Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 6 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.

See Rating Scale
Understanding Gateways

Alignment

|

Partially Meets Expectations

Gateway 1:

Focus & Coherence

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

Gateway 2:

Rigor & Mathematical Practices

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

Usability

|

Not Rated

Not Rated

Gateway 3:

Usability

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

Gateway One

Focus & Coherence

Meets Expectations

+
-
Gateway One Details

The materials reviewed for Grade 6 meet the expectations for Gateway 1. These materials do not assess above-grade-level content and spend the majority of the time on the major clusters of each grade level. Teachers using these materials as designed will use supporting clusters to enhance the major work of the grade. These materials are consistent with the mathematical progression in the standards, and students are offered extensive work with grade-level problems. Connections are made between clusters and domains where appropriate. Overall, the materials meet the expectations for focusing on the major work of the grade, and the materials also meet the expectations for coherence.

Criterion 1a

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

The instructional materials reviewed for Grade 6 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

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

The instructional materials reviewed for Grade 6 meet the expectation 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 I and Teacher Resources Part 2 Section U, 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 5 Test that addresses standards from 6.RP has students complete ratio tables, find the percent of a quantity, answer word problems using equivalent ratios, and represent different relationships with ratios.
  • In Teacher Resources Part 2, the Unit 3 Test that addresses standards from 6.EE.A,B has students writing and evaluating numerical expressions with whole-number exponents, writing algebraic expressions, and solving word problems by writing and solving one variable equations of the form x + p = q or px = q.

Criterion 1b

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

The instructional materials reviewed for Grade 6 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 65 percent. Overall, the instructional material spends the majority of class time on the major work of the grade.

Indicator 1b

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

The instructional materials reviewed for Grade 6 meet the expectations for spending the majority of class time on the major clusters of each grade. Overall, approximately 65 percent of class time is devoted to major work of the grade.

The materials for Grade 6 include 15 Units. In the materials, there are 171 lessons, and of those, 28 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 143 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 84 lessons addressing major work as indicated by the materials themselves to 92.5 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 65 percent, 92.5 out of 143; and
  • Days– Approximately 65 percent, 102.5 out of 158.

The number of instructional days, approximately 65 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.
8/8
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 6 meet the expectations for coherence. The materials use supporting content as a way to continue working with the major work of the grade and include a full program of study that is viable content for a school year including 158 days of lessons and assessment. Students are given extensive work on grade-level problems, and materials develop according to the grade-by-grade progressions in the Standards. These instructional materials are visibly shaped by the cluster headings in the standards, and connections are made between domains and clusters within the grade level. Overall, the Grade 6 materials support coherence and are consistent with the progressions in the standards.

Indicator 1c

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

The instructional materials reviewed for Grade 6 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 Lesson 4 of Unit 6 in Teacher Resources Part 1 and Lesson 25 of Unit 5 in Teacher Resources Part 2, the materials connect 6.NS.C with 6.G.3 as students graph points in the coordinate plane in order to solve mathematical problems about polygons.
  • In Lessons 12 and 13 of Unit 6 in Teacher Resources Part 1, the materials connect 6.EE.7 with 6.G.1 as students are expected to solve real-world and mathematical problems by writing and solving equations that arise from finding the area of triangles, parallelograms, and trapezoids.
  • In Lessons 33 and 41 of Unit 8 in Teacher Resources Part 2, the materials connect 6.EE.7 with 6.G.2 as students are expected to solve real-world and mathematical problems by writing and solving equations that arise from finding the volume of a right rectangular prism.

Indicator 1d

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

The instructional materials reviewed 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 158 days which is appropriate for a school year of approximately 140-190 days.

  • The materials are written with 15 units containing a total of 171 lessons.
  • Each lesson is designed to be implemented during the course of one 45 minute class period per day. In the materials, there are 171 lessons, and of those, 28 are Bridging lessons. Twenty-eight 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 143 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

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.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 6 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, and they 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 5, Geometry: Coordinate Grids, of Teacher Resources Part 2 describes the geometric topics students encountered in Grade 5, specifically graphing in the first quadrant of the coordinate plane, the work students will encounter graphing and solving problems in all four quadrants of the coordinate plane, and how the work of this unit will build to transformations and the Pythagorean Theorem 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 31 of Unit 4 in Teacher Resources Part 1 addresses multi-digit addition with positive integers, and the lesson is labeled as "preparation for 6.NS.3."

