Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 5 partially meet the expectations for alignment to the CCSSM. The materials meet the expectations for focus and coherence in Gateway 1, and they partially meet the expectations for rigor and the mathematical practices in Gateway 2. Since the materials partially meet the expectations for alignment, evidence concerning instructional supports and usability indicators in Gateway 3 was not collected.

See Rating Scale
Understanding Gateways

Alignment

|

Partially Meets Expectations

Gateway 1:

Focus & Coherence

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

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
11
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 5 meet the expectations for Gateway 1. Although there are some questions that align to and/or assess standards that are beyond Grade 5, the inclusion of these questions is either mathematically appropriate or, where not appropriate, their omission would not significantly alter the structure of the materials, and these materials 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. Although materials do not relate grade-level concepts explicitly to prior knowledge from earlier grades, the materials develop according to the grade-by-grade progressions in the Standards. Students are given extensive work on grade-level problems, and 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 5 JUMP Math meet the expectations for not assessing topics before the grade level in which the topic should be introduced. Although there are some questions that align to and/or assess standards that are beyond Grade 5, the inclusion of these questions is either mathematically appropriate or, where not appropriate, their omission would not significantly alter the structure of the materials.

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 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 K and Teacher Resources Part 2 Section U, along with the answer keys and "Scoring Guides and Rubrics," were reviewed for this indicator.

The assessments are mostly aligned to the standards of the grade-level, and assessment questions that are above grade-level/non-aligned can easily be modified or omitted without making a significant impact on the integrity of the materials.

Assessments containing off grade-level material include the following:

  • On the Teacher Resources Part 1 Unit 4 Quiz for Lessons 31 to 37, problems 3a, 3b, 3c and 4 imply the use of the standard algorithm for division by including a grid. The grid includes subtraction symbols next to space for the procedural steps.
  • On the Teacher Resources Part 1 Unit 4 Test for Lessons 27-37, problem 5 as well as problems 8 and 9 imply the use of standard algorithm for division by including a grid. The grid includes subtraction symbols next to space for the procedural steps.
  • On the Teacher Resources Part 2 Unit 1 Quiz for Lessons 2 to 5, problems 3 and 4 require students to evaluate translations which is a grade 8 standard.

Some assessments contain bonus questions. The rubric indicates that these questions should be marked correct or incorrect and not be assigned a point value. The bonus questions include items that might assess standards that are above grade-level, and in addition, the standard is not identified on the rubric.

  • On the Teacher Resources Part 1 Unit 4 Quiz for Lessons 31 to 37, the bonus problem implies the use of the standard algorithm for division by including a grid. The grid includes subtraction symbols next to space for the procedural steps.

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 5 meet the expectations for students and teachers using the materials as designed devoting the large majority of class time to the major work of the grade. Overall, the materials devote approximately 82 percent of class time to the major work of Grade 5.

Indicator 1b

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

The instructional materials reviewed for Grade 5 meet the expectations for spending the majority of class time on the major clusters of each grade. Overall, approximately 82 percent of class time is devoted to major work of the grade.

The materials for Grade 5 include 14 Units. In the materials, there are 170 lessons, and of those, 32 are Bridging lessons. According to the materials, Bridging lessons should not be “counted as part of the work of the year” (page A-59), so the number of lessons examined for this indicator is 138 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 79 percent, 11 out of 14;
  • Lessons– Approximately 82 percent, 113 out of 138; and
  • Days– Approximately 82 percent, 124 out of 152.

The number of instructional days, approximately 82 percent, devoted to major work is the most reflective for this indicator because it represents the total amount of class time that addresses major work.

Criterion 1c - 1f

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

The instructional materials reviewed for Grade 4 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 138 days of lessons and assessment. Students are given extensive work on grade-level problems. Materials develop according to the grade-by-grade progressions in the Standards, but materials do not relate grade-level concepts explicitly to prior knowledge from earlier grades. 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 4 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 5 meet the expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. When appropriate, the supporting work enhances and supports the major work of the grade.

