## Alignment: Overall Summary

The instructional materials for Primary Mathematics Common Core Edition Grade 4 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.

|

## Gateway 1:

### Focus & Coherence

0
7
12
14
5
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

## Gateway 2:

### Rigor & Mathematical Practices

0
10
16
18
N/A
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

|

## Gateway 3:

### Usability

0
22
31
38
N/A
31-38
Meets Expectations
23-30
Partially Meets Expectations
0-22
Does Not Meet Expectations

## The Report

- Collapsed Version + Full Length Version

## Focus & Coherence

#### Does Not Meet Expectations

+
-
Gateway One Details

The instructional materials for Primary Mathematics Common Core Edition Grade 4 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.

### Criterion 1a

Materials do not assess topics before the grade level in which the topic should be introduced.
0/2
+
-
Criterion Rating Details

The instructional materials reviewed for Primary Mathematics Common Core Edition Grade 4 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 material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.
0/2
+
-
Indicator Rating Details

The instructional materials reviewed for Primary Mathematics Common Core Edition Grade 4 do not meet expectations for assessing grade-level content. The materials include Differentiated Unit Tests and Continual Assessments (Books 4A and 4B). Overall, the instructional materials assess content from future grades within the majority of the Unit Tests and Continual Assessments. Above grade-level assessment items are present and could not be modified or omitted without a significant impact on the underlying structure of the instructional materials.

The assessments embedded in the Singapore Math Primary Mathematics Tests, Books A and B, include Unit Tests for each of the eleven units in the grade. Each Unit Test includes two separate tests, A and B. “Test A focuses on key concepts and include free response questions that demonstrate problem-solving skills. Test B focuses on application of analytical skills, thinking skills, and heuristics” (page 3, Test Books). Three Continual Assessments are also included and administered to students following Units 2, 5, and 7 respectively, and there is an End-of-Year Test.

Throughout the assessments, there were assessment items aligned to standards above grade level. For example:

• Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols (5.OA.1) Unit 1-Part 2, Test B, #10 “Insert parentheses to make the following equation true. 10 x 8 - 2 ÷ 2 = 120 ÷ 4”
• Add and subtract fractions with unlike denominators by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. (5.NF.1) Unit 4, Test B, #17 “Karim bought 2 kg of flour. He used 4/5 kg of flour to bake bread and 7/15 kg of flour to bake some cupcakes. How many kilograms of flour did he have left?”
• Read, write, and compare decimals to thousandths. (5.NBT.3) Continual Assessment 3, Test A, #17 “Arrange the decimals in order. Begin with the smallest. 4.075, 4.057, 4.705, 4.507”
• Interpret a fraction as division of the numerator by the denominator. (5.NF.3) Unit 3, Test A, #15 “Find the value of 14 ÷ 4. Give the answer as a fraction in its simplest form.”
• Add, subtract, multiply, and divide decimals to hundredths. (5.NBT.7) - For example: Continual Assessment 3, Test B, #28 “A piece of wire 21.8 m long is cut into 2 pieces. One piece is 3.6 m longer than the other piece. Find the length of the longer piece.”
• Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. (5.OA.2) Unit 2, Test B, #7 “Given that 359 x 12 = 4,308, what is the missing number below? 359 x 11 = 4,308 - ____”
• Recognize volume as an attribute of solid figures and understand concepts of volume measurement. (5.MD.3) Unit 11, Test A, #5 “What is the volume of this cuboid? [includes a diagram] A. $$24cm^3$$ B. $$12cm^3$$ C. $$15cm^3$$ D. $$96cm^3$$”

Examples of items that align to Grade 4 standards include:

• Unit 3, Test A, #18: "Elise bought 1 gallon of milk. She drank 1/16 of it. She used 4/16 of it to make pudding. How much milk was left?" (4.NF.3d)
• Unit 3, Test B, #20: “Some children shared a cake. When the cake was cut into eighths, each child received 2 equal slices. How many children shared the cake?" (4.NF.4c)
• Unit 9, Test A, #3: "The area of a square is 81 sq m. What is the perimeter of the square?" (4.MD.3)

