## Singapore Math: Primary Mathematics Common Core Edition

##### v1
###### Usability
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## Report for 5th Grade

### Overall Summary

The instructional materials for Primary Mathematics Common Core Edition Grade 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.

##### 5th Grade
###### Alignment
Does Not Meet Expectations
Not Rated

### Focus & Coherence

The instructional materials for Primary Mathematics Common Core Edition Grade 5 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
Does Not Meet Expectations

#### Criterion 1.1: Focus

Materials do not assess topics before the grade level in which the topic should be introduced.

The instructional materials reviewed for Primary Mathematics Common Core Edition Grade 5 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' | indicatorName}}
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.

The instructional materials reviewed for Primary Mathematics Common Core Edition Grade 5 do not meet expectations for assessing grade-level content. The materials include Differentiated Unit Tests and Continual Assessments (Books 5A and 5B). 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 5A and 5B, includes Unit Tests for each of the thirteen 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 3, 6, and 9 respectively, and there is an End-of-Year Test.

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

• Write and evaluate numerical expressions involving whole number exponents. (6.EE.1) Unit 1, Test B, #4: “Which of the following show the prime factorization for 36? A. $$2^2\times3^3$$ B. $$2^3\times3^6$$ C. $$2^3\times3$$ D. $$3\times6$$”
• Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. (6.NS.4) Unit 1, Test B, #8: “What is the lowest common multiple of 3 and 7?”
• Interpret and compute quotients of fractions. (6.NS.1) Unit 4, Test A, #13: 3/5 ÷ 3/10 = ______ ”
• Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes. (6.G.1) Unit 5, Test B, #7: “The figure below is made up of two identical rectangles ABCD and BCEF. The area of triangle ACE is 1/2 the area of which rectangle?” [Diagram included in question.]
• Summarize numerical data sets in relation to their context such as by giving quantitative measures of center (median and/or mean) and variability. (6.SP.5c) Unit 10, Test A, #9: “The average mass of three packages is 29.5 kg. If the total mass of Package A and Package B is 53.3 kg, what is the mass of Package C?”
• Find a percent of a quantity as a rate per 100; solve problems involving finding the whole, given a part and the percent. (6.RP.3c) Unit 12, Test A, # 5: “There are 150 passengers on board a train. Thirty of them are traveling to the airport, and the rest are traveling to work. What percentage of the passengers are traveling to work? A. 25% B. 20% C. 60% D. 80% “
• Understand ratio concepts and use ratio reasoning to solve problems. (6.RP.A) Unit 13, Test A, # 7, “A car travels a distance of 510 km on 30 liters of gasoline. The rate is _____ km per liter.”

The reviewers also noted test items that assessed grade-level content. For example:

• Continual Assessment 3, Test B, #8: "A jug contained 3 liters of milk. After 400 ml of milk was poured out, what was the volume of milk left in the jug?" (5.MD.1)
• Unit 4 Test A, #3: "Makayla cuts 1/3 of a pie into 3 pieces. What fraction of the whole pie is each piece?" (5.NF.7)

#### Criterion 1.2: Coherence

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.

The instructional materials reviewed for Primary Mathematics Common Core Edition Grade 5 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' | indicatorName}}
Instructional material spends the majority of class time on the major cluster of each grade.

The instructional materials reviewed for Primary Mathematics Common Core Edition Grade 5 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 14 out of 29, which is approximately 48 percent.
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 71 out of 144, which is approximately 49 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 49 percent of the instructional materials focus on major work of the grade.

#### Criterion 1.3: Coherence

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.

The instructional materials for Primary Mathematics Common Core Edition Grade 5 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, and miss connections between two or more clusters in a domain or two or more domains.

##### Indicator {{'1c' | indicatorName}}
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The instructional materials reviewed for Primary Mathematics Common Core Edition Grade 5 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 5 where connections are made between major and supporting work are not always noted in the Teacher’s Guide. Some examples of where the materials make connections between supporting and major work include:

