Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 5 do not meet the expectation for alignment to the CCSSM. The materials partially meet expectations in the areas of focus and coherence, and do not meet the expectations for alignment to the CCSSM in the areas of rigor and the MPs. In the area of focus within the grade, there is one above grade-level topic included in the assessments, but it does not impact the structure of the materials. The materials spend an appropriate amount of class time on major work. In the area of coherence, the materials include content that is shaped by the CCSSM clusters, but some standards require supplemental materials for the content to be viable for one school year and to meet the full depth of the standards. All students engage in extensive practice with grade-level problems for the majority of standard, and supporting and additional content do not always engage students in the major work of the grade. Some natural connections are missed between clusters and domains. In the area of rigor and balance, all three aspects of rigor are sometimes present in the materials, but more emphasis needs to be placed on conceptual understanding, procedural skill and fluency, and application to help students meet the Standards’ rigorous expectations. The three aspects of rigor are not well balanced. In the area of practice-content connections, the materials identify MPs, but they do not consistently enrich the content and do not attend to their full meaning. Students rarely construct viable arguments or analyze the arguments of others. Materials do not explicitly teach the specialized language of mathematics.

See Rating Scale
Understanding Gateways

Alignment

|

Does Not Meet Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
10
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
5
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

Partially Meets Expectations

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-
Gateway One Details

The instructional materials reviewed for Grade 5 partially meet expectations for major work and coherence. Stepping Stones does assess future grade-level content on five assessments by requiring students to use the standard algorithm for division. These test items could easily be modified and may be mathematically appropriate for some students. Additionally, the instructional materials appropriately allocate class time to major work of the grade. In some cases, the supporting work enhances and supports the major work of the grade level, and in others, it does not. There are several missed opportunities to connect supporting work to major work. Connections between supporting and major work are not explicitly identified in the program. However, mathematics standards can be seen under Lesson Objectives in the “steps” section and one can see if there is more than one standard listed. The amount of time needed to complete the lessons is appropriate for a school year of approximately 140-190 days, but some modifications would need to be made in order for students to be able to master all content. The instructional materials identify and connect prior or future grade-level work to Grade 5-level work. Materials also make connections to prior knowledge of learning in earlier grades. However, students are not consistently provided extensive work with Grade 5-level work. The standards are referred to throughout the materials. Most of the materials include learning objectives that are visibly shaped by CCSSM cluster headings. The instructional materials sometimes include problems and activities that serve to connect two or more clusters in a domain and two or more domains in a grade in cases where the connections are natural and important.

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 meet expectations for assessing grade-level content. For this indicator, the review team examined all summative assessments and determined that they do assess one topic that is beyond the expectations for the grade. The assessments could have items modified so as to align to Grade 5 expectations. Overall, the amount of modifications or omissions needed does not significantly impact the underlying structure of the instructional 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 5 meet expectations for assessing grade-level content. For this indicator, the review team examined all summative assessments and determined that they do assess one topic that is beyond the expectations for the grade. The assessments could have items modified so as to align to Grade 5 expectations. Overall, the amount of modifications or omissions needed does not significantly impact the underlying structure of the instructional materials.

  • Each module has “Check-Ups” which contain questions that require students to select the correct answer or provide a written response, “Performance Tasks” which are used to measure depth of understanding, and “Interviews” which assess a student's ability to rote count fluently. There are also four “Quarterly Tests” in Modules 3, 6, 9 and 12 which assess all learning targets from the three modules just taught (tests 1 and 2) or from the previous three modules (tests 3 and 4).
  • There are five examples of assessments requiring the standard algorithm for division (6.NS.2). These are labeled as above grade level, and all involve dividing by a single-digit divisor. These items could be easily modified by allowing students to use a strategy of their choice without compromising the items. The items are located on the following assessments: Module 8 Check-up 1, Item 3; Module 9 Quarter Test 1, Item 6, Quarter Test 2, Item 6, Quarter Test 3, Item 6 and Quarter Test 4, Item 6.

Criterion 1b

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

The instructional materials reviewed for Grade 5 meet the expectation of instructional materials spending the majority of class time on the major clusters of the grade. The materials devote approximately 67 percent of class time to major work of the grade. Of the 12 modules, 11 contain six or more lessons (half a module) devoted to major work of Grade 5. Overall, the instructional materials allocate adequate instructional time to clusters of standards that are 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 focus within major clusters. Overall, the instructional material spends the majority of class time on the major clusters of each grade.

