## Math Expressions

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###### Usability
Our Review Process

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### Overall Summary

The instructional materials reviewed for Math Expressions Grade 3 meet expectations for alignment to the CCSSM. The instructional materials meet expectations for Gateway 1, focus and coherence, by focusing on the major work of the grade and being coherent and consistent with the Standards. The instructional materials meet expectations for Gateway 2, rigor and balance and practice-content connections, by reflecting the balances in the Standards and helping students meet the Standards’ rigorous expectations by giving appropriate attention to the three aspects of rigor, and the materials connect the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

###### Alignment
Meets Expectations
###### Usability
Meets Expectations

### Focus & Coherence

The instructional materials reviewed for Math Expressions Grade 3 meet expectations for Gateway 1, focus and coherence. The instructional materials meet the expectations for focusing on the major work of the grade, and they also meet expectations for being coherent and consistent with the standards.

##### Gateway 1
Meets 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 Math Expressions Grade 3 meet expectations for not assessing topics before the grade level in which the topic should be introduced. The materials assess grade-level content and, if applicable, content from earlier grades.

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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 Math Expressions Grade 3 meet expectations that they assess grade-level content.

The assessments are aligned to grade-level standards and do not assess content from future grades. The Grade 3 Assessment Guide includes a Beginning of Year Test, Middle of Year Test, End of Year Test, and tests for each Unit. Each Unit Test includes multiple choice, multiple-select, short answer, constructed response, and a separate performance task assessment.  The materials include a form A and form B assessment for each unit.

Digitally available assessments are PARCC and Smarter Balanced aligned practice tests. Each digital platform includes a variety of practice tests. Digital assessments assess grade-level content.

Examples of on-grade level assessment items include:

• Unit 1, Form B, Item 21, “Michelle’s bookcase has 4 shelves. It holds 9 books on each shelf. How many books will fit in the bookcase altogether?" (3.OA.3)
• Unit 3, Performance Assessment, Item 3, “Alberto has 62 pennies, 41 nickels, and 29 dimes. What strategy can you use to find the total number of coins? Describe it and show your work.” (3.NBT.1 and 3.NBT.2)
• Unit 6, Form A, Item 12, “Kevin has 368 marbles in his collection. His mom gives him 42 more marbles. He then gives some marbles to his friend. Kevin now has 352 marbles. How many marbles does he give to his friend? Answer: 58 marbles Is the answer reasonable? Tell why or why not. Then write an equation and solve the problem.” (3.OA.8)
• Grade 3, End of Year Test, Item 11, “Write an equation and solve the problem. Show your work. There are 3 dance classes with 10 students in each class. All of the classes are divided into 6 groups for the dance recital. How many students are in each group?” (3.OA.8)
• Grade 3, Middle of Year Test, Item 28, “Marisa measures 8/4 cups of sugar and 6/2 cups of flour. Does she measure more sugar or flour? Explain.” (3.NF.3c.)
• Grade 3, Smarter Balanced Test Prep Practice Test, Item 5, “Eleni bought 3 packs of crayons. She then found 3 crayons in her desk. Eleni now has 24 crayons. How many crayons were in each pack she bought? Explain how you solved the problem.” (3.OA.8)

#### 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 Math Expressions Grade 3 meet expectations for students and teachers using the materials as designed devoting the large majority of class time to the major work of the grade. The instructional materials devote at least 65 percent of instructional time to the major clusters of the grade.

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Instructional material spends the majority of class time on the major cluster of each grade.

The instructional materials reviewed for Math Expressions Grade 3 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 5 out of 7, which is approximately 71%.
• The number of Big Ideas, CCSSM clusters, devoted to major work of the grade (including assessments and supporting work connected to the major work) is 13 out of 18 , which is approximately 72%.
• The number of lessons devoted to major work (including assessments and supporting work connected to the major work) is approximately 77 out of 112, which is approximately 69%.

A lesson level analysis is most representative of the instructional materials as the lessons include major work, supporting work, and the assessments embedded within each unit. As a result, approximately 69% 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 reviewed for Math Expressions Grade 3 meet expectations for being coherent and consistent with the standards. The instructional materials have content designated for one grade level that is viable for one school year; are consistent with the progressions in the standards; and foster coherence through connections at a single grade.

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Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The instructional materials reviewed for Math Expressions Grade 3 partially meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. The materials include some lessons where supporting work enhances and supports the major work of the grade. However, there are lessons that include missed opportunities for supporting work to enhance the major work of the grade.

Examples of connections between supporting work and major work include the following:

• In Unit 4, Lesson 1 (3.G.A), shapes and their attributes are used to support the development of understanding of fractions (3.NF.A). Students complete a fraction rectangle activity as teachers guide students to compare the sizes of the rectangles to conclude the four rectangles have equal areas.
• In Unit 4, Lesson 2 (3.G.A), students work with partitioning rectangles supports their work with identifying the unit fraction and building fractions less than one from the unit fractions (3.NF.A).
• In Unit 5, Lesson 10 (3.G.A), students work with folding a square piece of paper in half a given number of times supports their work with finding equivalent fractions using their partitioned square (3.NF.A).

Overall, this series misses opportunities to connect multiplication and division (3.OA.A) to one- and two-step word problems using scaled bar graphs and scaled pictographs (3.MD.3).

Examples of missed opportunities to make connections between supporting work and major work include the following:

• In Unit 1, Lesson 19, students construct a scaled pictograph (3.MD.3). This lesson missed the opportunity to multiply and divide to solve one- and two-step word problems (3.OA.A) with the scaled pictograph.
• In Unit 4, Lesson 15, students use a provided scaled bar graph to solve problems (3.MD.3). In Problem 5 students use multiplication in the first step. “There are 4 riders on each of the 5 teams. If each student completed the same number of miles, how many miles did each student ride on Wednesday?” The multiplication work is embedded in the question and not directly related to the scaled bar graph (3.OA.A).
• In Unit 4, Performance Assessment, Problem 3, students make a bar graph from a table that is provided (3.MD.3), where they need to solve one- and two-step problems. This is a missed opportunity to connect to major work (3.OA.A).
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The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.

The instructional materials for Math Expressions Grade 3 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 150 days. The Pacing Guide can be found on page I18 in the Teacher Edition. The suggested amount of time and expectations for teachers and students of the materials are viable for one school year as written and would not require significant modifications.

• The program is designed with seven units and 98 lessons. Most lessons require one day.
• The Pacing Guide notes 19 lessons that may take two days, but this is not noted in the Day at a Glance for each lesson.
• All Units designate two days for Unit Assessments.
• The instructional materials consist of 18 days of Quick Quizzes and Strategy or Fluency Checks which are listed in the Pacing Guide.
• Unit 1 designates one day for the Prerequisite Skills Inventory Test.

Teachers start each lesson with a 5-minute Quick Practice and each lesson is comprised of several activities with estimated time ranging from a total of 55-65 minutes per lesson. Math Activity Centers are tailored for all levels of achievement across readiness and learning styles. They can be completed within the lesson or after, however, the time required for the activity is unstated.

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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 Math Expressions Grade 3 meet expectations for the materials being consistent with the progressions in the Standards. Content from prior and future grades is identified and connected to grade-level work, and students are given extensive work with grade-level problems.

The materials clearly identify content from prior and future grades and connect concepts to grade level work. Each unit includes a Unit Overview providing a Learning Progression. The Learning Progression states connections between the standards of the prior grade, current grade, and future grade. Additionally, each unit contains a Math Background Section. This section contains in depth information for the teacher articulating the learning progressions and the progression of the content between lessons. For example:

• Unit 4, Math Background, contains quotes from the Learning Progressions for Fraction Concepts, “Grade 3 students start with unit fractions (fractions with numerator 1), which are formed by partitioning a whole into equal parts and taking one part…” This page also includes visual examples of fraction bars and a statement regarding prior work, “The work students have done with decomposing shapes gives them a foundation for this work with equal parts of a whole.”
• Unit 6, the Learning Progression chart shows connections between Grade 2, Grade 3, and Grade 4 within the Numbers and Operations in Base Ten and Operations and Algebraic Thinking domains. “In Grade 2, students used addition and subtraction within 100 to solve one- and two-step word problems and mastered using mental strategies to add and subtract within 20. In Grade 3, students will use drawings and equations with a symbol for the unknown number to represent the problem, write equations and solve types of word problems involving comparison and misleading language, and use properties of operations to explain patterns. In Grade 4, students will use drawings and equations with a symbol for the unknown number to represent the problem, represent verbal statements of multiplicative comparisons as multiplication equations, and write equations to represent problems with more than one step.”

