## Investigations in Number, Data, and Space, 3rd Edition

##### v1
###### Usability
Our Review Process

Title ISBN Edition Publisher Year
Investigations 3 Common Core Standards Practice Workbook Grade 2 (Student) 978-0-328-75685-8 Pearson 2017
Investigations 3 Common Core Standards Practice Workbook Grade 2 (Teacher Guide) 978-0-328-75692-6 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 2 Unit 1 978-0-328-85906-1 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 2 Unit 2 978-0-328-85907-8 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 2 Unit 3 978-0-328-85908-5 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 2 Unit 4 978-0-328-85909-2 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 2 Unit 5 978-0-328-85910-8 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 2 Unit 6 978-0-328-85911-5 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 2 Unit 7 978-0-328-85912-2 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 2 Unit 8 978-0-328-85913-9 Pearson 2017
Implementing Investigations in Grade 2 978-0-328-85941-2 Pearson 2017
Investigations 3 Common Core Assessment Sourcebook Grade 2 978-0-328-85965-8 Pearson 2017
Investigations and the Common Core Content Guide Grade 2 978-0-328-85971-9 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 5 Unit 1 978-0-328-85931-3 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 5 Unit 2 978-0-328-85932-0 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 5 Unit 3 978-0-328-85933-7 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 5 Unit 4 978-0-328-85934-4 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 5 Unit 5 978-0-328-85935-1 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 5 Unit 6 978-0-328-85936-8 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 5 Unit 7 978-0-328-85937-5 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 5 Unit 8 978-0-328-85938-2 Pearson 2017
Implementing Investigations in Grade 5 978-0-328-85944-3 Pearson 2017
Investigations 3 Common Core Assessment Sourcebook Grade 5 978-0-328-85968-9 Pearson 2017
Investigations and the Common Core Content Guide Grade 5 978-0-328-85974-0 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 3 Unit 1 978-0-328-85915-3 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 3 Unit 2 978-0-328-85916-8 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 3 Unit 3 978-0-328-85917-7 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 3 Unit 4 978-0-328-85918-4 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 3 Unit 5 978-0-328-85919-1 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 3 Unit 6 978-0-328-85920-7 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 3 Unit 7 978-0-328-85921-4 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 3 Unit 8 978-0-328-85922-1 Pearson 2017
Implementing Investigations in Grade 3 978-0-328-85942-9 Pearson 2017
Investigations 3 Common Core Assessment Sourcebook Grade 3 978-0-328-85966-5 Pearson 2017
Investigations and the Common Core Content Guide Grade 3 978-0-328-85972-6 Pearson 2017
Common Core Standards Practice Workbook Grade K (Student Guide) 978-0-328-75683-4 Pearson 2017
Common Core Standards Practice Workbook Grade K (Teacher Guide) 978-0-328-75690-2 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade K Unit 1 978-0-328-85890-3 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade K Unit 2 978-0-328-85891-7 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade K Unit 3 978-0-328-85892-7 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade K Unit 4 978-0-328-85893-4 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade K Unit 5 978-0-328-85894-1 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade K Unit 6 978-0-328-85895-8 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade K Unit 7 978-0-328-85896-5 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade K Unit 8 978-0-328-85897-2 Pearson 2017
Implementing Investigations in Kindergarten 978-0-328-85939-9 Pearson 2017
Investigations 3 Common Core Assessment Sourcebook Grade K 978-0-328-85963-4 Pearson 2017
Investigations and the Common Core Content Guide Grade K 978-0-328-85969-6 Pearson 2017
Investigations 3 Common Core Standards Practice Workbook Grade 1 (Student) 978-0-328-75684-1 Pearson 2017
Investigations 3 Common Core Standards Practice Workbook (Teacher Guide) 978-0-328-75691-9 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 1 Unit 1 978-0-328-85898-9 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 1 Unit 2 978-0-328-85899-6 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 1 Unit 3 978-0-328-85900-9 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 1 Unit 4 978-0-328-85901-6 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 1 Unit 5 978-0-328-85902-3 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 1 Unit 6 978-0-328-85903-0 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 1 Unit 7 978-0-328-85904-7 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 1 Unit 8 978-0-328-85905-4 Pearson 2017
Implementing Investigations in Grade 1 978-0-328-85940-5 Pearson 2017
Investigations 3 Common Core Assessment Sourcebook Grade 1 978-0-328-85964-1 Pearson 2017
Investigations and the Common Core Content Guide Grade 1 978-0-328-85970-2 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 4 Unit 1 978-0-328-85923-8 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 4 Unit 2 978-0-328-85924-5 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 4 Unit 3 978-0-328-85925-2 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 4 Unit 4 978-0-328-85926-9 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 4 Unit 5 978-0-328-85927-6 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 4 Unit 6 978-0-328-85928-3 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 4 Unit 7 978-0-328-85929-0 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 4 Unit 8 978-0-328-85930-6 Pearson 2017
Implementing Investigations in Grade 4 978-0-328-85943-6 Pearson 2017
Investigations 3 Common Core Assessment Sourcebook Grade 4 978-0-328-85967-2 Pearson 2017
Investigations and the Common Core Content Guide Grade 4 978-0-328-85973-3 Pearson 2017
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### Overall Summary