Examples where connections are present include the following:

  • 5.MD.1 supports the major work of 5.NBT.B.
    • Teacher Resources Part 1 Unit 7 Lessons 1 to 9, Teacher Resources Part 2 Unit 5 Lessons 11-16, and Teacher Resources Part 2 Unit 6 Lessons 33-38 use measurement in the metric system to support the work of multiplying by multiples of 10 through many opportunities to convert within this system.
  • 5.MD.2 supports the major work of 5.NF.
    • Teacher Resources Part 1 Unit 5 Lessons 10, 17, and 18 have students measure and draw line plots supporting the work of the Number and Operations- Fractions domain.

Indicator 1d

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

The instructional materials reviewed for Grade 5 meet the expectations for 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 138 days which is appropriate for a school year of approximately 140-190 days.

  • The materials are written with 14 units containing a total of 170 lessons.
  • Each lesson is designed to be implemented during the course of one 45 minute class period per day. In the materials, there are 170 lessons, and of those, 32 are Bridging lessons. Thirty-two 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 138 lessons.
  • There are 14 unit tests which are counted as 14 extra days of instruction.
  • There is a short quiz every 3-5 lessons. Materials expect these quizzes to take no more than 10 minutes, so they are not counted as extra days of instruction.

Indicator 1e

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

The instructional materials reviewed for Grade 5 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. Content from future grades is not always clearly identified but often related to grade-level work. The Teacher Resources contain sections that highlight the development of the grade-by-grade progressions in the materials, occasionally identify content from future grades, and state the relationship to grade-level work.

  • At the beginning of each unit, "This Unit in Context" provides a description of connections to concepts that have been taught earlier in the year and that will occur in future grade-levels. For example, "This Unit in Context" from Unit 3, Number and Operations in Base Ten: Multiplication, of Teacher Resource Part 1 describes how "in Grade 3 students were introduced to multiplication as repeated addition and they interpreted the product of two numbers as the total number of objects when given a number of equal groups and the number in each group (3.OA.1)." Connection to future content is also stated such as "In this unit, students will identify relationships between corresponding terms in sequences made with multiplication (5.OA.3). Identifying relationships between corresponding terms in two sequences is an essential prerequisite for when students write formulas to represent the rule of functions in Grade 8 (8.F.1)"

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

  • Whole class instruction is used in the lessons, and all students are expected to do the same work throughout the lesson. Individual, small-group, or whole-class instruction occurs in the lessons.
  • The problems in the Assessment & Practice books align to the content of the lessons, and they provide on grade-level problems that "were designed to help students develop confidence, fluency, and practice." (page A-56, Teacher Resources Part 1)
  • In the Extensions sections of the Lessons, students get the opportunity to engage with more difficult problems, but the problems are still aligned to grade-level standards. For example, the problems in Teacher Resource Part 2 Unit 6 Lesson 24 engage students in finding area of the rectangle, but these problems still align to 5.NF.4b.

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

  • Every lesson identifies "Prior Knowledge Required" even though the prior knowledge identified is not aligned to any grade-level standards. For example, Teacher Resource Part 2 Unit 5 Lesson 19 identifies that a student "(k)nows how to tell time using a 12-hour clock format,” “(k)nows that 1 h = 60 min,” “(c)an convert time from hours to minutes,” and “(i)s familiar with a.m./p.m. notation.”
  • There are 32 lessons identified as Bridging Lessons, and most of these lessons are not aligned to standards from prior grades but state for which grade-level standards they are preparation. Teacher Resource Part 2 Unit 7 Lesson 6, which has students identifying and drawing line segments, lines, rays, and angles, is preparation for 5.G.3 and 5.G.4.

Indicator 1f

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

The instructional materials reviewed for Grade 5 meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards. Overall, the materials include learning objectives that are visibly shaped by CCSSM cluster headings.