To determine focus on major work, three perspectives were evaluated: the number of modules devoted to major work, the number of lessons devoted to major work, and the amount of time devoted to major work. The number of lessons devoted to major work, which is approximately 67 percent, is aligned with this indicator because it specifically addresses the amount of standards instruction devoted to major work.

  • Grade 5 instruction is divided into 12 modules with 12 lessons in each module. Of the 144 lessons, 97 are aligned to major work of Grade 5. Therefore, approximately 67 percent of student instruction would be focused on major work.
  • Of the 12 modules, 11 have half, or more, of the instruction in the module focused on major work of Grade 5. Therefore, approximately 92 percent of student instruction would be focused on major work.
  • Grade 5 instruction is designed to be taught over 180 days (15 days per module). Of the 180 days, 97 days of instruction focus on major work of Grade 5. Therefore, approximately 54 percent of student instruction would be focused on major work.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
4/8
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 5 do not meet expectations for coherence. In some cases, the supporting work enhances and supports the major work of the grade level, and in others, it does not. There are several missed opportunities to connect supporting work to major work. Connections between supporting and major work are not explicitly identified in the program. However, mathematics standards can be seen under Lesson Objectives in the “steps” section and one can see if there is more than one standard listed. The amount of time needed to complete the lessons is appropriate for a school year of approximately 140-190 days, but some modifications would need to be made in order for students to be able to master all content. The instructional materials identify and connect prior or future grade-level work to Grade 5-level work. Materials also make connections to prior knowledge of learning in earlier grades. However, students are not consistently provided extensive work with Grade 5-level work. The standards are referred to throughout the materials. Most of the materials include learning objectives that are visibly shaped by CCSSM cluster headings. The instructional materials sometimes include problems and activities that serve to connect two or more clusters in a domain and two or more domains in a grade in cases where the connections are natural and important.

Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 5 partially meet expectations that supporting content enhances focus and coherence by engaging students in the major work of the grade. In some cases, the supporting work enhances and supports the major work of the grade level, and in others, it does not. There are several missed opportunities to connect supporting work to major work.

Connections between supporting and major work are not explicitly identified in the program. However, mathematics standards can be seen under Lesson Objectives in the “steps” section and one can see if there is more than one standard listed.

Connections between supporting and major work:

  • Metric conversion (5.MD.1) lessons are connected to the major work of computation with decimals (5.NBT.B). However, these connections are often not explicit and the ranges of numbers do not require students to do work at the expectation of standards of 5.NBT.7 and 5.NF.4.
  • Constructing line plot (5.MD.2) lessons are connected to solving operations using fractions (5.NF.A and B). However, students are asked to subtract fractions (find the difference between largest/smallest), but plots are only to the 1/2 unit, so students are adding/subtracting in Grade 4 value ranges.

Missed connections between supporting and major work:

  • Metric conversions (5.MD.1) is not connected to understanding place value (5.NBT.A). The materials miss the opportunity to discuss place value and powers of 10 when teaching/practicing unit conversions.

Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 5 partially meet the expectations for having an amount of content designated for one grade level as viable for one school year in order to foster coherence between grades. Overall, the amount of time needed to complete the lessons is appropriate for a school year of approximately 140-190 days, but some modifications would need to be made in order for students to be able to master all content.

  • There are 12 modules, each with 12 lessons, making a total of 144 lessons.
  • Lessons are designed to take 45-60 minutes.
  • Additional instructional time can be added using “More Math” activities which include investigations, problems solving activities, enrichment activities, and cross-curricular activities.
  • Standard 5.MD.2 does not reach the rigor of the grade level and would require the teacher to create/find additional resources.
    • In Lesson 6.12 students only plot to the nearest 1/2 unit. The standard expects work with 1/4 and 1/8 unit (5.MD.2).
    • In Lesson 9.12 students use line plots with whole numbers. Students do not have to use operations of fractions to solve problems (5.MD.2).

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 expectations for materials being consistent with the progressions in the standards. Overall, the instructional materials identify and connect prior or future grade-level work to Grade 5-level work. Materials also make connections to prior knowledge of learning in earlier grades. However, students are not consistently provided extensive work with Grade 5-level work.

i. Materials develop according to the grade-by-grade progressions. Prior and future content is clearly identified and relates to grade-level work.

  • Prior grade-level topics taught are identified: Lessons 1.1-1.7 working multi-digit whole numbers (4.NBT.2), Lessons 1.8-1.12 multiplying four digit whole numbers (4.NBT.5), and lesson 1.4 locating large numbers on a number line (2.MD.6).
  • Future grade-level topics taught are identified: Lesson 8.5-8.7 address using the standard division algorithm (6.NS.2).

ii. Materials consistently give students extensive work with grade-level problems.

