Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 5 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.

See Rating Scale
Understanding Gateways

Alignment

|

Partially Meets Expectations

Gateway 1:

Focus & Coherence

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

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
14
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

Usability

|

Not Rated

Not Rated

Gateway 3:

Usability

0
22
31
38
0
31-38
Meets Expectations
23-30
Partially Meets Expectations
0-22
Does Not Meet Expectations

Gateway One

Focus & Coherence

Meets Expectations

+
-
Gateway One Details

The instructional materials reviewed for Grade 5 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.

Criterion 1a

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

The instructional materials reviewed meet the expectation for not assessing topics before the grade-level in which the topic should be introduced. Overall, there are no assessment items that align to topics beyond Grade 5.

Indicator 1a

The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 5 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 5. 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:

  • Unit 6 Session 2.9 Resource Master A50: This assessment is used to assess addition and subtraction of decimals. The students are asked to solve and show how they solved problems. “In Darston it rained 2.26 inches on Monday and 0.33 inch on Tuesday. How much more did it rain on Monday than on Tuesday?”
  • Unit 7 Session 1.11, Resource Master A56: This assessment is used to assess dividing of fractions. The students are asked to solve each story problem, show a representation, and write an equation. “Six students equally shared ½ of a pan of brownies. What fraction of the whole pan of brownies did each student eat?”

Criterion 1b

Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.
4/4
+
-
Criterion Rating Details

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 5.

Indicator 1b

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

The instructional materials reviewed for Grade 5 meet the expectations for spending the majority of class time on the major clusters of the grade. Overall, approximately 75 percent of class time is spent on major work of the grade.

The instructional materials are separated into eight units. Each unit is composed of two or three 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 17 of the 23 investigations focus on major work of the grade. This represents approximately 74 percent of the investigations.
  • If the Ten-Minute Math activity times are added into the session minutes, approximately 7780 of the minutes focus on major work of the grade. This represents approximately 74 percent of the minutes.
  • Approximately 113 of 134 sessions focus on or support the major work of the grade. This represents approximately 84 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 75 percent of the materials focus on major work of the grade.

Criterion 1c - 1f

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

The instructional materials reviewed for Grade 5 partially meet the expectations for being coherent and consistent with the Standards. The instructional materials show strength in having an amount of content that is viable for one school year, but due to not always identifying work that is off grade-level, the materials are not always consistent with the progressions in the Standards. The materials do foster coherence through connections within the grade, but few of those connections are between major work of the grade and supporting work.

Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 5 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 3 Session 3.6 students represent and interpret data on a line plot by comparing to find the largest and smallest mixed number (5.MD.2), but they do not use the data to perform any mathematical operations.
  • In Unit 8, Sessions 1.1 through 1.5, students sort shapes by their attributes, categorize triangles and quadrilaterals, and identify triangles and quadrilaterals that can fit into more than one category (5.G.B).

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

  • In Unit 3 Session 3.4 two word problems ask students to perform mathematical operations to combine fractions (5.NF.A) found in data on a line plot (5.MD.2).

Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 5 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 134 sessions.
  • Each session is designed to be completed in 60 minutes. Each session is accompanied by a Ten-Minute Math activity that is designed to be completed in 10 minutes outside of math time.
  • Each unit consists of 2-3 Investigations. Each investigation ranges from 4-11 class sessions
  • Each unit takes between 2.5 to 5.5 weeks to complete according to the “Grade 5 Curriculum Units and Pacing Chart” on page 9 of the Implementing Investigations in Grade 5 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 158 days.

Indicator 1e

Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
1/2
+
-
Indicator Rating Details

The materials reviewed for Grade 5 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. An example of unclear identification includes:

  • Unit 5 Session 1.7 introduces students to a fictitious animal called a Fastwalker whose annual rate of growth is not linear. This content more closely aligns to 8.F.3, but it is not clearly identified as content from a future grade.

