## Alignment: Overall Summary

The instructional materials reviewed for JUMP Math Grade 4 partially meet expectations for alignment. The instructional materials meet expectations for focus and coherence by assessing grade-level content, devoting the majority of class time to the major work of the grade, and being coherent and consistent with the progressions in the Standards. The instructional materials partially meet expectations for rigor and the mathematical practices. The instructional materials partially meet the expectations for rigor by attending to conceptual understanding and procedural skill and fluency, and they also partially meet expectations for practice-content connections by identifying the mathematical practices and using them to enrich grade-level content.

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## Gateway 1:

### Focus & Coherence

0
7
12
14
13
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

## Gateway 2:

### Rigor & Mathematical Practices

0
10
16
18
12
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

|

## Gateway 3:

### Usability

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

## The Report

- Collapsed Version + Full Length Version

## Focus & Coherence

#### Meets Expectations

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Gateway One Details

The instructional materials reviewed for JUMP Math Grade 4 meet expectations for Gateway 1. The instructional materials meet expectations for focus within the grade by assessing grade-level content and spending the majority of class time on the major work of the grade. The instructional materials meet expectations for being coherent and consistent with the Standards as they connect supporting content to enhance focus and coherence, have an amount of content that is viable for one school year, and foster coherence through connections at a single grade.

### Criterion 1a

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

The instructional materials reviewed for JUMP Math Grade 4 meet expectations for not assessing topics before the grade level in which the topic should be introduced.

### 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
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Indicator Rating Details

The instructional materials reviewed for JUMP Math Grade 4 meet expectations for assessing grade-level content. Probability, statistical distribution, similarity, transformation, and congruence do not appear in the assessments. Examples of grade-level assessment items include:

• Student Resource, Assessment & Practice Book 1, Unit 3, OA4-17, Items 1-10, “Round each number to the nearest hundred. Then find the sum or difference.” (4.NBT.3)
• Teacher Resource, Sample Unit Tests and Quizzes, Book 1, Unit 6, Unit Test, Item 6,“A subway train is about 200m long. How many trains, lined end to end, would equal a. close to a kilometer? b. close to 3km?” (4.MD.1)
• Teacher Resource, Sample Unit Tests and Quizzes, Book 2, Unit 9, Geometry, Test, Item 7, “Find the measure of the whole angle by adding the measures of the small angles.” Two models of angles composed of two non-overlapping parts are provided. (4.MD.7)
• Student Resource,Assessment & Practice Book 2, Unit 4, NF4-22 “Write a fraction and a decimal for each shaded part in the boxed below.” (4.NF.6).

### 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
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Criterion Rating Details

The instructional materials reviewed for JUMP Math Grade 4 meet expectations for students and teachers using the materials as designed and devoting the majority of class time to the major work of the grade. Overall, instructional materials spend approximately 74 percent of class time on the major clusters of the grade.

### Indicator 1b

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

The instructional materials reviewed for JUMP Math Grade 4 meet expectations for spending the majority of class time on the major work of the grade. Overall, approximately 74 percent of class time is devoted to major work of the grade.

The materials for Grade 4 include 16 units. In the materials, there are 186 lessons, and of those, 36 are Bridging lessons. According to the materials, Bridging lessons should not be “counted as part of the work of the year” (page A-59), so the number of lessons examined for this indicator is 150 lessons. The supporting clusters were also reviewed to determine if they could be factored in due to how strongly they support major work of the grade. There were some connections found between supporting clusters and major clusters, and due to the strength of the connections found, the number of lessons addressing major work was increased from the approximately 112 lessons addressing major work, as indicated by the materials themselves, to 122 lessons.

Three perspectives were considered: the number of units devoted to major work, the number of lessons devoted to major work, and the number of instructional days devoted to major work including days for unit assessments.

The percentages for each of the three perspectives follow:

• Units – Approximately 67 percent, 10 out of 16;
• Lessons – Approximately 75 percent, 112 out of 150; and
• Days – Approximately 74 percent, 122.5 out of 166.

The number of instructional days, approximately 74 percent, devoted to major work is the most reflective for this indicator because it represents the total amount of class time that addresses major work.

### Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
7/8
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Criterion Rating Details

The instructional materials reviewed for JUMP Math Grade 4 meet expectations for being coherent and consistent with the Standards. The instructional materials connect supporting content to enhance focus and coherence, include an amount of content that is viable for one school year, and foster connections at a single grade. However, the instructional materials contain off-grade-level material and do not relate grade-level concepts explicitly to prior knowledge from earlier grades.