The instructional materials provide extensive work with grade-level problems. Students work with grade-level problems in each lesson. Within each lesson, students practice grade level problems within Quick Practice, Student Activity Book pages, Homework, and Remembering activities. During modeled and guided instruction, students are given opportunities to engage in the grade level work by doing various examples with teacher and peer support. The independent practice in the Student Activity Book aligns with the lesson and provides students the opportunity to work with grade level problems to extend concepts and skills. For example:

• Unit 2, Lesson 4, Activity 1, students work in pairs to test one another on math facts using provided study sheets, then work independently for a few minutes to study the study sheets. In Activity 2, students identify which type of problem (array, equal groups, or area) is being solved and which operation will be used. Finally, students complete an error analysis of a multiplication equation, then write and solve multiplication and division equations for nine real world problems. (3.OA.A)
• Unit 3, Lesson 12, Activity 1, students practice ungrouping tens as the teacher “models” the skill. In the Student Activity Book students are ungrouping tens in subtraction problems and include “proof drawings” representing how they got their answer. This lesson also includes additional opportunities to practice making “proof drawings” to support subtraction. The formative assessment, “Check Understanding”, contains one more problem for students to ungroup tens in a subtraction problem, “Subtract. 300-156. Make a proof drawing to show that your answer is correct.” (3.NBT.2)

Each lesson contains Math Center Activities, as well as Homework and Remembering (spiral reviews) pages which provide additional practice with grade-level problems. For example:

• Unit 1, Lesson 8, Homework, students write and solve multiplication and division equations to match a real world problem.
• Unit 2, Lesson 9, Remembering, students write and solve multiplication and division equations and find unknown numbers for Fast Array Drawings. In Stretch Your Thinking, students answer the following question, “Cecelia says she can use addition to solve multiplication problems. Is Cecelia correct? Explain.”
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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 Math Expressions Grade 3 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the Standards.

Each unit is structured by specific domains and Big Ideas. Learning objectives within the lessons are clearly shaped by CCSSM cluster headings. For example:

• Unit 1, Lesson 4, the lesson objective states, “Students will learn to relate division to multiplication with an unknown factor.” This is shaped by cluster 3.OA, “Represent and solve problems involving multiplication and division.”
• Unit 5, Lesson 8, the learning objective states, “Students will learn to use number lines to find two or more equivalent fractions.” This is shaped by 3.NF.A, “Develop understanding of fractions as numbers.”
• Unit 7, Big Idea 2, “Analyzing Triangles and Quadrilaterals” includes four lessons. This Big Idea is shaped by cluster 3.G.A, “Reason with shapes and their attributes.” Lesson objectives in this section include, “Students will learn to classify triangles according to their angle sizes and side lengths and to build and name polygons, students will learn about the relationships among different types of quadrilaterals, students will learn to draw quadrilaterals, students will learn to describe, sort, and draw quadrilaterals according to their attributes, and students will learn to use mathematical practices and content skills to solve problems about quadrilaterals.”

Materials include problems and activities connecting 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 3, Lesson 9, cluster 3.NBT.A connects to 3.OA.D, when students engage in addition and subtraction while they solve real world problems. Problem 20, “The florist ordered 398 roses and 562 tulips. How many flowers did the florist order in all?”
• Unit 4, Lesson 4, cluster 3.G.A connects to 3.NF.A, when students work with partitioning shapes relates to visual fraction models.
• Unit 6, Lesson 2, cluster 3.OA.A connects to 3.NBT.3, when students represent and solve word problems with unknown addends and unknown factors. Problem 8, “There are 56 cars in a parking lot. There are 8 rows and the same number of cars in each row. How many cars are in each row?”

### Rigor & Mathematical Practices

The instructional materials reviewed for Math Expressions Grade 3 meet expectations for Gateway 2, rigor and balance and practice-content connections. The instructional materials meet expectations for reflecting the balances in the standards and helping students meet the standards’ rigorous expectations by giving appropriate attention to the three aspects of rigor, and they meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

##### Gateway 2
Meets Expectations

#### 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.

The instructional materials reviewed for Math Expressions Grade 3 meet expectations for reflecting the balances in the standards and helping students meet the standards’ rigorous expectations, by giving appropriate attention to developing students’ conceptual understanding and procedural skill and fluency. The instructional materials also do not always treat the aspects of rigor separately or together.

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

The instructional materials for Math Expressions Grade 3 meet expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

The materials identify Five Core Structures: Helping Community, Building Concepts, Math Talk, Quick Practice, and Student Leaders as the organizational structures of the program. “Building Concepts in the classroom experiences in which students use objects, drawings, conceptual language, and real-world situations - all of which help students build mathematical ideas that make sense to them.”

The instructional materials present opportunities for students to develop conceptual understanding. For example:

• Unit 1, Lesson 2, students write multiplication equations for equal groups from pictures and tables to find the total number. “How many bananas?” requires students to write “4 x 3 = 12” from the figure. In the following activity, students make a drawing for each problem, label the drawing with a multiplication equation, and write the answer to the problem.
• Unit 2, Lesson 9, Activity 3, students interpret products and quotients of whole numbers. “Louis put 72 marbles in 8 bags. He put the same number of marbles in each bag.” The directions state, “Write a question for the given information and solve.” Students determine which operation to use and formulate a question that requires that operation.
• Unit 4, Lesson 1, Understand Fractions, Activity 1, "Students use what they have learned about decomposing shapes as a foundation for understanding unit fractions as equal parts of a whole." Activity 2, "Students use fraction bars to visualize and represent unit fractions as the elements for building other fractions."

The instructional materials present opportunities for students to independently demonstrate conceptual understanding. For example,

• Unit 1, Lesson 16, students determine the type of multiplication or division problem represented in word problems, and solve the word problems. For example, Problem 3, “Zamir bought 21 treats to the dog park. He divided the treats equally among the 7 dogs that were there. How many treats did each dog get?” Students need to determine this is an Equal Groups Division with an Unknown Multiplier (number of groups) problem, and write and solve the equation.
• In Unit 5, Lesson 2, students find the area and perimeter of rectangles. Check Understanding problem, “Draw a rectangle with an area of 36 centimeters square and one side length of 4 centimeters. Find the unknown side length. Then find the perimeter."
• Unit 6, Lesson 4, students engage with comparison problems. Students represent comparison problems in two ways: using a drawing and using a bar diagram and completing statements using more and fewer. For example, “Claire has 8 marbles. Sasha had 15 marbles.” Problem 17, “How many more marbles does Sasha have than Claire? Problem 18, “How many fewer marbles does Claire have than Sasha?”
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Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

The instructional materials for Math Expressions Grade 3 meet expectations for attending to those standards that set an expectation of procedural skill and fluency.

The instructional materials provide regular opportunities for students to attend to the standards. For example, 3.OA.7, fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division or properties of operation; and 3.NBT.2, fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

The instructional materials develop procedural skill and fluency throughout the grade-level. Each lesson includes a “Quick Practice” described as “routines [that] focus on vitally important skills and concepts that can be practiced in a whole-class activity with immediate feedback”. Quick Practice can be found at the beginning of every unit on the pages beginning with the letters QP. Student materials and instructions are also found in the Teacher Resource Book on pages beginning with Q. Examples include:

• The Introduction includes a chart “Path to Fluency: Kindergarten through Grade 6” which provides a pathway for fluency and memorization of basic facts, and operations with multi-digit operations. Also included are Reteach and Practice Sheets, Quick Practices, and Daily Routines supporting fluency.
• Unit 1, Teacher Resource Book, Multiplication Equations as Groups of 9, “The Student Leader points at the equation in the 9s column of the Multiplication Table Poster in order: 1x9=9, 2x9=18, 3x9=27, and so on. Class says: 9 is 1 group of 9 and raises 1 finger. 18 is 2 groups of 9 and raises 2 fingers. 27 is 3 groups of 9 and raises 3 fingers, and so on.”
• Unit 5, Teacher Resource Book, “Display these fractions bars. Student Leader 1 says two unit fractions with different denominators (such as 1/3 and 1/5 ) and asks which is greater and why. Class: 1/3 is greater because it has fewer unit fractions to make the same whole.” Students practice fraction fluency with students leading the activity.

