## Alignment: Overall Summary

The instructional materials reviewed for Grade 3 partially meet the expectations for alignment to the CCSSM. The materials partially meet the expectations for focus and coherence in Gateway 1, and they partially meet the expectations for rigor and the mathematical practices in Gateway 2. Since the materials partially meet the expectations for alignment, evidence concerning instructional supports and usability indicators in Gateway 3 was not collected.

|

## Gateway 1:

### Focus & Coherence

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

## Gateway 2:

### Rigor & Mathematical Practices

0
10
16
18
14
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

#### Partially Meets Expectations

+
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Gateway One Details

The instructional materials reviewed for Grade 3 partially meet the expectations for focus on major work and coherence. The instructional materials do not meet the expectations for focus due to not spending a majority of class time on major work. The instructional materials partially meet the expectations for coherence, and they show strengths in having an amount of content that is viable for one school year and fostering coherence through connections within the grade.

### Criterion 1a

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

The instructional materials reviewed meet the expectation for not assessing topics before the grade-level in which the topic should be introduced. Overall, there are assessment items that align to topics beyond Grade 3, but these items could be modified or omitted without affecting the underlying structure of the materials.

### 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.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 3 meet the expectations for assessing grade-level content. Most of the assessments include material that is appropriate for Grade 3. In the instances where material is above grade-level, the material could easily be omitted or modified by the teacher to assess the grade-level standards being addressed. Probability, statistical distributions, similarity, transformations and congruence do not appear in the assessments.

In the teacher’s edition, assessments for each unit are listed including portfolio opportunities recommending which student work would be appropriate. Assessments are found in the Assessment Sourcebook.

Content from future grades is introduced occasionally on Grade 3 assessments. These items could easily be modified to stay on grade-level.

• Unit 7 Quiz 2 asks students to add 3 digit numbers that go beyond 1,000 (3.NBT.2 calls for students to fluently add and subtract within 1000). “Three apples have a mass of 880 grams. Two plums have a mass of 375 grams. What is the total mass of these 5 pieces of fruit? A. 1,155 grams B. 1,250 grams C. 1,255 grams D. 1,265 grams”
• Unit 7 in the Solving Addition and Subtraction Problems assessment, found in the Assessment Sourcebook, asks students to add decimal monetary amounts (5.NBT.B). This assessment could be removed.

### 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
+
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Criterion Rating Details

The instructional materials reviewed do not meet the expectation for students and teachers devoting the large majority of class time to the major work of the grade when the materials are used as designed. Overall, the materials do not spend at least 65% of class time on the major work of Grade 3.

### Indicator 1b

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

The instructional materials reviewed for Grade 3 do not meet the expectations for spending the majority of class time on the major clusters of the grade. Overall, approximately 63 percent of class time is spent on major work of the grade.

The instructional materials are separated into eight units. Each unit is composed of two, three, or four investigations, and each investigation is divided into sessions. The Implementing Investigations guide states in Part 4 (Classroom Routines) within the Overview that each session includes a Classroom Routine activity that is “introduced as a session activity and are then used outside of math time (e.g., during morning meeting, just before or after lunch or recess, or at the beginning or end of the day) or integrated into the math lesson as the first 10 minutes of a 70-minute math block.” The Ten-Minute Math activity provides practice with current skills or review of previously learned skills. Each session requires sixty minutes. Three perspectives were used when calculating major work of the grade: number of investigations, number of minutes (including Ten-Minute Math), and number of sessions (excluding Ten-Minute Math).

• Approximately 15 of the 25 investigations focus on major work of the grade. This represents approximately 60 percent of the investigations.
• If the Ten-Minute Math activity times are added into the Session minutes, approximately 6,060 of the minutes focus on major work of the grade. This represents approximately 60 percent of the minutes.
• Approximately 90 of 144 sessions focus on or support the major work of the grade. This represents approximately 63 percent of the sessions.

The third perspective, number of Sessions, is the most reflective of the instructional materials because it is based on the Sessions which includes the instructional activities, review, and practice but does not include the Ten-Minute Math activity that is done outside of math time. As a result, approximately 63 percent of the materials focus on major work of the grade.

### Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
6/8
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 3 partially meet the expectations for being coherent and consistent with the Standards. The instructional materials show strength in having an amount of content that is viable for one school year, but due to not always identifying work that is off grade-level, the materials are not always consistent with the progressions in the Standards. The materials do foster coherence through connections within the grade, but few of those connections are between major work of the grade and supporting work.

### 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 Grade 3 partially meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. Supporting standards are not always used to support major work of the grade and often appear in lessons with few connections to the major work of the grade.

Although some attempts to connect supporting work to major work are made, students can often complete problems aligned to supporting work without engaging in the major work of the grade.

• In Unit 2 Session 1.5 on Student Activity Book page 82, students answer problems about paper airplanes using a scaled pictograph. The questions connect supporting work (3.MD.3) with major work of the grade (3.OA.A and 3.OA.D). However, in Unit 2 Session 5, students make a scaled pictograph to represent data about the favorite sports of students. Student Activity Book page 81 states that students should use their pictographs to answer questions; however, students have the numbers represented in the pictograph listed in table form. As a result, the questions that could require students to engage in the major work of multiplication (3.OA.A) can instead be answered with subtraction (1.OA.1). Also, in Unit 2 Section 1.4 students solve problems with scaled bar graphs, but the problems require students to read the graph, add numbers, or subtract numbers, which are not major work of Grade 3.
• Unit 4 Investigation 3 focuses on standard 3.G.1. Sessions 3.1 and 3.2 require students to build and identify triangles; these Sessions are below grade-level and not connected to major work of Grade 3. Sessions 3.3 and 3.4 focus on 3.G.1, but no connection to major work of the grade is made. In Session 3.5, students continue to work with standard 3.G.1. Session 3.5 includes one assessment problem that has alignment to the major work standard 3.MD.7d. The one assessment problem (page A46 of the Assessment Sourcebook) requires students to find the area of a shape. The Sessions in Unit 4 Investigation 3 do not clearly connect the supporting work standard 3.G.1 to the major work of the grade.

Occasionally supporting standards are used to support the major work of the grade.

• In Unit 6, materials aligned with the supporting standard 3.G.2 support students developing understanding of fractions, 3.NF.A. In Session 1.2 students make and label fractions sets and consider whether two differently shaped sixths of the same whole are equal. In Session 1.4 students make one whole with combinations of halves, thirds, and sixths by using pattern blocks. In Sessions 1.7 students share brownies to identify fractional parts and fraction expressions.

### 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

The instructional materials reviewed for Grade 3 meet the expectations for the amount of content being viable for one school year.

• The instructional materials are divided into 8 units that have a total of 144 sessions.
• Each session is designed to be completed in 60 minutes. Each session is accompanied by a Ten-Minute Math activity that is designed to be completed in 10 minutes outside of math time.
• Each unit consists of 2-5 investigations. Each investigation ranges from 4-9 class sessions.
• Each unit takes between 2.5 to 5.5 weeks to complete according to the “Grade 3 Curriculum Units and Pacing Chart” on page 9 of the Implementing Investigations in Grade 3 guide. Each unit includes an additional 2.5 days beyond the days required to finish the sessions. These days could be used to complete the Intervention, Practice, and/or Extension activities that are included at the end of each investigation.
• These instructional materials include approximately 164 days.

### 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 materials reviewed for Grade 3 partially meet the expectations for being consistent with the progressions in the Standards. In general, the materials develop according to the grade-by-grade progressions in the Standards, but content from future grades is not clearly identified. The materials provide extensive work with grade-level problems for most standards, but the materials do not relate grade-level concepts explicitly to prior knowledge from earlier grades.

The materials develop according to the grade-by-grade progressions in the Standards, but content from future grades is not clearly identified. Examples of unclear identification include:

• In Unit 2 students work with line plots. Questions guide students to discuss the shape of the data. The materials use terms like range, mode, and outliers, which are more closely aligned to 6.SP.B.
• In Unit 4 Session 2.5 students are finding the area of irregular shapes (6.G.1).
• In Unit 7 Session 2.4 students are asked to fluently add beyond 1000. The 3rd grade standard is for students to fluently add within 1000. In Session 3.6 students are asked to add and subtract monetary amounts in dollars and cents such as in the student activity book page 455 when students are asked how much change from various amounts ($0.47 from$1.00, $3.18 from$5.00, etc). The above-grade level content in these sessions is not identified as such and is treated as on-grade level.

