## JUMP Math

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

Showing:

### Overall Summary

The instructional materials reviewed for Grade 7 partially meet the expectations for alignment to the CCSSM. The materials meet the expectations for focus and coherence in Gateway 1, and they do not meet the expectations for rigor and the mathematical practices in Gateway 2. Since the materials partially meet the expectations for alignment, evidence concerning instructional supports and usability indicators in Gateway 3 was not collected.

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

### Focus & Coherence

##### Gateway 1
Meets Expectations

#### Criterion 1.1: Focus

Materials do not assess topics before the grade level in which the topic should be introduced.

The instructional materials reviewed for Grade 7 meet the expectations for not assessing any topics before the grade-level in which the topic should be introduced. All of the summative assessment questions focus on grade-level topics or below. Overall, the instructional materials do not assess any content from future grades.

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

The instructional materials reviewed for Grade 7 meet the expectations for assessing the grade-level content and, if applicable, content from earlier grades. The Sample Unit Quizzes and Tests included in the Teacher Resources Part 1 Section L and and Teacher Resources Part 2 Section V, along with the answer keys and "Scoring Guides and Rubrics," were reviewed for this indicator. Examples of Unit Tests that include great-level assessment items include the following:

• In Teacher Resources Part 1, the Unit 6 Test that addresses standards from 7.G.A has students construct triangles from given angle measurements or side lengths and solve problems involving scale drawings of geometric figures.
• In Teacher Resources Part 2, the Unit 2 Test that addresses standards from 7.NS.2 has students converting rational numbers to a decimal using long division and showing that the decimal form of a rational number terminates in 0s or eventually repeats.

#### Criterion 1.2: Coherence

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

The instructional materials reviewed for Grade 7 meet the expectations for, when used as designed, devoting the majority of class time in each grade to the major work of the grade. The amount of time spent on major work is approximately 73 percent. Overall, the instructional material spends the majority of class time on the major clusters of the grade.

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

The instructional materials reviewed for Grade 7 meet the expectations for spending the majority of class time on the major clusters of each grade. Overall, approximately 73 percent of class time is devoted to major work of the grade.

The materials for Grade 7 include 15 Units. In the materials, there are 168 lessons, and of those, 29 are Bridging lessons. According to the materials, Bridging lessons should not be “counted as part of the work of the year” (page A-56), so the number of lessons examined for this indicator is 139 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 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 96 lessons addressing major work as indicated by the materials themselves to 102 lessons.

Three perspectives were considered: 1) the number of units devoted to major work, 2) the number of lessons devoted to major work, and 3) 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 15;
• Lessons– Approximately 73 percent, 102 out of 139; and
• Days– Approximately 73 percent, 112 out of 154.

The number of instructional days, approximately 73 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 1.3: Coherence

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.

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

The instructional materials reviewed for Grade 7 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-level.

Examples where connections are present include the following:

• In Lessons 8, 9, and 10 of Unit 6 in Teacher Resources Part 1, the materials connect 7.RP.2 with 7.G.1 as students are expected to recognize and represent proportional relationships between quantities in order to solve problems involving scale drawings of geometric figures.
• In Lessons 11, 12, and 13 of Unit 4 in Teacher Resources Part 2, the materials connect 7.EE.4a with 7.G.5 as students are expected to solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers, that arise from using facts about supplementary, complementary, vertical, and adjacent angles in a figure.
• In Lessons 14, 15, and 16 of Unit 4 in Teacher Resources Part 2, the materials connect 7.EE.4 with 7.G.6 as students are expected to construct simple equations and inequalities to solve problems by reasoning about the quantities that arise from real-world and mathematical problems involving area of two-dimensional objects composed of triangles, quadrilaterals, and polygons.
• In Lesson 16 of Unit 7 in Teacher Resources Part 2, the materials connect 7.RP.2 with 7.SP.2 as students are expected to recognize and represent proportional relationships between quantities in order to draw inferences about a population with an unknown characteristic of interest.
##### Indicator {{'1d' | indicatorName}}
The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.

