Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 4 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

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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

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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 4 meet the expectations for Gateway 1. Although there are some questions that align to and/or assess standards that are beyond Grade 4, 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 4 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 4, 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 for Grade 4 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 W, 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 2 Unit 4 Quiz for Lessons 6 to 11, problems 2b, 2c, 3a, and 3b have fractions that have denominators exceeding the expectations of grade 4. Grade 4 is limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

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.

  • The Teacher Resources Part 1 Unit 4 Quiz for Lessons 32 to 36 emphasizes standard 4.NBT.5; however, the Bonus problem requires the multiplication of a seven digit number by a one-digit whole number.
  • The Teacher Resources Part 2 Unit 2 Quiz for Lessons 40 to 43 includes a bonus question that requires dividing a nine digit number by a one-digit whole number. Standard 4.NBT.6 addresses division with up to four-digit dividends and one-digit divisors.
  • The Teacher Resources Part 2 Unit 4 Quiz for Lessons 1 to 5 includes a bonus question that compares fractions with 1,000 and 10,000 as a denominator.

Some assessments contain advanced questions. The advanced questions are assigned points but are not included in the total score for the assessment. These questions might assess standards that are above grade-level, and in addition, the standard is not identified on the rubric.

  • On the Teacher Resources Part 2 Unit 4 Quiz for Lessons 6 to 11, problems 6 and 7 ask students to write "more" or "less" when comparing fractions that have denominators exceeding the expectations of grade 4. Grade 4 is limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Criterion 1b

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

The instructional materials reviewed for Grade 4 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 74 percent of class time to the major work of Grade 3.

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 4 meet the expectations for spending the majority of class time on the major clusters of each grade. Overall, approximately 74 percent of class time is devoted to major work of the grade.

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

Three perspectives were considered: 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 16;
  • Lessons– Approximately 75 percent, 112 out of 150; and
  • Days– Approximately 74 percent, 122.5 out of 166.

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

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
7/8
+
-
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 166 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 4 meet the expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. When appropriate, the supporting work enhances and supports the major work of the grade.

Examples where connections are present include the following:

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

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 166 days which is appropriate for a school year of approximately 140-190 days.

  • The materials are written with 16 units containing a total of 186 lessons.
  • Each lesson is designed to be implemented during the course of one 45 minute class period per day. In the materials, there are 186 lessons, and of those, 36 are Bridging lessons. Thirty-six 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 150 lessons.
  • There are 16 unit tests which are counted as 16 extra days of instruction.
  • There is a short quiz every 3-5 lessons. Materials expect these quizzes to take no more than 10 minutes, so they are not counted as extra days of instruction.

Indicator 1e

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

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

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

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

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

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

Indicator 1f

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

The instructional materials reviewed for Grade 4 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, in Teacher Resources Part 1 Unit 1 Operations and Algebraic Thinking: Patterns, Teacher Resources Part 1 Unit 3 Operations and Algebraic Thinking: Rounding, and Teacher Resources Part 1 Unit 5 Operations and Algebraic Thinking: Division are shaped by the Operations and Algebraic Thinking domain. Throughout the course, all standards are addressed, and within lessons, goals are written that are shaped by the CCSSM cluster headings. For example, in Teacher Resources Part 2 Unit 3, Lesson 35 connects all three of the standards in the 4.OA.A cluster in "Equations with Multiplication and Division."

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

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

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

  • Teacher Resources Part 2 Unit 2 Lessons 45 and 46 connect 4.NBT and 4.MD. In these lessons students divide 3-digit and 4-digit numbers by 1-digit numbers, including with a remainder.
  • In Teacher Resources Part 2 Unit 5 Lesson 33 4.NBT and 4.MD are connected. In this lesson students change measurements in pounds to ounces and solve problems involving mass in pounds and ounces.
  • Teacher Resources Part 2 Unit 6 Lesson 41 connects 4.OA and 4.NBT. In this lesson students find factors of numbers up to 100 and determine whether a given 1-digit number is a factor of a given whole number in the range 1-100.
  • Problem Solving Lesson 9 connects 4.NBT, 4.NF, and 4.MD. In this lesson students find the perimeter by converting fractional feet lengths to inches and adding the sides.