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

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

### Focus & Coherence

The instructional materials reviewed for Grade 2 meet the expectations for focus on major work and coherence. The instructional materials meet the expectations for focus through their assessments and design concerning class time spent on major work. The instructional materials partially meet the expectations for coherence, and they show strengths in having an amount of content that is viable for one school year and fostering coherence through connections within the grade.

##### 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 meet the expectation for not assessing topics before the grade-level in which the topic should be introduced. Overall, there are no assessment items that align to topics beyond Grade 2.

##### Indicator {{'1a' | indicatorName}}
The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.

The instructional materials reviewed for Grade 2 meet the expectations for focus within assessment. There are no above grade-level assessment questions, and the assessments include material that is appropriate for Grade 2. Probability, statistical distributions, similarity, transformations and congruence do not appear in the assessments.

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

Examples of quality assessments include:

• On Unit 2 Session 2.5 Assessment Sourcebook page A14, Quiz 1 assesses students on identifying triangles, quadrilaterals, pentagons, hexagons, and cubes (2.G.1), and there is an item where students have to match the name of each of these shapes to a picture of each shape.
• On Unit 5 Session 2.6 Assessment Sourcebook page A40, Quiz 1 assesses students on comparing two three-digit numbers (2.NBT.4), and there is an item that represents two three-digit numbers with base-10 blocks. Students are supposed to write the numbers and complete inequality statements once the numbers are written.

#### 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 meet the expectation for students and teachers devoting the large majority of class time to the major work of the grade when the materials are used as designed. Overall, the materials spend at least 65% of class time on the major work of Grade 2.

##### Indicator {{'1b' | indicatorName}}
Instructional material spends the majority of class time on the major cluster of each grade.

The instructional materials reviewed for Grade 2 meet the expectations for spending the majority of class time on the major clusters of the grade. Overall, approximately 70 percent of class time is spent on major work of the grade.

The instructional materials are separated into eight units. Each unit is composed of one, two, three, or four investigations, and each investigation is divided into sessions. The Implementing Investigations guide states in Part 4 (Classroom Routines) within the Overview that each session includes a Classroom Routine activity that is “introduced as a session activity and are then used outside of math time (e.g., during morning meeting, just before or after lunch or recess, or at the beginning or end of the day) or integrated into the math lesson as the first 10 minutes of a 70-minute math block.” The Classroom Routine activity requires 10-15 minutes which provides daily practice and review of previously learned skills. Each session requires sixty minutes. Three perspectives were used when calculating major work of the grade: number of units, number of investigations, and number of sessions.

• Approximately 5 of the 8 units focus on major work of the grade. This represents approximately 63 percent of the units.
• Approximately 13 of the 21 investigations focus on major work of the grade. This represents approximately 62 percent of the investigations.
• Approximately 100 of 143 sessions focus on or support the major work of the grade. This represents approximately 70 percent of the sessions.