The instructional materials reviewed meet the 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 154 days which is appropriate for a school year of approximately 140-190 days.

• The materials are written with 15 units containing a total of 168 lessons.
• Each lesson is designed to be implemented during the course of one 45 minute class period per day. In the materials, there are 168 lessons, and of those, 29 are Bridging lessons. Twenty-nine Bridging lessons have been removed from the count because the Teacher's Edition states that they are not counted as part of the work for the year, so the number of lessons examined for this indicator is 139 lessons.
• There are 15 unit tests which are counted as 15 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' | indicatorName}}
Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.

The instructional materials reviewed for Grade 7 partially meet the expectation for being consistent with the progressions in the Standards. Overall, the materials address the standards for this grade-level and provide all students with extensive work on 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, and content from prior or future grades is clearly identified and related to grade-level work. The Teacher Resources contain sections that highlight the development of the grade-by-grade progressions in the materials, identify content from prior or future grades, and state the relationship to grade-level work.

• At the beginning of each unit, "This Unit in Context" provides a description of prior concepts and standards students have encountered during the grade-levels before this one. The end of this section also makes connections to concepts that will occur in future grade-levels. For example, "This Unit in Context" from Unit 8, Statistics and Probability: Probability Models, of Teacher Resources Part 1 describes the topics from Measurement and Data that students encountered in Grades K through 5, specifically organizing and representing data with scaled picture and bar graphs and line plots with measurements in fractions of a unit, and from Statistics and Probability in Grade 6, specifically developing an understanding of statistical variability and summarizing and describing distributions. The description then includes the topic of probability, specifically referring to using different tools to find probabilities, and it concludes with how the work of this unit builds to the statistical topic of bivariate data in Grade 8.

There are some lesson that are not labeled Bridging Lessons that contain off grade-level material, but these lessons are labeled as “preparation for” and can be connected to grade-level work. For example, Lesson 33 of Unit 2 in Teacher Resources Part 2 addresses solving addition and multiplication equations including negative addends and coefficients, and the lesson is labeled as "preparation for 7.EE.4."

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-54, Teacher Resources)
• In the Advanced 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 Lesson 27 of Unit 3 in Teacher Resources Part 2 engage students in solving inequalities where the coefficient of the variable is negative, which is more difficult than when the coefficient is positive, but these problems still align to 7.EE.4b. Also, the problems in Lesson 52 of Unit 5 in Teacher Resources Part 2 that have students simplifying numerical expressions that include repeating decimals align to standards from 7.NS.

The instructional materials do not relate grade-level concepts explicitly to prior knowledge from earlier grades. Examples of 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, Lesson 28 of Unit 2 in Teacher Resources Part 2 states that its goal is to solve problems involving ratios with fractional terms, and the prior knowledge required is that students can divide fractions, can multiply fractions by whole numbers, can multiply whole numbers by fractions, can find equivalent ratios, and can understands ratio tables.
• There are 29 lessons identified as Bridging Lessons, but none of these lessons are explicitly aligned to standards from prior grades even though they do state for which grade-level standards they are preparation. For example, in Unit 4 of Teacher Resources Part 1, four of the seven lessons are Bridging Lessons labeled as "preparation for 7.NS.1," and two of the seven are Bridging Lessons labeled as "preparation for 7.NS.2." However, none of these six Bridging Lessons are explicitly aligned to standards prior to Grade 7. Also, Lesson 1 of Unit 3 in Teacher Resources Part 2 is a Bridging Lesson labeled as "preparation for 7.EE.4" that has students substituting values for a variable into an expression, but the lesson is not explicitly aligned to standards prior to Grade 7.
##### Indicator {{'1f' | indicatorName}}
Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.

The instructional materials reviewed for Grade 7 meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards. Overall, materials include learning objectives that are visibly shaped by CCSSM cluster headings and make connections within and across domains.