### Indicator 1c

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

The instructional materials reviewed for JUMP Math Grade 4 meet the expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. When appropriate, the supporting work enhances and supports the major work of the grade.

Examples where connections are present include the following:

• 4.MD.4 supports work with 4.NF.A,B and 4.OA. In Teacher Resource, Part 2, Unit 2, Lessons NBT4-27, NBT4-38, NBT4-39, and NBT4-40, students use line plots and measuring objects with a ruler. These are done with fractions as well as whole numbers, supporting the major work of Numbers and Operations with fractions.
• 4.MD.1 supports work from 4.OA.2. In Teacher Resource, Part 1, Unit 6, Lessons MD4-2, MD4-5, and MD4-6, students measure and convert within the metric system.

### 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
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Indicator Rating Details

The instructional materials reviewed for JUMP Math Grade 4 meet expectations for having an amount of content designated for one grade level that is viable for one school year in order to foster coherence between grades. Overall, the amount of time needed to complete the lessons is approximately 166 days, which is appropriate for a school year of approximately 140-190 days.

• The materials are written with 16 units containing a total of 186 lessons.
• Each lesson is designed to be implemented during the course of one 45 minute class period per day. In the materials, there are 186 lessons, and of those, 36 are Bridging lessons. Bridging lessons have been removed from the count because the Teacher Resource states that they are not counted as part of the work for the year, so the number of lessons examined for this indicator is 150 lessons.
• There are 16 unit tests which are counted as 16 extra days of instruction.
• There is a short quiz every 3-5 lessons. Materials expect these quizzes to take no more than 10 minutes, so they are not counted as extra days of instruction.

### 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
+
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Indicator Rating Details

The instructional materials reviewed for JUMP Math Grade 4 partially meet expectations for being consistent with the progressions in the Standards. Overall, the materials address the standards for this grade level and provide all students extensive work with grade-level problems. The materials make connections to content in future grades, but they do not explicitly relate grade-level concepts to prior knowledge from earlier grades.

The materials develop according to the grade-by-grade progressions in the Standards. Content from future grades is not always clearly identified but often related to grade-level work. The Teacher Resource contains sections that highlight the development of the grade-by-grade progressions in the materials, occasionally identify content from future grades, and state the relationship to grade-level work.

• At the beginning of each unit, This Unit in Context provides a description of connections to concepts that have been taught previously and that will occur in future grade levels. For example, This Unit in Context from Unit 4, Number and Operations in Base Ten: Multiplication, of Teacher Resource, Part 1, describes how "In Grade 3, students were introduced to multiplication as repeated addition, and they interpreted the product of two numbers as the total number of objects when given a number of equal groups and then number in each group (3.OA.A.1)." Connection to future content is also stated such as "In later grades, students will multiply multi-digit numbers by two-digit numbers (5.NBT.B.5) and multi-digit decimals (6.NS.B.3), including positive and negative decimals (7.NS.A.2a, c)."

The materials give all students extensive work with grade-level problems. The lessons also include Extensions, and the problems in these sections are on grade level.

• Whole class instruction is used in the lessons, and all students are expected to do the same work throughout the lesson. Individual, small-group, or whole-class instruction occurs in the lessons.
• The problems in the Assessment & Practice books align to the content of the lessons, and they provide on-grade-level problems that "were designed to help students develop confidence, fluency, and practice." (page A-56, Teacher Resource, Part 1)
• In the Extensions sections of the lessons, students get the opportunity to engage with more difficult problems, but the problems are still aligned to grade-level standards. For example, the problems in Teacher Resource, Part 1, Unit 3, Lesson NBT4-14 engage students in listing numbers that round to a given number, but these problems still align to 4.NBT.3.

The instructional materials do not relate grade-level concepts explicitly to prior knowledge from earlier grades. Examples of these missing explicit connections include:

• Every lesson identifies Prior Knowledge Required even though the prior knowledge identified is not aligned to any grade-level standards. For example, Teacher Resource, Part 2, Unit 4, Lesson NF4-6, identifies that prior to the lessons students "(c)an use pictures to name equivalent fractions" and "(c)an use the phrase 'times as many as' to compare two numbers."
• There are 36 lessons identified as Bridging lessons; most of these lessons are not aligned to standards from prior grades but state for which grade-level standards they are preparation. Teacher Resource, Part 2, Unit 2, Lesson NBT4-40, which has students using pictures to divide when there is a remainder, is preparation for 4.OA.3 and 4.NBT.6.

### 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
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-
Indicator Rating Details

The instructional materials reviewed for JUMP Math Grade 4 meet expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards. Overall, the materials include learning objectives that are visibly shaped by CCSSM cluster headings.