The third perspective, number of sessions, is the most reflective of the instructional materials because it is based on the sessions which includes the instructional activities, review, and practice. As a result, approximately 70 percent of the 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 Grade 2 partially meet the expectations for being coherent and consistent with the Standards. The instructional materials show strength in having an amount of content that is viable for one school year, but due to not always identifying work that is off grade-level, the materials are not always consistent with the progressions in the Standards. The materials do foster coherence through connections within the grade, but few of those connections are between major work of the grade and supporting work.

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

The instructional materials reviewed for Grade 2 partially meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. Throughout the instructional materials, major work of the grade is sometimes supported by non-major work. However, there are some missed natural connections, and the supporting standards occasionally appear in lessons with few connections to the major work of the grade.

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

• In Unit 4 Session 1.1 uses picture graphs (2.MD.10) to represent data not connected to major work.
• In Unit 4 Session 1.2 introduces bar graphs (2.MD.10) for 15 minutes of a 70 minute math class and then plays “Guess My Rule,” which is a game that identifies common attributes. There are no connections to major work.
• In Unit 4 Sessions 1.5 and 1.6 students do not work with the bar graph (2.MD.10) outside of creating it. Bar graphs could support the major work by having the students add or subtract with the data.
• There are missed opportunities to make connections between 2.MD.7 (time) and Numbers and Operations in Base Ten and Operations and Algebraic Thinking.