Gateway Two

Rigor & Mathematical Practices

Partially Meets Expectations

+
-
Gateway Two Details

The instructional materials reviewed for Grade 4 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 4 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 4 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

In Teacher Resources Part 2 Unit 4 Lessons 1-9 develop the conceptual understanding of 4.NF.A, extending understanding of fraction equivalence and ordering. Lessons 1-5 are used “in preparation for” 4.NF.A and address standards from 3.NF. Lessons 6-9 are on grade-level for 4th grade.

  • Visual fraction models are used to begin to develop conceptual understanding. Fraction circles and rectangles partitioned into equal parts are two visual models included in the instructional materials.
  • In Teacher Resources Part 2 Lesson 1, students are introduced to the BLM Fraction Memory activity. In this game cards match if the same fraction is shown. Students match different representations of the fractions, including visual fraction models.
  • In Teacher Resources Part 2 Lesson 6, students are introduced to finding equivalent fractions using multiplication, but the lesson includes visual fraction models to support student understanding of equivalent fractions. Students practice breaking all parts into two equal parts to create equivalent fractions and breaking all parts into the same number of equal parts to create equivalent fractions using fraction models. The materials “(h)ave students signal (by holding up the correct number of fingers) how many times as many parts the first picture has as the second picture.”

Clusters 4.NBT.A and 4.NBT.B focus on generalizing place value understanding for multi-digit whole numbers and using place value understanding and properties of operations to perform multi-digit arithmetic.

  • In Teacher Resources Part 1 Unit 2 Lesson 1, students are introduced to the place value chart as they work to identify the place value of digits in two, three, and four-digit numbers. (4.NBT.2)
  • In Teacher Resources Part 1 Unit 2 Lesson 4, students represent numbers with base ten blocks to build understanding of place value for multi-digit numbers. (2.NBT.2)
  • In Teacher Resources Part 1 Unit 2 Lesson 14, students use base ten blocks to regroup numbers as sums of ones, tens, hundreds, and thousands. In Lessons 15 and 16 students continue to use place value understanding to begin to add multi-digit whole numbers.
  • Teacher Resources Part 1 Unit 3 Lessons 13-16 develop conceptual understanding of 4.NBT.3, rounding multidigit numbers to any place value. Lesson 13 is mostly focused on the 3rd grade standard of rounding. Lessons 14-16 cover the 4th grade standards. Number lines and rounding grids are used to develop conceptual understanding.

Indicator 2b

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

The materials for Grade 4 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 and A-52 through A-54 give strategies for mental math. The strategies are not incorporated into the lesson plans for the teacher.
  • There is a game in the Teacher Resources Part 1 page A47-A48 that helps to build student fluency. This game focuses on knowing the pairs of one-digit numbers that add up to particular target numbers, but this game is not mentioned in the lessons.

Standard 4.NBT.4 requires students to fluently add and subtract multi-digit whole numbers using the standard algorithm.

  • Much of the work in Grade 4 is around adding and subtracting.
  • In Teacher Resources Part 1 Unit 1 Lesson 1, students practice finding the differences between numbers mentally and find a number that is more than another number by a given difference in order to prepare for 4.NBT.4.
  • In Teacher Resources Part 1 Unit 2 Lessons 10 thru 13, students work with coins to prepare for 4.NBT.4.
  • In Teacher Resources Part 1 Unit 2 Lessons 14 thru 21, students solve addition and subtraction problems, and in Lessons 25 thru 27 students reinforce the concepts.

Standard 4.NBT.5 requires students to multiply a whole number of up to four digits by a one-digit whole number and to multiply two two-digit numbers.

  • In Teacher Resources Part 1 Unit 4 Lesson 28, students find products by adding on to smaller products to prepare for 4.NBT.5.
  • In Teacher Resources Part 1 Unit 4 Lesson 31, students use doubles and doubling to multiply mentally to help prepare for 4.NBT.5.
  • In Teacher Resources Part 1 Unit 4 Lesson 30, students use arrays to understand the distributive property and multiply large numbers by breaking them into smaller numbers.
  • In Teacher Resources Part 1 Unit 4 Lessons 32 thru 39, students multiply various methods including the standard algorithm.