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

  • The materials have different types of practice for students during each lesson. There are Teaching Resources in the Resource Masters and Activities in the Student Activity Book which are both aids during lessons. There are Daily Practice and Homework pages in the Student Activity Book which are indicated to be session follow-ups that review and practice grade-level content.
  • Recommendations for differentiation allow students to primarily work with grade-level tasks.
  • The materials give students extensive work with most domains. However, 5.NF.B is addressed mainly in Unit 7. The materials do not provide any spiraling or application in other units for 5.MD.C to tie these standards to other math in the grade level.

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 Grades 3 and 4 “as students developed an understanding of the operations of multiplication and division and the relationship between the two operations.”
  • Unit 2 describes how students, in earlier grades, identified two and three dimensional shapes and worked with measurement which prepared them for measuring and finding area in Grade 5.
  • Unit 3 builds on the work students have done in Grades 3 and 4, as they worked with fractions including representing fractions on number lines and adding and subtracting fractions with like denominators.
  • Unit 5 refers back to work done in Grades 3 and 4 where students investigated mathematical situations and patterns governed by rules.
  • Unit 6 refers to work done in Grade 3 and 4 as well as earlier in Grade 5 to build understandings of fractions and mixed numbers including equivalences.
  • Unit 7 builds on the work done in Grade 4 when students multiplied a fraction by a whole number.
  • Unit 8 builds on Grades 3 and 4 work with polygons including triangles and quadrilaterals and with work in measurement including finding perimeter and area.

Indicator 1f

Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 5 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 5.

  • In Unit 1 Session 3.6 students compare division problems that involve multiples of 10 and work on strategies for solving division problems (5.NBT.B).
  • In Unit 3 Session 2.3 students solve problems involving addition of fractions using clock and rectangle representations (5.NF.A).
  • In Unit 3 Session 3.4 students represent a set of measurement data that includes fractions on a line plot and use that data to solve problems (5.MD.B).

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

  • In Unit 5, Sessions 1.3 through 1.7 have students creating tables of data from given rules, 5.OA.B, and this is connected to 5.G.A as students graph the tables of data on coordinate planes and use the graphs to solve real-world problems.
  • In Unit 6, Sessions 2.5 through 2.8 connect 5.NBT.A with 5.NBT.B as students use their understanding of the place value system to add and subtract decimals to hundredths.

Gateway Two

Rigor & Mathematical Practices

Partially Meets Expectations

+
-
Gateway Two Details

The instructional materials reviewed for Grade 5 partially meet the expectations for rigor and the mathematical practices. The materials meet the expectations for rigor as they help students develop conceptual understanding, procedural skill and fluency, and applications. However, the materials partially meet the expectations for mathematical practices as they do not attend to the full meaning for each of the MPs and rarely prompt, or have the teachers prompt, students to analyze the arguments of others.

Criterion 2a - 2d

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.
7/8
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 5 partially meet the expectations for rigor and the mathematical practices. The materials meet the expectations for rigor as they help students develop conceptual understanding, procedural skill and fluency, and applications. However, the materials partially meet the expectations for mathematical practices as they do not attend to the full meaning for each of the MPs and rarely prompt, or have the teachers prompt, students to analyze the arguments of others.

Indicator 2a

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
2/2
+
-
Indicator Rating Details