  • Differentiated instruction, at grade level, is available for each lesson (Extra Help, Extra Practice, and Extra Challenge). Connections to lessons in prior grades related to the standard being taught are also available.
  • Opportunities for enrichment, at grade level, are available for each module. Additionally there are separate investigations and problem solving activities for each module. They allow for small groups of students to gather, analyze and represent data to provide more extensive practice with the content.
  • Opportunities for fluency practice and practice of grade-level content from previous lessons is available in each module under "Ongoing Practice."
  • "Extra help" assignments are used to scaffold so grade-level content is more accessible.
  • Fundamental games reinforce and practice computational skills.
  • Reviewer Note: Graphing Points on a coordinate plane (5.G.A) is only covered in lesson 7.8 and 7.11. Constructing and interpreting line plots (5.MD.2) is only covered in lessons 9.12, 10.12 and 6.12. Relating fractions to division (5.NF.3) is only covered in lesson 11.1-11.2. Standards 5.NF.2, 5.NF.5 and 5.NF.6 are not addressed in the program. These lessons MAY NOT be enough to cover the true depth of the standard and supplemental material may need to be provided. Represent and interpret data (5.MD.2) does not get beyond Grade 3 use of line plots, which explicitly states that there should be grade level work with operations with fractions and the program does not provide this opportunity.

iii. Some materials explicitly relate grade-level concepts to prior knowledge from earlier grades.

  • 4.NBT.2: In lesson 1.1-1.7 students are extending their place value knowledge by working with larger numbers.
  • 2.MD.6: In lesson 1.4 students are extending their number line knowledge by focusing on seven-digit numbers and their place value understanding.
  • 4.NBT.5: In lessons 1.8-1.12 students are extending their conceptual understanding of multiplication to learn the standard algorithm of multiplication.
  • Module 1 reviews mental strategies learned in Grade 4 to multiply numbers beyond the fact range. These include: doubling and halving, factoring one or both products of two 2-digit numbers, applying properties, and using partial products to multiply two 2-digit numbers.
  • Module 4 reviews addition of common fractions with the same denominator that was introduced in Grade 4. The area and number line models are used to add fractions with related and unrelated denominators.
  • Module 5 reviews and builds on concepts of angles learned in Grade 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.
1/2
+
-
Indicator Rating Details

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

  • A comprehensive listing of the CCSSM and the correlating exercises are found under the drop down menu on the home page.
  • The cluster headings are clearly identified by hovering over the lesson title.
  • Learning targets are clearly marked in the materials. The learning targets identify objectives and standards of each module.
  • Connections are made to prior grade level content.

The instructional materials sometimes include problems and activities that serve to connect two or more clusters in a domain and two or more domains in a grade in cases where the connections are natural and important. The materials connect two or more clusters within the grade.

  • Representing data sets (5.MD.B) is connected to operations with fractions (5.NF.A and 5.NF.B) in lessons 6.12 and 10.12.
  • Graphing data (5.G.A) is connected to numerical patterns (5.OA.3) in lessons 7.10 and 7.11.
  • Converting like measurement units within the metric system (5.MD.1) is connected to multiplying decimals (5.NBT.B) in lessons 8.8-8.12, 10.10-10.11 and 12.10-12.12.
  • Understanding place value (5.NBT.A) is connected to performing operations with whole numbers and decimals (5.NBT.B) in lesson 10.7 and 12.7.
  • A connection between the calculation of finding volume (5.MD.C) with multiplying decimals (5.NBT.B) is missing in lessons 3.7-3.12.
  • There are instances where the work with the standard does not reach the expectation of the grade level. For instance, 5.MD.2 does not get beyond a Grade 3 level with the use of line plots. (5.MD.2 explicitly states that there should be grade-level work with operations with fractions that the curriculum does not provide.)

Gateway Two

Rigor & Mathematical Practices

Does Not Meet Expectations

+
-
Gateway Two Details

The instructional materials reviewed for Grade 5 Stepping Stones do not meet expectations for rigor and the MPs. The instructional materials do not consistently give appropriate attention to conceptual understanding, procedural skill and fluency, and application. The lesson and assessment materials do not consistently provide opportunities for students to work with each aspect of rigor in a balanced way. Overall, the instructional materials do not consistently reflect the balance in the CCSSM which helps students meet rigorous expectations by developing conceptual understanding, procedural skill and fluency, and application. The instructional materials do not support the MP's emphasis on mathematical reasoning. The students are given some opportunities to justify or explain their thinking, and there are very limited opportunities for evaluating the thinking of others. They do not consistently assist teachers in having students construct viable arguments or analyze other student arguments. They do not explicitly teach or attend to the specialized language of mathematics.