In the materials, the units are organized by domains and are clearly labeled. For example, Teacher Resources Part 1 Unit 3 is titled Expressions and Equations: Equivalent Expressions, and Teacher Resources Part 2 Unit 6 is titled Geometry: Volume, Surface Area, and Cross Sections. Within the units, there are goals for each lesson, and the language of the goals is visibly shaped by the CCSSM cluster headings. For example, in Unit 8 of Teacher Resources Part 1, the goal for Lesson 9 states "Students will design and use a simulation to determine probabilities of compound events." The language of this goal is visibly shaped by 7.SP.C, "Investigate chance processes and develop, use, and evaluate probability models."

The instructional materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade. Examples of these connections include the following:

• In Lessons 22 and 23 of Unit 4 in Teacher Resources Part 2, the materials connect 7.G.A with 7.G.B as students draw, construct, and describe geometrical figures; describe the relationships between them; and solve problems involving angle measure and area.
• In Lesson 13 of Unit 7 in Teacher Resources Part 2, the materials connect 7.SP.A with 7.SP.B as students use random sampling to draw inferences about a population and informal comparative inferences about two populations.
• In Lesson 19 of Unit 3 in Teacher Resources Part 2, the materials connect 7.RP with 7.EE as students are expected to recognize and represent proportional relationships between quantities and rewrite expressions in different forms in a problem context to shed light on the problem and how the quantities in it are related.
• In Lesson 18 of Unit 4 in Teacher Resources Part 2, the materials connect 7.RP with 7.G.A as students compute areas from scale drawings.

### Rigor & Mathematical Practices

The instructional materials reviewed for Grade 7 do not meet the expectations for rigor and mathematical practices. The instructional materials partially meet the expectations for rigor and do not meet the expectations for mathematical practices.

##### Gateway 2
Does Not Meet Expectations

#### Criterion 2.1: Rigor

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.

The instructional materials reviewed for Grade 7 partially meet expectations for rigor and balance. The materials include specific attention to both conceptual understanding and procedural skill and fluency; however, there are limited opportunities for students to work with engaging applications. As a result, the materials do not exhibit a balance of the three aspects of rigor.

##### Indicator {{'2a' | indicatorName}}
Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

The instructional materials for Grade 7 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

Cluster 7.NS.A focuses on extending previous understandings of operations with numbers to include operations with rational numbers.

• Teacher Resources Part 1 Unit 2 has students develop their understanding of adding and subtracting rational numbers through the use of number lines, drawings of protons (positive) and electrons (negative) as counters, and comparisons to using operations with positive numbers (7.NS.1).
• Teacher Resources Part 1 Unit 7 has students develop their understanding of multiplying and dividing integers (7.NS.2a,b,c) through the use of number lines and by extending the properties of operations to include negative numbers.
• Teacher Resources Part 2 Unit 1 has students develop their understanding of multiplying and dividing rational numbers (7.NS.2a,b,c) through the use of area models (rectangular and circular), 10 X 10 grids, number lines, and extending patterns of operations from integers and positive rational numbers.
• Teacher Resources Part 2 Unit 5 has students develop their understanding of rational numbers by examining repeating and terminating decimals (7.NS.2d). In Lesson 50, students use place value to position terminating decimals on number lines, and they also use number lines and place value to determine intervals in which repeating decimals would be.

Cluster 7.EE.A focuses on using the properties of operations to generate equivalent expressions.

• Teacher Resources Part 1 Unit 3 has students develop their understanding of equivalent expressions through the use of pictures, area models, substituting numbers for variables, and extending the properties of operations to include expressions with variables in them. Lesson 12 also includes pictures of objects that resemble algebra tiles as students write equivalent expressions for the area of a shaded figure.
##### Indicator {{'2b' | indicatorName}}
Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

The materials for Jump Math Grade 7 meet the expectations for procedural skill and fluency by giving attention throughout the year to individual standards which set an expectation of procedural skill and fluency.