The materials often give all students extensive work with grade-level problems.

• The materials have different types of practice for students during each lesson. There are Teaching Resources in the Resource Masters and Activities in the Student Activity Book which are both aids during lessons. There are Daily Practice and Homework pages in the Student Activity Book which are indicated to be session follow-ups that review and practice grade-level content.
• Recommendations for differentiation allow students to primarily work with grade-level tasks.
• The materials give students extensive work with most domains. However, 3.NF is found in Unit 6 in 13 sessions. Of these 13 sessions, eight sessions teach fractions as a part of an object or shape, three sessions demonstrate fractions on a number line, and two sessions ask students to represent fractions by drawing shape models. These sessions may not allow all students to develop understanding of fractions as numbers. 3.MD.A, tell time to the nearest minute and measure time intervals in minutes, is found in 19 Ten-Minute Math activities which may not provide enough explicit instruction or extensive practice with measuring time in intervals for all students.

The materials do not consistently relate grade-level concepts explicitly to prior knowledge from earlier grades. The scope and sequence found in the Implementing Investigations book gives some limited information relating to knowledge from earlier and future grades by listing major topics and which units in prior and future grades address those topics. Each unit has a “Connections: Looking Back” section at the beginning of the unit. Several units specifically refer to work from prior grades without providing explicit connections to specific standards.

• Unit 1 specifically says the unit builds on the work done in K-2 as students use knowledge of counting groups to work with equal-sized groups and rectangular arrays leading to an understanding of multiplication and division.
• Unit 2 describes how students will use learning from K-2 to represent data on bar and picture graphs with more than one-unit scales and on line graphs.
• Unit 3 states the unit builds on K-2 work with an understanding of place value to 1000, operations of addition and subtraction, and the properties of operations along with fluency in addition facts within 20 and adding and subtracting within 100.
• Unit 4 “builds on the work students have done in previous grades” in understanding the importance of standard units of measure and familiarity with measurement tools.
• Unit 6 refers back to work done in Grade 2 with understanding fractions and fraction notation and the idea that fractions represent part of a whole.

### 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.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 3 meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards.

The materials begin each investigation with a planner that lists objectives for each session, and in the session materials, Math Focus points are listed at the beginning of each session. The instructional materials include objectives and Math Focus points that are visibly shaped by the CCSSM cluster headings for Grade 3.

• In Unit 1 Session 1.1 the Math Focus Points are “understanding multiplication as combining equal groups” and “writing, representing, and solving multiplication problems in context.” These are visibly shaped by cluster 3.OA.A, represent and solve problems involving multiplication and division.
• In Unit 3 Session 4.3 in Math Workshop students work on a set of activities that involve finding the difference between 2-digit and 3-digit numbers under 200. They focus on the strategy of using 100 as a landmark number for finding the difference between these numbers (3.NBT.A).
• In Unit 6 Session 1.5 students represent halves, fourths, eighths, thirds, and sixths on a number line and discuss fractions equivalent to ½ and ⅓. This session is visibly shaped by cluster 3.NF.A, develop understanding of fractions as numbers.

The instructional materials include problems and activities that connect two or more clusters in a domain or two or more domains.

• Unit 5 Session 3.3 connects clusters 3.OA.A, 3.OA.B, and 3.OA.D as students solve multi-step contextual problems involving multiplication and addition.
• Unit 5 Session 1.3 connects 3.OA.A and 3.OA.D as students use cube trains to write equations to represent multiples and non-multiples.
• Unit 5 Session 2.1 connects 3.OA.A and 3.MD.C as students work with arrays and multiplication facts.

## Rigor & Mathematical Practices

#### Partially Meets Expectations

+
-
Gateway Two Details

The instructional materials reviewed for Grade 3 partially meet the expectations for rigor and the mathematical practices. The materials meet the expectations for rigor as they help students develop conceptual understanding, procedural skill and fluency, and applications. However, the materials partially meet the expectations for mathematical practices as they do not attend to the full meaning for each of the MPs and rarely prompt, or have the teachers prompt, students to analyze the arguments of others.