Overall, units are organized by domains and are clearly labeled. For example, in Teacher Resource, Part 1, Unit 1, Operations and Algebraic Thinking: Patterns, Teacher Resource, Part 1, Unit 3, Operations and Algebraic Thinking: Rounding, and Teacher Resource, Part 1, Unit 5, Operations and Algebraic Thinking: Division are shaped by the Operations and Algebraic Thinking domain. Throughout the course, all standards are addressed, and within lessons, goals are written that are shaped by the CCSSM cluster headings. For example, in Teacher Resource, Part 2, Unit 3, Lesson OA4-35, connects all three of the standards in the 4.OA.A cluster in Equations with Multiplication and Division.

The instructional materials do include some problems and activities that serve to connect two or more clusters in a domain. Instances where two or more clusters within a domain are connected include the following:

• In Teacher Resource, Part 1, Unit 2, Lesson NBT4-16, students add 2-digit numbers without regrouping. This lesson connects 4.NBT.A and 4.NBT.B.
• Teacher Resource, Part 2, Unit 2, Lesson NBT4-47 connects 4.NBT.A and 4.NBT.B. Students divide 1-digit multiples of powers of ten by the same multiple of a lesser power of ten and divide using expanded form when all digits are divisible by the divisor.
• Teacher Resource, Part 2, Unit 5, Lesson MD4-24 connects 4.NBT.A and 4.NBT.B, as well as 4.NF.B and 4.MD.A. In this lesson, students solve problems involving measurements of mass and capacity, including problems requiring conversions.

The instructional materials also include problems and activities that connect two or more domains in a grade, in cases where these connections are natural and important. Instances where two or more domains are connected include the following:

• Teacher Resource, Part 2, Unit 2, Lessons NBT4-45 and NBT4-46 connect 4.NBT and 4.MD. In these lessons, students divide 3-digit and 4-digit numbers by 1-digit numbers, including with a remainder.
• In Teacher Resource, Part 2, Unit 5, Lesson MD4-33, 4.NBT and 4.MD are connected. In this lesson, students change measurements in pounds to ounces and solve problems involving mass in pounds and ounces.
• Teacher Resource, Part 2, Unit 6, Lesson OA4-41 connects 4.OA and 4.NBT. In this lesson, students find factors of numbers up to 100 and determine whether a given 1-digit number is a factor of a given whole number in the range 1-100.

## Rigor & Mathematical Practices

#### Partially Meets Expectations

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Gateway Two Details

The instructional materials reviewed for JUMP Mathematics Grade 4 partially meet expectations for Gateway 2. The instructional materials partially meet expectations for rigor by developing conceptual understanding of key mathematical concepts, giving attention throughout the year to procedural skill and fluency, and spending some time working with routine applications. The instructional materials do not always treat the three aspects of rigor together or separately, but they do place heavier emphasis on procedural skill and fluency. The instructional materials partially meet expectations for practice-content connections. Although the instructional materials meet expectations for identifying and using the MPs to enrich mathematics content, they partially attend to the full meaning of each practice standard. The instructional materials partially attend to the specialized language of mathematics.

### 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.
6/8
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Criterion Rating Details

The instructional materials reviewed for JUMP Math Grade 4 partially meet expectations for rigor by developing conceptual understanding of key mathematical concepts, giving attention throughout the year to procedural skill and fluency, and spending some time working with routine applications. The instructional materials do not always treat the three aspects of rigor together or separately, but they do place heavier emphasis on procedural skill and fluency.

### 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
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Indicator Rating Details

The instructional materials reviewed for JUMP Math Grade 4 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. The materials include problems and questions that develop conceptual understanding throughout the grade level. The instructional materials provide students few opportunities to independently demonstrate conceptual understanding without teacher direction throughout the grade level.

4.NF.A extends fraction equivalence and ordering. Teacher Resources (Common Core State Standards Curriculum Correlations) state that 4.NF.A is addressed in Part 2 Unit 4. The materials provide opportunities to work with equivalent fractions and models. Examples include:

• Teacher Resource, Part 2, Unit 4, Lesson NF4-3 uses a variety of visual models and discussion to help students understand equivalency (“What fraction of each shape is shaded?” “Do they have the same shape shaded?” “Do they have the same amount shaded?”)
• Student Resource, Assessment & Practice Book, Part 2, Unit 4, Lesson NF4-6, Item 4, ”Write an equivalent fraction for the picture. Then write how many times as much the new numerator and denominator are.” Students use models to show equivalent fractions.
• Student Resource, Assessment & Practice Book, Part 2, Unit 4, Lesson NF4-9, Item 7 “Use centimeters and millimeters to write a fraction equivalent to $$\frac{2}{3}$$.” Students use a ruler to find equivalent fractions.