• The teacher's edition gives strategies for mental math starting on page A-32. The strategies are not incorporated into the lesson plans for the teacher.
• There is a game in the teacher's edition on pages A51-A52 that helps to build student fluency. This games focuses on addition and subtraction, but it is not mentioned in any of the lessons.

Cluster 7.NS.A develops procedural skill in completing addition, subtraction, multiplication, and division with rational numbers.

• Teacher Resources Part 1 Unit 2 has students build procedural skill with adding and subtracting rational numbers, in conjunction with developing their conceptual understanding, through the use of number lines, signed pictures, and comparisons to using operations with positive numbers (7.NS.1).
• Teacher Resources Part 1 Unit 7 and Teacher Resources Part 2 Unit 1 have students build procedural skill with multiplying and dividing rational numbers (7.NS.2a,b,c), in conjunction with developing their conceptual understanding, through the use of area models (rectangular and circular), 10 X 10 grids, number lines, and extending patterns of operations from integers and positive rational numbers.
• There are further opportunities for students to develop their procedural skill with the four operations and rational numbers within the Assessment & Practice books on pages 36-67 and 176-191 for Part 1 and pages 1-34 for Part 2.

Standard 7.EE.1 includes students developing procedural skill in developing equivalent, linear expressions with rational coefficients through addition, subtraction, factoring, and multiplication.

• Teacher Resources Part 1 Unit 3 has students build their procedural skill with developing equivalent expressions (7.EE.1), in conjunction with developing their conceptual understanding, through the use of pictures, area models, substituting numbers for variables, and extending the properties of operations to include expressions with variables in them.
• There are further opportunities for students to develop their procedural skill with developing equivalent expressions within the Assessment & Practice books on pages 83-98 for Part 1.

Standard 7.EE.4 expects students to develop procedural skill in constructing and solving linear equations and inequalities of the form px+q=r; p(x + q)=r; px+q&gt;r; and px+q&lt;r.

• Teacher Resources Part 2 Unit 3 has students build their procedural skill with constructing and solving linear equations and inequalities as different methods for solving equations are discussed and those methods are used to solve inequalities.
• Teacher Resources Part 2 Unit 4 offers more opportunities for students to develop procedural skill in constructing and solving linear equations and inequalities as students solve geometric problems involving angle relationships, area, surface area, and volume in Lessons 11-16.
• There are further opportunities for students to develop their procedural skill in constructing and solving linear equations and inequalities within the Assessment & Practice books on pages 64-103 and 104-118 for Part 2.
##### Indicator {{'2c' | indicatorName}}
Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade

The instructional materials do not meet the expectation for being 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. Overall, there is little evidence of the opportunity to work with engaging applications of the mathematics. There are few non-routine problems throughout the year. Word problems are present in the materials, but the context has limited bearing on the mathematics. However, there are ten Problem Solving Lessons designed to help students "isolate and focus on [problem solving] strategies."

Cluster 7.RP.A expects students to use proportional relationships to solve real-world and mathematical problems. The parts of this cluster that relate to applications, 7.RP.3 in particular, are primarily focused on in Teacher Resources Part 2 Unit 2, so the following evidence comes from that Book and Unit.

• In Lessons 31 and 32, students write proportions to solve problems involving percents. Both lessons are structured so that exercises for students to complete immediately follow examples that the teacher does which are exactly like the exercises. Many exercises also include contexts like the teacher-led examples. In the exercises where different contexts are presented, the wording of the exercises is very similar to the examples, so students still have a procedure for how to solve the problem in the new context.
• In Lessons 34 and 35, students solve mathematical problems involving proportional relationships, but none of the problems involve a context. Also, the problems are routine because students complete exercises that follow the process used in teacher-led examples.
• In Lesson 37, students are shown how to use tape diagrams to solve problems involving percent discounts and markups. The exercises that students are asked to complete are routine because, as in previous lessons, they immediately follow and are the same as teacher-led examples.