### 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.
7/8
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 3 partially meet the expectations for rigor and the mathematical practices. The materials meet the expectations for rigor as they help students develop conceptual understanding, procedural skill and fluency, and applications. However, the materials partially meet the expectations for mathematical practices as they do not attend to the full meaning for each of the MPs and rarely prompt, or have the teachers prompt, students to analyze the arguments of others.

### 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.
2/2
+
-
Indicator Rating Details

The materials reviewed for Grade 3 meet the expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. In the instructional materials visual representations, verbal explanations, and written equations are used to develop conceptual understanding.

• In Unit 1 Session 1.3 students interpret products of whole numbers by using given pictures to find the total number of objects when there are set groups with a different number of objects in each group (3.OA.1). Students also complete Student Activity Book pages 9-12 which require them to solve the problem, show their solution, and write an equation to represent what is being described.
• In Unit 6 Session 1.3 students understand fractional parts are constructed of unit fractions by folding pieces of paper into fourths, sixths, eighths, etc. and representing each section of the folded paper as a unit fraction (3.NF.A). Students also complete Student Activity Book page 353 where they are asked to draw lines to divide shapes into fractional pieces.
• In Unit 6 Session 2.2 students represent fractions on a number line by using number line resource masters labeled from 0-3 and working with others to visually represent fractions (3.NF.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.
2/2
+
-
Indicator Rating Details

The materials reviewed for Grade 3 meet the expectations for giving attention throughout the year to individual standards that set an expectation for procedural skill and fluency. The materials include opportunities to practice and review in order to build procedural skill and fluency. Students are provided Daily Practice in every session and Homework in many sessions.

Standard 3.OA.7 requires students to fluently find single-digit products and quotients.

• In Units 1 and 5 students identify the division/multiplication facts they need to know by sorting division cards into piles of know and still working on. Students then use facts they already know to help them with the facts that they don’t know.
• In Unit 8 and 10 sessions focus on division fact fluency.
• All of the Ten-Minute Math activities indirectly work on fluency but do not provide direct fluency practice for products of two one-digit numbers. In Units 5 and 8, during “Closest Estimate” students view addition/subtraction and multiplication/division problems with three estimates and determine which of the three is the closest to the actual answer. In Units 1, 2, and 7, during “Counting Around the Class” students estimate then count around the class to practice multiples. Variations of this include "How Many Students are in the Class?" and "Counting Around the Class by Fractions." In Units 2, 3, and 6, during “Today’s Number” students write several different expressions that equal a given number. In Units 4 and 5 during “Quick Images” students visualize and analyze the structure of an arrangement of dots or 2-D images and write equations.

Standard 3.NBT.2 requires students to fluently add and subtract within 1000.

• In Unit 3 Session 1.3 students solve addition word problems within 1000 in the “More Sticker Station Problems” activity in the Student Activity Book, page 125.
• In Unit 3 Session 1.4 the Ten-Minute Math activity asks students to create expression that equal 289. They must use multiples of 10 in each equation such as 209 + 50 +30.
• In Unit 3 Session 5.4 students solve subtraction word problems within 1000 in the “How Many Are Left?” activity in the Student Activity Book, pages 197-198.
• In Unit 7 Session 2.5 students solve addition and subtraction problems within 1000 in the “Addition and Subtraction: Related Problems 2” activity in the Student Activity Book, pages 429.

### 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
2/2
+
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Indicator Rating Details

The materials reviewed for Grade 3 meet the expectations for teachers and students spending sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade.

Practice for 3.OA.3, use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, is found in three units of instruction. Within Units 1, 5, and 8 materials focus on one-step problems, scaffolded two-step problems, or two-step problems with inverse operations. In Units 5 and 8, there are six lessons that focus on the concept of division. The students solve single-step, division word problems such as “There are 24 students in Ms Smith’s class. She wants to place them into 4 equal groups. How many students are in each group?”