The instructional materials provide opportunities for student to independently demonstrate procedural skill and fluency throughout the grade-level. These include: Path to Fluency Practice, and Fluency Checks. For example:

• Unit 1, Lesson 14, Activity 2, students review strategies for multiplying and dividing. The Student Activity Book includes questions that “focus on using strategies students were introduced to in previous lessons.” “Emily knows that 4 x 10 = 40.  How can she use subtraction and multiples of 9 to find 4 x 9?” (3.OA.7)
• Unit 1, Lesson 3, Path to Fluency, students practice “count bys”, mixed up multiplication, and mixed up division facts for 5s, 2s, 10s, and 9s.
• Unit 3, Fluency Check 3, students practice single digit by single digit multiplication. For example, Problem 10, “9 x 3 = __.”
• Student Activity Book, Unit 3, Lesson 8, students practice writing addition problems vertically by lining up the place values correctly before adding. (3.NBT.2)

In addition, Homework and Remembering activity pages found at the end of each lesson provide additional practice to build procedural skill and fluency.

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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

The instructional materials for Math Expressions Grade 3 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied.

Students engage with application problems in many lessons for the standards that address application in solving real-word problems. For example, in the Student Activity Book, Unit 4, Lesson 9, students solve application problems involving elapsed time. “Berto spent from 3:45 p.m. to 4:15 p.m. doing math homework and from 4:30 p.m. to 5:10 p.m. doing social studies homework. How much time did he spend on his math and social studies homework?”

Each lesson includes an Anytime Problem listed in the lesson at a glance, and Anytime Problems include both routine and non-routine application problems. For example:

• In Unit 4, Lesson 12, Anytime Problem, “Sarah spent $5 from her savings to buy a book. Then, she spent half of her remaining savings when she paid$9 for a shirt. How much money did Sarah have in savings before she bought the book and the shirt?”
• Unit 1, Lesson 2, Anytime Problem, “Dulal, Lien, and Kate have either the bird, the cat, or the fish. Dulal does not have the bird. Lien does not have the cat. Kate does not have the fish or the cat. Which pet does each person have?”

The instructional materials present opportunities for students to engage in routine application throughout the grade-level. Examples of routine applications of grade-level mathematics are found in the Student Activity Book. For example:

• Unit 1, Lesson 15, “There are 3 shelves in a bookshelf. Each shelf has 2 piles of books on it. If there are 3 books in each pile, how many books are in the bookshelf?”
• Unit 2, Lesson 2, Student Activity Book, “Ana has a ribbon that is 18 inches long. She cut the ribbon into 3 equal pieces. Then she cut each of those pieces in half. How many small pieces of ribbon are there? How long is each piece?”
• Unit 3, Lesson 3, students use place value drawings to assist in solving problems. “Scott made a batch of rolls. He gave a bag of 10 rolls to each of 7 friends. He kept 1 bag for himself. How many rolls did he bake in all?”
• Unit 6, Lesson 6, Problem 2, “Mark has 6 shirts and 5 pairs of pants. Today his aunt gave him 4 more shirts and another pair of pants. How many shirts does he have now?”

Remembering pages at the end of each lesson are designed for Spiral Review anytime after the lesson occurs. One feature of the Remembering problems are those titled Stretch Your Thinking, which often present opportunities for students to engage with non-routine problems. For example:

• Unit 2, Lesson 15, Remembering, Stretch Your Thinking, Exercise 14, “Matt runs four days a week. On the first day he runs 30 minutes. On the second day he runs 5 minutes more than the first day. On the third day, he runs the same number of minutes as on the second day. On the fourth day, he runs 10 minutes more than the previous day. After Matt runds on the fourth day, how many minutes in all has he run?”
• Unit 3, Lesson 5, Remembering, Stretch Your Thinking, Exercise 17, “Adult and student tickets were sold for a concert. When the numbers of adult tickets and students tickets are rounded, the total number of tickets sold was about 1,200. List four different combinations of adult and students tickets that might have been sold.”
• Unit 7, Lesson 4, Remembering, Stretch Your Thinking, Exercise 7, “Jake has 12 liters of water. Name four different ways he can divide the water into buckets so each bucket has the same number of liters.”
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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.

The instructional materials for Math Expressions Grade 3 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately.

All three aspects of rigor are represented in the materials, for example:

• Each lesson has a 5-minute Quick Practice providing practice with skills that should be mastered throughout the year.
• There are Performance Tasks throughout the series, where students use conceptual understanding to perform a mathematical task. For example, Unit 3, Problem 4, “June, Ella, and Joshua are collecting pennies for the service project. June collected 324 pennies. Ella collected 442 pennies, and Joshua collected 248 pennies… Part C: How many more pennies do the students need to collect to buy a second flat of flowers? Show your work.”
• Fluency Checks are included throughout the series, where students practice procedural skills and fluency. For example, Student Activity Book, Lesson 19, Fluency Check, Problem 3, “Add: 8+5=_.”
• Application problems are embedded into practice in the Student Activity Book. For example, Unit 5, Lesson 5, Solve Perimeter and Area Problems, Problem 1, “The dimensions of a rectangular picture frame are 9 inches and 6 inches. What is the greatest size picture that would fit in the frame?”

Examples where student engage in multiple aspects of rigor:

• Unit 3, Lesson 7, students are introduced to proof drawing addition. This lesson builds students conceptual understanding of addition by asking students to visualize and model regrouping by making proof drawings to illustrate adding two 3-digit numbers. Students are introduced to four methods for solving addition problems: Show All Totals Method, New Groups Below Method, New Groups Above Method, and Proof Drawing. Students use each method to solve: “Tonya and Mark collect seashells. Tonya has 249 shells and Mark has 386 shells. How many do they have in all?”
• Unit 3, Lesson 16, students practice and discuss addition and subtraction methods. In Activity 1, students create an addition word problem using the given numbers 672 and 228. Students then create a subtraction problem using the given numbers 814 and 439. Students create a Math Mountain for those numbers, and then find addition problems that match the mountain. Students apply learned skills by creating word problems. They use procedures to solve the equations in the problems.

#### Criterion 2.2: Math Practices

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

The instructional materials reviewed for Math Expressions Grade 3 meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs). The MPs are identified and use accurate mathematical terminology. The instructional materials also partially support teachers and students in students constructing viable arguments and analyzing the arguments of others.

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

The instructional materials reviewed for Math Expressions Grade 3 meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade level.

Mathematical Practice Standards are clearly identified in a variety of places throughout the materials. For example:

• The Mathematical Practices are identified in both volumes of the Teacher’s Edition. Within the introduction, on page I13 in the section titled The Problem Solving Process, the publisher groups the Mathematical Practices into four categories according to how students will use the practices in the problem solving process. Mathematical Practices are also identified within each lesson.
• Each time a Mathematical Practice is referenced it is listed in red with a brief description of the practice.
• At the beginning of each Unit is a section devoted to the Mathematical Practices titled "Using the Common Core Standards for Mathematical Practices". Within this section, each Mathematical Practice is defined in detail. In addition, an example from the Unit is provided for each practice. For example, Unit 1, “Using the Common Core Standards for Mathematical Practices” illustrates how MP2 is used in Lesson 1-1 and Lesson 1-3.
• The Mathematical Practices align and connect with the content of daily lessons, rather than being included as stand-alone topics.

Examples of Mathematical Practices that are identified, and enrich the mathematical content include:

• Unit 1, Lesson 4, MP7 - Look for Structure | Identify Relationships, “Emphasize that division undoes multiplication. In multiplication, start with the factors and then find the product. In division, start with the product and one of the factors and then find the other factor." Student rewrite division equations as an unknown multiplication equation.
• Unit 1, Lesson 10, Teaching the Lesson, MP8 - Use Repeated Reasoning/Identify a Pattern, “Ask what patterns students see in the count-bys and equation. Two common patterns are: The sums of the digits of the count-bys follow the pattern 3, 6, 9, 3, 6, 9; and the products follow the pattern odd even, odd, even,...”
• Unit 2, Lesson 15, Teaching the Lesson, MP1 - Make Sense of Problems, teachers are given no guidance to support students as they “have Student Pairs work together to make sense of Problems 1 and 2 and to decide what operations to use.”
• Unit 3, Lesson 4, Teaching the Lesson, MP7 - Use Structure, “Allow time for students to build the number using their Secret Code Cards. What number did you build? [1,278] How is this exercise different from the first one? [The place values are given out of order.]”
• Unit 5, Lesson 9, Teaching the Lesson, MP2 - Reason Abstractly and Quantitatively, “Why can you use different fractions to name 1/2?”

It should be noted that while the Mathematical Practices are clearly identified in the teacher materials, they appear to be over identified. Many lessons have multiple Mathematical Practices listed.