### Criterion 1b

Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.
0/4
+
-
Criterion Rating Details

The instructional materials reviewed for Primary Mathematics Common Core Edition Grade 4 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

Instructional material spends the majority of class time on the major cluster of each grade.
0/4
+
-
Indicator Rating Details

The instructional materials reviewed for Primary Mathematics Common Core Edition Grade 4 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 4, which is approximately 31 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.
• 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 143, which is approximately 47 percent.

A lesson-level analysis (which includes lessons and sub lessons) is most representative of the instructional materials because it addresses the amount of class time students are engaged in major work throughout the school year. As a result, approximately 47 percent of the instructional materials focus on major work of the grade.

### Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
5/8
+
-
Criterion Rating Details

The instructional materials for Primary Mathematics Common Core Edition Grade 4 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

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Primary Mathematics Common Core Edition Grade 4 partially meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The examples from Primary Mathematics Common Core Edition Grade 4 where connections are made between major and supporting work were not always noted in the Teacher’s Guide. Some examples of where the materials make connections between supporting and major work include:

• Unit 1, Lesson 1d connects generating and analyzing patterns (supporting standard, 4.OA.5) with place-value understanding (major work, 4.NBT.1). Student Workbook 4A, page 14, #3 says: “Create a regular number pattern that starts with 493,070 and increase each number by 10,000.” This connection is not noted in the Teacher’s Guide.
• Unit 5, Lesson 1a connects conversion of units (4.MD.A) to the major work of extending understanding of fraction equivalence and ordering (4.NF.A) and building fractions from unit fractions by applying and extending previous understandings of operations on whole numbers (4.NF.B). Student Textbook 4A, page 150, #2 says: “How many months are there in 5/6 of a year?” This connection is not noted in the Teacher’s Guide.
• Unit 10, Lesson 2a connects generating and analyzing measurement data by making a line plot to display a data set including measurement sin fractions of a unit (4.MD.4) to the major work of adding fractions (4.NF.3). Student Textbook 4B, page 132, #3 says: “Carla measured the length of some earthworms to the nearest quarter of an inch. She also noted whether the worm had a swelling along its length or not.” [Students are given the data in a line plot and asked 7 questions related to the data.” These connections are not noted in the Teacher’s Guide.

Examples where units and/or lessons did not make connections between major and supporting work include:

• In Unit 8, Lessons 8.1a, 8.4a-b, 8.5a-b, 8.6a-b, and 8.8a-c address the supporting standards 4.G.1 and 4.G.2, involving measuring angles, without connections to major work.
• In Unit 9, there are missed opportunities to connect area and perimeter (supporting work, 4.MD.A) to the major work of fraction operations (4.NF.C). However, there are two questions including fractions of a whole number in the Review lesson.

### Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
2/2
+
-
Indicator Rating Details

Instructional materials for Primary Mathematics Common Core Edition Grade 4 meet expectations that the amount of content designated for one grade-level is viable for one year.

As designed, the instructional materials can be completed in 143 days. The total days were computed in the following manner:

• Each lesson was counted as 1 day of instruction. If a lesson was listed as 1-2 days, 2 days were counted. There was no indication in the Teacher's Guide of how many minutes each lesson would take.
• Any lesson that did not have an indication of days of completion was counted as 1 day.
• One day was counted for each review day indicated in the Teacher's Guide, each assessment, each Continual Assessment, and the End-of-Year Assessment.

In the Teacher's Guide is reference to a technology resource named “Primary Digital.” This is an “online digital curriculum that is designed to complement the core math materials in Singapore Math, Primary Mathematics.” The days indicated above do not count any days for using the online digital curriculum. The days noted above also do not include the mental math and reinforcement activities.