The materials provide some problems that provide opportunities for students to demonstrate conceptual understanding. Examples include but are not limited to:

• Teacher Resource, Part 2, Unit 4, Lesson NF4-3, Extensions, Item 1, ”On grid paper, draw three 4 by 4 grids. Show three different ways to shade half of the grid. Hint: The picture shows one way.” (4.NF.2)
• Teacher Resource, Part 1, Unit 4, Lesson NBT4-30, Extensions, Item 3, “Have the students do Questions 1 and 2 on BLM Using Area to Find Equal Products. Students will discover that multiplying by one factor in a product by 2 and dividing the other factor by 2 results in the same answer. They do this by cutting rectangles in half and gluing them together again in a different way. So 6 x 10= 3 x 20.” (4.NBT.5)

### 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
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Indicator Rating Details

The instructional materials reviewed for JUMP Math Grade 4 meet expectations for attending to those standards that set an expectation of procedural skill and fluency. The instructional materials develop procedural skill and fluency throughout the grade level. The materials provide opportunities for students to independently demonstrate procedural skill and fluency across the grade.

Examples that show the development of procedural skill and fluency include:

• Student Resource, Assessment & Practice Book, Part 1, Lesson NBT4-18, Item 8, “Add, regrouping where necessary. 6a. 5,328 + 1,234 + 6,762 6b. 3,658 + 6,343 + 4.534.” (4.NBT.4)
• Teacher Resource, Book 1, Unit 4, Lesson NBT4-35, Item 8 a-j, “Multiply. You will need to copy questions f. to j. onto grid paper. a. 523 x 4 b. 631 x 5 c. 264x3 d. 153x9.” (4.NBT.5)

Examples that show opportunities for students to independently demonstrate procedural skill and fluency include:

• Student Resource, Assessment & Practice Book, Part 1, Lesson NBT4-18, includes 54 problems where students are required to add and regroup using the standard algorithm. (4.NBT.4)
• In Student Resource, Assessment & Practice Book, Part 1, Lesson NBT4-35, students must complete 46 problems (a variety of problem types) by using the multiplication algorithm to multiply one-digit numbers by numbers with up to four digits. (4.NBT.5)
• Student Resource, Assessment & Practice Book, Part 2, Lesson NBT4-45, Item 3a-g, “Divide. There will be fewer hundreds than the number of groups. Write ‘0’ in the hundreds position to show this. The first one has been started for you” 3b. 5⟌348” (4.NBT.6)

### 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
1/2
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Indicator Rating Details

The instructional materials reviewed for JUMP Math Grade 4 partially meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single- and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied. The materials include limited opportunities for students to independently engage in the application of nonroutine problems. Most problems are routine in nature and provide few opportunities for students to independently demonstrate the use of mathematics flexibly.

The instructional materials have few opportunities for students to engage in non-routine application throughout the grade level. There is little variety in situational contexts/problem types. Engaging applications include single- and multi-step word problems presented in a context in which the mathematics is applied; however, these problems are often routine, and students have few opportunities to engage with non-routine application problems. Examples of routine application problems include:

• Teacher Resource, Part 1, Unit 4, Lesson NBT4-29, Extensions, 2, “Fred has $2347 and Marcel has$3653. Jennifer has 3 times as much money as Fred and Marchel put together. How much money does Jennifer have?”
• Teacher Resource, Part 2, Unit 3, Lesson OA4-32, Exercises, “Solve. 1a. John has 12 blue marbles. He has 9 more red marbles tha blue marbles. How many red marbles does he have? b. John also has 7 fewer green marbles than red marbles. How many green marbles does he have? c. How many red, blue, and green marbles does he have altogether?”
• Teacher Resource, Part 2 Unit 9, Lesson G4-16, Extensions, 4, “Aputik is fixing up her basement bathroom. She is going to need a total of 28 tiles and 6 yards of wood. Tiles come in packs of 5 and cost $8 a pack. Wood is sold by the foot and costs$7 per foot. How much will it cost Auptik to fix up her basement bathroom?” Students are solving a routine multi-step problem.
• Teacher Resource, Part 2, Unit 3,OA4-36, Exercises, Bonus, d. “A jackpine is 35 feet tall. A red pine is three times as tall as a jack pine. A giant sequoia is eight times as tall as a jack pine. How tall is each tree?”