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-51, 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 28 of Unit 5 in Teacher Resources Part 2 engage students in reflecting points across one axis and then the other, but these problems still align to 6.NS.6. Also, the problems in Lesson 41 of Unit 8 in Teacher Resources Part 2 that have students solving problems involving volume and surface area of prisms and pyramids align to standards from 6.NS, 6.EE, and 6.G.

The instructional materials relate grade-level concepts explicitly to prior knowledge from earlier grades. Examples of these 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 9 of Unit 3 in Teacher Resources Part 2 identifies knowing addition and subtraction, along with multiplication and division, as inverse operations in order for students to accomplish the goal of the lesson, which is solving one-step equations using logic and the concept of operations.
  • There are 28 lessons identified as Bridging Lessons, and most of these lessons are aligned to standards from prior grades and also state for which grade-level standards they are preparation. Lesson 2 of Unit 3 in Teacher Resources Part 1, which has students write and solve addition equations, is aligned to 4.OA.3 and is in preparation for 6.EE.2 and 6.EE.5. Also, Lessons 1 and 3 of Unit 6 in Teacher Resources Part 1, which have students identify right angles, parallel lines and perpendicular lines, are aligned to 4.G.1 and 4.G.2 and are in preparation for 6.G.3.

Indicator 1f

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

The instructional materials reviewed for Grade 6 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 entitled Expressions and Equations: Variables and Equations, and Teacher Resources Part 2 Unit 9 is entitled Statistics and Probability: Distribution. 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 2, the goal for Lesson 41 states "Students will solve problems involving the surface area of rectangular and triangular pyramids and prisms and the volume of rectangular prisms." The language of this goal is visibly shaped by 6.G.A, "Solve real-world and mathematical problems involving area, surface area, and volume."

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 Lesson 36 of Unit 4 in Teacher Resources Part 1 and Lessons 23 and 24 of Unit 5 in Part 2, the materials connect 6.NS.B with 6.NS.C as students compute fluently with multi-digit numbers and order rational numbers.
  • In Lessons 10 and 11 of Unit 6 in Teacher Resources Part 1, the materials connect 6.EE.A with 6.EE.B as students evaluate expressions at specific values of their variables and solve real-world and mathematical problems by writing and solving equations.
  • In Lessons 5 through 9 of Unit 9 in Teacher Resources Part 2, the materials connect 6.SP.A with 6.SP.B as students develop an understanding of statistical variability and summarize and describe distributions.
  • In Lesson 5 of Unit 6 in Teacher Resources Part 1, the materials connect 6.NS with 6.EE as students solve real-world and mathematical problems by graphing points and writing and solving equations.
  • In Lessons 39 and 40 of Unit 8 in Teacher Resources Part 2, the materials connect 6.G with 6.NS as students represent three-dimensional figures using nets made up of rectangles and triangles, use the nets to find the surface area of these figures, and compute fluently with multi-digit numbers.

Gateway Two

Rigor & Mathematical Practices

Does Not Meet Expectations

+
-
Gateway Two Details

The instructional materials reviewed for Grade 6 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.

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.
5/8
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 6 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

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

The instructional materials for Grade 6 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

Cluster 6.RP.A focuses on understanding the concept of ratios and of a unit rate.

  • Teacher Resources Part 1 Unit 1 Lessons 6-9, 11, and 12 have students develop their understanding of ratios and unit rate through ratio tables and using ratio tables to find equivalent rates and a unit rate.
  • Teacher Resources Part 1 Unit 1 Lesson 10 introduces double number lines as a way to model equivalent rates and further develop students' understanding of ratios and unit rate.
  • Teacher Resources Part 1 Unit 5 Lesson 13, 15, and 17 introduce percents of quantities as a rate per 100; discuss the relationship between fractions, decimals, and percents; and use base-10 blocks to model the relationship between decimals and percents. The content of these three lessons focuses on students' understanding of ratios and unit rate by illustrating the connections between ratios written in different forms.

Cluster 6.NS.C focuses on applying and extending previous understandings of numbers to the system of rational numbers.

  • Teacher Resources Part 2 Unit 4 has students develop their understanding of negative numbers through the use of number lines, drawings of protons (positive) and electrons (negative) as counters, and different contexts that promote an understanding of negative numbers, such as credits/debits and temperatures.