### Indicator 1e

Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
1/2
+
-
Indicator Rating Details

The instructional materials for Primary Mathematics Common Core Edition Grade 4 partially meet expectations for the materials being consistent with the progressions in the standards. Overall, materials develop according to the grade-by-grade progressions of the standards; however, some of the content within Grade 4 reflects standards above grade level. Materials make connections to previous grades; however, content from future grades is not identified. For example:

• Students solve problems aligned to 5.NF.2, (Solve word problems involving addition and subtraction of fractions referring to the same whole…)
• In Unit 3, students work with fractions beyond those expected in Grade 4. In Student Textbook 4A page 109: “Gwen bought 1 liter of tomato juice. She drank 2/7 of it in the morning. She drank 4/7 of it in the evening. How much tomato juice was left?” (5.NF.2)
• In Unit 4, Student Workbook 4A page 124, students add/subtract with unlike denominators. For example, “Mrs. Lopez bought 3 3/4 kg of beans, 1 1/2 kg of lettuce, and 1 3/4 kg of carrots. How many kilograms of vegetables did she buy altogether?”
• Students solve problems aligned to 5.NBT.3 (Read, write, and compare decimals to thousandths.)
• In Unit 6, Student Textbook 4B page 26, students read, write, and compare decimals to the thousandths (5.NBT.3). For example, “Arrange the numbers in increasing order…(b) 9.047, 9.076, 9.074, 9.067”
• There are 12 games/activities offered as reinforcement in the back of Teacher’s Guide 4A. One of these activities compares decimals to the thousandths, which is above grade level.
• In Unit 7, Student Workbook 4B page 46, students perform decimal operations to the hundredths (5.NBT.7). For example, “Mitchell jogged 5.85 km on Saturday. He jogged 1.7 km less on Sunday than on Saturday. What was the total distance he jogged on the two days?”
• There are 10 games/activities offered as reinforcement in the back of Teacher’s Guide 4B. One of the games (1.5a) relates to order of operations (6.EE.2).

The Grade 4 Teacher’s Guides (4A and 4B) include a Developmental Continuum (4A-page vi-x and 4B page vi-x) that contains an overview of topics and skills for each grade level, K-5, but no specific standards are indicated. Standards specific to units and lessons are listed in the introduction to each unit. There are no connections to future grade-level content. In each Teacher’s Guide, there is a Notes section at the beginning of each lesson that includes work learned in previous grade levels as well as the connection to the current work in the lesson. For example:

• Unit 2 in Teacher’s Guide 4A, page 81 states, “In Primary Mathematics 3, students learned how to add and subtract 4-digit numbers using the standard algorithm, how to draw bar models for word problems, and how to use some mental-math techniques in addition and subtraction. Here they will review the addition and subtraction of numbers up to 4 digits and use the bar modes. Also, they will learn some new mental math strategies.”
• Unit 1 in Teacher’s Guide 4A, (page 5), states, “In Primary Mathematics 3A, students learned to interpret a 4-digit number in terms of thousands, hundreds, tens and ones. These are called place values. These concepts are reinforced and extended to numbers up to 1,000,000.”
• Unit 7 in Teacher’s Guide 4B, page 91 states, “In Primary Mathematics 3A, students learned the formal algorithm for multiplying a whole number by a one-digit whole number. The formal algorithm will be extended to decimals in this lesson. Students should know the basic multiplication facts well and have a good understanding of place value. Mental-math strategies will also be applied in this lesson.”

Students in Grade 4 do not have extensive work with grade-level problems due to the amount of above grade-level work in the lessons which detracts from the grade-level work. There are limited opportunities for enrichment and reinforcement of grade-level work.