• In Unit 8, Lesson 5a (Teacher’s Guide 3B, page 204/Student Textbook, page 128) students convert measurements involving decimals (5MD.A) which supports and connects to the work of 5.NBT.A, understanding the place-value system.
• In Unit 8, Lessons 8.5a and 8.5b, students convert a decimal measurement to a smaller unit or a compound unit and convert a measurement unit to a larger unit as a decimal (supporting standard, 5.MD.1). There are natural connections made to the major work of multiplication of decimals (5.NBT.5). Student Textbook, page 54, #1a says, “Express 0.75 m in centimeters. 0.75 m = 0.75 x 100 cm = _____ cm” The connection is not noted in the Teacher’s Guide.
• In Unit 10, Lesson 10.2a, students work with line plots (supporting standard, 5.MD.2), which is connected to the major work of adding and subtracting fractions with unlike denominators (5.NF.1). Student Workbook 5B, page 73, #1 says, “The following are measurements of the amount of time it took to do an activity to the nearest twelfth of an hour - 1 2/3, 1 5/6, 1 1/2, 1 1/3, 1 2/3, 1 2/3, 1 1/4, 1 7/12, 1 3/4, 1 5/6, 1 1/4, 1 5/12.” [Students need to plot the measurements and answer questions related to the measurements.] This connection is not noted in the Teacher’s Guide.

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

• Unit 2, Lessons 1a and 1b addresses operations and algebraic thinking (5.OA) without any connection to major work of Grade 5, such as 5.NBT.A and 5.NBT.B.
• In Unit 11, students work with two-dimensional figures and subcategories of categories and classify 2-D figures based on properties (supporting standards 5.G.3,4) without connections to major work of the grade.
##### Indicator {{'1d' | indicatorName}}
The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.

Instructional materials for Primary Mathematics Common Core Edition Grade 5 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 144 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' | indicatorName}}
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.

The instructional materials for Primary Mathematics Common Core Edition Grade 5 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 5 reflects standards above grade level. Materials make connections to previous grades; however, content from future grades is not identified. For example:

• In Unit 1, the mathematics includes finding the lowest common multiple and greatest common factor of pairs of numbers (6.NS.4). For example, “Find the lowest common multiple of each set of numbers. (a) 3 and 5; (b) 6 and 8; (c) 4, 6, and 9” in Student Workbook 5A, page 14.
• In Unit 1, the mathematics includes finding the prime factorization of a number (6.EE.1). For example, “List the composite numbers between 47 and 51 and show the prime factorization of each” in Student Workbook 5A, page 15.
• In Unit 2, the mathematics includes applying the order of operations to expressions with and without parenthesis (6.EE.2). For example, “Find the value of each of the following. (a) 7 x 9 + 1 ÷ 1 - 6 x 3; (b) (108 + 12) ÷ 5 x 6; (c) 60 ÷ 5 + 24” in Student Workbook 5A, page 31.
• In Unit 6, the mathematics includes ratios that align with Grade 6 CCSS (6.RP.1, 6.RP.2, 6.RP.3). For example, “The ratio of Gary’s mass to Andy’s mass is 4:5. Their total mass is 117 kg. (a) Find Andy’s mass. (b) Find Gary’s mass” in Student Workbook 5A, page 174.

The Grade 5 Teacher’s Guides (5A and 5B) include a Developmental Continuum (5A-page vii-xi and 5B page vii-xi) 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 1 in Teacher’s Guide 5A, page 4 states, “In Primary Mathematics 3A, students learned to relate 4-digit numbers to the place-value concept. In Primary Mathematics 4A, the place-value concept was reinforced and extended to 6-digit numbers. In this lesson, the place-value concept will be extended to hundred billions, or numbers with 12 digits.”
• Unit 7 in Teacher’s Guide 5B, page 13 states, “In Primary Mathematics 3A, students learned to round numbers of up to four digits to the nearest ten, hundred, or thousand. In Primary Mathematics 4A, they learned to round larger numbers to the nearest hundred, thousand, ten thousand, and hundred thousand. In Primary Mathematics 4B, students learned to round decimals to a whole number and to one decimal place. In this lesson, students will review rounding decimals to a whole number or one decimal place and extend this to rounding decimals to two decimal places.”
• Unit 10 in Teacher’s Guide 5B, page 142 states, “In earlier levels of Primary Mathematics, students learned how to locate points on both horizontal and vertical number lines. In this lesson, students will learn to graph positive points on a plane by using a coordinate grid.”

In Grade 5, students have extensive work with grade-level problems. In each lesson, students are guided through the topic of the day with problems demonstrated by the teacher, discussion problems (which include problems in the student workbook), assessment problems (which are formative assessment problems in the student workbook), and practice problems (which students complete on their own in the workbook). For example, Unit 3, Lesson 2 Fractions and Division, Textbook 5A, page 63 focuses on 5.NF.3 and gives the students two illustrations with explanation on how 3 divided by 4 is 3/4 and how 5 divided by 4 is 5/4. Students show “another way” to use the standard algorithm for division of 5 divided by 4. Students then complete eight problems, varying from procedural to conceptual/word problems (one problem (#2 on page 64), students need to answer using two methods). The workbook pages that correlate give the students 16 problems to solve using their knowledge learned.