The materials reviewed for Grade 5 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 6 Session 2.2 students use representations to add tenths, hundredths, and thousandths through reasoning about place value, equivalents, and representations by creating posters that show their solution to a problem with adding decimals. Their posters show, “How did you add the decimals? Make sure you explain your method carefully on your posters. If [someone] walked in, would that person be able to understand clearly what problem you were solving and how you solved it from your poster?” (5.NBT.A)
  • In Unit 7 Session 1.1 students use representations to multiply a fraction and a whole number by first creating a representation of a multiplication problem making sure to use a few different representations such as number lines, shapes divided into fractional parts, and equations. Students also complete Student Activity Book pages 421-424 which require them to make a representation, write a multiplication equation, and solve the problem (5.NF.B).
  • In Unit 7 Session 1.5 students represent a fractional part of a fractional quantity by using fraction bars and tables to talk through what each of the numbers refers to in the representations given (5.NF.B). Students also complete Student Activity Book pages 443-447 which require them to use fraction bars and explain their thinking and representations.
  • In Unit 7 Session 1.7 students use arrays to represent multiplication of fractions and also understand the relationship between the denominator and numerator of factors and relationship between the denominator and numerator of products. Students solve problems by using unmarked arrays to express the fractions making sure to keep track of what the whole is and how each vertical and horizontal line should be placed and what needs to be shaded to represent the fraction problem given (5.NF.B). Students also complete Student Activity Book pages 453-456 which require them to not only solve a story problem using an array, but then also write an equation based off of what is represented.

Indicator 2b

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
2/2
+
-
Indicator Rating Details

The materials reviewed for Grade 5 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, 5.NBT.5, and additional practice is provided.

Standard 5.NBT.5 requires students to fluently multiply multi-digit numbers using the standard algorithm.

  • The Ten-Minute Math activities indirectly work on the requirement for fluency of the grade. The Ten-Minute Math activities addressing 5.NBT.5 begin in Unit 3 before the algorithm is taught in Unit 4. In Unit 3, “Today’s Number,” students create expressions that equal (n), use multiplication, and use no more than 2 factors.
  • In Unit 5 Session 1.1 students solve multi-digit multiplication problems in the “Solve Two Ways” activity in the Student Activity Book page 276.
  • Unit 4- all of Investigation 1; Sessions 2.4, 2.5, 2.7; and all of Investigation 3- provide opportunities to practice procedural skill and fluency of the grade. During Session 1.1 students review multiplication strategies by breaking numbers apart, changing one factor and adjusting, and creating an equivalent problem. During Session 1.2 students estimate products by rounding numbers. During Session 1.3 students are shown solutions to the same problem solved using two different algorithms followed by the teacher working through a problem step-by-step using the US standard algorithm for multi-digit multiplication.

Indicator 2c

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade
2/2
+
-
Indicator Rating Details

The materials reviewed for Grade 5 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. Though at times the problems are scaffolded in such a way the students are guided through the question, they are engaged consistently in problem solving during the year.

Practice with application of 5.NF.6 is found in two Units, Units 7 and 8. Unit 7 provides practice with real-world application of 5.NF.6. Sessions 1.1, 1.2, 1.3, 1.4, 1.7, and 1.8 require students to solve real-world problems such as “Janet is using a recipe for muffins that calls for ¾ cup of of milk. She is going to make 3 times the recipe. How many cups of milk does she need?” Unit 8 Session 2.4 provides practice with finding the area of different size rectangles for a class garden.

Work for standard 5.NF.7c, solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem is found in Unit 7. In Sessions 1.9, 1.10, and 1.11 students are guided through problems that either divide a whole number by a fraction or divide a fraction by a whole number. Students practice these real world problems in the Student Activity Book Daily Practice. Most of the Daily Practice problems follow the same format such as “Felix has 2 yards of ribbon. He needs ¼ yard to make 1 bow. How many bows can Felix make?” or “How much popcorn would each person get if 2 people shared ½ of a bag of popcorn equally?”

Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 5 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 2e - 2g.iii

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

The instructional materials reviewed for Grade 5 partially meet the expectations for practice-content connections. Overall, the materials show strengths in identifying and using the MPs to enrich the content along with attending to the specialize language of mathematics. However, the materials do not always attend to the full meaning of each MP, and there are few opportunities for students to analyze the arguments of others either through prompts from the materials or from their teachers.

Indicator 2e

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

The instructional materials for Grade 5 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 MP4 and MP5. An example of MP4 from Session 2.3 is included.
  • The Unit 7 “Mathematical Practices in this Unit” is found on pages 10-13. This unit focuses on MP1 and MP8. An example of MP1 from Session 1.4 is included.