Overall, units are organized by domains and are clearly labeled. For example, Teacher Resource Part 1 Unit 1 Operations and Algebraic Thinking: Patterns and Teacher Resources Part 1 Unit 5 Number and Operations-Fractions: Fractions are shaped by the Operations and Algebraic Thinking and Number and Operations-Fractions domains. Throughout the course, all standards are addressed, and within lessons, goals are written that are shaped by the CCSSM cluster headings.

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

  • In Teacher Resource Part 1 Unit 3 Lesson 17, students write a power as a product and a product as a power. This lesson connects 5.NBT.A and 5.NBT.B.
  • In Teacher Resource Part 1 Unit 5 Lesson 19, students compare fractions, review equivalent fractions, and solve word problems connecting 5.NF.A and 5.NF.B.
  • In Teacher Resource Part 2 Unit 4 Lesson 55, students multiply fractions and then their corresponding decimals. This lesson connects 5.NBT.A and 5.NBT.B.

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

  • In Teacher Resource Part 2 Unit 5 Lesson 15, students convert between pounds and ounces connecting 5.MD and 5.NF.
  • In Teacher Resource Part 2 Unit 6 Lesson 25, students solve problems connected to the area of rectangles connecting 5.NF and 5.NBT.
  • In Problem Solving Lesson 2, students write and interpret expressions involving quotients connecting 5.OA and 5.NBT.

Gateway Two

Rigor & Mathematical Practices

Partially Meets Expectations

+
-
Gateway Two Details

The instructional materials reviewed for Grade 5 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.
6/8
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 5 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 5 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

Clusters 5.NF.A and 5.NF.B focus on using equivalent fractions as a strategy to add and subtract fractions and applying and extending previous understanding of multiplication and division to multiply and divide fractions.

  • Teacher Resources Part 1 Unit 5 has students use shapes, Geoboards, bar diagrams, tables, grids, fraction strips, number lines, and Pattern Blocks to develop fraction understanding and use that understanding to find a fraction of a whole number. In Lesson 13 students use fraction strips to show subtraction of fractions with unlike denominators, and in Lesson 15 students use number lines to find least common denominators. (5.NF.1 and 5.NF.2).
  • Teacher Resources Part 2 Unit 2 has students use shapes, rulers, area models, fraction parts and wholes, and number lines to develop and apply the formula for multiplying and dividing fractions. In Lesson 22 students use area models find half of a given fraction (5.NF.4).
  • Teacher Resources Part 2 Unit 2 Lesson 28 has students use the given Blackline Masters of fraction parts and wholes to divide whole numbers by unit fractions (5.NF.7).

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 Grade 5 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.

  • In the Teacher Resources Part 1 pages A-35 through A-46 give strategies for mental math and pages A-52 through A-54 demonstrate “How to Learn Your Times Tables in a Week.” The strategies are not incorporated into the lesson plans for the teacher.
  • A game that helps to build student fluency is provided in the Teacher Resources Part 1 on pages A-47 and 48. This game focuses on knowing the pairs of one-digit numbers that add up to particular target numbers so that students will be able to mentally break sums into easier sums, but this game is not mentioned in the lessons.

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

  • Much of the work in Grade 5 is directly related to the clusters that address procedural skill and fluency and the strategies that develop the procedural skill and fluency such as examples and repetition in the class lesson, reinforcement in the Assessment and Practice book specific to the class lesson, and providing guided scaffolding. Teacher Resources Part 1 Units 2, 3, 4, and 6 focus on Numbers and Operations in Base Ten and Teacher Resources Part 2 Unit 4 also focuses on Numbers and Operations in Base Ten.
  • Teacher Resources Part 1 Unit 3 Lesson 19 has students developing fluency by multiplying 2-digit numbers by 1-digit numbers using the standard algorithm, area models, grids, and finding missing numbers in problems that are partially worked out. Students prepare for 5.NBT.5 in Lessons 13, 14, 15, 16, and 17 and then continue towards fluency by multiplying with more than 2-digit by 1-digit in the remaining lessons of the unit and following units.