Standard 7.NS.3 sets an expectation that students solve real-world and mathematical problems involving the four operations with rational numbers.

• In Lessons 28 and 29 of Unit 7 in Teacher Resources Part 1, students are presented with few opportunities to solve real-world problems involving the four operations with rational numbers, and the few problems they are given are routine as they follow exercises with which they are very similar. Also, the contexts for the problems do not vary.
• In Lessons 30 and 31 of Unit 7 in Teacher Resources Part 1, students are presented with numerical expressions involving the four operations that they are supposed to simplify. The students do not create any of the expressions, and contexts are not presented with the expressions.
• In Lessons 39 and 44 of Unit 1 in Teacher Resources Part 2, students are presented with some word problems that require them to multiply or divide rational numbers, but these problems are routine. They follow exercises with which they are similar, and the contexts do not have bearing on them.

Standard 7.EE.3 includes solving problems with rational numbers using tools strategically, applying properties of operations to calculate with numbers, converting between different forms of numbers as appropriate, and assessing the reasonableness of answers. This standard is primarily addressed in Unit 5 of Teacher Resources Part 1.

• In Lessons 17 through 25, students are given some opportunities to solve problems with rational numbers, but the problems are routine, and tools are given to students. For example, in Lesson 23 students are shown how to use tape diagrams for solving problems that involve percents and told to use tape diagrams when completing the exercises. In Lesson 25, there are some exercises at the end of the lesson where the context could have a bearing on the students solving a problem, but these exercises at the end are routine because they have the same format and use the same wording as the preceding exercises in the lesson. For example, there are a series of exercises where students work in the context of the ratio of boys to girls in a classroom and are supposed to use a tape diagram to help them answer the exercises , but these follow a teacher-led example that also uses the context of the ratio of boys to girls in a classroom and a tape diagram.

In Problem Solving Lesson PS7-5 students are presented with two problem solving strategies: using tape diagrams and using algebra to solve multi-step ratio problems. The teacher-led exercises scaffold students through the strategies in a variety of applications. In one instance in the lesson, teachers are prompted to ask students what is the same between the two strategies. The Problem Bank provides students opportunities to work independently on routine tasks that are similar to the exercises. Students were directed to use both strategies learned in the lesson. Teachers were guided to ask students which strategy they prefer and why but were not guided to connect application of the strategies to the mathematics.

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

The instructional materials partially meet the expectation that the materials balance all three aspects of rigor with the three aspects almost always treated separately within the curriculum including within and during lessons and practice. Overall, many of the lessons focus on procedural skills and fluency with few opportunities for students to apply procedures for themselves. There is a not a balance of the three aspects of rigor within the grade.

• The three aspects of rigor are not pursued with equal intensity in this program.
• Conceptual knowledge and procedural skill and fluency are evident in the instructional materials. There are multiple lessons where conceptual development is the clear focus.
• The instructional materials lack opportunities for students to engage in application and problem solving in real world situations.
• There are very few lessons that treat all three aspects together due to the relative weakness in application. However, there are several lessons that include conceptual development leading to procedural practice and fluency.
• There are minimal opportunities for students to engage in cognitively demanding tasks and applications that would call for them to use the math they know to solve problems and integrate their understanding into real-world applications.

#### Criterion 2.2: Math Practices

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

The instructional materials reviewed for Jump Math Grade 7 do not meet the expectations for practice-content connections. Although the materials meet expectations for identifying and using the MPs to enrich mathematics content, they do not attend to the full meaning of each practice standard. Overall, in order to meet the expectations for meaningfully connecting the Standards for Mathematical Content and the MPs, the instructional materials should carefully pay attention to the full meaning of each MP, especially MP3 in regards to students critiquing the reasoning of other students and teachers engaging students in constructing viable arguments and analyzing the arguments of others.

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

The instructional materials reviewed for Grade 7 meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.