• In Primary Mathematics Teacher’s Guide 4A, Lesson 1.4 - Factors, page 47 under the “Notes” section, states, “In Primary Mathematics 3, students learned the term product. Here, they will learn the term factor, how to find factors of whole numbers, and how to find common factors.” (first paragraph) Further down the page it states, “Finding the greatest common factor will only be covered in Grade 5, though you may point out the greatest common factor when appropriate.” This should be noted as a Grade 6 standard (6.NS.4).

### Indicator 1f

Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.
1/2
+
-
Indicator Rating Details

The instructional materials for Primary Mathematics Common Core Edition Grade 4 partially meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the standards.

The materials for Primary Mathematics Common Core Edition for Grade 4 include learning objectives that are visibly shaped by the CCSSM cluster headings. For example:

• In Unit 1, Lesson 1.1 (Teacher’s Guide 4A, page 5), students find the standard, expanded, and written forms of numbers to the hundred-thousands place value (4.NBT.2), which is shaped by 4.NBT.A: “Generalize place value understanding for multi-digit whole numbers.” For example, Student Workbook 4A, page 7: “Mr. Royce sold his car for this amount of money [diagram included of 10,000s, 1,000s, and 100s]. (a) Write the amount of money in figures. (b) Write the amount of money in words.”
• In Unit 3, Lesson 3.2a (Teacher’s Guide 4A, page 172), students add fractions with like denominators using models and digits (4.NF.3a and 4.NF.3b), which is shaped by 4.NF.B: “Build fractions from unit fractions.” For example, in Student Textbook 4A, page 91, “Lila drank 1/5 liters of milk. Her brother drank 2/5 liters of milk. How much did they drink together?” [Students are given pictures of measuring cups indicating the level of milk in each.]
• In Unit 8, Lesson 8.1a (Teacher’s Guide 4B, page 139), students distinguish between and identify points, lines, line segments, rays, and angles, both in isolation and within figures (4.G.1), which is shaped by the 4.G.A: “Draw and identify lines and angles, and classify shapes by properties of their lines and angles.”

The materials for Primary Mathematics Common Core Edition Grade 4 include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important. For example:

• Unit 2, Lesson 2.2c (Teacher’s Guide 4A, page 111) connects the major cluster, “Use the four operations with whole numbers to solve problems” (4.OA.A) with major cluster, “Use place-value understanding and properties of operations to perform multi-digit arithmetic” (4.NBT.B). Students solve multi-step problems, most involving money to the one thousands place and involving addition, subtraction, and multiplication. For example, in Student Textbook 4A, page 56: “Mr. Cohen earns $2,935 a month. If he spends$1,780 each month and saves the rest, how much will he save in 6 months?”
• Unit 11, Lesson 11.1d (Teacher’s Guide 4B, page 245) connects the supporting cluster, “Solve problems involving measurement and conversion of measurements” (4.MD.A) with the supporting cluster, “Represent and interpret data” (4.MD.B). Students build different shapes with the same number of cubes and find the volume of multiple solids.

The materials in Primary Mathematics Common Core Edition Grade 4 include problems and materials that do not make connections with two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.

• Unit 3 - Fractions (Teacher’s Guide 4A, pages 157-203) and Unit 4 - Operations on Fractions (Teacher’s Guide 4A, pages 204-266) focus on Domain “Numbers and Operations - Fractions” and the major clusters within the domain without any connections to other domains or clusters. Connecting this work to the major cluster “Uses place-value understanding and properties of operations to perform multi-digit arithmetic," (4.NBT.B) represents a missed opportunity.
• Unit 5 - Measures (Teacher’s Guide 4A, pp.267-302) addresses the cluster, “Solve problems involving measurement and conversion of measurements” without connections to other clusters or domains. Connecting this mathematics to the cluster within the same domain, “Represent and interpret data,” would be natural and important.

## Rigor & Mathematical Practices

#### Not Rated

+
-
Gateway Two Details
Materials were not reviewed for Gateway Two because materials did not meet or partially meet expectations for Gateway One

### Criterion 2a - 2d

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.

