Investigations in Number, Data, and Space, 3rd Edition
Downloadable Resources
Publisher Response
2017

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

Publisher
Savvas Learning Company f/k/a Pearson
Subject
Math
Grades
K-5
Report Release
03/03/2017
Review Tool Version
v1.0
Format
Core: Comprehensive

EdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Partially Meets Expectations

Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
NE = Not Eligible. Product did not meet the threshold for review.
Not Eligible
Downloadable Resources
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Showing:
4th Grade

About This Report

Report for 4th Grade

Alignment Summary

The instructional materials reviewed for Grade 4 partially meet the expectations for alignment to the CCSSM. The materials partially meet the expectations for focus and coherence in Gateway 1, and they partially meet the expectations for rigor and the mathematical practices in Gateway 2. Since the materials partially meet the expectations for alignment, evidence concerning instructional supports and usability indicators in Gateway 3 was not collected.

4th Grade
Gateway 1

Focus & Coherence
10/14
0
7
12
14
Gateway 2

Rigor & Mathematical Practices
14/18
0
10
16
18
Alignment (Gateway 1 & 2)
Partially Meets Expectations
Gateway 3

Usability
Usability (Gateway 3)
Not Rated
Gateway 1
Gateway 2
Gateway 3
Viewing:
Gateway 1
Overview of Gateway 1

Focus & Coherence

The instructional materials reviewed for Grade 4 partially meet the expectations for focus on major work and coherence. The instructional materials do not meet the expectations for focus due to assessing topics from grade-levels before they should be introduced. 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
v1.0
Gateway 1

Focus & Coherence
10/14
0
7
12
14
Criterion 1.1: Focus
00/02
Criterion 1.2: Coherence
04/04
Criterion 1.3: Coherence
06/08
Partially Meets Expectations

Criterion 1.1: Focus
00/02
Materials do not assess topics before the grade level in which the topic should be introduced.

The instructional materials reviewed do not meet the expectation for not assessing topics before the grade-level in which the topic should be introduced. Overall, there are assessment items that align to topics beyond Grade 4.

Indicator 1A
00/02
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 4 do not meet expectations for focus within assessment. Most of the assessments include materials appropriate for Grade 4, however, there are two assessment items that assess above grade level probability and statistics.

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

In Unit 2, Generating and Representing Measurement Data, there are two assessment items that use language and contexts more appropriate for probability and statistics in Grade 6 (6.SP.4):

  • In Unit 2 students are given a line plot and asked to identify the outlier.
  • In Unit 2, “Comparing Numbers of Cavities,” students are given the following prompt: “Consider the highest and lowest number of cavities and the outliers. Consider also where the data are concentrated and what you think is typical.”

In Unit 1, Quiz 2, Question 1 asks “Which number is a factor of 200?” This question is aligned to Standard 4.OA.4 (finding all factor pairs for a whole number in the range 1-100) but asks for a factor of a number outside of the range indicated by the standard. However, this question is could be modified to stay on grade level.

Criterion 1.1: Focus
00/02
Indicator 1A
00/02

Criterion 1.2: Coherence

04/04
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 4.

Indicator 1B
04/04
Instructional material spends the majority of class time on the major cluster of each grade.

The instructional materials reviewed for Grade 4 meet the expectations for spending the majority of class time on the major clusters of the grade. Overall, approximately 68 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 Ten-Minute Math activity provides practice with current skills or review of previously learned skills. Each session requires sixty minutes. Three perspectives were used when calculating major work of the grade: number of investigations, number of minutes (including Ten-Minute Math), and number of sessions (excluding Ten-Minute Math).

  • Approximately 15 of the 22 investigations focus on major work of the grade. This represents approximately 68 percent of the investigations.
  • If the Ten-Minute Math activity times are added into the session minutes, approximately 6290 of the minutes focus on major work of the grade. This represents approximately 68 percent of the minutes.
  • Approximately 90 of 132 sessions focus on or support the major work of the grade. This represents approximately 68 percent of the sessions.