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 4 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 4 there are several standards that call for application. Standard 4.OA.3 requires students to solve word problems posed with whole numbers and having whole number answers using the four operations, including problems in which remainders must be interpreted. Standard 4.MD.3 requires students to apply the area and perimeter formulas for rectangles in real world and mathematical problems. Standard 4.MD.7 requires that students solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems. Standard 4.NF.3d requires that students solve word problems involving addition and subtraction of fraction referring to the same whole and having like denominators, and Standard 4.NF.4c requires students solve word problems involving multiplication of fraction by a whole number. The instructional materials include some problems that allow students to engage in applications of the mathematics.

  • Assessment and Practice Part 1 Unit 2 Lesson 23 Problem 3 consists of three multi-step word problems. Problem 2a states: “There are 7 dogs at the shelter. There are three more cats than dogs at the shelter. How many cats and dogs are at the shelter?” Problem 2b states: “There are apples and pears on the table. There are 8 apples and 3 fewer pears. How many apples and pears are on the table?” Problem 2c states: “Darya invited 17 friends to a birthday party. Seven of them are boys. How many more girls than boys did Darya invite to her party?”
  • Assessment and Practice Part 1 Unit 3 Lesson 17 Problem 6 asks: “Class 4A collected 287 books and class 4B collected 476 books for charity. A) About how many books did 4A and 4B collect together? B) Is your estimate higher or lower than the actual answer? How do you know?” This problem requires students to make estimates and use their estimates to reason about the actual answer.
  • Assessment and Practice Part 2 Unit 3 Lesson 38 includes multi-step word problems. For example, Problem 2 asks “Diana is two years older than Farhad. Farhad is 10 years old. Farhad is 7 years older than Chen. How old are Diana and Chen? Diana is ______ years old and Chen is ______ years old.” However, not all problems in this lesson are multi-step word problems. For example, Problem 11 asks “An elephant weighs 13,000 pounds and is 13 feet tall. Is this elephant 1,000 times heavier than it is tall? Explain.”

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.

  • Teacher Resources Part 2 Unit 3 Lesson 32 includes scaffolded problems such as "There are 32 children in a class. 13 of them are boys. a) How many girls are there? b) How many more girls are there than boys?"
  • Teacher Resources Part 2 Unit 3 Lesson 32 includes one-step problems such as "A book costs $10. A poster is $4 cheaper than the book. How much does the poster cost?"
  • Teacher Resources Part 2 Unit 3 Lesson 35 is aligned to 4.OA.3, but the problems are one-step multiplication word problems. For example, "Alex is 8 years old. Jo is three times as old as Alex. How old is Jo?"
  • Teacher Resources Part 2 Unit 4 Lesson 11 includes routine word problems. Students answer questions about pizzas and pies.
  • Teacher Resources Part 2 Unit 8 Lesson 26 lists 4.NF.3 and 4.NF.4. This lesson focuses on measuring and drawing line segments and objects of a given length in inches, to the quarter of an inch. There is not a clear focus on solving word problems.
  • Teacher Resources Part 2 Unit 8 Lesson 27 lists 4.NF.3 and 4.NF.4. This lesson focuses on measuring and drawing line segments and objects of a given length in inches, to the closest eighth of an inch. There is not a clear focus on solving word problems.
  • Assessment and Practice Part 2 Unit 3 Lesson 32 focuses on Addition and Subtraction Word Problems. In Problem 1, students complete a chart that scaffolds the problem into parts. Problems 3-6 are word problems that follow the same routine without the chart.
  • Assessment and Practice Part 2 Unit 3 Lesson 33 includes word problems using diagrams with multiple steps that are scaffolded for students. In Lessons 4-34 through 4-36, students are provided with either a sample response, a chart to complete, or some other form of scaffolding for each problem set rendering each problem routine.

Problem Solving Lessons include word problems but are often heavily scaffolded and focused on the use of a particular problem-solving strategy. However, there are some instances where application problems are found. For example, Problem Solving Lesson 6 includes problems such as "A school fundraiser has a bake sale that sells muffins and cake. A muffin costs $2 and a piece of cake costs $3. The bake sale sold 30 items altogether and made $71. How many muffins and how many pieces of cake were sold?"

Advanced Lessons often contain application problems; however, they are optional and not assigned to all students and therefore not included in this Report. For example, Teacher Resources Part 2 Unit 3 Lesson 36 (Advanced) includes problems such as "Barret reads 7 books over the holidays. Henry reads three times as many books as Barret. How many more books did Henry read?" Teacher Resources Part 2 Unit 3 Lesson 37 (Advanced) includes problems such as "In a class library, there are four times as many chapter books as non-fiction books. There are three times as many nonfiction books as comics. There are 160 books in total. How many books of each kind are in the library?" Students may not complete these word problems.