Criterion 2a - 2d

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.
4/8
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 5 Stepping Stones do not meet expectations for rigor and balance. The instructional materials do not consistently give appropriate attention to conceptual understanding, procedural skill and fluency, and application. The lesson and assessment materials do not consistently provide opportunities for students to work with each aspect of rigor in a balanced way. Overall, the instructional materials do not consistency reflect the balance in the CCSSM which helps students meet rigorous expectations by developing conceptual understanding, procedural skill and fluency, and application.

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.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 5 partially meet the expectations for developing conceptual understanding of key mathematical concepts. Overall, the instructional materials do not consistently offer opportunities to use manipulatives and models to develop conceptual understanding. Also, more emphasis should be placed on discussion of mathematical concepts.

  • Lessons 9.1-9.9 address the conceptual understanding of multiplying fractions (5.NF.4).
  • Lessons 1.2-1.3 and 1.5-1.8 address the conceptual understanding of place value (5.NBT.A).
  • Lessons 2.7-2.12 and 5.1-5.2 address the conceptual understanding of division (5.NBT.B).
  • Several lessons are focused specifically on the conceptual understanding standards.
  • The “Number Case” and “Fundamentals” channels provide resources for students to use models.
  • In lesson 9.1, students use array models to multiply a whole number by a fraction (5.NF.4).
  • In lesson 9.3, student use area models to multiply two fractions (5.NF.4).
  • In lesson 1.1, students use an abacus to represent 6-digit numbers (5.NBT.A).
  • In lesson 2.7, students use hundreds grids to represent fractions (5.NF.4).
  • In lesson 1.8, students use many different ways to model and support multi-digit number work (i.e., place value charts and arrays) to help answer questions.
  • In lessons 11.1 and 11.2, during whole group application problems, students use visual fractions models and are encouraged to make sketches of fractions to develop the understanding of fractions and their relation to division equations.
  • In lesson 1.12, during whole group discussion students are asked to show models and support their strategies for solving problems. Student practice problems, however, are mostly focused on procedural fluency.
  • In lesson 9.6, an explicit connection to Grade 4 multiplicative comparison problems is made to a tape diagram. These strategies make conceptual comparisons to multiplication with fractions, however there is no discussion on the differences between multiplication with only whole numbers and when one factor is a fraction.
  • In lesson 9.7, students engage in whole group discussion and procedural questions regarding the size of fractions. Student work is primarily procedural, and the format of the questions primarily prompts students to solve the problems first rather than reason about the size. Also, no visual models are used to justify or prove answers.
  • Lessons 11.7 and 11.8 provide a few whole group examples that model situations involving the division of fractions. However, seldom does the student work require students to use models to show their conceptual understanding of the division of fractions.
  • Module 1, Lesson 8, involves many links to conceptual models (e.g., place value charts; area models) to help see patterns when multiplying with larger digits and make connections to x10 patterns in place value.
  • Module 1, Lessons 10 and 12, provide teachers with guidance in leading discussions on different strategies and encourages discussion about specific strategies; student work provides procedural practice, although there is limited connection to students explaining using 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.
1/2
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-
Indicator Rating Details

The Grade 5 materials partially meet the expectations for procedural skill and fluency. They give some attention to individual standards that set an expectation of procedural skill and fluency. Lessons contain multiple examples of fluency practice pages.

  • “Fundamental Games” provides opportunities for students to practice fluency through games.
  • Ongoing practice in computation fluency is provided in only lesson 3, lesson 7 and lesson 11 of every module; however, only 13 of the 36 lessons that have this additional practice are focused on multiplication fluency. Only three of these lessons involve multiplication with 2-digits x 2-digits, and no lessons involve more than 2-digit numbers.
  • Only one interview assessment is focused on multiplication fluency (interview 1 - applying the double/half strategy).
  • Some lessons offer opportunities to develop multiplication fluency with multi-digit whole numbers within 1 million (5.NBT.5). (Modules 1 and 3)
  • Work with fluency in multi-digit multiplication does involve multiple links to the conceptual development built in Grade 5 and prior grades. However, there is little evidence of repeated practice that is interwoven throughout the year that supports the development of the expectation set in the standard.