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

• In Unit 1 the Session 3.3 Collect $0.50 activity connects supporting work naturally to major work. Money is a supporting standard (2.MD.8), but students are working on adding the value of the coins together which directly supports major work of the grade (2.NBT.6). • In Unit 3 Session 1.4 major work is supported through the use of bar graph data (2.MD.10) for adding and subtracting during the discussion portion (2.OA.1). • In Unit 7 Sessions 2.1 and 2.2 students are working with the supporting cluster 2.OA.C. Students are skip counting and adding within 100, which supports the major work of the grade. (2.NBT.A). ##### Indicator {{'1d' | indicatorName}} The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades. The instructional materials reviewed for Grade 2 meet the expectations for the amount of content being viable for one school year. • The instructional materials are divided into 8 units that have a total of 143 sessions. • Assessments are done during sessions and are not counted as extra days. • Each session is designed to be completed in 60-70 minutes with the majority of the sessions being 70 minutes. Each session is accompanied by a Ten-Minute Math activity that is designed to be completed in 10 minutes outside of math time. • Each unit takes between 2 to 5.5 weeks to complete according to the “Grade 2 Curriculum Units and Pacing Chart” on page 9 of the Implementing Investigations in Grade 2 guide. Each unit includes an additional day beyond the days required to finish the sessions. This day could be used to complete the Intervention, Practice, and/or Extension activities that are included at the end of each investigation. • The pacing chart on page 9 of the Implementing Investigations In Grade 2 guide suggests a total of approximately 28.5-32.5 weeks or 140-165 days. ##### Indicator {{'1e' | indicatorName}} Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades. The materials reviewed for Grade 2 partially meet the expectations for being consistent with the progressions in the Standards. In general, the materials develop according to the grade-by-grade progressions in the Standards, but content from future grades is not clearly identified. The materials provide extensive work with grade-level problems for most standards, but the materials do not relate grade-level concepts explicitly to prior knowledge from earlier grades. The materials develop according to the grade-by-grade progressions in the Standards, but content from future grades is not clearly identified. Examples of unclear identification include: • Unit 2 Sessions 3.5 and 3.6 have students notating fractions (3.NF.1). • In Unit 2 Session 2.4 students build and count arrays of more than 5 x 5, which is above the grade-level standard. • In Unit 4 Session 2.5 students analyze numerical data in line plots. In grade 2, line plot data is limited to measurement data (2.MD.9). Some of the above grade-level content is identified as above grade-level. • Unit 8 describes the unit as laying a piece of the foundation for the work students do in Grade 3 and beyond as they build their understanding of the operations of multiplication and division. The materials often give all students extensive work with grade-level problems. • Recommendations for differentiation allow students to primarily work with grade-level tasks. • The standards are addressed throughout the entire series, and no standards were completely omitted. Overall, the materials were on grade-level, and students had a variety of opportunities to engage in grade-level problems. • The materials give students extensive work with most domains. However, 2.MD.2 is addressed in three sessions within Unit 6. These sessions may not allow all students to master measuring the length of an object twice, using length units of different lengths for the two measurements, and describing how the two measurements relate to the size of the unit chosen. • Standard 2.MD.3- estimate lengths using units of inches, feet, centimeters, and meters- is addressed in five lessons within Unit 6. This may not provide enough explicit instruction with measurement for all students. The materials do not consistently relate grade-level concepts explicitly to prior knowledge from earlier grades. The scope and sequence found in the Implementing Investigations book gives some limited information relating to knowledge from earlier and future grades by listing major topics and which units in prior and future grades address those topics. Each unit has a “Connections: Looking Back” section at the beginning of the unit. Several units specifically refer to work from prior grades without providing explicit connections to specific standards. • Unit 1 says that the unit builds on all of the Kindergarten and Grade 1 number units, which focused in large part on counting, composing and decomposing numbers, fluency with single-digit computation within 10, and representing and solving a variety of types of addition and subtraction problems. ##### Indicator {{'1f' | indicatorName}} Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important. The instructional materials reviewed for Grade 2 meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards. The materials begin each investigation with a planner that lists objectives for each session, and in the session materials, Math Focus points are listed at the beginning of each session. The instructional materials include objectives and Math Focus points that are visibly shaped by the CCSSM cluster headings for Grade 2. • In Unit 3 Session 3.3 the Math Focus Point is “Developing fluency with addition and subtraction within 20.” This is visibly shaped by cluster 2.OA.B, Add and subtract within 20. • In Unit 6 Session 2.1 the Math Focus Points are “Becoming familiar with the terms inches, feet, and yards as standard units of measure," "Using a ruler as a standard measuring tool," and "Measuring and comparing lengths.” These are visibly shaped by cluster 2.MD.A, Measure and estimate lengths in standard units. • In Unit 7 Session 2.4 the Math Focus Points are “Describing the relationship between a number of equal groups and their total," "Representing multiplicative relationships with tables," and "Using an equation to model adding equal groups.” These are visibly shaped by cluster 2.OA.C, Work with equal groups of objects to gain foundations for multiplication. The instructional materials include problems and activities that connect two or more clusters in a domain or two or more domains. • In Unit 3, Sessions 3.3 and 3.4 connect 2.OA.A, 2.OA.B, 2.NBT.A, 2.NBT.B, and 2.MD.B as students solve problems by using their understanding of place value to add and subtract within 20 along with relating addition and subtraction to length. • In Unit 8, Sessions 2.1 through 2.4 connect 2.NBT.A and 2.NBT.B as students use their understandings of place value and properties of operations to add and subtract within 20. ###### Overview of Gateway 2 ### Rigor & Mathematical Practices The instructional materials reviewed for Grade 2 partially meet the expectations for rigor and the mathematical practices. The materials meet the expectations for rigor as they help students develop conceptual understanding, procedural skill and fluency, and applications. However, the materials partially meet the expectations for mathematical practices as they do not attend to the full meaning for each of the MPs and rarely prompt, or have the teachers prompt, students to analyze the arguments of others. ##### Gateway 2 Partially 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 Grade 2 partially meet the expectations for rigor and the mathematical practices. The materials meet the expectations for rigor as they help students develop conceptual understanding, procedural skill and fluency, and applications. However, the materials partially meet the expectations for mathematical practices as they do not attend to the full meaning for each of the MPs and rarely prompt, or have the teachers prompt, students to analyze the arguments of others. ##### Indicator {{'2a' | indicatorName}} Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings. The materials reviewed for Grade 2 meet the expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. Overall, the instructional materials often call for visual representations, verbal explanations, and written equations. • In Unit 1 Session 1.5 students develop the conceptual understanding of understanding that the three digits of a three-digit number represent amounts of hundreds, tens, and ones (2.NBT.1). Students are filling in the missing numbers on the hundreds chart that starts at 101. Students have to answer addition and subtraction problems that relate to the missing numbers such as "100+3=?" • In Unit 1 Session 2.3 students develop their understanding of the Commutative Property of Addition (2.NBT.9). Students work with different colored counting cubes to see that the order that numbers are added in does not matter. • In Unit 7 Session 1.1 students explore even and odd (2.OA.3) by modeling with cubes, drawing pictures, and explaining their strategies for determining if a number is even or odd. • In Unit 7 Session 2.1 students explore arrays (2.OA.4) to find how many rooms are in a building that has three floors using cubes and drawing pictures. ##### Indicator {{'2b' | indicatorName}} Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency. The materials reviewed for Grade 2 meet the expectations for giving attention throughout the year to individual standards that set an expectation for procedural skill and fluency. The materials include opportunities to review and practice in order to build procedural skill and fluency in the Classroom Routines, Daily Practice, Homework, and Games. Standard 2.OA.2 requires students to fluently find single-digit sums and differences. • In Unit 1, Sessions 2.1 thru 2.8, students work on properties of operations, addition of two or more numbers, and subtraction facts. • In Unit 3 Session 2.1 students use Resource Master-G22 to complete the activity “Close to 20.” Students choose three cards to get a sum as close to 20 as possible. • In Unit 3 Session 2.3 the classroom routine provides students practice with fluency by requiring students to create their own near doubles equation for given equations. Standard 2.NBT.5 requires students to add and subtract within 100. • In Unit 1 Session 3.3 the “Collect$0.50” activity provides students with the opportunity to work on procedural skill and fluency by working with coins that add up to $0.50. • In Unit 3, Sessions 3.1 thru 3.7, students work with word problems requiring addition and subtraction within 100. • In Unit 5 Session 1.4 students are engaged in creating combinations of coins that add up to$1.00.
• In Unit 5 Session 1.5 students complete problems on Student Activity Book page 311, “Capture 5,” that requires addition and subtraction of numbers within 100.
• In Unit 7 Sessions 2.1 and 2.2 students skip count and add within 100.
##### Indicator {{'2c' | indicatorName}}
Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade

The materials reviewed for Grade 2 meet the expectations for teachers and students spending sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade.

Practice with application of the major work in addition and subtraction is found throughout six units of instruction. Students have many opportunities to work with standard 2.OA.1, use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g. by using drawings and equations with a symbol for the unknown number to represent the problem.

In Unit 1 students are introduced to problems with multiple addends and use cubes to model. Within Sessions 4.1 through 4.5, students focus on word problems using strategies for solving addition and subtraction word problems through modeling, drawing pictures, and class discussions.

In Unit 3 students use sticker strips, hundred charts, number lines, and strategies based on place value and coins (dimes and pennies) to model word problems with 2-digit numbers. In Unit 4 students answer questions about data found on graphs and line plots. In Unit 5 students solve word problems with the goal of getting to 100. “How Many More?” asks students to solve the real world question of “Jake has 23 bird stickers. Franco gave him 31 more stickers. How many bird stickers does Jake have now? Color the grid to show Jake’s stickers. How many more stickers does Jake need to have 100 bird stickers?” The materials then apply this skill to working with money. In Unit 6 students use addition and subtraction to compare measurement data. In Unit 8 students focus on comparison word problems.

##### Indicator {{'2d' | indicatorName}}
Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.

The instructional materials reviewed for Grade 2 partially meet the expectations for balance of the three aspects of rigor within a grade. Although the instructional materials meet expectations for each aspect of rigor, these aspects of rigor are often addressed in separate parts of the Sessions. Materials targeting application are often scaffolded, detracting from the balance of rigor. Overall, the three aspects of rigor are most commonly treated separately.

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

#### Criterion 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 Grade 2 partially meet the expectations for practice-content connections. Overall, the materials show strengths in identifying and using the MPs to enrich the content along with attending to the specialize language of mathematics. However, the materials do not always attend to the full meaning of each MP, and there are few opportunities for students to analyze the arguments of others either through prompts from the materials or from their teachers.