The third perspective, number of sessions, is the most reflective of the instructional materials because it is based on the sessions which includes the instructional activities, review, and practice but does not include the Ten-Minute Math activity that is done outside of math time. As a result, approximately 68 percent of the materials focus on major work of the grade.

Criterion 1.2: Coherence
04/04
Indicator 1B
04/04

Criterion 1.3: Coherence
06/08
Coherence: Each grade's instructional materials are coherent and consistent with the Standards.

The instructional materials reviewed for Grade 4 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
01/02
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The instructional materials reviewed for Grade 4 partially meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. Supporting standards are not always used to support major work of the grade and often appear in lessons with few connections to the major work of the grade.

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

  • In Unit 2 Sessions 1.2, 1.3, and 1.4 students work with height data to record and compare data and develop arguments about what the data shows (4.MD.A) with no support for the major work standards (4.NF and/or 4.OA.A). In Sessions 2.1 through 2.6, students work with data in various way; for example, students are representing and interpreting data on a graph, constructing arguments, and describing data (4.MD.A). There is no support within these lessons for the major work standards (4.NF and/or 4.OA.A).

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

  • In Unit 1 Sessions 1.1 through 1.4 students work with arrays and answer questions such as how many items are found in an array. The questions and activities in these sessions connect the supporting work (4.OA.B) with major work of the grade (4.NBT.B).
Indicator 1D
02/02
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 4 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 132 sessions
  • Each session is designed to be completed in 60 minutes. Each session is accompanied by a Ten-Minute Math activity that is designed to be completed in 10 minutes outside of math time.
  • Each unit consists of 1-4 Investigations. Each investigation ranges from 4-10 class sessions
  • Each unit takes between 2.5 to 5.5 weeks to complete according to the “Grade 4 Curriculum Units and Pacing Chart” on page 9 of the Implementing Investigations in Grade 4 guide. Each unit includes an additional 2.5 days beyond the days required to finish the sessions. These days could be used to complete the Intervention, Practice, and/or Extension activities that are included at the end of each investigation.
  • These instructional materials include approximately 153 days.
Indicator 1E
01/02
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 4 partially meet the expectations for being consistent with the progressions in the Standards. In general, the materials develop according to the grade-by-grade progressions in the Standards, but content from future grades is not clearly identified. The materials provide extensive work with grade-level problems for most standards, but the materials do not relate grade-level concepts explicitly to prior knowledge from earlier grades.

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

  • In Unit 2, students make line plots to represent data, 4.MD.4, but they also use terms such as range, mode, and outlier to describe the sets of data, 6.SP.B, and compare two sets of data, 7.SP.B. The content from future grades is not identified as such.
  • In Unit 4 Session 4.4 students find the area of irregular polygons by decomposing the shapes into rectangles and triangles, 6.G.1. The content from future grades is not identified as such.
  • In Unit 8, Session 1.5 has students generate two numerical patterns from two given rules, and the students are also asked questions that compare the two patterns created. This content more closely aligns to 5.OA.3, but it is not clearly identified as content from a future grade.

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

  • Recommendations for differentiation allow students to primarily work with grade-level tasks.
  • The materials have different types of practice for students during each lesson. There are Teaching Resources in the Resource Masters and Activities in the Student Activity Book which are both aids during lessons. There are Daily Practice and Homework pages in the Student Activity Book which are indicated to be session follow-ups that review and practice grade-level content.
  • The materials give students extensive work with most domains. However, 4.NBT.A is only found in Unit 5 in eight sessions and Unit 6 in one session. There are 17 ten-minute math practices that also address this standard which is an important standard for “applying concepts of place value and division.” This may not be extensive enough for all students to develop understanding of place value for multi-digit whole numbers. The major work clusters of 4.NF.A, 4.NF.B and 4.NF.C are taught in Unit 6.