Indicator 2c

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade
1/2
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-
Indicator Rating Details

The instructional materials for Grade 5 partially 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, although word problems are included in the instructional materials, the problems are often routine. Many problems are single-step, and problems that are multi-step are often scaffolded. However, there are ten Problem Solving Lessons designed to help students "isolate and focus on [problem solving] strategies."

In Grade 5 there are several standards that call for application. Standard 5.NF.2 requires students solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators. Standard 5.NF.6 requires that students solve word problems involving multiplication of fractions and mixed numbers. Standard 5.NF.7c requires students solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, and Standard 5.MD.5b requires that students apply the formulas V=l x w x h and V= b x h for rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. Standard 5.MD.5c requires students to recognize volume as additive and find volumes of solid figures composed of two non-overlapping parts, applying this technique to solve real world problems. The instructional materials include some problems that allow students to engage in applications of the mathematics.

  • Assessment and Practice Part 1 Unit 5 Lesson 8 aligns to 5.NF.2: “Kim needs 2 1/3 cups of flour to make bread and 3 cups of flour to make dumplings. How much flour does she need altogether?”
  • Assessment and Practice Part 1 Unit 5 Lesson 18 Problems 8 and 9 have students multiply a fraction by a whole number. Question 8 states “To make 1 pie, a recipe calls for ¼ of a cup of blueberries. How many cups of blueberries are needed for 8 pies?” Question 9 states “Farah’s exercise routine takes ⅓ of an hour. She exercises 6 days a week. How many hours a week does she exercise?” (5.NF.6).
  • In Teacher Resources Part 2 Unit 2, Lessons 29 and 30 have the teacher showing students a ⅓ cup measure, a 1 cup measure and enough counters to fill up the 1 cup measure. The teacher tells students that the small measure is labeled as ⅓ cup and the big measure as 1 cup. The teacher asks the following: “'How many small cupfuls should fill up the big cup?' (3) Ask a volunteer to check that this is the case. Tell students that a recipe calls for cups of flour but you only have the ⅓ cup measure. Teacher asks: 'How many cupfuls do you need?' (6) Have a volunteer write the division question (2 ⅓ = 6)." The sequencing of questions in this problem scaffolds the problem. (5.NF.6)
  • In the Teacher Resources Part 2 Unit 2 Lesson 33 Cumulative Review the teacher tells students that some problems that involve division will have a mixed number answer but that the answer needs to be a whole number. The teacher writes on board "Nomi can carry 16 lbs. How many books weighing 1 ½ pounds each can she carry?" There are exercises a-d that are similar for students to practice. (5.NF.7c)
  • Assessment and Practice Part 2 Unit 6 Lesson 27 Problem 7 asks students to estimate the answer and then use a calculator to find the actual value. Problem 7a states “The tower of the Aon center in Chicago, IL is a rectangular prism that is 194 ft. wide, 194 ft. long, and 1,123 ft. tall. What is the volume of the tower?” Problem 7b states “The Cheung Kong Center Tower in Hong Kong, China is a rectangular prism 154 ft. wide, 154 ft. long, and 928 ft. tall. What is the volume of the tower?” Problem 7c asks “Which tower has the greatest volume, the Aon Center of the Cheung Kong Center Tower? What is the difference between them?” (5.MD.5b)
  • Assessment and Practice Part 2 Unit 6 Lesson 32 Problem 5 states “A skyscraper has three rectangular towers. a) What is the area of the ground floor of the skyscraper? b) What is the area of the top floor of the skyscraper? c) What is the total volume of the skyscraper?” Note – this problem is accompanied by two diagrams. Diagram 1 includes the measures for the ground floor of the skyscraper. Diagram 2 includes the height for each tower. (5.MD.5c)

Word problems can be found in many lessons throughout the instructional materials; however, they are mostly routine, similar to problems previously encountered by students, and/or encourage the use of strategies modeled in the Teacher Resource. As a result, the instructional materials do not present sufficient opportunity for students to engage in non-routine application problems.