##### Indicator {{'2e' | indicatorName}}
The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.

The instructional materials for Grade 2 meet the expectations for identifying the Standards for Mathematical Practice (MPs) and using them to enrich the mathematical content. The MPs are clearly identified in Implementing Investigations on page 44 and can also be found in each unit. The instructional materials highlight two MPs in every Unit. During the Sessions, Math Practice Notes dialogue boxes are given to provide tips to the teacher on how to engage students in the MPs. Additionally, Math Practice Notes are provided for the MPs that are not highlighted so students continue to work on the practices all year.

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

• The Unit 7 “Mathematical Practices in this Unit” is found on pages 6-9. This unit focuses on MP3 and MP2. An example of MP2 from Session 2.2 is included.
• The Unit 3 “Mathematical Practices in this Unit” is found on pages 8-11. This unit focuses on MP5 and MP2. An example of MP5 from the activity “Sticker Station” is included.

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

• Unit 3 Session 1.3 includes a Math Practice Note for MP7, a practice not highlighted in the unit. Students are recognizing that problems about 32 stickers and 32 cents are the same.
• Unit 4 Session 1.1 includes a Math Practice Note for MP4 and MP6, practices highlighted in the unit. The MP4 note discusses tables, tallies, and equations being mathematical models of the classroom data. The MP6 note describes what students need to include in a representation to communicate clearly.
• Unit 5 Session 1.1 includes a Math Practice Note for MP7, a practice highlighted in the unit. The note discusses how solving pairs of related problems can help students see connections between related facts. It also includes a Math Practice Note for MP6 and MP8, practices not highlighted in the unit. The note discusses the importance of explaining a pattern once it has been recognized.
• Unit 7 Session 2.6 includes a Math Practice Note for MP2 and MP3, practices highlighted in the unit. The MP2 note states that students are recognizing that the same tables match different contexts. The note for MP3 describes how the students can make arguments describing common structure.
##### Indicator {{'2f' | indicatorName}}
Materials carefully attend to the full meaning of each practice standard

The instructional materials reviewed for Grade 2 partially meet expectations that materials carefully attend to the full meaning of each practice standard (MP). Although the instructional materials attend to the full meaning of some of the MPs, there are some MPs for which the full meaning is not developed.

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

• The Unit 1 Session 2.7 Math Practice Note lists MP5 and has students play "Quick Images." This is a game that uses Ten Frames instead of coins. The Math Practice Note talks specifically about the Ten Frame that highlights the structure of 10, combinations of ten, teen numbers as ten plus some amount, and 2-digit numbers as groups of ten and some number of ones. Students are not able to choose a tool in this session.
• The Unit 1 Session 3.1 Math Practice Note lists MP1 and has students work together to figure out how many children are in the class. They solve the problem in two different ways. The teacher asks students if she will get the same answer if she adds the number of boys to girls and if she adds the girls to the boys and encourages students to explain their thinking. The students are encouraged to explain their thinking and discuss if their answer makes sense. They are not having to persevere through this problem.
• The Unit 8 Session 1.1 Math Practice Note lists MP4 and introduces students to comparison problems with a smaller unknown. The teacher displays a story problem on the board and then draws a sketch to show what is being seen. She draws two bars to show the students number of stickers from the problem. In this session the teacher is doing all of the work, the student is not engaged in modeling with mathematics on their own.
• The Unit 8 Session 2.8 Math Practice Note lists MP1 and has students breaking up a hundred and some tens. The following question is posed: If a student started with 235 stickers and needs to take away 158, with 150 being taken away so far, how many stickers are left to take? The students are taken through this problem step-by-step and work on this as a whole group. This discussion of the activity does not have a student persevere or make sense of the problem.

At times, the instructional materials fully attend to a specific MP. The following are examples:

• The Unit 4 Session 2.2 Math Practice Note lists MP1 and has students in pairs discuss and decide how they will collect their data about the number of teeth lost by students in other classes. They perform the same task with teeth lost in their classroom first. The Math Practice Note explains to the teacher that the step prior to collecting data is to devise a plan. Students are engaging in perseverance if they need to devise a plan and be clear about the question they will ask to be able to gather accurate data for their survey.
• The Unit 4 Session 2.3 Math Practice Note lists MP4 and has students predicting the number of teeth lost by students in other classrooms. They are asked to collect the data, make predictions about the data, and display the data. The representation of data students collected allowed them to make the predictions about the other classrooms. This is a real-world problem that uses a model to express the data.
##### Indicator {{'2g' | indicatorName}}
Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
##### Indicator {{'2g.i' | indicatorName}}
Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.