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

  • Unit 2 Session 1.1 includes a Math Practice Note for MP1 and MP4. MP4 is a practice highlighted in the unit. Students are developing approaches for determining the volume of a rectangular solid which will lead to formulas for volume.
  • Unit 4 Session 3.5 includes a Math Practice Note for MP1, a practice not highlighted in the unit. The note describes how students compare approaches for multiplying and dividing large numbers with known strategies.
  • Unit 5 Session 2.5 includes a Math Practice Note for MP4 and MP5, practices that are highlighted in the unit. The note discusses how choosing from various tools allows students to model with mathematics in different ways.
  • Unit 7 Session 1.8 includes a Math Practice Note for MP2 and MP8. MP8 is a practice highlighted in the unit. Students are discussing problems related to the multiplication of fractions.

Indicator 2f

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

The instructional materials reviewed for Grade 5 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 2 Session 2.1 Math Practice Note lists MP5 and has students determining the volume in cubic centimeters of a small prism. The Math Practice Note states that “students might use centimeter cubes or a centimeter ruler to find the dimensions.” In this activity, students are told which tools to use.
  • The Unit 7 Session 1.1 Math Practice Note lists MP1. The teacher states, “Earlier in the year you worked on adding and subtracting fractions, and in the last unit you worked on adding and subtracting decimals. In this unit you will be multiplying and dividing fractions and decimals. We are going to begin with multiplying fractions.” The Math Practice Note discusses that part of making sense of problems is being able to connect unfamiliar work with prior learning. However, the statements to be made by the teacher explicitly guide students to where connections could be made, and the session itself does not assist the teachers or students to make or discuss these connections.
  • The Unit 7 Session 2.1 Math Practice Note lists MP1 and has students making sense of the problem by recognizing that different pathways to a solution may yield answers that look different even if they are equivalent. However, they are not persevering in solving the problems given.
  • The Unit 7 Session 2.2 Math Practice Note lists MP5 and has students identifying decimal and fraction equivalence through the use of a calculator. The Math Practice Note states that in this activity, students explore how to use a calculator to determine the records of several basketball players. This activity tells students which tool to use.

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

  • The Unit 1 Session 2.6 Math Practice Note lists MP5 and has students reminded of the various tools, such as story contexts and arrays, that they can use to represent not only the problem but also the steps of their solutions to solve multiplication problems. They are never specifically told which tool to use and are able to choose the tool that is most appropriate for them and the lesson.
  • The Unit 4 Session 1.1 Math Practice Note lists MP6 and has students describing and comparing strategies used to solve multi-digit multiplication problems. The Math Practice Note specifically calls out that in the discussions students need to explain the steps of their solution, name the strategy used, and question classmates making sure to develop clear explanations and concise notation for their work.
  • The Unit 7 Session 1.5 Math Practice Note lists MP6 and asks students to make a conjecture about what happens when they multiply a number by a fraction smaller than 1. The Math Practice Note discusses that articulating conjectures requires that students attend carefully to the language they use and to state all components of their reasoning.

Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
0/0

Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 5 partially meet the expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade level mathematics.

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

  • In Unit 6 Session 1.2 students neither construct an argument nor critique the arguments of others when the materials reference MP3 and direct students to “make sure that they think about how many parts out of 1,000 are shaded.”
  • In Unit 6 Session 1.5 MP3 is referenced when students are asked to “share their responses and justifications with the whole class.” The students are not required to analyze the arguments of others.
  • In Unit 7 Session 1.1 MP3 is referenced when students are asked to share their solutions and equations for Problem 1 on Student Activity Book page 421.