  • Assessment and Practice Part 2 Unit 2 Lesson 21 Question 7 states: "Mike is making ½ of a recipe for raisin bread. The recipe calls for ⅓ of a cup of raisins. What fraction of a cup of raisins does Mike need?"
  • Assessment and Practice Part 2 Unit 2 Lesson 23 Question 4 has students multiplying mixed numbers and mixed numbers by a fraction. Question 4 states: "Luis is making ⅗ of a recipe for mushroom soup. The recipe calls for 3 ½ cups of milk. a) How much milk does he need? Hint: Change 3 ½ to an improper fraction. b) Luis uses 2 cups of milk. Will his recipe work?" The hint scaffolds this problem for students.
  • Assessment and Practice Part 2 Unit 2 Lesson 28 Question 8 has students dividing a fraction by a whole number. Question 8 states "Ethan has a scoop that measures a ½ cup. He needs 3 cups of flour. How many spoonfuls of flour does he need?"
  • Teacher Resources Part 2 Unit 2 Lesson 29 and 30: "Rosa has two apples. She cuts them each into fourths. How many pieces does she have?"
  • Teacher Resources Part 2 Unit 2 Lesson 29 and 30: "Julie baked five muffins that weigh 1 ¾ pounds total. How much does each muffin weigh?"
  • Assessment and Practice Part 2 Unit 3 Lesson 13 focuses on Multiplication and Word problems. Students are presented with multiple problems that ask them to identify the larger and smaller quantities in the problem prior to solving the problems. Problem 6, the only word problem, states “Write the equation and replace the correct letter with the given number. If the unknown is not by itself, write the equation that means the same thing. Solve the equation to solve the problem.” Problem 6c states “A snake is 5 times as long as a lizard. The snake is 125 cm long. How long is the lizard?” This is a routine problem using the same strategies used in problems throughout the lesson.

Problem Solving Lessons include word problems that are heavily scaffolded and focused on the use of a particular problem-solving strategy. In Grade 5, none of the Problem Solving Lessons align to application standards.

Indicator 2d

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

The instructional materials for Grade 5 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 deep 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 5 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
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-
Indicator Rating Details

The instructional materials reviewed for Grade 5 meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.

In Teacher Resources Part 1, a description of each MP is given on pages A-22 to A-26. According to a statement in the materials, “opportunities to develop or assess the mathematical practice standards can occur in classroom discussions, exercises, activities, or extensions.” 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-22 in Teacher Resources Part 1, "While these opportunities occur in virtually every lesson, only some opportunities have been 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
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-
Indicator Rating Details