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 the unit builds on the work done in Grade 3 “as students developed an understanding of multiplication and division through work with equal-sized groups, arrays, and area models.”
  • Unit 2 describes how students will use learning from Grade 3 where students worked with categorical and numerical data represented by line plots, bar graphs, and pictographs.
  • Unit 4 describes building on the work students have done in previous grades that includes measuring with a variety of units of length, finding perimeter and area, and reasoning about 2-dimensional shapes and their attributes.
  • Unit 5 “builds on the work students have done in Grade 3 on addition and subtraction, as they extended their ideas about place value and the operations of addition and subtraction.”
  • Unit 6 refers back to work done in Grade 3 “as students worked with fractions with denominators of 2, 3, 4, 6, and 8” with various representations including drawing, number lines, and pattern blocks.
  • Unit 8 refers to work done in Grade 3 in multiplication and division when students analyzed number sequences from repeating patterns.
Indicator 1F
02/02
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 4 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 4.

  • In Unit 1 Sessions 1.3 and 1.4 students use what they know about multiplication to find all the arrays for given numbers. They discuss special features of some numbers, including prime and square numbers (4.OA.B).
  • In Unit 4 Session 2.3 students sort quadrilaterals according to a variety of criteria and construct quadrilaterals with specific attributes (4.G.A).
  • In Unit 7 Session 3.4 students represent multi-step problems with equations and solve the problems. They continue to solve division problems and discuss solving division problems efficiently (4.OA.A).
  • In Unit 1 Session 1.1 the Math Focus Point is “representing multiplication situations with arrays.” This is visibly shaped by cluster 4.NBT.B, use place value understanding and properties of operations to perform multi-digit arithmetic.

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

  • In Unit 2, Sessions 2.5 and 2.6 connect 4.MD.A and 4.MD.B as students solve problems involving measurement and conversion of measurements based on representations and interpretations of data sets.
  • In Unit 5, Session 3.3 connects 4.OA.A with 4.NBT.A as students use place-value understanding of multi-digit whole numbers in order to solve word problems.
Criterion 1.3: Coherence
06/08
Indicator 1C
01/02
Indicator 1D
02/02
Indicator 1E
01/02
Indicator 1F
02/02
Overview of Gateway 2

Rigor & Mathematical Practices

The instructional materials reviewed for Grade 4 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
v1.0
Gateway 2

Rigor & Mathematical Practices
14/18
0
10
16
18
Criterion 2.1: Rigor
07/08
Criterion 2.2: Math Practices
07/10
Partially Meets Expectations

Criterion 2.1: Rigor
07/08
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 4 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
02/02
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 4 meet the expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. In the instructional materials visual representations, verbal explanations, and written equations are used to develop conceptual understanding.

  • In Unit 6 Session 1.3 students use visual fraction models to generate equivalent fractions (4.NF.1). While working, students share their ideas with another student. Students also complete Student Activity Book pages 348 and 349 which require them to find equivalent fractions using fraction models and then provide a written explanation of how they know that the fractions are equivalent.
  • In Unit 6 Session 2.3 student view Fraction Cards and are asked to determine which fraction is greater (4.NF.2). Students are told to use the picture on the cards and other knowledge that they have about fractions to help them decide. Teachers are told to listen for the use of “landmark fractions” in the student explanations. Students continue comparing fractions playing the game Capture Fractions and record equivalent fractions on Student Activity Book page 371.
  • In Unit 5 Sessions 3.1 and 3.2 students create and hang a 10,000 chart in order to recognize that a digit in one place represents ten times what it represents in the place to its right (4.NBT.1).
  • In Unit 1 Session 1.1 students draw rectangular arrays, write problems to represent the arrays, and calculate how many items are in an array (4.NBT.5). For Daily Practice, students are given real-world pictures of arrays and are asked to find the total and dimensions and draw the arrays.
Indicator 2B
02/02
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 4 meet the expectations for giving attention throughout the year to individual standards that set an expectation for procedural skill and fluency. The materials include opportunities to practice and review in order to build procedural skill and fluency. Students are provided Daily Practice in every session and Homework in many sessions. The instructional materials provide direct instruction regarding the standard algorithm, 4.NBT.4, and additional practice is provided.