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 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 4 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 4 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
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 4 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. In Teacher Resources Part 1 Unit 3 Lesson 16, MP1 is identified for the question “What is the smallest number that rounds to 800 when rounded to the nearest hundred? How many numbers round to 800 when rounded to the nearest hundred?” However, students are given a “hint” in order find the answer instead of persevering to solving the problems.
  • MP2: In Teacher Resources Part 2 Unit 2 Lesson 41, students are given five division problems and are told to divide by skip counting. Students have already been solving division problems using skip counting, so these problems do not require students to reason abstractly or quantitatively.
  • MP4: In Teacher Resources Part 1 Unit 2 Lesson 13, students are presented with the following problem: "You would like to buy a postcard that costs 55 cents, but you only have a dollar bill to pay with. How much change should you get back?" This problem is included in a section about counting up by different denominations to find change. Students are expected to solve the problem using this one method. There is no opportunity for students to model mathematics themselves.
  • MP6: In Teacher Resources Part 1 Unit 4 Lesson 35, students solve three multiplication problems using the standard algorithm. Students are told to check to see if their answers are correct. Students are not specifically attending to precision while checking their answers.
  • 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 1, Unit 2, Lesson 21, students are subtracting from 100 and 1000. Students do not construct knowledge about regrouping. Instead, they are told, “A shortcut for regrouping from 100.” This will lead to misconceptions when students regroup for subtracting as they did not construct the knowledge; they learned the shortcut or traditional algorithm. In Teacher Resources Part 1 Unit 2 Lesson 7, students are asked to subtract 1,010 from four different numbers. Teachers are told that students who have difficulty can do the subtraction in two steps "8,549 - 1000 = 7,549, then 7,549 - 10 = 7,539." Students do not determine the 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.
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Indicator Rating Details

The instructional materials reviewed for Grade 4 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 8 Lesson 30, students are converting mixed measurements to measurements in inches. The teacher is prompted to "have students think of how to convert a mixed measurement, such as 3 ft 4 in, into a measurement in inches only. They can discuss the ideas in pairs, then in groups of four. To prompt students to think of the method shown below, ask them to recall what they did with other units of measurement, such as centimeters and meters, or liters and milliliters." Although students are talking in small groups, the discussion is centered around solving a problem in the same manner of previous problem and does not address MP3 by having students construct their own arguments and/or critiquing the reasoning of others. Another example is found in Teacher Resources Part 1 Unit 1 Lesson 12 page 40: "There are counters of two colors. Try to find a way to have 12 counters so that there are four times as many of one color as the other. Then explain why it is not possible." The students are told from the beginning that there is no possible solution. In Teacher Resources Part 2 Lesson 44 page 19, students are asked to "(f)ind and correct the mistake in the long divisions." Students are told from the beginning that the original reasoning is incorrect.

In the Assessment and Practice Books, students are sometimes prompted to construct an argument. For example, in Assessment and Practice Book Part 1 page 1 question 2 asks “ Are all multiple of 8 even? Explain.” Another example is Assessment and Practice Book Part 2 page 23 question 58: “Kyle has 6 books. Ron has three times as many books. How many books does Ron have? Explain how you know.” 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 instructional materials, 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, often they are often told up front if the student is correct or incorrect or are provided hints. For example, in Assessment and Practice Book 2 page 8 question 9 provides a pattern. Three rules are provided to describe the pattern. Students are prompted to say whose rule is correct, and students are asked what mistakes did the others make. The problem is suggesting that one is correct and two are incorrect.

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.
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Indicator Rating Details

The materials reviewed for Grade 4 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.

In the Teacher's Guide, p. A-23, MP 3 is discussed in detail. Examples are provided to clarify the reasoning behind the labeling of MP3 in the materials although examples are not necessarily on grade level.

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 "chose 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.