The Standards for Mathematical Practice (MPs) are identified in Teachers Resources Parts 1 and 2 in most lessons. The MPs are not listed in the beginning with the lesson goals but in parentheses in bold within the lesson at the part where they occur. As stated on page A-21 in the Teacher Resources Part 1, “We guide students to develop the Mathematical Practice Standards by explicitly teaching the skills required. While the development of these practices occurs in virtually every lesson, only some lessons have grade-level applications of the standards. These grade-level applications are identified in the margin.”

Overall, the materials clearly identify the MPs and incorporate them into the lessons. The MPs are incorporated into almost every lesson; they are not taught as separate lessons. All of the MPs are represented and attended to multiple times throughout the year, though not equally. In particular, MP5 receives the least attention.

##### Indicator {{'2f' | indicatorName}}
Materials carefully attend to the full meaning of each practice standard

The instructional materials reviewed for Grade 7 do not meet the expectations for carefully attending to the full meaning of each practice standard. The publisher rarely addresses the Mathematical Practice Standards in a meaningful way.

The materials identify examples of the Standards for Mathematical Practice (MPs), so the teacher does not always know when a MP is being carefully attended to. MPs are marked throughout the curriculum, but sometimes the problems are routine problems that do not cover the depth of the Math Practices. Many times the MPs are marked where teachers are doing the work.

Examples where the material does not meet the expectation for the full meaning of the identified MP:

• MP1: In Teacher Resources Part 1 Unit 8 Lesson 6, students are asked to make an organized list from an already completed tree diagram and a separate list from a chart. Both of these exercises resemble examples that are completed by the teacher immediately preceding the exercises. Another example is in Teacher Resource Part 1 Unit 8 Lesson 8. A task asks students to, “Check that the numbers in Part C actually add to 1,000 and that the numbers in the Bonus question add to 10,000 or that their percents add to 100%.” These are not examples of MP1 as they do not require students to make sense of problems or persevere in solving them.
• MP4: In Teacher Resources Part 2 Unit 3, Lesson 18 asks students to choose two variables and write an equation, and this exercise does not show the full meaning of modeling with mathematics. Also, in Teacher Resources Part 2 Unit 1 Lesson 32, students are asked to determine if a recipe will turn out by multiplying two fractions. These exercises follow teacher-led examples exactly like them, and there is not an opportunity for students to say what changes would need to be made if they determine the recipe will not turn out.
• MP4: While the publisher attaches MP4 to many lessons, there are occasions when the activities students are completing do not have them model with mathematics. For example, in Teacher Resources Part 1 Unit 3 Lesson 6, there are exercises with instructions to "write a subtraction expression for the change (in dollars) from \$20 as the price of a CD is ...". From the instructions, students are told to subtract from 20 and that the units will be dollars. Although, the answer is a mathematical model, the directions give the format of the model to the students, and by giving the units, students are not able to identify any important quantities. Also in Lesson 6, students are to complete three exercises where an algebraic expression is given to them, and they are to evaluate the expression by substituting a given value for the variable. In these exercises, students do not have the opportunity to make assumptions or approximations in a complex situation, identify important quantities and represent their relationships, draw conclusions, or interpret the results of a problem and make improvements if needed.
• MP5: In Teacher Resources Part 1 Unit 5, Lesson 16 says, “Explain that you can use estimation to check the answer.” There is no choosing of tools. In Teacher Resources Part 1 Unit 8, Lesson 9 has the teacher telling students “it can be tedious to find theoretical probabilities of compound events using a tree diagram, chart, or organized list.” This does not require the students to use tools strategically.
• MP7: While MP7 is indicated in many lessons, sometimes the structure is found in the standard itself and not the indicated exercise or a rule is being provided. For example, in Teacher Resources Part 2 Unit 6 Lesson 28, students are finding the surface area of composite shapes. The teacher then guides them through the process of separating prisms and each of their corresponding calculations. In this exercise, students are not discerning anything about the decomposition of three-dimensional composite shapes; they are simply following the teacher and the instruction given.
##### Indicator {{'2g' | indicatorName}}
Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
##### Indicator {{'2g.i' | indicatorName}}
Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.