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Materials carefully attend to the full meaning of each practice standard

The instructional materials reviewed for Math Expressions Grade 3 partially meet expectations for carefully attending to the full meaning of each practice standard.

The materials do not attend to the full meaning of Mathematical Practice 5.

Mathematical Practice 5: The instructional materials often dictate what tools the students use, thus providing few opportunities for students to choose tools strategically. For example:

• Unit 3, Lesson 1, students are directed to use the dot side of their MathBoards to make drawings of numbers.
• Unit 4, Lesson 3, students are directed to use a number line.
• Unit 4, Lesson 16, students are directed to use a measuring tape to measure student jumps.
• Unit 7, Lesson 5, students are directed to use straws and chenille sticks to form various angles.
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Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
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Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.

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

Math Expressions includes a Focus on Mathematical Practices lesson as the last lesson within each unit. Activity 3 of each of these lessons prompts students to determine whether a mathematical statement is true or false or to establish an arguable position surrounding a mathematical statement. These activities provide students opportunities to construct an argument and critique the reasoning of others. Student volunteers ask questions of other students to verify or correct their reasoning. Examples of Focus on Mathematical Practices lessons include, but are not limited to:

• In Unit 2, Lesson 15, students defend their position of the following statement, “You can always break an 8s multiplication into two equal addends.” Students are asked to “Establish an arguable position by writing or stating sentences that support a specific point of view.” Student work should include examples or counterexamples to justify their position. Volunteers are invited to share their positions with the class. Classmates are encouraged to ask questions to verify reasoning or correct reasoning errors.
• In Unit 3, Lesson 18, students establish an arguable position by writing or stating sentences or equations supporting a specific point of view. “If you add two 3-digit numbers, the sum will always be a 3-digit number.” Students share their positions and explanations with the class and verify their reasoning.
• In Unit 5, Lesson 10, students determine a position for the following statement, “When comparing two fractions with the same numerators and different denominators, the fraction with the smaller denominator is greater than the fraction with the larger denominator.” Classmates are encouraged to ask questions to verify reasoning or correct reasoning errors.

Puzzled Penguin problems are found throughout the materials and provide students an opportunity to correct errors in the penguin’s work. These tasks focus on error analysis, and many of the errors presented are procedural. Examples of Puzzled Penguin problems include:

• In Unit 1, Lesson 4, Puzzled Penguin problem, students identify that the penguin made a computation error when relating a division fact with the inverse multiplication fact and correct it.
• In Unit 2, Lesson 4, Puzzled Penguin problem, students identify that the penguin added instead of multiplying.
• In Unit 4, Lesson 2, Puzzled Penguin problem, students identify the error to 8 x 6 = 14.

In addition, Remembering pages at the end of each lesson often present opportunities for students to construct arguments and/or critique the reasoning of others. For example:

• Unit 2, Lesson 6, Remembering, Stretch Your Thinking, Exercise 8, “Explain two different squares that can be made using the number 9.”
• Unit 3, Lesson 2, Remembering, Stretch Your Thinking, Exercise 5, “Anton says 2,000 + 300 + 70 + 5 is the same as 23 hundreds + 7 tens + 5 ones. Is he correct? Explain.”
• Unit 4, Lesson 3, Remembering, Stretch Your Thinking, Exercise 6, “Use the numbers 3 and 4 to make a fraction that is greater than 1 and a fraction that is less than 1. Explain how you made your fractions without using a number line.”
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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.

The instructional materials reviewed for Math Expressions Grade 3 partially meet expectations that the instructional materials assist teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. Overall, the teacher materials provide students multiple opportunities to construct viable arguments, however there are missed opportunities to support teachers in engaging students in analyzing the arguments of others throughout the materials.

Throughout the Teacher Edition, the MP3 is identified with explanations and guidance for teachers, either in reference to specific parts of the lesson, or in specific activities such as Math Talks. However, this guidance often supports teachers to engage students in explaining their methods, instead of constructing arguments or critiquing reasoning. For example:

• Unit 3, Lesson 15, Math Talk, “Ask students to compare the two methods, explaining what is different and what is the same. Then, have students complete the subtraction.”

Puzzled Penguin activities are present throughout the series in the Student Activity Book. In some activities, the Teacher Edition includes guidance to support the teacher to engage students in MP3, but there are also missed opportunities. For example:

• Unit 1, Lesson 12, Puzzled Penguin, student analyze the work of the Puzzled Penguin. Teachers are supported to facilitate student discussion through sample student work. There is a missed opportunity to offer guidance to teachers on how to use the mathematics to analyze the error.
• Unit 3, Lesson 2, Puzzled Penguin problem, students critique the reasoning of the Puzzled Penguin regarding building a three-digit number using place value strategies. Student pairs analyze what he did wrong and respond to him in written form. Teachers are given the error Puzzled Penguin made, but not provided with any prompts or question stems to use with students.

There are instances where MP3 is identified in A Day at a Glance for a lesson, but there is no guidance for teachers on how to engage students to construct arguments or analyze the arguments of others.

##### Indicator {{'2g.iii' | indicatorName}}
Materials explicitly attend to the specialized language of mathematics.

The instructional materials reviewed for Math Expressions Grade 3 meet expectations that materials use accurate mathematical terminology.

• New vocabulary is introduced at the beginning of a Lesson or Activity.
• The Teacher Edition provides instruction for teachers on how to develop the vocabulary, with guidance for teachers to discuss and use of the vocabulary.
• The student materials include Unit Vocabulary Cards that students can cut out and use in school or at home to review vocabulary terms.
• The Student Activity resource contains activities that students can do with the vocabulary cards; however, the teacher materials do not provide guidance as to when students should engage in these activities to support learning the vocabulary.
• There is an eGlossary providing audio, graphics, and animations in both English and Spanish of the vocabulary needed in the lessons.
• Study POP! is an interactive digital charades app that includes Math Expressions vocabulary to help students practice and develop mathematical vocabulary. Study POP! is listed at the beginning of many lessons, but is not referenced during the lesson.

Examples of how vocabulary is incorporated within lessons include:

• Unit 1, Lesson 1, the terms equation, multiplication, factor, and product are listed in the student materials. The Teacher Edition suggests teachers may want to add these words to a vocabulary list on chart paper.
• Unit 5, Lesson 1, the terms area, perimeter, and unit square are listed in the student materials. Students use perimeter and area as they work on their Math Boards with rectangles. Students use unit squares to find the area of the rectangles. Students use 1-inch unit squares and a ruler to determine the area and perimeter of a rectangle.
• Unit 7, Lesson 5, the terms ray, angle, right angle, triangle, quadrilateral, polygon, concave, convex, pentagon, hexagon, decagon, and octagon are listed in the student materials.  Students work with the vocabulary terms throughout the lesson in multiple activities. Definitions and visual examples are provided for the vocabulary words.

In addition, there are instances where teachers are told to look for precise use of words, facts, and symbols. For example:

• Unit 2, Lesson 15, “MP6-Attend to Precision: The sentences must include precise mathematical words, facts, and symbols.” Students use precise mathematical language to defend their position on the statement, “You can always break an 8s multiplication into two equal addends.”
• Unit 5, Lesson 10, “MP6-Attend to Precision: The sentences must include precise mathematical words, facts, and symbols.” Students use precise mathematical language to defend their position on the statement, “When comparing two fractions with the same numerators and different denominators, the fraction with the smaller denominator is greater than the fraction with the larger denominator.”

### Usability

##### Gateway 3
Meets Expectations

#### Criterion 3.1: Use & Design

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

The instructional materials reviewed for Math Expressions Grade 3 meet expectations for being well-designed and taking into account effective lesson structure and pacing. The instructional materials include an underlying design that distinguishes between problems and exercises, assignments that are not haphazard with exercises given in intentional sequences, variety in what students are asked to produce, and manipulatives that are faithful representations of the mathematical objects they represent.

##### 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.

The instructional materials for Math Expressions Grade 3 meet expectations that materials distinguish between problems and exercises.

Materials provide the opportunity for students to learn new mathematics through problem solving activities. In a typical lesson, Activity 1 and Activity 2 develop the new math content of the lesson. Lessons are outlined according to an Inquiry Lesson Path based on four phases: Phase 1 Guided Introduction, Phase 2 Learning Unfolds, Phase 3 Knead Knowledge (practice stage), and Phase 4 Maintaining and Integrating Fluency. Students build mastery through practice problems/exercises. In a typical lesson, during Activity 2 and Activity 3, students complete problems in the Student Activity Book which provide practice with the math content. The purpose of each Activity within a unit is explained in the “Teaching the Lesson Section” found on the first page of each lesson.