The instructional materials reviewed for Grade 2 partially meet the expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade level mathematics.

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

• In Unit 2 Session 2.2 students are asked to sort shapes into two categories, 4 sides with 4 right angles or 4 sides but not 4 right angles. The materials state, “If there is a disagreement, have students explain how they determine whether an angle is a right angle or not, and have them show how they “measure” the angles of the shape with the square tile?” This is an opportunity for students to construct their own viable argument, but there are no specific prompts or questions for analyzing the arguments of others, just agreeing or disagreeing.
• In Unit 5 Session 2.2 students are playing a game where they determine what number should be added to 79 in order to obtain a sum of 100, and the students are prompted to consider how they would answer this question knowing that 80 + 20 = 100. The students are prompted to construct other strategies besides the one that is presented, but there is not an opportunity for students to analyze the alternative strategies that are presented.
• In Unit 8 Session 1.2 students are prompted to construct arguments that support why certain subtraction expressions have a difference of 10. In this example, students are also prompted to construct their arguments in a specific way, and there are also no opportunities for students to analyze other arguments that might be presented.

There are a few places where the materials prompt students to construct viable arguments and analyze the arguments of others.

• In Unit 1 Session 1.6 students are asked to figure out what part of the counting strip is incorrect, and they are supposed to discuss what is wrong, how they know, and how they could fix it. Students are also supposed to include why someone might have made the errors.
##### Indicator {{'2g.ii' | indicatorName}}
Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.

The instructional materials reviewed for Grade 2 partially meet the expectations for assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards. Overall, teachers are instructed to have students share or explain their solutions and occasionally ask questions of other students, but these questions or prompts generally do not assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others.

• The Unit 3 Session 2.4 Math Practice Note states, “When students notice a numerical pattern such as this one- that when 10 is added to a number, the tens place increases by 1 and the ones place stays the same- it is important that they explain why this pattern holds. Does this happen only for the numbers we have looked at, or will it happen for other numbers, too?” This note assists teachers in helping students construct viable arguments, but there is no assistance for analyzing the arguments of others.
• In Unit 6 Session 1.2 while students are comparing measurements with different units, the teacher is directed to ask, “(Holly’s) number is higher than anyone else’s? Does that mean that (her) jump was the longest? Why does (Holly) have the highest number?” These questions and the accompanying Math Practice Note assist teachers in engaging students in constructing an argument, but there are no questions or prompts to assist teachers in having students analyze the arguments of others.
• In Unit 8 Session 2.4 students are asked to examine three different strategies for adding two three-digit numbers, and the teacher is prompted to have “students share their understanding of why the two problems (one of the three strategies) are equivalent.” Through this prompt, students could begin to construct a viable argument, but there are no other questions or prompts to help students who are not able to construct an argument. There are also no questions or prompts for students to analyze the arguments of others.

There are a few places where the materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others.

• In Unit 1 Session 3.1 teachers are prompted to lead a discussion with the following: “First let’s see what people have for an answer to this problem. [Katrina] thinks 12. Who has a different answer?...Did anyone have another answer? People found a few different answers to this problem. Let’s hear how some of you solved the problem and see whether we can figure out why there are different answers. Last year, some of my students used the number line or the 100 chart to solve Enough for the Class? problems. How do you think they used these tools?” These questions assist the teacher in prompting students to construct their own argument, and they also provide different strategies that the students could use in analyzing the arguments of others.
##### Indicator {{'2g.iii' | indicatorName}}
Materials explicitly attend to the specialized language of mathematics.

The instructional materials reviewed for Grade 2 meet the expectations for explicitly attending to the specialized language of mathematics.