However, as noted previously in this report, the presence of above grade-level work represented in the units detracts from the grade-level work. There are limited opportunities for enrichment and reinforcement of grade-level work.

##### Indicator {{'1f' | indicatorName}}
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.

The instructional materials for Primary Mathematics Common Core Edition Grade 5 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 5 include learning objectives that are visibly shaped by the CCSSM cluster headings. For example:

• In Unit 8, Lesson 8.5a (Teacher’s Guide 5B, page 78), students convert meters to centimeters, feet to inches, quarts to cups, gallons to quarts, pounds to ounces, kilometers to meters and vice versa (5.MD.1). This lesson is shaped by 5.MD.A, “Convert like measurement units within a given measurement system." For example, Student Textbook 5B, page 55, “Express 4.2 L in liters and milliliters.”
• In Unit 9, Lesson 9.1a (Teacher’s Guide 5B, page 93), students find the volume of solids made up of 1-cm cubes (5.MD.3), which is shaped by 5.MD.C, “Geometric measurement: Understand concepts of volume.” For example, in Student Workbook, page 48, “How many 1-cm cubes are needed to fill a rectangular container that measures 3 cm by 3 cm by 4 cm?”
• In Unit 3, Lesson 3.5a (Teacher’s Guide 5A, page 140), students utilize pictures, models and number lines to multiply a fraction by a whole number (5.NF.4), which is shaped by 5.NF.B, “Apply and extend previous understandings of multiplication and division.”

The materials for Primary Mathematics Common Core Edition Grade 5 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 5, Lesson 5.2a (Teacher’s Guide 5A, page 227) connects the major cluster, “Use equivalent fractions as a strategy to add and subtract fractions” (5.NF.A) to the major cluster, “Apply and extend previous understandings of multiplication and division” (5.NF.B). Students find the area of a composite figure, including sides with fractional lengths. For example, in Student Workbook 5A, page 141, students find the area of figures where some of the figures have side lengths of mixed numbers. (Figure D - 10 1/2 inch sides, Figure E - 8 2/3 inch side)
• Unit 7, Lesson 7.4d (Teacher’s Guide 5B, page 30) connects the major cluster, “Apply and extend previous understandings of multiplication and division” (5.NF.B) to the major cluster, “Perform operations with multi-digit whole numbers and with decimals to hundredths” (5.NBT.B). Students express a fraction as a decimal correct to two decimal places. For example, in Student Textbook 5B, page 27 #22, “Express each fraction as a decimal correct to 2 decimal places: (a) 3/7, (b) 5/8.”
• Unit 9, Lesson 9.1c connects the major cluster, “Use equivalent fractions as a strategy to add and subtract fractions" (3.NF.2) and the major cluster, “Apply and extend previous understandings of multiplication and division" (3.NF.3d).

The materials in Primary Mathematics Common Core Edition Grade 5 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 4 - Multiply and Divide Fractions (Teacher’s Guide 5A, pages 160-216) contains lessons that focus on one CCSSM cluster. For example, in the first lesson (4.1a, Product of Fractions, Teacher’s Guide 5A, page 165), the mathematics is focused on developing the concept of multiplying a fraction by another fraction (5.NF.B), using pictures, models, and number lines. A natural connection in this unit is, “Use equivalent fractions as a strategy to add and subtract fractions,” (5.NF.B) as students develop multiple strategies to multiply and divide fractions.
• Unit 9 - Volume (Teacher’s Guide 5B, pages 89-123) addresses the major cluster (5.MD.C) without any connection to other domains or clusters. For example, in Lesson 9.2a (Teacher’s Guide 5B, pages 99-102), the mathematics involves finding the volume of rectangular prisms, given the length, width, and height. A natural connection in this unit is the major cluster, “Performs operations with multi-digit whole numbers and with decimals to hundredths” (5.NBT.B). Problems that contain side lengths with decimal values would have connected the work of the major cluster (5.MD.C) with the major cluster (5.NBT.B).