Examples include but are not limited to:

• In Unit 3, Lesson 4, Teaching the Lesson Section, Activity 1, Quick Practice Routines: Represent Hundreds, Tens, and Ones, is stated as important because “Students create place value drawings to help conceptualize 2-digit and 3-digit numbers.” Activity 2, Place Value Drawings for Thousands, Hundreds, Tens, and Ones, is stated as important because “Students represent numbers through thousands with place value drawings.”  Activity 3, Use Place Value to Compare Numbers, is stated as important because “Students use place value drawings to visualize and compare numbers of increasing value.”
• In the Student Activity Book, Unit 6, Lesson 2, Activity 2, students solve real world problems with unknown addends: “There were 90 girls and some boys in an after-school program. 160 children were in the program in all. How many boys were in the after-school program?” In Activity 3, students are introduced to word problems with unknown factors: “A toymaker has 36 boxes of toy trains to ship to 4 toy shops. Each shop will get the same number of boxes. How many boxes of toy trains will each shop get?”
##### Indicator {{'3b' | indicatorName}}
Design of assignments is not haphazard: exercises are given in intentional sequences.

The instructional materials for Math Expressions Grade 3 meet expectations that materials provide tasks in an intentional sequence.

The design of the assignments follows a natural progression leading, to full understanding and mastery of new mathematics. Lessons follow a consistent pattern of two or three activities per lesson. Activity 1 usually focuses on the new learning. This learning is reinforced in Activity 2, and then students practice the new learning by completing Student Activity Book pages during Activity 3. Activity 3 either reinforces the new skill, or it reviews previously learned content.

Examples include but are not limited to:

• In Unit 1, Lesson 11, students review multiplication facts for 2, 3, 5, 9, and 10 using strategy cards (flashcards). Next students write multiplication equations to represent areas of rectangles and draw rectangles whose areas represent multiplication equations. Finally, students use the area model and distributive property to develop a multiplication strategy.
• In Unit 4, Lesson 4, students compare fractions using fraction bars looking for patterns, then students use number lines to compare fractions.
• In Unit 6, Lesson 1, students use Math Mountains to break-apart numbers and turn the Math Mountains into addition equations with total and 2 addends. Then students are able to solve story problems in the Student Activity Book.
##### 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.

The instructional materials for Math Expressions Grade 3 meet expectations that materials provide varied opportunities for students to present their mathematical knowledge.

Examples of how students produce answers and solutions include but are not limited to:

• Using Math Mountains to put together and take apart numbers
• Using Arrays and Area Models to solve multiplication problems
• Using drawings to make sense of mathematics
• Representing 3-digit numbers with Secret Code Cards
• Providing thinking explanations as they answer Check for Understanding questions in the Student Activity Book
• Completing fluency checks and practice in the Student Activity Book
• Critiquing the Reasoning of others by asking “good thinker questions” and using “good justifications”
• Practicing “good explanations”
• Identifying the error and correcting it (Puzzled Penguin)
• Solving problems and exercises in the Student Activity Book
##### Indicator {{'3d' | indicatorName}}
Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.

The instructional materials for Math Expressions Grade 3 meet expectations that materials provide virtual and physical manipulatives that are faithful representations of the mathematical objects they represent and are connected to the written material.

Students use a variety of manipulatives including MathBoards, Secret Code Cards, base-ten blocks, Square Inch Tiles, fraction bars, number lines, Math Mountains, and Math Mountain Cards. Most of the manipulatives are available virtually in the itools found in ThinkCentral. Manipulatives are often connected to written methods when appropriate.

Examples include but are not limited to:

• Unit 1, Lesson 3, students use arrays to solve and write multiplication problems.
• Unit 1, Lesson 11, students use Square Inch Tiles to make area models to write and solve multiplication problems.
• Unit 4, Lesson 2 students use fraction bars to break apart 1 whole into equal fractional parts and use number lines to represent fractions less than 1 whole.
##### 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.

The instructional materials for Math Expressions Grade 3 meet expectations that materials provide a visual design that is not distracting or chaotic but supports students in engaging thoughtfully with the mathematics.

Student Activity Book pages include many exercises per page, but they follow a consistent layout and do not feel cluttered because there are no extra and unnecessary pictures on the pages. Additionally, students are provided ample space to show their work. When needed, models, which are consistent with the materials used in the lesson, are included on the pages. For example, on Student Activity Book page 19, Arrays are shown, and students write multiplication equations for the corresponding arrays.

In the Teacher Guide, lessons follow a consistent layout, moving from one activity to another. Each Activity includes a large blue box that highlights the mathematical content and practice standards, the focus of the lesson, and materials needed. Parts of the lesson, such as MathTalk, are clearly labeled. For example, in Unit 4, Lesson 4, a MathTalk in Action box shows examples of how students might share their methods for comparing unit fractions.

The digital interactive game, Poggles, includes simple, appealing characters that do not distract students as they practice addition and subtraction. Poggles are small squarish characters with animated faces whose appearance can be changed by adding hair and hats to the Poggle squares.

#### Criterion 3.2: Teacher Planning

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

The instructional materials reviewed for Math Expressions Grade 3 meet expectations for supporting teacher learning and understanding of the CCSSM. The instructional materials include: quality questions to support teachers in planning and providing effective learning experiences, a teacher edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials, a teacher edition that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons, and explanations of the role of the specific grade-level mathematics in the context of the overall mathematics curriculum.

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

The instructional materials for Math Expressions Grade 3 meet expectations that materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students’ mathematical development.

Examples of teacher support include but are not limited to:

• Questions for teachers to pose are consistently included in the lesson narrative. They are italicized, making them easily visible.
• MathTalk in Action boxes include questions for the teacher to ask and potential student responses. For example, in Unit 2, Lesson 6, the teacher is guided to ask the questions: “What patterns do you see in the square numbers?, Why do you think those numbers are the same? Who can give an example?, Why is there no matching product for a square number?”
• Teacher Notes are also provided at the bottom of the lesson pages and include questions to deepen students understanding of the mathematics. For example, in Unit 6, Lesson 4, the Language and Vocabulary notes provide several probes to promote student thinking and discussion: “How many more does B have than A? How many fewer does A have than B?”
##### 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.

The instructional materials for Math Expressions Grade 3 meet expectations that 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. Materials also, when necessary provide teacher guidance for the use of embedded technology to support and enhance student learning.

Ample guidance is provided in the Teacher Guide for planning. The Pacing Guide provides guidance for each unit. Charts show the Learning Progression for the Content Standards Across Grades for the standards addressed in the Unit. A Planning Chart for each Unit that includes Math Activity Center Resources, Big Idea Resources, and Lesson Resources is provided. The Planning Chart also includes the standards addressed in each lesson, the digital and print resources for each lesson, and the assessments for the Unit. A table of the Standards for Mathematical Practice and the lessons where each is embedded is included. Also, a Table of the Math Content Standards and the lessons where they are taught is provided. Finally, a list of Assessment, Review, and Intervention Resources for the Unit is provided.

Examples include but are not limited to:

• Each lesson includes guidance on the focus of each Activity and why it is important. For example, in Unit 2, Lesson 1, Activity 1, 6s Multiplications and Divisions, is stated as important because “Students use patterns as a strategy to multiply and divide by 6.”
• Each Activity includes an explanation of what the teacher should do or say and includes possible correct responses to questions posed by the teacher.
• Formative Assessment and Check for Understanding questions are highlighted in the Teacher Guide.
• Math Practices are highlighted in the lesson narratives.
• A list of questions that can be used to build a Math Talk community is included at the beginning of each Unit.
• Notes at the bottom of each page of the lesson narrative give useful suggestions for implementing the lesson, asking questions, acquiring vocabulary, and building concepts. For example, in Unit 3, Lesson 1, the Teaching Notes for Faster Ten Sticks states, “Point out the small circles along two edges of the dot array. Explain that there are 5 dots between each pair of circles. Students can use the circles as a guide to help them draw ten sticks quickly.”
• Digital Resources for each lesson are highlighted on the first page of the lesson, and itools, which include virtual manipulatives, are shown in the lesson narrative when it may be beneficial to use them. For example, in Unit 4, Lesson 2, a picture of itools Fraction Bars and Number Lines are shown because they may be used in the lesson.
##### 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.

The instructional materials for Math Expressions Grade 3 meet expectations that materials contain a teacher’s edition that contains full, adult-level explanations and examples of the more advanced mathematics concepts and the mathematical practices so that teachers can improve their own knowledge of the subject, as necessary.