Standard 4.NBT.4 requires students to fluently add and subtract multi-digit whole numbers using the standard algorithm.

  • In Unit 4, nine Ten-Minute Math activities address 4.NBT.4. The Ten-Minute Math activities are titled “Broken Calculator” and are found in Sessions 1.1, 1.2, 1.3, 1.4, 1.5, 3.1, 3.2, 3.3, and 3.4. These activities are presented to students without any explicit instruction on the standard algorithm, and many of these numbers are less than 1,000 or use 0 in the tens and ones place. For example, in Session 1.1 students are asked to create five expressions that equal 1,800. They can use either subtraction or addition and the 1 and 8 keys are broken. In Session 1.2 students create five expressions that 2,600 using addition and subtraction, and 2 and 6 broken. These Ten-Minute Math activities are not aligned to 4.NBT.4.
  • In Unit 5, ten sessions- 1.4, 1.5, 1.6, 2.4, 2.5, 2.6, 2.7, 3.4, 3.5, and 3.6- provide the formal instruction for 4.NBT.4. Session 1.4 is the first time that students are formally taught the standard algorithm. In the opening activity students discuss and explain how two different algorithms work. The Discussion section provides support for the teacher to explicitly model the standard US algorithm. Practice is provided in student activity book pages 278-279. Session 1.5 provides more practice but no further review or instruction for using the standard algorithm. Session 1.6 provides support to review the steps with students. Session 2.4 includes an opening activity that provides an example of subtracting by place. This section explains how the standard US algorithm works step-by-step and includes Student Activity Book pages 298, 299, and 300. In Session 2.5 students practice and talk through the steps of subtraction problems, and in Session 2.6 students continue to subtract using the standard algorithm and practice problems including items with a story context. In Session 2.7 students subtract a number from a number with a zero in the tens place. Students talk through the steps of the problem without the teacher modeling or providing instruction. Sections 3.4, 3.5, and 3.6 provide practice with the standard algorithm.
  • In Unit 6 students are provided with five formal opportunities to practice 4.NBT.4. In the Daily Practice portion of Sessions 1.1, 1.3, 1.4, 1.5, and 2.5 students are provided opportunities to add or subtract using the standard algorithm.
  • In Unit 7 students are provided with another formal opportunity to practice 4.NBT.4 in the Daily Practice portion of Session 1.3.
Indicator 2C
02/02
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 4 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 fractions is limited to Unit 6. Standard 4.NF.3d, solve real-world problems involving addition and subtraction of fractions referring to the same whole and having like denominators, is found within Sessions 3.1, 3.2, 3.4, 4.2, 4.3, and 4.4. Standard 4.NF.4c, solve word problems involving multiplication of a fraction by a whole number, is in Sessions 4.1, 4.2, 4.3, and 4.4. For example, in Session 4.1 (4.NF.3d) students are required to solve word problems like “Jake bought three kinds of pizza for a party. Each pizza was the same size. By the end of the party, ¾ of the pizza was eaten. How much pizza was eaten in all?”

Practice for 4.OA.3 is found throughout five units of instruction. Through the first four units, materials focus on one-step problems, scaffolded two-step problems, or two-step problems with inverse operations. In Unit 8, Analyzing Patterns and Rules, the full intent of the standard is reached. In this Unit, students are generating tables from situations and then generating and/or using rules from those tables to solve word problems. However, often the activities are still very scaffolded.

Much of Unit 2 provides real-world application of 4.MD.A and 4.MD.B. Sessions include “How Many Raisins in a Box,” “How Tall are Fourth Graders,” and “How Tall are First Graders.” Students collect data from the real-world and use that data to create representations, compare data, and analyze data.