  • Teacher Resources Part 1 Unit 1 Lesson 4 page 15: “Find the missing number in each pattern. Explain the strategy you used to find the number.” These are fill-in-the-blank problems that require very brief explanations.
  • Teacher Resources Part 1 Unit 2 Lesson 1 page 2: "Ask students to write a few numbers the Egyptian way and to translate those Egyptian numbers into regular numbers (using Arabic numerals). Have students write a number that is really long to write the Egyptian way (Example: 798). ASK: How is our system more convenient? What is it helpful to have a place value system (i.e., to have the ones, tens, and so on always in the same place)?" The focus of this activity is on writing and translating numbers, and the teacher is not given guidance on how to engage students in MP3 other than to have students notice that our number system is more convenient.
  • Teacher Resources Part 1 Unit 2 Lesson 4 page 15: "You have one set of blocks that makes the number 13 and one set of blocks that makes the number 22. Can you have the same number of blocks in both sets?" This question can be answer with a yes or no, and the teacher is not given support to help students engage in MP3.
  • Teacher Resources Part 1 Unit 2 Lesson 14 page 43: "Write on the board: 83 hundreds + 7 tens + 5 ones = ___ thousands + ____ hundreds + ____ tens + ____ ones. Have a volunteer fill in the blanks. Point out that now we can write the number by writing the digits from left to right. ASK: What would happen if we ddid that with the original representation, 83 hundreds + 7 tens + 5 ones. Would we still get the same answer? (yes!) Discuss why that is the case. Emphasize that because hundreds are the largest place value, regrouping the hundreds won't affect how we write the number." The original question is a fill-in-the-blank problem completed by one volunteer. One of the questions is a yes or no question, and the teacher guidance about the discussion downplays regrouping, the focus of the lesson.
  • Teacher Resources Part 2 Unit 3 Lesson 34 page 28: "Draw the tape diagrams below and ask which of them would fit the situation and which would not. Have students explain why the diagrams that do not fit the situation do not work." For the tape diagrams that do fit the situation, no explanation of student reasoning is required, and for the tape diagrams that do not fit the situation, the explanation provided to the teacher is very brief. No guidance for the teacher to support students struggling with interpreting tape diagrams.
  • Teacher Resources Part 2 Unit 3 Lesson 3 page 12: "Five eights of a pizza was eaten. What fraction is left? (3/8) How do you know?" Although students are asked to explain how they knew their answer, this question could simply be answered by showing work. The teacher is not provided any guidance around how to get students deeply engaged in MP3 with this question.
  • Teacher Resources Part 2 Unit 3 Lesson 6 page 22: "Is there a fraction equivalent to 3/8 with an odd denominator? Explain. Answer: No. The denominator will always be a multiple of 8, so it will always be even." Teachers are not given guidance or examples of student work to help them support students in developing their answers.
  • Teacher Resources Part 2 Unit 6 Lesson 41 page 9: "Can 13 be a factor of 12? (no) How do you know? (because 13 is greater than 12; no whole number times 13 can equal 12)." No follow-up discussion or support for the teacher is provided with these questions.

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 are needed.

Indicator 2g.iii

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

The materials reviewed for Jump Math Grade 4 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 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.

  • Unit introductions sometimes include vocabulary. For example, in Teacher Resources Part 2 Unit 9 page T-1, the definition of an angle is provided.
  • Vocabulary words are listed at the beginning of each lesson plan in the Teacher’s Guide, but definitions, if any, are within the lesson.
  • Teacher Resources part 1 page A-30 states that for vocabulary words listed for each lesson teachers should “explain the meaning of these terms and write them on the board as they appear in 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 9 Lesson 14, vocabulary includes the terms endpoint, intersect, intersection point, line, line segment, point, and ray. 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.
  • 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.
  • Some activities include words that do not attend to the specialized language of mathematics. For example, in the Assessment and Practice Part 2 page 5, students are prompted to write fill a blank to indicate how many dots are remaining even though the lesson itself included vocabulary like remainder.
  • At times the words themselves are the focus, not the language of mathematics. For example, Teacher Resources part 1 page A-17 states that “In some areas of math (e.g., geometry), the greatest difficulty that students face is in learning the terminology. If you include mathematical terms in your spelling lessons, students will find it easier to remember the terms and to communicate about their work.”

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).
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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:
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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 4 (U.S. Common Core Edition) 978-1-927457-12-2 JUMP Math 2014
Jump Math Teacher Resources Grade 4 (U.S. Common Core Edition) 978-1-927457-29-0 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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