Standard 6.EE.3 has students applying the properties of operations to generate equivalent expressions.

  • Teacher Resources Part 2 Unit 6 Lesson 16 has students use area of rectangles to compare two expressions. The teacher draws rectangles and asks students to find the area of them. The teacher then adds more rectangles to the original, and students find the new area and write equivalent expressions in a table. Students then go on to use properties of operations- Commutative, Associative, and Distributive- to write equivalent expressions as well as use a GCF to multiply to factor the expression.

Indicator 2b

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

The materials for Jump Math Grade 6 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-30. The strategies are not incorporated into the lesson plans for the teacher.
  • There is a game in the teacher's edition pages A42-A43 that helps to build student fluency. This games focuses on addition and subtraction, but it is not mentioned in any of the lessons.

Standard 6.NS.2 expects fluency in dividing multi-digit numbers using the standard algorithm.

  • Teacher Resources Part 2 Unit 1 Lessons 57-62 offer students opportunities to develop fluency in dividing multi-digit numbers using the standard algorithm through practice dividing by single-digit positive integers, decimals, and multi-digit positive integers.
  • There are further opportunities for students to develop their fluency with dividing multi-digit numbers using the standard algorithm within the Assessment & Practice books on pages 29-40 for Part 2.

Standard 6.NS.3 expects students to fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

  • Teacher Resources Part 1 Unit 4 Lesson 33 offers students an opportunity to fluently add and subtract multi-digit decimals using the standard algorithm. The lesson involves decimals to the hundredths place, and it also gives students the opportunity to reinforce their understanding of adding and subtracting multi-digit decimals through the use of number lines and base-10 blocks.
  • Teacher Resources Part 1 Unit 4 Lesson 41 helps to develop fluency by having students multiply decimals to the thousandths place by whole numbers.
  • Teacher Resources Part 2 Unit 1 Lessons 48, 57, and 58 offer students opportunities to fluently multiply and divide multi-digit decimals using the standard algorithms. In addition to the standard algorithms, students' fluency is also developed through the use of number lines and the comparison of multiplying decimals to the process of multiplying fractions.
  • There are further opportunities for students to fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation within the Assessment & Practice books on pages 105-108 and 125 for Part 1 and pages 13-14 and 29-32 for Part 2.

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
0/2
+
-
Indicator Rating Details

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. There are ten Problem Solving Lessons designed to help students "isolate and focus on [problem solving] strategies."

6.RP.3 asks students to use ratio and rate reasoning to solve real-world and mathematical problems.

  • In Lessons 8 and 9 of Unit 1 in Teacher Resources Part 1, there are word problems that include real-life contexts, but the word problems follow teacher-led examples which the students can mimic when completing their word problems. By following the teacher-led examples, the word problems become routine, and the real-world context does not have any bearing on students chances of successfully completing the word problems.
  • In Lesson 19 of Unit 5 in Teacher Resources Part 1, students are asked to complete several word problems involving percents. In the exercises where different contexts are presented, the wording of the exercises is very similar to the teacher-led examples, so students still have a procedure for how to solve the problem in the new context.
  • In Unit 2 of Teacher Resources Part 2, Lessons 25-30 include many word problems. In these lessons, the problems are routine because students are presented with procedures or specific models to use to solve the problem through teacher-led examples. In the instances where the context could have bearing on the problem, the structure of the wording of the problem closely resembles the structure of the examples, so the context does not have bearing on solving the problem. For example, in Lesson 25, there is an exercise that states "There are 12 cats for every 10 dogs. If there are 15 dogs, how many cats are there?" This follows a teacher-led example that states "In a pet shop, there are 6 cats for every 8 dogs. There are 12 dogs in the shop. How many cats are there?"
  • The performance task In Problem Solving 6-5 engages students in a real-world task for "Making Punch;" however, the placement of this task after problem solving lessons on the use of a specific strategy removes application of math from the task.

Standard 6.EE.7 asks students to solve real-world and mathematical problems by writing and solving equations of the form x+p = q and px=q for cases in which p, q and x are all nonnegative rational numbers.