Notes are provided at the bottom of each lesson narrative in the Teacher Edition to deepen teacher understanding of the mathematics and to improve instruction. Math Background Notes provide information about the math topic to deepen teacher’s understanding. Watch For! Notes provide information about potential misconceptions and things to watch for as students complete the lesson. What to Expect from Students notes provide information about how students might engage with the math and why the math is important. Building Concepts notes provide explanations of the math and how students learn.

Examples include but are not limited to:

• Path to Fluency Charts are provided.
• Chart of the Addition/Subtraction and Multiplication/Division problem types is provided.
• Table of the Major Work and Major Clusters of the Grade is provided.
• Table of the Common Core State Standards for Mathematical Content is provided.
• Table of the Common Core State Standards for Mathematical Practice with an explanation for each Mathematical Practice is provided.
• The Putting Research into Practice section at the beginning of each unit provides research about best practices in teaching children mathematics.
• The Math Background section, prior to each unit, includes sections that deepen teacher knowledge of the math in the unit. Examples include Learning Path in the Common Core Standards, Help Students Avoid Common Errors, Effective Practice Routines, Relate Mathematics to the Real World, and Focus on Mathematical Practices.
• The Math Background section, prior to each unit, provides excerpts from the Progressions for the Common Core State Standards.
• The Mathematical Practices section, prior to each unit, provides information on how students will engage with the Practice Standards throughout the unit.
• A Teacher Glossary is provided.
##### 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.

The instructional materials for Math Expressions Grade 3 meet expectations that materials contain a teacher’s edition that explains the role of the specific mathematics standards in the context of the overall series.

A Path to Fluency: Kindergarten through Grade 6 Chart is provided and highlights the fluency requirements of each grade level, activities that target fluency, and interventions for Grades 3, 4, 5, and 6. Also, a Major Work and Major Clusters of the Grade Chart for Grades K-6 is provided. Finally, for each unit, a Learning Progressions for the Common Core State Standards Chart for the domains addressed in the unit, which includes the current, prior, and next grade level standards is provided.

##### 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).

The instructional materials for Math Expressions Grade 3 provide a list of lessons in the teacher's edition, cross-referencing the standards addressed and providing an estimated instructional time for each lesson, chapter, and unit.

Math Expressions does not include chapters, but rather units which are divided by Big Ideas, which are further divided into lessons. The Pacing Guide provides estimated instructional time for lessons and units. This Pacing Guide provides an estimated number of days for each unit, including lessons that may take two days and the number of days for assessments and quizzes. It should be noted that Lessons identified as taking two days in the Pacing Guide are not identified in the lesson narratives, nor is a breaking point indicated.

Examples include but are not limited to:

• The Table of Contents provided in the introduction to the materials includes standards for all units’ Big Ideas.
• The Chart of the Common Core State Standards for Mathematical Content provided identifies the lessons in which each standard will be addressed.
• The Chart of the Common Core State Standards for Mathematical Practice provided identifies the lessons in which each Mathematical Practice will be addressed.
• A Planning Chart is provided in the Overview for each unit that includes the standards that are addressed in each lesson.
• Charts of the Math Content Standards and Math Practice Standards are provided in the Overview for each unit. These charts include a list of each standard and the lessons where they are addressed.
• The Content and Practice Standards are identified on the first page of each lesson. The standards are also listed for each Activity within a lesson.
##### 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.

The instructional materials for Math Expressions Grade 3 contain strategies for informing students, parents, or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

Family Letters for each unit are found in the Student Activity Book. These letters explain content, manipulatives students may use, and an explanation of terminology that may be unfamiliar to parents. Most units include between 1-3 Family Letters. Spanish versions of the letters are also included in the Student Activity Book.

##### Indicator {{'3l' | indicatorName}}
Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.

The instructional materials for Math Expressions Grade 3 contain explanations of the instructional approaches of the program and identification of the research-based strategies.

The Teacher Edition contains explanations of the program’s instructional approaches and research-based strategies. An Inquiry Learning Path describes the four phases of the Math Expressions classroom: Guided Introduction, Learning Unfolds, Knead Knowledge, and Maintaining and Integrating Fluency. The Putting Research into Practice pages at the beginning of each Unit explain best practices related to the content of the Unit. Excerpts from the Progressions for the Common Core State Standards are included in the Math Background section of each Unit. Research Notes are sometimes included in the Teaching Notes at the bottom of the lesson narrative in the Teacher Edition. For example, the Teaching Notes in Unit 2, Lesson 8, Activity 2, Organizing Fluency Study state, “The Unit 1 Overview lists all practice materials for Unit 1. The Unit 2 Overview lists the practices materials in Unit 2 and describes how to continue fluency practice all year. These pages will give you an overview to manage the different needs of your students, who are in different places in the progression of fluency materials.”

#### Criterion 3.3: Assessment

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

The instructional materials reviewed for Math Expressions Grade 3 meet expectations for offering teachers resources and tools to collect ongoing data about student progress on the CCSSM. The instructional materials provide strategies for gathering information about students’ prior knowledge, strategies for teachers to identify and address common student errors and misconceptions, and assessments that clearly denote which standards are being emphasized.

##### Indicator {{'3m' | indicatorName}}
Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.

The instructional materials for Math Expressions Grade 3 meet expectations that materials provide strategies for gathering information about students’ prior knowledge within and across grade levels.

Examples include but are not limited to:

• The Assessment Guide contains a Prerequisite Skills Inventory Test, organized by Domains, and a corresponding Prerequisite Skills Inventory Test Correlation document. The correlation aligns each question with a description of the prerequisite skill addressed, as well as the DoK level of the question. This correlation document is formatted as a table so each student’s performance by question/skill can be recorded. The Prerequisite Skills Inventory Test  is designed to be administered at the beginning of the school year.
• When a student completes practice opportunities and tests in the Personal Math Trainer, all of the performance data and adaptive learning information follows each student to the next grade.
• The Math Background section for each unit alerts teachers to prior knowledge opportunities. For example, in Unit 4, the Math Background for Time states, “In the previous grade, students found elapsed time in hours and half hours from a start time and an end time. In this unit students find elapsed time in hours and minutes and use these skills to solve real world problems.” It is noted that number lines and clock models may be needed to help students calculate elapsed time.
• Quick Practice activities at the beginning of each lesson are designed to “provide opportunities for students to call to mind their prior understanding of a topic that has already been discussed in class or to begin to build a prerequisite skill for a topic that is to come later” (Teacher Edition page I4).
• Quick Quizzes and Fluency Checks are embedded within the units to check understanding of Big Ideas prior to moving on to the next Big Idea instruction, and to monitor progress toward computational fluency. For example, Fluency Check 9 assesses student multiplication and division facts (3.OA.7) and addition and subtraction of 3-digit numbers (3.NBT.2).
• Students take three progress monitoring assessments to assess grade level skills and concepts students have learned. The Beginning of Year test assesses concepts they will learn throughout the year, the Middle of Year Test shows progress made in the first half of the year, and the End of Year Test measures growth throughout the school year.
##### Indicator {{'3n' | indicatorName}}
Materials provide strategies for teachers to identify and address common student errors and misconceptions.

The instructional materials for Math Expressions Grade 3 meet expectations that materials provide support for teachers to identify and address common student errors and misconceptions.

Examples include but are not limited to:

• Common student errors are identified for each Unit Review/Test question along with a direction on how to help students. For example, on the Unit 4 Review/Test, if a student misses Question 6 or 9, the common error identified states, “Students can’t use information from graph to solve.” Teachers are directed to “Review how to read a bar graph, pictograph, or line plot. Have students look at headings, titles, and labels before reading the numbers presented in the data.”
• The Math Background section of each Unit provides a narrative called “Help Students Avoid Common Errors”.
• Puzzled Penguin activities highlight typical student mistakes and misconceptions by challenging students to find the Puzzled Penguin’s mistake and correct it. Teachers are provided questions in order to lead classroom conversations through a MathTalk format that revolve around the mistake and its correction, helping students understand the mathematics.
• Watch For! are teaching notes periodically found in each unit. These notes alert teachers to common misconceptions they should be on the lookout for. For example, in Unit 3, Lesson 1, the Watch For! note states, “Be sure students understand that a thousand bar doesn’t have to be the size of 10 hunderd boxes. Whenever they see or draw a long, skinny stip in a place value drawing, they will know that it is a thousand bar and it is equivalent to 10 hundreds.”
##### Indicator {{'3o' | indicatorName}}
Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

The instructional materials for Math Expressions Grade 3 meet expectations that materials provide support for ongoing review and practice, with feedback, for students in learning both concepts and skills.