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

  • In Unit 1 Session 1.2 students are told “[Hana] and [Yumiko] say that all these numbers are multiples of 12 and that any solution to this number puzzle will be a multiple of 12. Do you agree? Why or why not?”
  • In Unit 6 Session 1.7 the following guided exchange supports students in critiquing the arguments of others: “[Stuart] says that we can’t play the card because, in the bottom row, we’ve already played 825 thousandths and 975 thousandths, and this card goes in between them. Are there any comments? [Shandra] disagrees. she says that we could play it in the last spot in the middle row because it’s greater than 6 tenths and goes between 45 hundredths and 975 thousandths in the last column. Are there any comments? [Shandra] is right; we can play the card there. Remember the rules: the decimals have to be in order from left to right and from top to bottom, but it’s all right if the last card in one row is bigger than a card in the first one or two spaces of the next row.”

Indicator 2g.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 5 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 3 Session 3.3 students are playing a game, and the teacher says, “a player wins a round if the sum of his or her two cards is greater than the sum of the other player’s cards. Who has the greater sum? How do you know?” These questions would prompt students to construct their own 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.
  • In Unit 5 Session 1.4 there are a series of scaffolded questions for teachers that would assist them in having students construct arguments from graphs about the height and age of two people. There are no questions or prompts for teachers to assist them in having students analyze others’ arguments when different interpretations might arise.
  • In Unit 8 Session 2.3 students are asked to explain their thinking about how the perimeter and area of rectangles change when each dimension is doubled. There are question that assist the teacher with engaging students in constructing their own arguments, but there are no questions or prompts to assist teachers with having students analyze the arguments of others.

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

  • In Unit 3 Session 1.1 teachers are prompted to provide the students with questions such as, “How did you know how many marbles to circle in Problem 5a?....Deon says that since there are 12 marbles, ⅓ is four marbles. Deon , how do you know that? Who has another way to think abou this problem? I noticed in Problem 7 that almost everyone agrees ⅔ is greater than 2/6, but who can explain why this is true?” The Math Practice Note tells teachers to ask students to paraphrase each other’s explanations or to ask one another questions to encourage students’ working to make sense of each other’s approaches.

Indicator 2g.iii

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

The instructional materials reviewed for Grade 5 meet the expectations for explicitly attending to the specialized language of mathematics.

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

  • In Unit 1 Session 1.4 students are introduced to the order of operations. The materials prompt the teacher to state, “Mathematicians realized that when you have more than one operation in an expression like this, people could have different interpretations of how to solve it. We don’t want to have two different answers for the same computation. So mathematicians agreed on rules for what you do first. This is called the order of operations.”
  • In Unit 3 Session 3.4 students are adding and subtracting mixed numbers. The materials prompt the teacher to state, “You used many of the same strategies for adding and subtracting mixed numbers that you have used for adding and subtracting whole numbers. It seems as though the main difference is sometimes you have to find ways to deal with adding or subtracting fractions that have different denominators.”
  • In Unit 7 Session 2.1 students are dividing fractions. The materials prompt the teacher to state, “You know that ⅜ is a fraction, and it can also be used to represent a division problem, just like the other notations. In the next few sessions, we’re going to continue to think about fractions as division, and we’re also going to look at their decimal equivalents.”

Gateway Three

Usability

Not Rated

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
0/8

Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
0/2

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
0/2

Indicator 3c

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
0/2

Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
0/2

Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
0/0

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
0/8

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
0/2

Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
0/2

Indicator 3h

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.
0/2

Indicator 3i

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.
0/2

Indicator 3j

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
0/0

Indicator 3k

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
0/0

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
0/0

Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
0/10

Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
0/2

Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
0/2

Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
0/2

Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
0/2

Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
0/2

Indicator 3q

Materials encourage students to monitor their own progress.
0/0

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
0/12

Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
0/2

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
0/2

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
0/2

Indicator 3u

Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
0/2

Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
0/2

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
0/2

Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
0/0

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
0/0

Criterion 3aa - 3z

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
0/0

Indicator 3aa

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
0/0

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
0/0

Indicator 3ac

Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
0/0

Indicator 3ad

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.).
0/0

Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
0/0

Additional Publication Details

Report Published Date: Fri Feb 10 00:00:00 UTC 2017

Report Edition: 2017

Title ISBN Edition Publisher Year
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

About Publishers Responses

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

The K-8 Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

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