Indicator 2D
01/02
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 4 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 adequately addressed in the Sessions; however, for the most part they are addressed in separate sections of the instructional materials. Conceptual understanding is typically addressed in the Discussion and Math Workshop portions of 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 2.1: Rigor
07/08
Indicator 2A
02/02
Indicator 2B
02/02
Indicator 2C
02/02
Indicator 2D
01/02

Criterion 2.2: Math Practices
07/10
Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice

The instructional materials reviewed for Grade 4 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
02/02
The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.

The instructional materials for Grade 4 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 that students continue to work on the practices all year.

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

  • The Unit 2 “Mathematical Practices in this Unit” is found on pages 8-11. This unit focuses on MP2 and MP7. An example of MP2 from Session 2.2 is included.
  • The Unit 8 “Mathematical Practices in this Unit” is found on pages 8-11. This unit focuses on MP4 and MP8. An example of MP4 from Session 1.2 is included, and an example of MP8 from Session 1.3 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 1 Session 1.6 includes a Math Practice Note for MP7, a practice not highlighted in the unit. Students are noticing and using the properties of multiplication.
  • Unit 4 Session 1.2 includes a Math Practice Note for MP6, a practice highlighted in the unit. The note discusses measurement differences.
  • Unit 5 Session 3.1 includes a Math Practice Note for MP5 and MP7, practices highlighted in the unit. The note discusses how the 10,000 chart is a tool for understanding the structure of the base-10 system.
  • Unit 7 Session 3.5 includes a Math Practice Note for MP8, a practice not highlighted in the unit. Students are working with problems that emphasize the relationship between multiplication and division.
Indicator 2F
01/02
Materials carefully attend to the full meaning of each practice standard

The instructional materials reviewed for Grade 4 partially meet expectations that materials carefully attend to the full meaning of each practice standard (MP). Although the instructional materials attend to the full meaning of some of the MPs, there are some MPs for which the full meaning is not developed.

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

  • Unit 1 Session 1.1 in the Math Practice Note it lists MP5 and has students represent multiplication situations with arrays. The Math Practice Note talks specifically about what a rectangular array is and how it provides images students use to understand key properties. This activity only has students using arrays and does not allow them to choose any other tool.
  • Unit 3, Session 2.2 in the Math Practice Note it lists MP4 and has students learning how to represent remainders in a division problem. In the Math Practice Note it states that while students are learning the division notations, teachers should emphasize “reading”each equation with meaning by referring to the context it is modeling. This session doesn’t allow for students to realize the mathematics present in the real-world problem, but has them notate and solve the problem and then refer back to it to find the meaning.
  • Unit 3 Session 2.4 in the Math Practice Note it lists MP5 and has students play a Missing Factors game. In the Math Practice Note they state that this game is to learn how to use the rectangular array to model division. Students are not able to choose any tool other than an array in this lesson.
  • Unit 6 Session 1.2 in the Math Practice Note it lists MP5 and has students finding fractional parts of a rectangle. In the Math Practice Note students are told to use a 4X6 rectangle.

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

  • Unit 6, Session 3.2 in the Math Practice Note it lists MP5 and has students adding fractions. In the Math Practice Note it states students choose which mathematical tool to use and the session supports this choice while offering suggestions such as number lines and rectangles, to represent addition of fractions. This session attends to the full meaning of MP5.
  • Unit 8, Session 1.6 in the Math Practice Note it lists MP4 and has students work on a Window and Tower Activity where they can use tables and arithmetic expressions to model the number of floors and windows they would have in a tower taking into consideration if it is a single or double tower. This session allows for students to engage in real world problem situations.
Indicator 2G
Read
Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
Indicator 2G.i
01/02
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 4 partially meet the expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade level mathematics.