Examples include but are not limited to:

• Homework and Remembering pages provide a review of recently taught topics as well as a spiral review throughout the year. The Personal Math Trainer online platform allows students to complete homework tasks for each lesson, receive instant feedback, and  step-by-step guidance if needed.
• Unit Review/Test and Performance Tasks for each unit are found in the Student Activity Book. The author states, You can use this Unit Review/Test as an end-of-unit review to determine if children have mastered the content of the unit. You can assess children’s knowledge with one of the forms of the Unit 1 Test in the Assessment Guide.” Teachers are provided with a Data-Driven Decision Making Table which suggests specific reteaching activities for students who incorrectly answer the correlated questions, as well as suggestions for which Standards Quiz to assign in the Personal Math Trainer which provides a personalized intervention for the student. The Performance Task includes a detailed scoring rubric which can be used to provide feedback to students.
• The Personal Math Trainer can be used for homework practice, fluency practice, standards practice, unit pre-tests with instant feedback, and step-by-step guidance when needed. Everything a student completes in the platform helps to improve the adaptive workflow (powered by Knewton Adaptivity) for the student throughout the year.
• The Knewton Adaptivity, Homework with Daily Intervention and Enrichment can be used in multiple ways in the classroom. A 5-minute Warm-Up provides students with personalized review prior to the assignment. On-level and advanced students may receive less or no warm-up, as determined by Knewton. After the warm-up, the HMH pre-built assignment is given to students. A 10-minute personalized enrichment is provided for students who demonstrate mastery (95% or higher) on the assignment.  Enrichment shows students proximate, forward-looking concepts based on the assignment content.
• Other Formative Assessment opportunities include: daily Check Understanding tasks on select Student Activity Book pages, daily observation with anecdotal notes, observations during Math Talk conversations, and analyzing student work samples and student responses in the Student Activity Book. Portfolio suggestions are also provided at the end of each unit.
##### Indicator {{'3p' | indicatorName}}
Materials offer ongoing formative and summative assessments:
##### Indicator {{'3p.i' | indicatorName}}
Assessments clearly denote which standards are being emphasized.

The materials reviewed for Math Expressions Grade 3 meet the expectation for offering ongoing assessments that clearly denote which standards are being emphasized.

Examples include but are not limited to:

• Every unit includes two versions of a Unit Assessment, Form A and Form B, found in the Assessment Guide. Both assessments provide PARCC and Smarter Balance question formats and a Standards Correlation Document which can be used to collect student performance data. This document also aligns each question to a DoK Level and Standard(s).
• Each unit contains a Performance Assessment which can be found in the Assessment Guide. The standards are clearly noted for the assessment as a whole, and not by specific question.
• There are three Benchmark Assessments (Beginning of the Year Inventory, Middle of the Year Inventory and End of Year Assessment) found in the Assessment Guide. Standards for these assessments are clearly noted on the Correlation Document and DoK Levels are noted.
##### 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.

The instructional materials for Math Expressions Grade 3 meet expectations that assessments provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

Examples include but are not limited to:

• Scoring Guides are provided for each Unit Performance Assessment found in the Assessment Guide. Each question is assigned a point value and a rubric is provided to determine Performance Levels 0-3 based on the number of points earned. Additionally, each Performance Level is further defined on a task-specific basis and indicates specifics about student understanding to assist teachers in interpreting student work. Sample student work for each Performance Level is also provided in the Assessment Guide.
• Answer keys for the Unit Assessments, Form A and Form B, are located in the back of the Assessment Guide. However, no guidance or suggestions for follow-up instruction are included in the Assessment Guide.
• The online Personal Math Trainer can be utilized to administer Beginning, Middle and End of Year Tests, Unit Assessments, and Fluency Checks. The data from these assessments is collected and analyzed, and a Personal Study Plan is prescribed through Adaptive Workflow settings (through Knewton Adaptivity) based on the data and the mastery threshold percentage established for the assessment. The primary use is for end of the unit assessments, or to provide targeted students with occasional review, intervention, and re-assessment opportunities. Students must complete an initial assignment (test). Students who do not demonstrate mastery receive a Personal Study Plan, consisting of a personalized review and intervention assignment lasting 15 minutes. After completing the Personal Study Plan, the initial assignment is given again, but numbers in the assessment are changed.
##### Indicator {{'3q' | indicatorName}}
Materials encourage students to monitor their own progress.

The instructional materials for Math Expressions Grade 3 do not encourage students to monitor their own progress and do not provide direction for teachers to encourage students to monitor their progress.

#### Criterion 3.4: Differentiation

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

The instructional materials reviewed for Math Expressions Grade 3 meet expectations for supporting teachers in differentiating instruction for diverse learners within and across grades. The instructional materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners and strategies for meeting the needs of a range of learners. The materials embed tasks with multiple entry points that can be solved using a variety of solution strategies or representations, and they provide opportunities for advanced students to investigate mathematics content at greater depth. The instructional materials also suggest support, accommodations, and modifications for English Language Learners and other special populations and provide a balanced portrayal of various demographic and personal characteristics.

##### Indicator {{'3r' | indicatorName}}
Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

The instructional materials for Math Expressions Grade 3 meet expectations that materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

Teachers guide students through an inquiry path to become mathematically proficient. The four stages of the path to learning are guided introduction, learning unfolds, knead knowledge through practice, and maintain fluency. As stated by the publisher, “Within the curriculum, a series of learning progressions reflect research on students’ natural learning stages when mastering concepts such as computation and problem-solving strategies. These learning stages informed the order of concepts, the sequence of units, and the positioning of topics in Math Expressions.”

Examples include but are not limited to:

• Unit 1, Lesson 6, students build fluency with 2s and 5s. Prompts are given for EL students at three different levels: emerging, expanding, bridging. A teaching note is included to help teachers diagnose if students are at an Emerging, Expanding, or Bridging level. Teachers are instructed, “Draw a 3 x 4 array. Write the words row and column.” Emerging: “Point to the rows. Rows go across. There are 3 rows. Point to the columns. Columns go down. There are 4 columns. Have students repeat.” Expanding: “Rows go across. How many rows are there? Columns go down. How many columns are there?” Bridging: “Have students tell the difference between rows and columns.”
• In Unit 3, Lesson 1, the Universal Access/Extra Help teaching note instructs teachers, “If students are not convinced the 5 x 20 boxes represent 100, have them draw horizontal ten sticks.”
• In Unit 5, Lesson 6, students use tangrams to find area. The Universal Access/Special Needs teacher notes state, “If students have difficulty manipulating paper manipulatives, laminate the page before you cut out the materials. Pair the students with a Helping Partner so they can work through the activity together.”
##### Indicator {{'3s' | indicatorName}}
Materials provide teachers with strategies for meeting the needs of a range of learners.

The instructional materials for Math Expressions Grade 3 meet expectations that materials provide teachers with strategies for meeting the needs of a range of learners.

Examples include but are not limited to:

• An explanation of differentiated instruction is provided in the Teacher Edition.
• A list of intervention resources is provided for each unit in the Unit Overview Assessment.
• Math Activity Centers resources for on-level, challenge, and intervention are provided for each unit’s lessons.
• Teaching notes for English Learners are provided for emerging, expanding, and bridging students and are provided for each unit’s lessons.
• Some lessons have Differentiated Instruction notes provided for universal access/extra help.
##### Indicator {{'3t' | indicatorName}}
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

The instructional materials for Math Expressions Grade 3 meet expectations that materials embed tasks with multiple entry points that can be solved using a variety of solution strategies or representations.

MathTalks provide “an inquiry environment that encourages constructive discussion of problem-solving methods through well-defined classroom activity structures. . . comprises four components: questioning, explaining math thinking, contributing math ideas, and taking responsibility for learning” (Teacher Edition page I3). Initially, teachers model MathTalks and then students run the MathTalk. For example, in Unit 1, Lesson 2, the MathTalk states, “The Solve and Discuss structure of conversation is used throughout the Math Expressions program. The teacher selects four or five students to go to the board and solve a problem using any method they choose. The other students work on the same problem at their desks. Then the teacher asks the students at the board to explain their methods. Students at their desks are encouraged to ask questions and to assist each other in understanding the problem. Thus students solve, explain, question, and justify. It is best to ask only two or three students at the board to explain. This avoids having the seated students become restless. Time is better spent on the next issue. Be sure to have students stand beside their work and point to parts of it as they explain it. Using a pointer that does not obscure any work enables watchers to see the part of the drawing or math symbols that are being discussed at that moment.”