Few opportunities for non-routine applications of mathematics are provided in the extensions and in the Assessment and Practice Books. Examples include:

• Student Resource, Assessment & Practice, Part 2, Lesson OA4-37, Item 8, “Javier is four times as old as Kong. Kong is 3 years younger than Ewa. Javier is 9 years older than Ewa. How old is each person?”
• Teacher Resource, Part 1, Unit 6, Lesson MD4-14, Extensions, Item 2, “Simon and Maria played a video game. Simon got five times as many points as Maria did in round one. Maria got three times as many points as Simaon did round two. Maria got more points overall. Give an example of Simon and Maria’s possible points.”

### 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
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Indicator Rating Details

The instructional materials reviewed for JUMP Math Grade 4 partially meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. All three aspects of rigor are present in the materials, but there is an over-emphasis on procedural skills and fluency.

The curriculum addresses conceptual understanding, procedural skill and fluency, and application standards, when called for, and evidence of opportunities where multiple aspects of rigor are used to support student learning and mastery of the standards. There are multiple lessons where one aspect of rigor is emphasized. The materials emphasize fluency, procedures, and algorithms.

Examples of conceptual understanding, procedural skill and fluency, and application presented separately in the materials include:

• Conceptual Understanding: Student Resource, Assessment & Practice Book, Part 2, Lesson NBT4-43, Item 2, “Divide 12 hundreds among 3 equal groups. Then finish the division equation. 12 hundreds / 3 = ___ hundreds so 1200 / 3 = _____.” Students develop conceptual understanding by using base-10 blocks to model division of a multi-digit number by a one-digit number.
• Procedural Skill and Fluency: Student Resource, Assessment & Practice Book, Part 1, Lesson MD4-6, Item 6, “Convert the mixed measurements to measurements in centimeters. a. 3 m 1 cm = 301 cm (6 Items a-f).”
• Application: Student Resource, Assessment & Practice Book, Part 1, Lesson NBT4-36, Item 2, “On average, every American uses 147 gallons of water each day. a. About how much water does each American use in a week? b. About how much water would a family of 4 use in a day?”

Examples of where conceptual understanding, procedural skill and fluency, and application are presented together in the materials include:

• Student Resource, Assessment & Practice Book, Part 1, Lesson NBT4-35, Item 11, “An octopus has 8 arms and 240 suckers on each arm. How many suckers does an octopus have?” Students are employ the standard algorithm to multiply in word problems that apply mathematics to real-world contexts.
• Student Resource, Assessment & Practice Book, Part 2, Lesson NF4-7, Item 14, “Quentin ate $$\frac{3}{5}$$ of a pizza and Jasmine ate $$\frac{1}{3}$$ of the pizza. Who ate more pizza?” Students engage in conceptual understanding and application as they use fraction models to compare fractions,
• Student Resource, Assessment & Practice Book, Part 2, Item 8, “Tyrell has $$\frac{4}{10}$$ of a dollar and Tania has $$\frac{7}{100}$$ of a dollar. What fraction of a dollar do they have altogether?” Students use conceptual understanding, procedural skill, and fluency as they add tenths and hundredths, base-10 models are used to develop conceptual understanding. Students also demonstrate procedural skill and application in converting between tenths and hundredths and adding tenths and hundredths.

### Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
6/10
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Criterion Rating Details

The instructional materials reviewed for JUMP Math Grade 4 partially meet expectations for practice-content connections. Although the instructional materials meet expectations for identifying and using the MPs to enrich mathematics content, they partially attend to the full meaning of each practice standard. The instructional materials partially attend to the specialized language of mathematics.

### Indicator 2e

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

The instructional materials reviewed for JUMP Math Grade 4 meet expectations for identifying the Standards for Mathematical Practice and using them to enrich mathematics content within and throughout the grade level.

All 8 MPs are clearly identified throughout the materials, with few or no exceptions. Examples include:

• The Mathematical Practices are identified at the beginning of each unit in the Mathematical Practices in this Unit.
• Mathematical Practices in this Unit gives suggestions on how students can show they have met a Mathematical Practice. For example, in Unit 6 Operations and Algebraic Thinking: Factors, “MP.1: In OA4-43 Extension 6, students make sense of a non-routine problem when they analyze the conditions a number satisfies to find the number.”
• Mathematical Practices in this Unit gives the Mathematical Practices that can be assessed in the unit. For example, in Unit 6, Operations and Algebraic Thinking: Factors “In this unit, you will have the opportunity to assess MP.1 to MP.8.”
• The Mathematical Practices are also identified in the materials in the lesson margins.
• In optional Problem Solving Lessons designed to develop specific problem-solving strategies, MPs are identified in specific components/problems in the lesson.