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

  • Unit 6 Session 1.2 directs students to talk with a partner and find a way to explain whether ⅓ = ⅙ while directing teachers to “listen for explanations that focus on the relationship between thirds and sixths.” Students do not critique the reasoning of others during this activity.
  • Unit 8 Session 1.8 asks students to explain how one penny jar will catch up to another and provides other students the opportunity to ask questions. However, those questions may not necessarily be a critique of the explanations originally offered.

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

  • In Unit 6 Session 2.4 students work in groups to compare fraction cards to ½ by placing fraction cards between landmarks. This activity encourages group discussion with language such as “I understand your thinking, but here is my reason for placing this one (card) here.”
Indicator 2G.ii
01/02
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 4 partially meet the expectations for assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.

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

  • In Unit 1 Session 2.2 the teacher asks, “What strategies are you using to find the factors of 200 and 300?” The Math Practice Note connects this to critiquing the arguments of others. However, students do not critique, and no assistance is provided for the teacher to engage students in such a discussion.
  • In Unit 2 Sessions 1.2 and 1.4 students are asked to construct arguments about height based on data. The teachers is assisted in supporting students with sentence stems like “Can anyone finish a sentence that starts ‘More than half our class…’ or ‘About half our class…’ The Math Practice Note focuses teacher attention on the construction of arguments based on data modeling.
  • In Unit 6 Session 1.1 the teacher is instructed to provide the following directions: “Work with a partner to shade in and label these fourths and eighths on the 4 X 6 rectangles. You don't each have to do all of the fractions, but between the two of you, do all of them; and you have to agree that the fractions your partner did are correct.” This does not support the student in how to critique or express disagreement if the fractions done are incorrect.
  • In Unit 6 Session 1.6 the teacher ask students to bring an activity book page to a discussion. The students are asked to show and explain how they know each pair of fractions is equivalent. The Math Practice Note states that “In this discussion, students connect the numerator and denominator with the ideas of the number of pieces and the size of the pieces, respectively, in order to begin to make arguments about equivalence.”

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

  • In Unit 2 Session 1.5 the teacher is prompted to provide the students with questions such as “What do you think of [___]’s idea?” or “How is [__] supporting what she is saying with evidence from the data?”
  • In Unit 7 Session 2.2 the teacher is is given the following guided questions: “Let’s talk about Set A. The problem you want to solve is 37x52. Who wants to explain what cluster problems they used to help them solve 37x52? ...[Marisol] noticed she could multiply by 50s to get her answer, and [Emann] used what he knew about multiplying by 3 to multiply by 30. Did other people recognize multiplication facts or problems that you saw right way you could easily solve?”
Indicator 2G.iii
02/02
Materials explicitly attend to the specialized language of mathematics.

The instructional materials reviewed for Grade 4 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 2.2 students are collecting data about shoe size. The materials prompt the teacher to state, “You’ve been collecting data that includes the fraction ½ . To think about how we might display that data using a line plot, let’s do a quick data collection.”
  • In Unit 4 Session 2.1 students are identifying lines. The materials prompt the teacher to state, “There are two special kinds of lines we’re going to learn about-parallel lines and perpendicular lines.”
  • In Unit 6 Session 2.5 students are comparing fractions. The materials prompt the teacher to state, “Could these two fractions be equal? Why or why not? Could thinking about equivalent fractions help? How?”
Criterion 2.2: Math Practices
07/10
Indicator 2E
02/02
Indicator 2F
01/02
Indicator 2G
Read
Indicator 2G.i
01/02
Indicator 2G.ii
01/02
Indicator 2G.iii
02/02
Overview of Gateway 3

Usability

This material was not reviewed for Gateway Three because it did not meet expectations for Gateways One and Two
Gateway 3
v1.0
Gateway 3