##### 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).

The instructional materials for Math Expressions Grade 3 meet expectations that 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.

Examples include but are not limited to:

• Scaffolding of vocabulary is provided. For example, in Unit 3, Lesson 1, the words circles, ten sticks, and boxes are explained for EL students. Teachers are instructed to say, “‘This is a circle. It equals 1. Its value is 1.’ Have students repeat. Continue with ten sticks and boxes.”
• Extra support is provided for EL students. For example, in Unit 5, Lesson 7, students are introduced to equivalency with fractions. Teachers are instructed to “Point out that the word equivalent has equal in it. Cross out the ‘i’, ‘v’, and ‘ent’ in equivalent to see the word equal. We show that fractions are equivalent using an equal sign.”
• Each unit lesson contains a Math Activity Center with activities and resources for students who are on-level and those needing challenge and intervention.
• Teaching notes included in some lessons provide specific guidance for teachers to support students who are emerging, expanding, and bridging language acquisition.
##### Indicator {{'3v' | indicatorName}}
Materials provide opportunities for advanced students to investigate mathematics content at greater depth.

The instructional materials for Math Expressions Grade 3 meet expectations that materials provide opportunities for advanced students to investigate mathematics content at greater depth.

Examples include but are not limited to:

• Math Lessons contain Differentiated Instruction Math Activity Centers. Challenge Resources specify which Activity Card will challenge advanced students.
• The online Personal Math Trainer provides personalized enrichment with learning supports.
• Challenge worksheets for each lesson are available in print and digitally and are noted on the Differentiated Instruction page for each lesson.
• Math Readers, books in the Math Activity Center, place math content in the context of stories and support higher levels of critical thinking.
##### Indicator {{'3w' | indicatorName}}
Materials provide a balanced portrayal of various demographic and personal characteristics.

The instructional materials for Math Expressions Grade 3 meet expectations that materials provide a balanced portrayal of various demographic and personal characteristics.

Examples include but are not limited to:

• Puzzled Penguin appears throughout the unit to provide opportunities to help students avoid common errors. These errors are presented as letters to students. Students teach Puzzled Penguin the correct way and explain why the penguin is wrong.
##### Indicator {{'3x' | indicatorName}}
Materials provide opportunities for teachers to use a variety of grouping strategies.

The instructional materials for Math Expressions Grade 3 provide opportunities for teachers to use a variety of grouping strategies.

Examples include but are not limited to:

• Math Activity Centers are provided at the conclusion of each lesson and students can be grouped individually, in pairs, or in groups to complete the Activity Cards. For example, in Unit 3, Lesson 1, Intervention Activity card 3-1, students find the sum of two dice when rolled then determine if the sum can be regrouped into a ten and some ones.
• Math Writing Prompts are part of the Math Activity Centers and provide opportunities for students to work individually, in pairs, or in groups. For example, in Unit 6, Lesson 4, the Challenge Math Writing Prompt states, “Would you solve a comparison problem with an unknown difference the same way you would solve a comparison problem with an unknown larger or smaller amount? Explain your thinking.”
• MathTalks provide various grouping structures. During Solve and Discuss, 4-5 students go to the board and solve the problem while the rest of the class is solving independently or as part of a small group consisting of 2-3 students. During Scenarios, a group of students act out a particular mathematical situation for other students to see.
##### Indicator {{'3y' | indicatorName}}
Materials encourage teachers to draw upon home language and culture to facilitate learning.

The instructional materials for Math Expressions Grade 3 sometimes encourage teachers to draw upon home language and culture to facilitate learning.

Family Letters for each unit are found in the Student Activity Book. Spanish versions of these letters are also included in the Student Activity Book. However, instructional materials do not encourage teachers to draw upon home language and culture to facilitate learning. English Learner notes in the Teacher Edition do not reference Spanish vocabulary 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.

The instructional materials reviewed for Math Expressions Grade 3: integrate technology in ways that engage students in the Mathematical Practices; are web-­based and compatible with multiple internet browsers; include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology; are intended to be easily customized for individual learners; and do not include technology that provides opportunities for teachers and/or students to collaborate with each other.

##### 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.

The instructional materials for Math Expressions Grade 3 are web-based and compatible with multiple internet browsers. In addition, materials are platform neutral and allow the use of tablets and mobile devices.

Web-based instructional materials for both teachers and students can be accessed using multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, both students and teachers can use multiple devices to access instructional materials (desktop computer, tablet, iPad, Smartboard, laptop, or cellphone). Students with disabilities can use mobile devices, assistive technology, or PCs to access materials. For example, non-readers have the option to have the entire text in an audio format. Additionally, the materials are platform-neutral for a variety of operating systems.

##### Indicator {{'3ab' | indicatorName}}
Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.

The instructional materials for Math Expressions Grade 3 provide opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.

Online assessments are available. Teachers have the ability to create their own assessments or customize those provided by the program. A variety of assessment types are provided: multi-step, fill in the blank, multiple-choice, or teacher-created questions. For example, teachers giving the computer adaptive test may edit the format and/or values of the text causing the corresponding complexity of the lesson to change accordingly.

The Personal Math Trainer is an online adaptive assessment and learning system of mathematical understanding and procedural skill/fluency. Teachers can identify question types, assignment type, or standard tested. Once students have completed the task or assessment, various charts and graphs can be generated based on standards to inform instruction. Reports are available for individual students and the entire class.

##### 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.

The instructional materials for Math Expressions Grade 3 include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations.

Teachers can manipulate the Personal Math Trainer to create learning experiences for students targeting their needs. Additionally, teachers can create lesson materials that are specific to the learning targets for specific unit lessons. For example, in Unit 3, Lesson 1, students can use the digital dotted MathBoard to make ten sticks and circle ones to represent numbers like 76.

The instructional materials for Math Expressions Grade 3 can be easily customized for local use.

Digital materials include adaptive technological innovations for teachers to personalize learning for students. Digital materials can be differentiated based on individual student’s needs. For example, when using the Personal Math Trainer, teachers can add or modify existing tasks to a student’s personalized learning path. Additionally, adaptive technology allows teachers to provide two flexible differentiated styles (Daily Intervention and Enrichment or Personal Study Plan) for students.

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.).

The instructional materials for Math Expressions Grade 3 do not include reference technology that provides opportunities for teachers and/or students to collaborate with each other.

Materials do not provide opportunities for students and teachers to participate in discussion groups using technology.

##### 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.

The instructional materials for Math Expressions Grade 3 integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.

Examples include but are not limited to:

• The Student Activity eBook provides audio, ability to submit answers online, a drawing tool for math drawings, guided practice to help students solve problems, and virtual manipulatives.
• The Personal Math Trainer is an online adaptive assessment and personalized learning system for students. It analyzes student activity to determine strengths, weaknesses, learning style preferences, and pace. It provides a personalized learning path for students and generates reports for teachers to inform instruction.
• The online Math Activity Center provides online differentiated instruction opportunities for practice, reteach, and challenge. Teachers can assign RTI assignments to students who struggle on Big Idea Quick Quizzes. Fluency Builders develop students’ basic facts and automaticity.
• OSMO is an interactive gaming system for iPads to build students' fluency and problem-solving skills. It offers physical manipulatives and provides immediate feedback.

## Report Overview

### Summary of Alignment & Usability for Math Expressions | Math

#### Math K-2

The instructional materials reviewed for Math Expressions Grade K-2 meet expectations for alignment to the Standards. The instructional materials meet expectations for Gateway 1, focus and coherence, Gateway 2, rigor and balance and practice-content connections, and Gateway 3, instructional supports and usability indicators.

##### Kindergarten
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations

#### Math 3-5

The instructional materials reviewed for Math Expressions Grades 3-6 vary in alignment to the CCSSM. All Grades 3-6 meet the expectations for Gateway 1, focus and coherence. The instructional materials for Grades 3-5 meet the expectations for Gateway 2, rigor and practice-content connections, but Grade 6 partially meets due to partially connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs). Since the materials for Grade 6 partially meet expectations for alignment, they were not reviewed for usability in Gateway 3. The materials for Grades 3-5 meet the expectations for alignment as they meet expectations for focus, coherence, rigor, and practice-content connections. The instructional materials for Grades 3-5 meet the expectations for usability in Gateway 3.

###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Partially Meets Expectations
Not Rated

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### Overall Summary

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###### Usability
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