  • In Lessons 14, 15, and 18 of Unit 6 in Teacher Resources Part 1, students are asked to solve problems involving the area of geometric figures. Before solving these problems, students are reminded of the formulas they would use to find the area of different shapes, and there are teacher-led examples completed for them. In addition, students are given a specific way to organize information from the problems and shown how to use key words to substitute specific values into the formulas in order to solve the problems.
  • In Lesson 10 of Unit 3 in Teacher Resources Part 2, there is a set of four exercises where students are supposed to complete the four word problems on their own, but the directions before them tell teachers to "work through the first problem together, then have students work individually." The wording of the remaining three exercises matches the wording of other teacher-led examples found in the lesson.

Standard 6.EE.9 has students use variables to represent two quantities in a real-world problem that change in relationship to one another and write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable.

  • Lesson 19 of Unit 6 in Teacher Resources Part 2 is supposed to address 6.EE.9, but the exercises that are presented for students to complete do not involve any real-world contexts. The extension problem in the lesson includes money, but the use of money as a context does not have any bearing on students completing the extension problem.
  • In Lesson 20 of Unit 6 in Teacher Resources Part 2, students are presented with one set of exercises to complete, but the units for the independent variable are the same as in the teacher-led example, and although the units for the dependent variable are different from the teacher-led example, the scale and range (from 0 to 10 counting by 1s) on the graphs provided are the same.

Indicator 2d

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

The instructional materials 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 address 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 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
5/10
+
-
Criterion Rating Details

The instructional materials reviewed for Jump Math Grade 6 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

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

The instructional materials reviewed for Grade 6 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 Practices (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 noted in parentheses and with an arrow within the lesson at the part where they occur. As stated on page A-22 in 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

Materials carefully attend to the full meaning of each practice standard
0/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 6 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 2 Unit 1 Lesson 45, students are given exercises and asked to use multiplication to check the answer to each division problem. Also, Teacher Resource Part 2 Unit 1 Lesson 46 asks students to "use a calculator to check your answers to the questions on AP Book 6.2 p. 9." While students need to be mathematically accurate, they are not making sense of problems or persevering in solving them.
  • MP1: In Lesson 11 of Unit 2 in Teacher Resources Part 1, this MP is noted next to three problems where students are supposed to place improper fractions on a number line that is already subdivided into equal intervals. These three problems follow multiple teacher-led examples that have the same structure and format. The students do not have to make sense of the problem because the number lines are already subdivided, and they do not have to persevere because examples like their problems have already been completed in the lessons.
  • MP2: In Lesson 5 of Unit 6 in Teacher Resources Part 1, there are three problems where students plot points on a coordinate grid and determine either coordinates for missing vertices of a quadrilateral or what type of quadrilateral is defined by four coordinate pairs. In these problems, students do not have to reason quantitatively because there are no units involved in the problem, and they also know that the quadrilateral will be either a square or a rectangle.
  • MP4: In Lesson 32 of Unit 8 in Teacher Resources Part 2, the second extension problem is labeled with this MP, but the students are provided with diagrams that helps them visually model the problem. Also, since all of the problems in the lesson are about finding the volume of rectangular prisms, students would already know which calculations need to be made. Lastly, the statement of the problem limits the way in which some prisms can be arranged, so there is no reason for students to determine if other solutions might be better than the first one they obtain.
  • MP4: In Teacher Resources Part 2 Unit 2, Lesson 26 has a section titled “Word problems involving ratios.” In this section, the teacher leads students through solving a word problem using a ratio table as had been done in a previous problem. In this problem, as with many other problems where MP4 is noted, 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 2 Unit 8, Lesson 33 asks students to use a calculator to check their answers. In instances where MP5 is noted, students do not get to choose and use appropriate tools strategically.
  • MP7: In Teacher Resources Part 1 Unit 1 Lesson 7, students are learning how to create a ratio table. Students do not have look for or make use of structure as the rules used to create the ratio table are clearly shown (x2, x3). Because the teacher has given them the answer, students are not required to look closely to discern a pattern or structure.
  • MP8: In Teacher Resources Part 2 Unit 4 Lesson 67, students are asked how far apart given integers are. Students do not have an opportunity to look for repeated reasoning when understanding the distance between numbers on a number line.