The instructional materials reviewed for Grade 5 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 only identify examples of the Standards for Mathematical Practice, 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: Sometimes the extent of scaffolding takes away the student's opportunity to reason and persevere. For example, in Teacher Resources Part 2 Unit 6 Lesson 52 in the Exercises, students are multiplying and dividing by powers of 10. The exercises are procedural in nature (example: 0.082 x 10), and the purpose of the exercises is for students to use “strategies for remembering which way to move the decimal point.” The students are not persevering because the teacher is instructed to prompt students to “Remember: Multiplying by 10, 100 or 1,000 makes the number bigger, so the decimal point moves right.” In Teacher Resources Part 2 Unit 5 Lesson 11, Using division to convert measurements in inches to feet, Exercises a-d are marked as MP1. The exercises have students rewrite basic division problems such as 28 divided by 12 as fractions in lowest terms and then solve. The teacher is asked to point out that there is another way to solve the problem by converting the 28 inches to feet by dividing by 12 to get 2 R4. The answer would be 2 4/12. Then reduce the fractional part of the mixed number, so 28 ft = 2 ⅓ ft. Students are then to go back and use this alternative way to check their answers to the exercise questions. Though the student is checking their answers to problems using a different method given to them by their teacher, they are not continually asking themselves, “Does this make sense?” nor making their own connections as to why this alternate way works.
  • MP5: In Teacher Resources Part 2 Unit 5 Lesson 10, Extension 1 is marked as MP5. In this extension students are identifying marks for halves, quarters, and eighths on a number line with sixteenths marked. The teacher is told to point out that students’ rulers have more than eight marks between the whole inch marks. The teacher asks, “How many parts is each inch divided into on your rulers?" Student should answer 16, and then the teacher is supposed to remind students that taking half of a fraction means dividing each part of the fraction into two parts so that the number of parts is doubled. There are no opportunities for students to select tools.
  • MP6: In Teacher Resources Part 1 Unit 2 Lesson 1, a portion of the lesson is marked as MP6. The teacher writes 28,306 on the board and tells students, “The number 28,306 is a 5-digit number. What is the place value of the digit 2?" The teacher answers, “The 2 is in the ten thousands place, so it stands for 20,000. What does the digit 8 stand for?” If students answer with 8,000 they are answering a specific question that was given them by their teacher, not meeting the full meaning of the standard by using precise language in communicating with others,.
  • 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 4 Lesson 54, students are multiplying decimals by whole numbers (example: 3.64 x 2). Students do not construct knowledge about decimal point placement in the product. Instead, they are told, “When you multiply a decimal number by a whole number, place the decimal point in the answer underneath the decimal point in the decimal number.” This may lead to misconceptions when students multiply decimals by decimals because they do not understand the structure. In Teacher Resources Part 1 Unit 2 Lesson 3, a portion of the lesson is marked as MP7. The teacher is writing the numbers 435 and 425 in expanded form on the board and asks students, “Which number is greater? How can you easily tell from the expanded form that it is greater?” Student should answer that 30 is more than 20 while everything else stays the same. Teacher then circles the 30 and the 20 to emphasize this. Though the student is supposed to tell the teacher why the greater number is easy to see when written in expanded form and there are four exercises that the teacher does with the students, the teacher is doing most of the work, and the students aren’t closely discerning a pattern or structure on their own.

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
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-
Indicator Rating Details

The instructional materials reviewed for Grade 5 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 Part 1 and 2, examples identified as MP3 are almost always in a whole group discussion, though there are occasional suggestions for students to work in 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 the Teacher Resources Part 2 Unit 5 Lesson 14, the teacher draws a rectangle and labels two sides as 5 inches and 2 feet. The teacher tells the students that she thinks the perimeter of this rectangle is 14 inches. "Is that correct? (no) Have students explain the mistake. (you cannot add feet to inches; you first need to convert the measurements to the same unit) Have students convert both measurements to inches and find the perimeter. (2 ft = 24 in, so (5 in + 24 in) x 2 = perimeter 58 in) Then have students find the perimeter of a rectangle that measures 5 ¾ in by 1 ¼ ft. (1 ¼ ft = 15 in, so the perimeter is 41 ½ in)." This portion of the lesson is labeled with MP3. Although students have to figure out if the answer is correct or not, they aren’t really reaching the full depth of MP3. The teacher talks the students through figuring out the actual perimeter, and the only time that students are constructing an argument themselves is when they are asked to explain the teacher’s mistake. Another example is in Teacher Resources Part 2 Unit 6 Lesson 38. The teacher asks “How many fluid ounces are in 1 gallon? (128) Which fraction of a gallon is 1 cubic inch? (1/231) Which fraction of a gallon is 1 fluid ounce? (1/128) What is larger, 1 cubic inch or 1 fluid ounce? (1 fl oz) How do you know? (231>128, so 1/128>1/231, so 1 fl oz > 1 cubic inch).” These questions lead to understanding but do not address MP3 by having students construct their own arguments and/or critiquing the reasoning of others.