The instructional materials reviewed for Grade 7 partially meet expectations that the materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.

Materials occasionally prompt students to construct viable arguments or analyze the arguments of others concerning key grade-level mathematics detailed in the content standards; however, there are very few opportunities for students to both construct arguments and analyze the arguments of others together. In the lessons provided in the Teacher Resources Parts 1 and 2, examples identified as MP3 are typically in a whole group discussion, though there are occasional suggestions for students to work in small groups. Students rarely have the opportunity to either construct viable arguments or to critique the reasoning of others in a meaningful way because of the heavy scaffolding of the program. For example, in Teacher Resources Part 2 Unit 4 Lesson 12, the teacher walks students through word problems asking specific questions. “SAY: In these diagrams, x and y are vertical angles. Point to the first picture and ASK: What is x? How do you know? What is y? How do you know?" In Teacher Resource Part 1 Unit 3 Lesson 9, students are asked, “What property of addition is being used?” These questions lead to understanding but do not address MP3 by having students construct their own arguments and/or critiquing the reasoning of others.

##### Indicator {{'2g.ii' | indicatorName}}
Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.

The materials reviewed for Grade 7 partially meet the expectation of 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.

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 re-direct students who didn’t understand. Examples of how the materials supply some questions for teachers to ask but have limited additional support include:

• In Teacher Resources Part 1 Unit 3, Lesson 2 directs the teacher to: "Write on board: (5 - 2) x 4 = (2 - 5) x 4 by the commutative property. Tell students that you saw someone make this claim. ASK: Is this correct? (no) What mistake did the person make? (they thought subtraction was commutative).” There are no additional questions provided for teachers to assist students who are not able to answer either or both of the questions correctly.
• In Teacher Resources Part 1 Unit 7 Lesson 27, a teacher-led example is called "Moving negative signs around in a product" and states “Have volunteers dictate the answers.”
• In Teacher Resources Part 1 Unit 7, the first example of Lesson 29 is labeled with MP3, but in it, teachers are told to tell the students that the relationship between multiplication and division can be applied to negative numbers. By telling the students that the relationship between multiplication and division can be applied to negative numbers, the teacher is constructing the argument for the students and not assisting them in constructing their own argument.
• In Teacher Resources Part 2 Unit 4, Lesson 18 has teachers ask, "How can you get the area of a scale drawing if you know the scale and the area of the original drawing?” Then, teachers are supposed to write the correct answer on the board. The materials do not indicate any additional questions to ask to assist students in constructing their own argument if they are unable to answer the initial question or assist students in analyzing the arguments of others if the correct answer is not initially given.
• In Teacher Resources Part 2 Unit 4, the last example in Lesson 22 includes “SAY: One of the angles measures 90 degrees. Can the 90 degree angle be one of the two equal angles? (no) Why not? (because a triangle cannot have two 90 degree angles) SAY: So in this example, there is only one case because the other case is impossible.” In this example, students get to construct their own argument, but there is no assistance given to teachers to help students who may not initially know the correct answer or to have students analyze the arguments of others if different solutions are given.

Overall, some questions are provided for teachers to assist their students in engaging students in constructing viable arguments and analyzing the arguments of others; however, additional follow-up questions and direct support for teachers is needed.

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

The materials reviewed for Jump Math Grade 7 partially meet the expectation for attending to the specialized language of mathematics. Overall, there are several examples of the mathematical language being introduced and appropriately reinforced throughout the unit, but there are times the materials do not attend to the specialized language of mathematics.

Although no glossary is provided in the materials, each unit introduction includes a list of important vocabulary, and each lesson includes a list of vocabulary that will be used in that lesson. The teacher is provided with explanations of the meanings of some words.