### Indicator 2a

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
N/A

### Indicator 2b

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
N/A

### Indicator 2c

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade
N/A

### Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.
N/A

### Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice

### Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
N/A

### Indicator 2f

Materials carefully attend to the full meaning of each practice standard
N/A

### Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
N/A

### Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
N/A

### Indicator 2g.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.
N/A

### Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
N/A

## Usability

#### Not Rated

+
-
Gateway Three Details
This material was not reviewed for Gateway Three because it did not meet expectations for Gateways One and Two

### Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.

### Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
N/A

### Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
N/A

### Indicator 3c

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
N/A

### Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
N/A

### Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
N/A

### Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.

### Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
N/A

### Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
N/A

### Indicator 3h

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.
N/A

### Indicator 3i

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.
N/A

### Indicator 3j

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
N/A

### Indicator 3k

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
N/A

### Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
N/A

### Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.

### Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
N/A

### Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
N/A

### Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
N/A

### Indicator 3p

Materials offer ongoing formative and summative assessments:
N/A

### Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
N/A

### Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
N/A

### Indicator 3q

Materials encourage students to monitor their own progress.
N/A

### Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.

### Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
N/A

### Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
N/A

### Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
N/A

### Indicator 3u

Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
N/A

### Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
N/A

### Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
N/A

### Indicator 3x

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

### Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
N/A

### Criterion 3aa - 3z

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.

### Indicator 3aa

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
N/A

### Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
N/A

### Indicator 3ac

Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
N/A

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
N/A

### Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
N/A
abc123

Report Published Date: 2018/11/12

Report Edition: 2014-2017

Title ISBN Edition Publisher Year
Singapore Math Common Core Tests 4A 978‑1‑932906‑54‑7 Marshall Cavendish Education Pte Ltd 2017
Singapore Math Common Core Tests 4B 978‑1‑932906‑55‑4 Marshall Cavendish Education Pte Ltd 2017
Primary Mathematics Common Core Edition Teacher's Guide 4A 978‑981‑01‑9835‑0 Marshall Cavendish Education Pte Ltd 2014
Primary Mathematics Common Core Edition Teacher's Guide 4B 978‑981‑01‑9836‑7 Marshall Cavendish Education Pte Ltd 2014
Primary Mathematics Common Core Edition Workbook 4A 978‑981‑01‑9847‑3 Marshall Cavendish Education Pte Ltd 2014
Primary Mathematics Common Core Edition Workbook 4B 978‑981‑01‑9848‑0 Marshall Cavendish Education Pte Ltd 2014
Primary Mathematics Common Core Edition Textbook 4A 978‑981‑01‑9859‑6 Marshall Cavendish Education Pte Ltd 2014
Primary Mathematics Common Core Edition Textbook 4B 978‑981‑01‑9860‑2 Marshall Cavendish Education Pte Ltd 2014

## Math K-8 Review Tool

The mathematics review criteria identifies the indicators for high-quality instructional materials. The review criteria supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our review criteria evaluates materials based on:

• Focus and Coherence

• Rigor and Mathematical Practices

• Instructional Supports and Usability

The K-8 Evidence Guides complements the review criteria by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

## Math K-8

K‑8 Evidence Guide K‑8 Review Criteria

The EdReports rubric supports a sequential review process through three gateways. These gateways reflect the importance of alignment to college and career ready standards and considers other attributes of high-quality curriculum, such as usability and design, as recommended by educators.

Materials must meet or partially meet expectations for the first set of indicators (gateway 1) to move to the other gateways.

Gateways 1 and 2 focus on questions of alignment to the standards. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?

Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom.

In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

For ELA and math, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to college- and career-ready standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For science, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to the Next Generation Science Standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For all content areas, usability ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for effective practices (as outlined in the evaluation tool) for use and design, teacher planning and learning, assessment, differentiated instruction, and effective technology use.