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

• In Unit 2 Session 1.1 students are introduced to 2-D and 3-D shapes. The teacher is prompted to state, “Sometimes we will be working with images of flat shapes, like the rectangle. They are called two-dimensional shapes. Other times we will be using solid objects like the Geoblocks. They are called three-dimensional shapes.”
• In Unit 2 Session 3.2 students are asked to describe what one-half of a given rectangular prism would look like. The materials prompt the teacher to ask, “Is this block one half of this block? How could you prove it? Could there be a different block that is also one half of this block?”
• In Unit 7 Session 2.2 students are asked to write an equation from a given array. The materials prompt the teacher to ask the following questions: “How many squares are in each column? How many columns are in this array? How can I write an equation that shows the total number of squares as the sum of equal addends?”

### Usability

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

#### Criterion 3.1: Use & Design

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
##### Indicator {{'3a' | indicatorName}}
The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
##### Indicator {{'3b' | indicatorName}}
Design of assignments is not haphazard: exercises are given in intentional sequences.
##### Indicator {{'3c' | indicatorName}}
There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
##### Indicator {{'3d' | indicatorName}}
Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
##### Indicator {{'3e' | indicatorName}}
The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

#### Criterion 3.2: Teacher Planning

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
##### Indicator {{'3f' | indicatorName}}
Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
##### Indicator {{'3g' | indicatorName}}
Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
##### Indicator {{'3h' | indicatorName}}
Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.
##### Indicator {{'3i' | indicatorName}}
Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.
##### Indicator {{'3j' | indicatorName}}
Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
##### Indicator {{'3k' | indicatorName}}
Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
##### Indicator {{'3l' | indicatorName}}
Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.

#### Criterion 3.3: Assessment

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

#### Criterion 3.4: Differentiation

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
##### Indicator {{'3r' | indicatorName}}
Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
##### Indicator {{'3s' | indicatorName}}
Materials provide teachers with strategies for meeting the needs of a range of learners.
##### Indicator {{'3t' | indicatorName}}
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
##### Indicator {{'3u' | indicatorName}}
Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
##### Indicator {{'3v' | indicatorName}}
Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
##### Indicator {{'3w' | indicatorName}}
Materials provide a balanced portrayal of various demographic and personal characteristics.
##### Indicator {{'3x' | indicatorName}}
Materials provide opportunities for teachers to use a variety of grouping strategies.
##### Indicator {{'3y' | indicatorName}}
Materials encourage teachers to draw upon home language and culture to facilitate learning.

#### Criterion 3.5: Technology

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
##### Indicator {{'3aa' | indicatorName}}
Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
##### Indicator {{'3ab' | indicatorName}}
Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
##### Indicator {{'3ac' | indicatorName}}
Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
##### Indicator {{'3z' | indicatorName}}
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.

## Report Overview

### Summary of Alignment & Usability for Investigations in Number, Data, and Space, 3rd Edition | Math

#### Math K-2

The instructional materials reviewed for Grades K-2 meet the expectations for focus and coherence in Gateway 1. The materials meet the expectations for focus as they assess grade-level topics and spend the majority of class time on major work of the grade. Even though the materials are viable for one school year and foster coherence through connections within the grade, the materials partially meet the expectations for coherence. The materials partially meet the expectations for rigor and the mathematical practices (MPs) in Gateway 2. The materials partially meet the expectations for rigor as they develop conceptual understanding and procedural skill and fluency, and even though the materials identify and use the MPs to enrich the content along with attending to the specialized language of mathematics, the materials partially meet the expectations for the MPs.

##### Kindergarten
###### Alignment
Partially Meets Expectations
Not Rated
###### Alignment
Partially Meets Expectations
Not Rated
###### Alignment
Partially Meets Expectations
Not Rated

#### Math 3-5

The instructional materials reviewed for Grades 3-5 partially meet the expectations for focus and coherence in Gateway 1. The materials meet the expectations for focus as they assess grade-level topics, except in Grade 4, and spend the majority of class time on major work of the grade, except in Grade 3. Even though the materials are viable for one school year and foster coherence through connections within the grade, the materials partially meet the expectations for coherence. The materials partially meet the expectations for rigor and the mathematical practices (MPs) in Gateway 2. The materials meet the expectations for rigor as they develop conceptual understanding, procedural skill and fluency, and application, and even though the materials identify and use the MPs to enrich the content along with attending to the specialized language of mathematics, the materials partially meet the expectations for the MPs.

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

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### Overall Summary

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###### Usability
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