Usability
NE = Not Eligible. Product did not meet the threshold for review.
NE
0
22
31
38
Criterion 3.1: Use & Design
NE = Not Eligible. Product did not meet the threshold for review.
NE
Criterion 3.2: Teacher Planning
NE = Not Eligible. Product did not meet the threshold for review.
NE
Criterion 3.3: Assessment
NE = Not Eligible. Product did not meet the threshold for review.
NE
Criterion 3.4: Differentiation
NE = Not Eligible. Product did not meet the threshold for review.
NE
Criterion 3.5: Technology
NE = Not Eligible. Product did not meet the threshold for review.
NE
Not Rated

Criterion 3.1: Use & Design

NE = Not Eligible. Product did not meet the threshold for review.
NE
Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
Indicator 3A
00/02
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
00/02
Design of assignments is not haphazard: exercises are given in intentional sequences.
Indicator 3C
00/02
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
00/02
Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
Indicator 3E
Read
The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
Criterion 3.1: Use & Design
NE = Not Eligible. Product did not meet the threshold for review.
NE
Indicator 3A
00/02
Indicator 3B
00/02
Indicator 3C
00/02
Indicator 3D
00/02
Indicator 3E
Read

Criterion 3.2: Teacher Planning

NE = Not Eligible. Product did not meet the threshold for review.
NE
Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
Indicator 3F
00/02
Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
Indicator 3G
00/02
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
00/02
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
00/02
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
Read
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
Read
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
Read
Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
Criterion 3.2: Teacher Planning
NE = Not Eligible. Product did not meet the threshold for review.
NE
Indicator 3F
00/02
Indicator 3G
00/02
Indicator 3H
00/02
Indicator 3I
00/02
Indicator 3J
Read
Indicator 3K
Read
Indicator 3L
Read

Criterion 3.3: Assessment

NE = Not Eligible. Product did not meet the threshold for review.
NE
Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
Indicator 3M
00/02
Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
Indicator 3N
00/02
Materials provide strategies for teachers to identify and address common student errors and misconceptions.
Indicator 3O
00/02
Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
Indicator 3P
Read
Materials offer ongoing formative and summative assessments:
Indicator 3P.i
00/02
Assessments clearly denote which standards are being emphasized.
Indicator 3P.ii
00/02
Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
Indicator 3Q
Read
Materials encourage students to monitor their own progress.
Criterion 3.3: Assessment
NE = Not Eligible. Product did not meet the threshold for review.
NE
Indicator 3M
00/02
Indicator 3N
00/02
Indicator 3O
00/02
Indicator 3P
Read
Indicator 3P.i
00/02
Indicator 3P.ii
00/02
Indicator 3Q
Read

Criterion 3.4: Differentiation

NE = Not Eligible. Product did not meet the threshold for review.
NE
Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
Indicator 3R
00/02
Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
Indicator 3S
00/02
Materials provide teachers with strategies for meeting the needs of a range of learners.
Indicator 3T
00/02
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
Indicator 3U
00/02
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
00/02
Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
Indicator 3W
00/02
Materials provide a balanced portrayal of various demographic and personal characteristics.
Indicator 3X
Read
Materials provide opportunities for teachers to use a variety of grouping strategies.
Indicator 3Y
Read
Materials encourage teachers to draw upon home language and culture to facilitate learning.
Criterion 3.4: Differentiation
NE = Not Eligible. Product did not meet the threshold for review.
NE
Indicator 3R
00/02
Indicator 3S
00/02
Indicator 3T
00/02
Indicator 3U
00/02
Indicator 3V
00/02
Indicator 3W
00/02
Indicator 3X
Read
Indicator 3Y
Read

Criterion 3.5: Technology

NE = Not Eligible. Product did not meet the threshold for review.
NE
Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
Indicator 3AA
Read
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
Read
Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
Indicator 3AC
Read
Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
Indicator 3AD
Read
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
Read
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
Criterion 3.5: Technology
NE = Not Eligible. Product did not meet the threshold for review.
NE
Indicator 3AA
Read
Indicator 3AB
Read
Indicator 3AC
Read
Indicator 3AD
Read
Indicator 3Z
Read
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