Practice with application of 3.OA.8 is found throughout five units of instruction. Standard 3.OA.8, solve two-step word problems using the four operations, is found in sessions within Units 2, 4, 5, 7, and 8. In Unit 5 Session 3.3 students are asked to solve multi-step word problems including “Arthur orders eight 70-packs of balloons and two 9-packs of marbles to sell at his party store. How many items does he order from The Toy Factory?”

### 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.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 3 partially meet the expectations for balance of the three aspects of rigor within a grade. Although the instructional materials meet expectations for each aspect of rigor, these aspects of rigor are often addressed in separate parts of the Sessions. Materials targeting application are often scaffolded, detracting from the balance of rigor. Overall, the three aspects of rigor are most commonly treated separately.

In general, conceptual understanding, procedural skill and fluency, and application are all adequately addressed in the Sessions; however, for the most part they are addressed in separate sections of the instructional materials. Conceptual understanding is typically addressed in the Discussion and Math Workshop portions of Sessions. Procedural skill and fluency is typically introduced in separate Sessions and then practiced in the Daily Practice portion of sessions. Application consists of routine word problems in the instructional materials. As a result, all aspects of rigor are almost always treated separately within the curriculum including within and during Sessions, Practice, and Homework.

### Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
7/10
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 3 partially meet the expectations for practice-content connections. Overall, the materials show strengths in identifying and using the MPs to enrich the content along with attending to the specialize language of mathematics. However, the materials do not always attend to the full meaning of each MP, and there are few opportunities for students to analyze the arguments of others either through prompts from the materials or from their teachers.

### Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
2/2
+
-
Indicator Rating Details

The instructional materials for Grade 3 meet the expectations for identifying the Standards for Mathematical Practice (MPs) and using them to enrich the mathematical content. The MPs are clearly identified in Implementing Investigations on page 44 and can also be found in each unit. The instructional materials highlight two MPs in every unit. During the sessions, Math Practice Notes dialogue boxes are given to provide tips to the teacher on how to engage students in the MPs. Additionally, Math Practice Notes are provided for the MPs that are not highlighted so students continue to work on the practices all year.

The Introduction and Overview of each unit includes a “Mathematical Practices in this Unit” section. This section of each unit highlights the two MPs that are the focus of the unit. The MPs are described and examples from the unit are provided. A chart showing where Mathematical Practice Notes occur and when the MP is assessed is also included in this section.

• The Unit 2 “Mathematical Practices in this Unit” is found on pages 8-11. This unit focuses on MP4 and MP5. An example of MP4 from Session 2.1 is included.
• The Unit 7 “Mathematical Practices in this Unit” is found on pages 8-11. This unit focuses on MP1 and MP3. An example of MP1 from Session 1.4 is included.

Math Practice Notes are provided in sessions alongside content. Math Practice notes are provided for the MPs highlighted within the unit and MPs that are not the highlighted practices for the unit.

• Unit 2 Session 2.3 includes a Math Practice Note for MP6, a practice not highlighted in the unit. Students are using tools accurately and learning the importance of repeated measurement for precision.
• Unit 5 Session 1.5 includes a Math Practice Note for MP3 and MP7. MP7 is a practice highlighted in the unit. The note discusses how students gain a deeper understanding of how the action and result of one operation is related to the other.
• Unit 6 Session 1.7 includes a Math Practice Note for MP8, a practice not highlighted in the unit. As students examine the relationship between the numerators and denominators of fractions that are equivalent to 1, they are able to look for and express regularity in repeated reasoning.

### Indicator 2f

Materials carefully attend to the full meaning of each practice standard
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 3 partially meet expectations that materials carefully attend to the full meaning of each practice standard (MP). Although the instructional materials attend to the full meaning of some of the MPs, there are some MPs for which the full meaning is not developed.