In the Assessment and Practice Books, students are sometimes prompted to construct an argument. For example, in Assessment and Practice Book Part 1 page 105 question 8 asks: “A turtle weighs 4/9 kg and a lizard weighs 5/11 kg. Which animal is heavier? Explain how you know.” Another example is Assessment and Practice Book Part 1 page 18 question 8: “Mona wants to build a model of the number six thousand, five hundred ninety. She has 5 thousands blocks, and 30 tens blocks. Can she build the model? Use diagrams and numbers to support your answer.” Although students are prompted to provide written arguments, often using the word “explain,” students are not provided with formal opportunities to share these written arguments with classmates.

In the Assessment and Practice Books, students are rarely provided opportunities to analyze the arguments of others. When items are included that ask for students to critique the reasoning of others, they are told up front that the student is incorrect. For example, in Assessment and Practice Book 1 page 4 question 9 states “Look at the sequence: 5, 9, 13, 17, 21, … Jake says the rule is : ‘Start at 5 and subtract 4 each time.’ Anika says the rule is: ‘Start at 5 and add 5 each time.’ Ethan says the rule is: ‘Start at 5 and add 4 each time.’ a) Whose rule is correct? b) What mistakes did the others make?”.

Indicator 2g.ii

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

The materials reviewed for Grade 5 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 redirect students who didn’t understand. Few problems or activities are labeled as MP3.

  • Teacher Resources Part 1 Unit 1 Lesson 4 : “Draw the table on the board. Tell students you have a riddle for them: you extended the first sequence for many terms, and you want the students to figure out what the term is in a certain row but in the second sequence. Ask students to explain how they find the answer. (Students need to figure out the rule to get from one sequence to the other, and then to use the rule to determine the number.)” The prompts do not assist teachers in engaging students in both constructing viable arguments and analyzing the arguments of others to deeply engage in MP3.
  • Teacher Resources Part 1 Unit 5 Lesson 8: In the extension section question 2 the directions state, "Is there a fraction equivalent to ⅜ with an odd denominator? Explain. Answer: No. The denominator is a multiple of 8, so it is even.” There are no directions for the teacher in how to help students engage in constructing viable arguments or analyzing the arguments of others, nor does this help to redirect students who do not understand.
  • Teacher Resources Part 2 Unit 7 Lesson 10: In the Acctivity section, students are working with empty regions of Venn diagrams. The directions state: “Have students think for some time to arrive at the conclusion that a shape like that does not exist. Ask them to explain why there cannot be a shape that is both a polygon and a circle. (a polygon has only straight sides, a circle has only one curved side; a polygon has vertices, a circle has no vertices; etc.)” There is no information or directions for the teacher to foster students ability to construct arguments and analyze the arguments of others which does not encourage students to deeply engage in MP3.

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
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Indicator Rating Details

The materials reviewed for Grade 5 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 “vocabulary words are listed at the beginning of each lesson plan. Make sure students are familiar with the vocabulary words. Make some of the words, such as geometrical terms, part of your spelling lessons.”
  • 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 1 Lesson 1 vocabulary includes the terms array, column, coordinates, ordered pair, and row. Each time, however, that these words are used in the lesson, they are used by the teacher. The student is not required to provide an explanation or justification for their answers that would allow them to use the words in this lesson. After the students do an activity in the lesson it states: "Explain that mathematicians around the world have agreed to give the location of a point by two numbers in parentheses. The column number is always on the left and the row number is always on the right: (column, row). SAY: This means that the numbers in the pair have a specific order, so we call them an ordered pair. Give students several ordered pairs and ask them to identify the corresponding points in an array of dots. Explain that the ordered pair of numbers can also be called the coordinates of the point."
  • 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.

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 Assessment & Practice Grade 5 (U.S. Common Core Edition) 978-1-927457-14-6 JUMP Math 2014
Jump Math Teacher Resources Grade 5 (U.S. Common Core Edition) 978-1-927457-31-3 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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