### Indicator 2f

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

The instructional materials reviewed for JUMP Math Grade 4 partially meet expectations for carefully attending to the full meaning of each practice standard. The materials do not attend to the full meaning of MPs 4 and 5.

Examples of the materials carefully attending to the meaning of some MPs include:

• MP1: Teacher Resource, Part 1, Unit 1, Lesson OA4-5, Extension 2, “To make a sequence, Ben picks a starting number and Maria picks a number to add each time. When they write the sequence, the terms switch between odd and even numbers. a. Talk with a partner about what it means for the terms to switch between odd and even numbers. b. What can you say about Maria’s number? Explain.” Students make sense of word problems related to number patterns and plan pathways to solutions using what they know about numbers.
• MP2: Teacher Resource, Part 1, Unit 2, Lesson NBT4-23, Extensions, Item 2: “Write your answer to the question as a full sentence. What fact did you not need to use? Jay has 7 oranges. He has 8 more apples than oranges. He has 3 times as many apples as pears. How many apples does he have?” Students reason abstractly and quantitatively to decontextualize and apply mathematical operations to solve word problems, then contextualize the solutions in order to write a full sentence to answer the problem.
• MP6: In Teacher Resource, Part 1, Unit 7, G4-4, Extensions, Item 3, students make use of structures related to place value in rounding numbers: “Make up an addition where rounding to the nearest thousand is higher than the actual answer, but rounding to the nearest hundred is lower than the actual answer.”
• MP7: Teacher Resource, Part 1, Unit 2, Lesson NBT4-18, Extensions, Item 6, “Subtract mentally. (Items 6a-f include a 4 or 5 digit number - 1,010).” Students make use of structure to realize that they take one away from the thousands and tens, as well as occasions where this strategy doesn’t work (there is a zero in one of those places).
• MP8: Teacher Resource, Part 1, Unit 2, Lesson NBT4-4, Lesson Activities, “Give students ones and tens blocks. ASK: Which numbers have standard base-10 representations that can be arranged as rectangles of width at least 2? That is, if the blocks are arranged horizontally, there are at least 2 rows.” Students use repeated reasoning to notice patterns in forming rectangles with ones and tens.

For MP4, students are given models to use and have few opportunities to develop their own mathematical models. In addition, students have few opportunities to compare different models in problem contexts. Examples include:

• Teacher Resource, Part 1, Unit 2, Lesson NBT4-1, Extensions, Item 3, “A plant is 4 cm tall and grows 3 cm each week. a. How tall will the plant be after 8 weeks? Use multiplication and addition to answer the question. b. Check your answer to part a with a T-table. Use clear labels. Explain how the T-table shows your equation. c. Will the plant be an even or odd number of cm tall after 1 year (52 weeks)? Find a quick way to answer the question. Explain.”
• Teacher Resource, Part 2, Unit 4, Lesson NBT4-35, Extensions, Item 3, “Sam has three times as much money as Megan. How much more money does Sam have than Megan? Show your work using equations. Write your answer as a complete sentence. a. Megan has $14. b. Megan has$124. c. Megan has \$2,314.”
• Teacher Resource, Part 2, Unit 6, Lesson OA4-43, Extensions, Item 7, “Arsham made orange juice to have with breakfast. He squeezed 9 oranges, all the same size, to get 558 mL of juice. He shared the juice equally between himself, his sister, and his brother. After he poured the juice, his sister said, ‘That’s not enough juice!’ So he squeezed another orange and gave it all to his sister. Now how much juice does she have? Use equations to show your work. Explain what each step means in the situation.”

For MP5, students are given few opportunities to use tools strategically, as they are most often given the tools to use for a problem. Examples include:

• Teacher Resource, Part 1 Unit 4, Lesson NBT4-35, Extensions, Item 4, “Find a shortcut way to do each problem in Extension 3 without using subtraction. Explain why the shortcut works using one of the following tools: a number line, an array, or base-10 blocks.”
• Teacher Resource, Part 2 Unit 4, Lesson NF4-5, Extensions, Item 4, “Which fraction is greater, $$\frac{3}{4}$$ or $$\frac{7}{12}$$? Use one or more of the following tools to find the answer: an array, a clock, a table, grid paper, a number line, pattern blocks.”

### Indicator 2g

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

### Indicator 2g.i

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

The instructional materials reviewed for JUMP Math Grade 4 partially meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.