At times, the instructional materials only attend superficially to MPs. The following are examples:

• Unit 1, Session 1.1 in the Math Practice Note it lists MP1 and has students asking multiplication questions. In the Math Practice Note it just reminds teachers to notice how students are entering problems, choosing strategies, and how they are making use of drawings or cubes to solve problems. This session poses questions such as, “We agree that there are usually five toes on a person’s foot. How many toes would there be on four feet?” These questions do not lend themselves to students having to persevere in solving them.
• Unit 1, Session 3.1 in the Math Practice Note it lists MP5 and has students represent multiplication situations with arrays. The Math Practice Note talks specifically about what a rectangular array is and how it provides images students use to understand key properties. This activity only has students using arrays and does not allow them to choose any other tool.
• Unit 4, Session 2.2 in the Math Practice Note it lists MP4 and has students compare fractions on a number line. This is a literal model not attending to the full meaning of MP4 because it does not solve a real world problem. In the Math Practice Note it states that each time students place a fraction on the number line, they are modeling where that number fits in our system, and its relationship to whole numbers and to other fractions.
• Unit 5, Session 2.2 in the Math Practice Note it lists MP5 and has students using arrays to break up multiplication facts. The Math Practice Note talks specifically about using arrays and the story context to solve problems. This session does not allow them to choose any other tool.
• Unit 5, Session 3.3 in the Math Practice Note it lists MP1 and has students working with multi-step word problems. This is a new kind of problem structure for these students and they are not asked to solve anything. The Math Practice Note just informs teachers to help students focus on making sense of each problem, does not have them persevere through any of this session’s work.
• Unit 6, Session 1.2 in the Math Practice Note it lists MP5 and has students making fraction sets. In the Math Practice Note it comments about students using tools such as brownies and fraction sets to visualize an area model for fractions, however, it then specifically states that in this session they will be given pattern blocks to represent fractions and fraction relationships. This session does not allow students to choose their tool.
• Unit 6, Session 1.3 in the Math Practice Note it lists MP4 and has students create and label fraction pieces. This is a literal model not attending to the full meaning of MP4 because it does not solve a real world problem nor are students modeling to solve a mathematical problem.
• Unit 8, Session 3.4, in the Student Activity Book page 527 students write problems using a letter to represent the unknown, but it is not tied to word problems. The problem reads: “This equation is about Zupin’s marbles: z = 20 + (18 x 4). What does Z mean? What does the 20 represent? What does the 18 represent?” This does not attend to the full meaning of MP4 because it does not relate the mathematics needed to solving a real world problem.

At times, the instructional materials fully attend to a specific MP. The following is an example:

• Unit 1, Session 4.6 in the Math Practice Note it lists MP1 and has students making sense of problems, sharing problems, and understanding different solutions. This session has students solving division problems and then discussing questions such as, “How did you start solving this division problem? Is there a multiplication fact you know that might help you? What part of the problem have you solved? What is left over?” In the Math Practice Note it states that these questions communicate to students that they are not expected to immediately know the answer, but they are expected to think about what knowledge and tools they have to help them get started to figure it out.

### Indicator 2g

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

### 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.
1/2
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Indicator Rating Details

The instructional materials reviewed for Grade 3 partially meet the expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

When MP3 is referenced, students are often asked to solve and share solutions. The independent work of the student is most often about finding the solution to a problem without creating a viable argument. Students often listen to peer solutions without being asked to critique the reasoning of the other student. Much of the student engagement in the class discussion is teacher prompted without giving students the opportunity to create their own authentic inquiry in the thinking of others.

• In Unit 4 Session 2.3 students are asked to discuss the area of a shape in their Student Activity Book with a partner. “How do you know that it’s 4 square inches? Who can explain how these triangles and squares go to together. Discuss with a partner.” There is no evidence that students are being guided to construct or critique mathematical reasoning.
• In Unit 6 Session 2.2 the teacher asks the students about the placement of a fraction on a numberline. “If I wanted to mark 2/4 on the number line, where would I mark it?” The students are neither constructing arguments nor analyzing the arguments of others.

At times, the materials prompt students to construct viable arguments and analyze the arguments of others.

• In Unit 8 Session 2.5 students are asked to explain why their solution to a problem makes sense while other students are encouraged to ask questions in order to help other students state their justifications clearly. By focusing questions that students will ask each other in this way, students are more clearly guided to critique the arguments of others and provide peer feedback.

### 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.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 3 partially meet the expectations for assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.

Most of the time when MP3 is referenced, teachers are asked to have students share or explain their solutions. Teachers are also directed to have students ask questions but are not supported in focusing those questions toward critiquing the arguments of others.