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
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 5 partially meet the expectations for students spending sufficient time working with engaging applications of the mathematics. Overall, the instructional materials do not consistently offer opportunities for students to engage in application of learning to real-world situations.

  • Lessons 9.8 and 9.9 focus on solving real world problems with multiplying fractions (5.NF.6).
  • Lessons 11.3 - 11.7 focus on solving real world problems with dividing fractions (5.NF.7).
  • Some lessons specifically focus on application of mathematics standards (5.NF.6 and 6.NF.7).
  • “Financial Literacy” offers lessons requiring application.
  • Each module contains three investigations that require application.
  • The lessons that are explicitly tied to word problem/application standards are inconsistent. Some lessons (i.e., 9.8, 11.5 and 11.7) involve little to no word problem work in the whole or small group portions or student journal.
  • Word problems on student work are usually one-step problems. Lesson 9.8 has a good balance of one-step, two-step, and some non-routine problems, but this is not the norm.

Indicator 2d

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

The materials reviewed for Grade 5 partially meet the expectations for balance between the three aspects of rigor with the grade.

  • Although all three aspects of rigor are present in the materials, there is not a balance among the three aspects of rigor. There is an under-emphasis on application work compared with the emphasis given to fluency.
  • There are few to no lessons that bring multiple aspects of rigor together. For example, lessons 3.7 - 3.11 only require students to use conceptual understanding to find volume of prisms. There is a missed opportunity to demonstrate application or procedural fluency in multiplication.
  • Module 4 does not contain any lessons that specifically address conceptual knowledge or application standards.
  • Student assessments do not offer a balance of rigor and are often missing questions requiring application. For example, summative assessment 7 (checkup, interview and performance task) does not assess application.

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
1/10
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 5 do not meet the expectation for supporting the MP's emphasis on mathematical reasoning. The students are given some opportunities to justify or explain their thinking, and there are very limited opportunities for evaluating the thinking of others. They do not consistently assist teachers in having students construct viable arguments or analyze other student arguments. They do not explicitly teach or attend to the specialized language of mathematics.

Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 5 partially meet the expectations for identifying the MPs and using them to enrich mathematics content within and throughout Grade 5. Overall, the instructional materials identify the mathematical practices but do not consistently use them to enrich the content. Also, some mathematical practices are over-identified and some are under-identified.

  • MPs are identified in the “Steps” portion of each module lesson.
  • MPs are identified in most lessons with at least one MP as the focus.
  • MPs are embedded within lessons.
  • A chart, for each module, under the Mathematics tab identifies MPs by lesson
  • Videos can be found under the Resources tab which explain the MPs and Habits of Mind.
  • MPs are not specifically listed on assessments.
  • Explanations of how the MPs are being used and what to expect from students to show growth or mastery is not provided in the “Steps” portion of the lesson.
  • The following lessons do not contain MPs to enrich the lesson content: 1.1, 1.3, 2.4, 2.5, 3.4, 4.4, 5.3, 5.4, 7.4, 7.5, 7.6, 8.4, 9.1, 9.5, 10.3, 10.4, 10.5, 11.3, 11.5, 12.4 and 12.5.
  • The MPs are not treated equally. For example MP7 is identified in 72 lessons, whereas MP5 is only identified in 6 lessons and MP5 only identified in 10 lessons.

Indicator 2f

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

The instructional materials reviewed for Grade 5 do not meet the expectations for materials carefully attending to the full meaning of each MP. Overall, the instructional materials do not meet the full meaning of four or more MPs.