There are few opportunities in the Teacher Resource or the Assessment & Practice for students to construct viable arguments or analyze the arguments or the work of others. MP3 is identified in the margins of the lesson. Examples of where the materials prompt students to construct viable arguments or analyze the arguments of others include, but are not limited to:

• Student Resource, Assessment & Practice Book, Part 2, Unit 4, Lesson NF4-7, Item 6, “Lina thinks $$\frac{4}{3}$$ is less than $$\frac{99}{100}$$ because the numbers are smaller. Is she right? Explain how you know?”
• Teacher Resource, Part 1, Unit 3, Lesson OA4-15, Extensions, Item 2, “Ethan says that he found another way to round a number to the nearest ten: Add 5 to the number and then replace the ones digit with zero. Does Ethan’s rule work? Explain why or why not using examples.” Then in Extension 2 a. Make a rule like Ethan’s rule from Extension 1, but for rounding to any place value. B. In pairs, explain your rule and why it works. Do you agree with each other? Discuss why or why not.” Students critique the reasoning of others.
• Teacher Resource, Part 1, Unit 3, Lesson OA4-4, Extensions, Item 4, “c. Write down a statement you think will be true for each sequence that adds 3 each time. Be as specific as you can. d. In pairs, explain why your statement is true for each sequence. Do you agree with each other? Discuss Why or why not.”

Examples where the materials miss opportunities to prompt students to construct viable arguments or analyze the arguments of others include, but are not limited to:

• Teacher Resource, Part 2, Unit 2, Lesson NBT4-43, Extensions, Item 4, “Lela reads 5 pages of a book. It takes her 37 days to finish the book. What are the possible numbers of pages in the book? Explain how you know.” Students do not construct a viable argument or analyze the arguments of others, only explain the solution.
• In Teacher Resource, Part 1 Unit 2, Lesson NBT4-8, Extensions, students write rules related to place value and operations and “agree with a partner on wording your rule.” In this problem, “agree with your partner on the wording rule” is not giving the student an opportunity to construct a viable argument or analyze the arguments of others, just agree on wording.
• In Student Resource, Assessment & Practice Book, Part 2, Lesson NF4-28, Item 4, students critique (the fictional) Sarah’s argument that 0.25 is more than 0.3 because more is shaded in on picture compared to another. However, this problem is a slight variation of a problem the teacher already covered in the group instruction, so it doesn’t indicate that the student constructed a viable argument. It verifies if the students understood the argument taught in class.

### 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
+
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Indicator Rating Details

The instructional materials reviewed for JUMP Math Grade 4 partially meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Teacher guidance and questions are found in the lessons. In some lessons, teachers are given questions that prompt mathematical discussions and engage students to construct viable arguments, and in other lessons, teachers are provided questions and sentence stems to facilitate students in analyzing the arguments of others, and to justify their answers. Also, on page A49 in the “How to use the lesson plans flexibly” states, “When students work with a partner, many of them will benefit from some guidance, such as displaying question or sentence stems on the board to encourage partners to understand and challenge each other’s thinking, use of vocabulary, or choice of tools or strategies, For example:

• I did ___ the same way but got a different answer. Let’s compare our work.
• What does ___ mean?
• Why is ___ true?
• Why do you think that ___ ?
• I don’t understand ___. Can you explain it a different way?
• Why did you use ___? (a particular strategy or tool)
• How did you come up with ___? (an idea or strategy)”

These sentence stems are used consistently during the Lessons and Extensions.

Examples where teachers are provided guidance to engage students in constructing viable arguments and/or analyze the arguments of others include, but are not limited to:

• Teacher Resource, Part 1 Unit 2, Lesson NBT4-2, Extensions, Item 3, “ASK: what strategy did you use to solve this problem?”
• Teacher Resource, Part 1, Unit 2, Lesson NBT4-17, Extensions, Item 4, “In part B encourage partners to ask questions to understand and challenge each other’s thinking (see p A-49 for sample sentence and question stems).”
• Teacher Resource, Part 1 Unit 2, Lesson NBT4-21, Extensions, Item 3, “Have students discuss their strategy with a partner, then have volunteers share with the whole class.”
• Teacher Resource, Part 1 Unit 3, Lessons OA4-13 and OA4-24, “ASK: What does the pattern say you are adding to get from the top number to the bottom number? Can you explain why that happens?”
• Teacher Resource, Part 1, Unit 5, Lesson OA4-24, Extensions, “Encourage partners to ask questions to understand and challenge each other’s thinking, choice of strategy, and choice of tool. Take up several strategies. Also, discuss different tools that can be used to show why the method works.”