• In Unit 2 Session 1.2 the teacher is prompted to comment on how different organizations of the data allowed students to answer different questions. No question or comments allow for students to construct and/or analyze viable arguments.
• In Unit 2 Session 2.4 the teacher prompts include: “What can we say about our class as a whole? What can you say about our data? Talk to a neighbor about the things you notice.” No question or comments allow for students to construct and/or analyze viable arguments.
• In Unit 4 Session 3.3 teacher prompts include: "What is the same about the shapes that are in this row labeled 'Quadrilaterals'? What is true of all quadrilaterals?" Then the teacher is told to post a chart and record student’s responses. The students are never prompted to argue or analyze with this line of questioning. The Math Practice Note for the teacher states, “you might want to talk explicitly with students about how using definitions of shapes in mathematics is not about opinion, but is about looking carefully at what properties the shape you’re considering does and does not have.”
• In Unit 7 Session 3.3 The Math Practice Note states, “some students may be able to use the context to explain what is happening…” and provides no support for students in critiquing the explanations of others.

The materials assist teachers, at times, in engaging students in constructing viable and analyzing the argument of others.

• In Unit 4 Session 2.2 teacher prompts include: "Which shapes worked to completely cover the rectangle? Does everyone agree? Anyone disagree? Can you talk about why you think these two shapes didn't work?"
• In Unit 4 Session 2.5 teacher prompts include: " Ask students how they solved the the problem. Does everyone agree the area of this shape is 55 square centimeters? Then, I noticed that Kim made a 4 x 10 and a 3 x 5 rectangle and Dwayne made a 7 x 5 and 4 x 5 rectangle. Why do these two different ways of finding area of 55 sq. cm both work? Take a minute to talk to a neighbor."

### Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 3 meet the expectations for explicitly attending to the specialized language of mathematics.

The instructional materials provide opportunities for teachers to say mathematical terms to students during the whole group portion of the lessons. The materials use precise and accurate terminology when describing mathematics. New terminology is introduced on the summary page of the TE at the beginning of the session where it will first be used. The mathematical terminology is highlighted in italics throughout the sessions within the TE. There is also an index at the end of each unit manual in which math terms are listed for the unit.

• In Unit 1 Session 1.4 students are creating and illustrating a multiplication situation. The materials prompt the teacher to state, “Just like before, write three sentences about your picture that tell the number of groups you drew, the number in each group, and the total number. Be sure to write a multiplication equation.”
• In Unit 4 Session 1.2 students are discussing how far an ant would walk if it walked around the edge of a piece of paper. The materials prompt the teacher to state, “Your job is to work in pairs to find out how far this ant would have to walk to get all the way around the perimeter of this paper, in other words, to walk all the way around and end up just where she started. How could you figure this out?” The math word that is the focus is "perimeter."
• In Unit 2 Session 1.1 students are discussing places that they like to eat and recording students’ favorite places to eat. The materials prompt the teacher to state, “ Data are pieces of information. We can collect data by counting something, measuring something, or doing experiments.” The math word that is the focus is "data."

## 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: 2017/02/10

Report Edition: 2017

Title ISBN Edition Publisher Year
Investigations 3 Common Core Curriculum Unit (TE) Grade 3 Unit 1 978‑0‑328‑85915‑3 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 3 Unit 2 978‑0‑328‑85916‑8 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 3 Unit 3 978‑0‑328‑85917‑7 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 3 Unit 4 978‑0‑328‑85918‑4 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 3 Unit 5 978‑0‑328‑85919‑1 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 3 Unit 6 978‑0‑328‑85920‑7 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 3 Unit 7 978‑0‑328‑85921‑4 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 3 Unit 8 978‑0‑328‑85922‑1 Pearson 2017
Implementing Investigations in Grade 3 978‑0‑328‑85942‑9 Pearson 2017
Investigations 3 Common Core Assessment Sourcebook Grade 3 978‑0‑328‑85966‑5 Pearson 2017
Investigations and the Common Core Content Guide Grade 3 978‑0‑328‑85972‑6 Pearson 2017

## 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.

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.