit 11, three connections are made between hands-on measuring and line plots. For example, in Student Textbook 2B page 93, the directions state, “Measure the length of the right feet of 15 classmates to the nearest centimeter. … Create a line plot showing the length of the feet of your classmates in centimeters.”
- Connections are made as students use their understanding of the major work of solving addition and subtraction word problems within 100 (2.OA.1) to solving word problems with money (2.MD.8). For example, on Workbook page 85, students solve the following problem: “Matthew counted his money. He had 2 twenty-dollar bills, 3 five-dollar bills, 6 one-dollar bills, 8 quarters, 4 dimes, 3 nickels, and 18 pennies. How much money did he have altogether?”
Supporting standards are often taught in isolation. Some connections are implicitly made; however, the connections are not fully explored. For example:
- Supporting standard 2.OA.4, Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. In Teacher’s Guide Lesson 4.1c, page 174, two examples of repeated addition are given; however, the focus of the chapter is moving students directly to multiplication aligned to 3.OA rather than on using arrays to build a foundation for multiplication in Grade 3.
- Materials do not sufficiently connect the supporting domain of Geometry to major work of Grade 2. In Unit 12 Geometry, one of the 7 seven lessons connects to 2.OA.2. In Lesson 12.3, students write an equation for, “How many more sides does a hexagon have than a quadrilateral?” This is the connection to 2.OA.2, and there are missed opportunities to connect 2.OA.2 to 2.G.2. For example, workbook page 163, students fill in a table on sides/angles of a shape, and natural connection would be to compare sides/angles using addition/subtraction.
Indicator 1D
Instructional materials for Primary Mathematics Common Core Edition Grade 2 meet expectations that the amount of content designated for one grade level is viable for one year.
- Instructional materials can be completed in 146 days.
- Materials include 130 instructional days and 16 days for assessment (one day per assessment), totalling 146 days.
- The suggested pacing from the publisher is one day per lesson. Each lesson is 60 minutes.
- No specific day or time for assessments is included in the Teacher’s Guide. There are assessments for each unit, three continual assessments, and an End-of-Year Assessment.
- According to the publisher, a teacher may need to supplement lessons in the book with outside resources. Teacher Edition 2B, page 200 states, “The lessons in this chapter are short and not likely difficult. You can extend the lessons easily with activities involving tangrams or pattern blocks. There are a number of sites on the Internet as well as books from which you can print out puzzles for students to form larger shapes from pattern blocks or tangrams. There are also sites on the Internet that allow students to manipulate shapes online.”
Indicator 1E
The instructional materials for Primary Mathematics Common Core Edition Grade 2 partially meet expectations for the materials being consistent with the progressions in the standards. Content from prior or future grades is not clearly identified in the materials and does not support the progressions of the grade-level standards. Materials do always relate grade-level concepts explicitly to prior knowledge.
- Each unit does begin with prerequisite skills. For example, Teacher’s Guide 2A, Unit 2, page 40 lists prerequisites: Students should have a good knowledge of place value concepts within 100 and should know addition and subtraction facts within 10.
- The Notes section in Teacher’s Guide 2A, pages 6-10 describes the continuum of skills present in each unit.
However, content from prior or future grades are not clearly identified in the materials and do not support the progressions of the grade-level standards. For example:
- In Unit 8, students work with money using decimal points. (4.NF.4)
- Workbook 2A, page 51, Problem 3: "Mr. Cohen sold 242 books. He had 304 books left. How many books did he have at first?" The problem situation uses numbers above Grade 2 standards and is not identified as such in the materials.
Materials require significant redesign in order to align them to Grade 2 standards. For example, Teacher’s Guide 2A, Unit 4, pages 163 -164 maps out approximately nine instructional days worth of lessons. However, the majority of these lessons align to Grade 3 standards. Units 4, 5, 7, and 9 address Grade 3 multiplication and division standards. The Grade 3 standards are listed in the Teacher’s Guide at the beginning of each of these units.
Primary Mathematics Common Core Edition Grade 2 materials do not provide all students extensive work with grade-level problems. Materials contain a large amount of lessons above grade level; there is not an extensive amount of time and practice for students with on grade-level problems. Less than 50 percent of the materials (70 of the 146 lessons) align to grade-level standards. There is limited practice on Standard 2.MD.10. Students are given three opportunities to complete a bar graph with information given. Two of these opportunities (Workbook 2B, pages 138 and 141) do not have “single scale units” as specified in Grade 2 CCSSM.
Indicator 1F
The instructional materials for Primary Mathematics Common Core Edition Grade 2 partially meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the standards.
Materials include learning objectives that are not consistently shaped by CCSSM cluster headings. Additionally, the cluster headings are not explicitly identified within the materials.
- Materials are not visibly shaped by the CCSSM cluster headings. Connections made are not specifically stated to the teacher and/or students.
- Several units include math that is not related to cluster headings, such as: Unit 4 Multiplication and Division, Unit 5 Multiplication Tables of 2 and 3, and Unit 7 Multiplication and Division.
- Lesson 8.1, Workbook 2B pages 66-68 include money with decimals, which do not support the Grade 2 cluster heading and go beyond Grade 2 standards.
- An NBT cluster heading for Grade 2 is, “Use place-value understanding and properties of operations to add and subtract.” Unit 2 includes several lessons that connect to this cluster heading. For example, in Teacher’s Guide, Lesson 2.1a pages 45 – 48, students add 2 one-digit numbers by decomposing one of the addends to make a partner-of-ten fact. In Teacher’s Guide, Lesson 2.2a pages 68 – 69, students use place-value disks to solve two- and three-digit addition problems.
- Workbook 2B, Lesson 10.1 pages 120-124 partially supports the cluster, "Work with time and money," by giving students the opportunity to tell and write the time from analog and digital clocks.
Materials sometimes include problems and activities that serve to connect two or more clusters in a domain; however, important connections are missed.
- An important connection between the number line and measurement is not made and opportunities to connect 1.OA.A.1 with place-value understanding are not developed.
- Unit 1: Connections are missed between 2.NBT.A.2 and 2.NBT.B.4, although both standards are identified for the lesson. In Textbook, page 25 Problem 5b, students “Count on in steps of 10: 475, 485, 495, … 535.” The opportunity to connect this to addition is missed. In Lesson 1.2b, a connection between 1.NBT.A and 1.NBT.B.7 is not identified as students write numbers within 1,000 using expanded form.
- Unit 2: Connections are made between 2.OA.A, 2.OA.B, 2.NBT.A, and 2.NBT.B. For example, in Lesson 2.2b, students solve addition and subtraction word problems using base-ten understanding. In Textbook 2A, page 44, students solve the following word problem: “There are 236 boys and 362 girls. How many children are there altogether?”
- Unit 3: Connections are made between length and addition and subtraction as students solve word problems related to length. (2.OA.A, 2.MD.A, and 2.MD.B). For example, in Textbook 2A, page 86, students solve the following word problem; “The grasshopper is 4 cm long. The fish is 6 cm long. The grasshopper is ___ cm shorter than the fish. The fish is ___ cm longer than the grasshopper.”
- Unit 6: Connections between NBT and OA are not fully developed in the chapter on addition and subtraction. There are few examples of word problems in the unit. The focus of the unit is computation.