• In Teacher Resources Part 1, page A-21 states that “words being introduced and defined for the first time are presented in bold font in the list and in italics in the lesson plans.”
• Vocabulary words are listed at the beginning of each lesson plan in the Teacher’s Guide, but definitions, if any, are within the lesson.

While the materials attend to the specialized language of mathematics most of the time, there are instances where this is not the case.

• In Lesson 26 of Unit 2 in Teacher Resources Part 2, the materials introduce the word "canceling" and treat it as a mathematical term or operation that can be used when students are multiplying fractions. The materials do not consistently have students "divide factors that equal 1," which would enable students to attend to precision through the specialized language of mathematics. The term "canceling" is also used in subsequent lessons.
• In Lesson 28 of Unit 2 in Teacher Resources Part 2, the materials refer to the "invert-and-multiply rule" for dividing fractions. The materials do not relate dividing by a number to multiplying by the reciprocal of the divisor, which would enable students to attend to precision through the specialized language of mathematics. The term "invert-and-multiply rule" is also used in subsequent lessons.
• In Lesson 34 of Unit 2 in Teacher Resources Part 2, the materials introduce the term "cross-multiply" and use it as a method for solving equations that involve proportional relationships. The use of "cross-multiply" obscures the precise, mathematical process that is occurring and does not attend to the specialized language of mathematics, such as properties of equality, involved in the process. The term "cross-multiply" is also used in subsequent lessons.

### Usability

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

#### Criterion 3.1: Use & Design

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

#### Criterion 3.2: Teacher Planning

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

#### Criterion 3.3: Assessment

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

#### Criterion 3.4: Differentiation

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

#### Criterion 3.5: Technology

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

## Report Overview

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

#### Math K-2

The instructional materials reviewed for Kindergarten and Grade 1 meet the expectations for focus and coherence in Gateway 1. The materials in both grades meet the expectation for focus as they assess grade-level topics and spend the majority of class time on major work of the grade. The materials for Kindergarten and Grade 1 are also coherent and consistent with the Standards. The materials for Kindergarten and Grade 1 do not meet expectations for rigor and the mathematical practices (MPs) in Gateway 2. The materials partially meet the expectations for rigor as they develop conceptual understand and procedural fluency, and even though the materials identify and use the MPs to enrich the mathematical content, the materials do not meet the expectations for the MPs.

Grade 2 materials are currently under revision by the publisher. EdReports will re-review and publish the grade-level report upon the completion of the materials revision.

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

#### Math 3-5

The instructional materials reviewed for Grade 4 and Grade 5 meet the expectations for focus and coherence in Gateway 1. The materials in both grades meet the expectation for focus as they assess grade-level topics and spend the majority of class time on major work of the grade. The materials for Grade 4 and Grade 5 are also coherent and consistent with the Standards. The materials for Grade 4 and Grade 5 do not meet expectations for rigor and the mathematical practices (MPs) in Gateway 2. The materials partially meet the expectations for rigor as they develop conceptual understand and procedural fluency, and even though the materials identify and use the MPs to enrich the mathematical content, the materials do not meet the expectations for the MPs.

Grade 3 materials are currently under revision by the publisher. EdReports will re-review and publish the grade-level report upon the completion of the materials revision.

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

#### Math 6-8

The instructional materials reviewed for Grades 6-8 meet the expectations for focus and coherence in Gateway 1. The materials for all three grades meet the expectations for focus as they assess grade-level topics and spend the majority of class time on major work of the grade, and the instructional materials for all three grades meet the expectations for being coherent and consistent with the Standards. The materials for all three grades do not meet the expectations for rigor and the mathematical practices (MPs) in Gateway 2. The materials partially meet the expectations for rigor as they develop conceptual understanding and procedural skill and fluency, and even though the materials identify and use the MPs to enrich the mathematical content, the materials do not meet the expectations for the MPs.

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

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###### Usability
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