There were three units where the Review lesson made connections with two or more clusters in a domain, or two or more domains in a grade:

• In Units 1 and 2, the Review lessons connect two or more clusters in a domain: “Understand the place value system,” (5.NBT.A) and “Perform operations with multi-digit whole numbers and with decimals to hundredths” (5.NBT.B). For example, in the Unit 1 Review, students are asked to find the value of expressions that include exponents and solve problems that require a “quick estimate.”
• In Unit 3, the Review lesson connects two or more clusters in a domain: “Use equivalent fractions as a strategy to add and subtract fractions,” (5.NF.A) and “Apply and extend previous understandings of multiplication and division to multiply and divide fractions” (5.NF.B). For example, “A piece of wood is 5 ft long. Juan used 3/4 of it to make a shelf. What is the length in feet of wood left?” (Student Workbook, page 94, #12)

### Rigor & Mathematical Practices

Materials were not reviewed for Gateway Two because materials did not meet or partially meet expectations for Gateway One
Not Rated

#### Criterion 2.1: Rigor

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' | indicatorName}}
Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
##### Indicator {{'2b' | indicatorName}}
Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
##### Indicator {{'2c' | indicatorName}}
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
##### Indicator {{'2d' | indicatorName}}
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.

#### Criterion 2.2: Math Practices

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
##### Indicator {{'2e' | indicatorName}}
The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
##### Indicator {{'2f' | indicatorName}}
Materials carefully attend to the full meaning of each practice standard
##### Indicator {{'2g' | indicatorName}}
Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
##### Indicator {{'2g.i' | indicatorName}}
Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
##### Indicator {{'2g.ii' | indicatorName}}
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.
##### Indicator {{'2g.iii' | indicatorName}}
Materials explicitly attend to the specialized language of mathematics.

### Usability

This material was not reviewed for Gateway Three because it did not meet expectations for Gateways One and Two
Not Rated

#### Criterion 3.1: Use & Design

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
##### Indicator {{'3a' | indicatorName}}
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.
##### Indicator {{'3b' | indicatorName}}
Design of assignments is not haphazard: exercises are given in intentional sequences.
##### Indicator {{'3c' | indicatorName}}
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.
##### Indicator {{'3d' | indicatorName}}
Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
##### Indicator {{'3e' | indicatorName}}
The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

#### Criterion 3.2: Teacher Planning

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
##### Indicator {{'3f' | indicatorName}}
Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
##### Indicator {{'3g' | indicatorName}}
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.
##### Indicator {{'3h' | indicatorName}}
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.
##### Indicator {{'3i' | indicatorName}}
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.
##### Indicator {{'3j' | indicatorName}}
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).
##### Indicator {{'3k' | indicatorName}}
Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
##### Indicator {{'3l' | indicatorName}}
Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.

#### Criterion 3.3: Assessment

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
##### Indicator {{'3m' | indicatorName}}
Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
##### Indicator {{'3n' | indicatorName}}
Materials provide strategies for teachers to identify and address common student errors and misconceptions.
##### Indicator {{'3o' | indicatorName}}
Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
##### Indicator {{'3p' | indicatorName}}
Materials offer ongoing formative and summative assessments:
##### Indicator {{'3p.i' | indicatorName}}
Assessments clearly denote which standards are being emphasized.
##### Indicator {{'3p.ii' | indicatorName}}
Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
##### Indicator {{'3q' | indicatorName}}
Materials encourage students to monitor their own progress.

#### Criterion 3.4: Differentiation

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
##### Indicator {{'3r' | indicatorName}}
Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
##### Indicator {{'3s' | indicatorName}}
Materials provide teachers with strategies for meeting the needs of a range of learners.
##### Indicator {{'3t' | indicatorName}}
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
##### Indicator {{'3u' | indicatorName}}
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).
##### Indicator {{'3v' | indicatorName}}
Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
##### Indicator {{'3w' | indicatorName}}
Materials provide a balanced portrayal of various demographic and personal characteristics.
##### Indicator {{'3x' | indicatorName}}
Materials provide opportunities for teachers to use a variety of grouping strategies.
##### Indicator {{'3y' | indicatorName}}
Materials encourage teachers to draw upon home language and culture to facilitate learning.

#### Criterion 3.5: Technology

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
##### Indicator {{'3aa' | indicatorName}}
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.
##### Indicator {{'3ab' | indicatorName}}
Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
##### Indicator {{'3ac' | indicatorName}}
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.
##### Indicator {{'3ad' | indicatorName}}
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.).
##### Indicator {{'3z' | indicatorName}}
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.

## Report Overview

### Summary of Alignment & Usability for 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
###### Alignment
Does Not Meet Expectations
Not Rated
##### 2nd Grade
###### Alignment
Does Not Meet Expectations
Not Rated

#### 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
###### Alignment
Does Not Meet Expectations
Not Rated
##### 4th Grade
###### Alignment
Does Not Meet Expectations
Not Rated
##### 5th Grade
###### Alignment
Does Not Meet Expectations
Not Rated

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### Overall Summary

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###### Usability
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