Within lessons, the teacher materials are not always clear about how teachers will engage and support students in constructing viable arguments or critiquing the reasoning of others. Materials identified with the MP3 standard often direct teachers to “choose a student to answer” or “have a volunteer fill in the blank.” Questions are provided but often do not encourage students to deeply engage in MP3. In addition, although answers are provided, there are no follow up questions to help redirect students who didn’t understand. Examples include:

• Teacher Resource, Part 1, Unit 2, Lesson NBT4-14, Extensions, Item 1, "a. Marko writes the number 5 hundreds + 43 tens + 6 ones as 5,436. Is Marko correct? Explain why or why not. b. Alice writes the number 54 hundreds + 3 tens + 6 ones as 5,436. Is Alice correct? Explain why or why not." Teacher instructions in the problem tell students to "explain why or why not" but don't give specific guidance for constructing viable arguments specific to the mathematics in this lesson.
• Teacher Resource, Part 2, Unit 4, Lesson NF4-3, Extensions, Item 3, "Tasha cuts a rectangle into four parts, as shown below. (picture of a rectangle with diagonal lines connecting opposite corners). Do the four parts have the same area? Explain how you know." Teacher instructions in the problem tell students to "explain how you know" but don't give specific guidance for constructing viable arguments specific to the mathematics in this lesson.
• Teacher Resource, Part 2, Unit 6, Lesson OA4-44, Extensions, Item 6 "a. Name a prime number that has 5 as a factor. b. Can a prime number have 8 as a factor? Explain." Teacher instructions in the problem tell students to "explain" but don't give specific guidance for constructing viable arguments specific to the mathematics in this lesson.

### Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
1/2
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Indicator Rating Details

The instructional materials reviewed for JUMP Math Grade 4 partially meet expectations for explicitly attending to the specialized language of mathematics.

Accurate mathematics vocabulary is present in the materials; however, while vocabulary is identified throughout the materials, there is no explicit direction for instruction of the vocabulary in the teacher materials of the lesson. Examples include, but are not limited to:

• Vocabulary is identified in the Terminology section at the beginning of each unit.
• Vocabulary is identified at the beginning of each lesson.
• The vocabulary words and definitions are bold within the lesson.
• There is not a glossary.
• There is not a place for the students to practice the new vocabulary in the lessons.
• Teacher Resource, Part 2, Unit 3, Lesson OA4-36, Vocabulary, materials use “scale factor” instead of multiplicative reasoning.

## Usability

#### Not Rated

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

### Criterion 3a - 3e

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

### Indicator 3a

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

### Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
N/A

### Indicator 3c

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

### Indicator 3d

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

### Indicator 3e

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

### Criterion 3f - 3l

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

### Indicator 3f

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

### Indicator 3g

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

### Indicator 3h

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

### Indicator 3i

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

### Indicator 3j

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

### Indicator 3k

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

### Indicator 3l

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

### Criterion 3m - 3q

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

### Indicator 3m

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

### Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
N/A

### Indicator 3o

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

### Indicator 3p

Materials offer ongoing formative and summative assessments:
N/A

### Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
N/A

### Indicator 3p.ii

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

### Indicator 3q

Materials encourage students to monitor their own progress.
N/A

### Criterion 3r - 3y

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

### Indicator 3r

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

### Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
N/A

### Indicator 3t

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

### Indicator 3u

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

### Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
N/A

### Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
N/A

### Indicator 3x

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

### Indicator 3y

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

### Criterion 3aa - 3z

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

### Indicator 3aa

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

### Indicator 3ab

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

### Indicator 3ac

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

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
N/A

### Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
N/A
abc123

Report Published Date: 2020/09/17

Report Edition: 2019

Title ISBN Edition Publisher Year
Teacher Resource for Grade 4, New US Edition 978‑1‑77395‑039‑6 JUMP Math 2019
Student Assessment & Practice Book 4.1 978‑1‑927457‑12‑2 JUMP Math 2019
Student Assessment & Practice Book 4.2 978‑1‑927457‑13‑9 JUMP Math 2019

## Math K-8 Review Tool

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

For math, our review criteria evaluates materials based on:

• Focus and Coherence

• Rigor and Mathematical Practices

• Instructional Supports and Usability

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

The EdReports rubric supports a sequential review process through three gateways. These gateways reflect the importance of alignment to college and career ready standards and considers other attributes of high-quality curriculum, such as usability and design, as recommended by educators.

Materials must meet or partially meet expectations for the first set of indicators (gateway 1) to move to the other gateways.

Gateways 1 and 2 focus on questions of alignment to the standards. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?

Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom.

In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

For ELA and math, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to college- and career-ready standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For science, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to the Next Generation Science Standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For all content areas, usability ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for effective practices (as outlined in the evaluation tool) for use and design, teacher planning and learning, assessment, differentiated instruction, and effective technology use.