Indicator 2g

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

Indicator 2g.i

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

The instructional materials reviewed for Grade 6 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 are identified as MP3 when the material is asking the students questions. 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, Teacher Resources Part 2 Unit 4 Lesson 69 asks students in the exercises "Which is closer to sea level: the bird or the fish?" This question leads to understanding of absolute value, but it does not address MP3 by having students construct their own arguments and/or critique the reasoning of others. Also, in Teacher Resources Part 2 Unit 8, Lesson 41 has students find the mistake made when simplifying a numerical expression that represents the surface area of a cube, but the students are notified there is a mistake before looking at the expression. This does not allow students to critique the reasoning of others because they already know there is a mistake.

Indicator 2g.ii

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

The materials reviewed for Grade 6 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 1 Lesson 10, teachers are instructed to draw a ratio table on the board, and then they are directed to "ASK: Is this a ratio table? (Yes) How do you know? How did I find the second row from the first? (multiplied both numbers by 2) Ask a volunteer to come and complete the third row in the ratio table." The teacher is not given any possible answers for the second question, and there is not any assistance for the teacher as to how students might discus the volunteer's solution once it is presented.
  • In Teacher Resources Part 1 Unit 6 Lesson 12, teachers are instructed to draw a triangle on the board during the third extension problem and ask the students how to draw the height in the triangle. The materials tell teachers that if the solution does not arise then they should tell the students the correct answers. There are no follow-up questions or prompts provided that could help students in constructing their own argument as to how the height could be drawn.
  • In Teacher Resources Part 2 Unit 1 Lesson 52, teachers are instructed to “ASK: How many 1/5s fit into 6?” and “How many 3/5s fit into 6? How do you know?” There are no additional questions or prompts for teachers to ask if students are not able to initially answer, and there is no assistance given for teachers to help students analyze each others' arguments.
  • Teacher Resources Part 2 Unit 4 Lesson 69: “Answer these questions. Did you compare the absolute values or the actual values of the integers?” The materials provide teachers with answers to the questions, but there is no assistance given to teachers for helping students construct their own arguments to support their answers or analyze the arguments of other students with which there might be disagreements in the answers.

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

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

The materials reviewed for Jump Math Grade 6 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: “Vocabulary words are listed at the beginning of each lesson plan. Make sure students are familiar with the vocabulary words.”
  • 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.

  • Often students are not required to provide explanations and justifications, especially in writing, which would allow them to attend to the specialized language of mathematics. For example, in Teacher Resources Part 2 Unit 7 Lesson 3, the teacher begins this lesson by introducing the term frequency with students. The students are not required to provide an explanation or justification for their answers that would allow them to use the word frequency in this lesson.
  • Many of the discussion prompts provided are guided by the teacher so that the student is merely repeating the teacher's language. This limits student ability to actively use mathematical language. For example, Teacher Resource Part 2 Unit 5 Lesson 27 starts with the teacher introducing new vocabulary (line of symmetry, reflect, image) to help students understand where the lesson is heading.

Gateway Three

Usability

Not Rated

Criterion 3a - 3e

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

Indicator 3a

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

Indicator 3b

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

Indicator 3c

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

Indicator 3d

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

Indicator 3e

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

Criterion 3f - 3l

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

Indicator 3f

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

Indicator 3g

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

Indicator 3h

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

Indicator 3i

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

Indicator 3j

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

Indicator 3k

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

Indicator 3l

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

Criterion 3m - 3q

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

Indicator 3m

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

Indicator 3n

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

Indicator 3o

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

Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

Indicator 3p.i

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

Indicator 3p.ii

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

Indicator 3q

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

Criterion 3r - 3y

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

Indicator 3r

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

Indicator 3s

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

Indicator 3t

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

Indicator 3u

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

Indicator 3v

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

Indicator 3w

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

Indicator 3x

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

Indicator 3y

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

Criterion 3aa - 3z

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

Indicator 3aa

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

Indicator 3ab

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

Indicator 3ac

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

Indicator 3ad

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
0/0

Indicator 3z

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

Additional Publication Details

Report Published Date: Wed Oct 18 00:00:00 UTC 2017

Report Edition: 2013

Title ISBN Edition Publisher Year
JUMP Math 6.1 Assessment & Practice 978-1-927457-06-1 JUMP Math 2013
JUMP Math 6.2 Assessment & Practice 978-1-927457-07-8 JUMP Math 2013
JUMP Math 6 Teacher Resources 978-1-927457-30-6 JUMP Math 2014

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Math K-8 Rubric and Evidence Guides

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

For math, our rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

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

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