  • MP1: MP1 is not referenced in Modules 1, 2, 5 or 7. There is little problem-solving in the Grade 5 program that requires multi-step work or that involves contexts that aren't clearly indicated by the lesson title and procedural work included in the lesson. MP1 is usually assigned whenever students are working on traditionally "harder" problems (i.e., problems involving unit conversion 6.10). There is little evidence this MP is addressed regularly on student independent work or on assessments. In lesson 12.12, students are shown a pan balance with a missing value. The students are asked in whole group to explain how they could find the missing value instead of working independently and then sharing their thinking.
  • MP2: MP2 is not referenced in Module 8. In Module 7 students are reasoning quantitatively but do not use abstract thinking. In lesson 6.3, students are told to use multiplication to create equivalent fractions instead of getting the opportunity to reason abstractly and quantitatively about the context.
  • MP4: MP4 is not referenced in Modules 1, 3, 8 or 11. Modeling is misidentified in lesson 9.6 when students are provided the sentence stem, “___ is 3 times as much as ___.” Students rarely create their own mathematical models for solving or reasoning about a real-life problem. Models, when used, are provided for the students to complete (i.e., tables, extending patterns). Lesson 9.6 has students using a tape diagram to model comparative expressions, but the lesson does not have a real-life context. Lesson 7.11 involves graphing data on a coordinate plane, but no other aspects of the modeling process are present in the lesson. Lesson 4.11 involves using expressions to model problems, but again, no other aspects of the modeling process are present in the lesson.
  • MP5: MP5 is not referenced in Modules 1, 2, 4, 6, 9, 10, 11 or 12. Lessons 8.3, 8.5, 7.11 and 7.12 are labeled in the MP chart as focusing on MP5, but do not. In lesson 3.8 students are finding volume and are given cubes to use. Other tools to fill the containers can be suggested by students, but are not available. Lesson 5.2 students are using a place value chart to demonstrate numbers in the thousandths, but then in lesson 5.4 they are using a “flare” number line. Students are rarely given opportunities to choose tools appropriately but rather provided the mathematical tool which is the lesson focus. In lesson 5.2 students use a number line to compare and no choice for comparison is available. In lesson 7.11 students use a coordinate plane or graph and no choice is available.

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.
0/2
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-
Indicator Rating Details

The instructional materials reviewed for Grade 5 do not meet the expectation for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards. Overall, the students are given some opportunities to justify or explain their thinking. There are very limited opportunities for evaluating the thinking of others.

  • The materials sometimes prompt students to explain and justify their thinking, but, opportunities for constructing arguments are not found in the student journal.
  • Most lessons reviewed that were labeled as using MP.3 involved students explaining their strategies or steps (for example Module 1, Lesson 9; Module 2, Lesson 4; Module 4, Lesson 6); but few involved critiques from other students.
  • There are no opportunities for students to reconsider their own argument in response to the critique of others.
  • There were 37 lessons out of 144 that specifically referenced MP3. Module 12 did not identify MP3 at all.
  • There are many missed opportunities including:
    • Module 1 Lesson 7-This lesson does not support the full intent of the standard. Students are only required to share strategies.
    • Module 2, Lesson 4- Students are prompted to share strategies. At no time are students required to critique the reasoning of others.

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.
0/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 5 do not meet the expectation for 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. Overall, the materials do not consistently assist teachers in having students construct viable arguments or analyze other students' arguments.

  • Teacher materials prompt students to have discussions or share their work, but do not provide true opportunities for students to construct arguments or analyze the arguments of others. For example, in Module 4, Lesson 2 students are only prompted to explain how they knew which fraction to rewrite. They did not have to justify to their peers why their answer was correct.
  • There are few opportunities for students to engage in meaningful arguments or analyze others' arguments.
  • There is little evidence of teachers engaging students in both constructing viable arguments and analyzing the arguments of others.
  • There are times when the teacher's guide gives recommendations on what teachers should pull out of or focus on when students respond/explain (for example in Lesson 3 of Module 1, the materials prompt teachers to "encourage students to explain that zeros" are used when there is no value in that place); but there are no directions on how to construct a strong argument.
  • There is no support for teachers in how to support students when they critique each other.
  • MP3 is not addressed in Module 12. In other modules, students are sometimes constructing viable arguments but are rarely asked to critique the work of others. Many lessons involve explaining steps or strategies, but few prompt the teacher or students to go into more depth. Lessons do not require these types of explanations or justifications in student writing in their daily work. In lesson 4.4 students are adding mixed numbers using a number line. At the end of the lesson students are asked to reflect why they used one of three methods in problem solving. Students are not asked to share with classmates to discuss their reasoning.

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
0/2
+
-
Indicator Rating Details

The materials reviewed for Grade 5 do not meet the expectation for attending to the specialized language of mathematics.

  • There is limited explicit instruction on how to use the language of mathematics. The materials do not prompt the teacher sufficiently to require precise vocabulary from students on a regular basis.
  • Vocabulary is in "Steps" but not in the student pages.
  • There are little opportunities for students to provide oral or written responses where the vocabulary may be expected.
  • The materials use precise and accurate mathematical language some of the time. There are side bars on student journals that define words (e.g., "expression" in lesson 4-11), but there is no expectation for students to use this precise vocabulary in their speech or student journals.

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: Fri Apr 08 00:00:00 UTC 2016

Report Edition: 0

Title ISBN Edition Publisher Year
null 978-1-921959-79-0 null null null

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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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