Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 4 partially meet the expectation for alignment to the CCSSM. The materials meet expectations in the areas of focus and coherence, but they 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, no above grade-level topics are included in the assessments. 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 with enough work to be viable for one school year. All students engage in extensive practice with grade-level problems, but supporting and additional content do not always engage students in the major work of the grade. Natural connections are made 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 the full meaning of the MPs. 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

|

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
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

Meets Expectations

+
-
Gateway One Details

The instructional materials reviewed for Grade 4 meet expectations for major work and coherence. Stepping Stones does not assess future grade level content. Additionally, the instructional materials devote an appropriate amount of 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, math 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. The instructional materials identify and connect prior or future grade-level work to Grade 4-level work. Additionally, students are consistently provided extensive work with Grade 4-level work and connections are made to prior knowledge from earlier grades. Materials develop according to the grade-by-grade progressions. The materials include learning objectives that are visibly shaped by CCSSM cluster headings. They 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, and they connect two or more clusters within the grade.

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 meet expectations for assessing grade-level content. For this indicator, the review team examined all summative assessments. Overall, there is no content from future grades assessed.

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 expectations for assessing grade-level content. For this indicator, the review team examined all summative assessments. Overall, there is no content from future grades assessed.

  • 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 students’ 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).

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 4 meet the expectation of instructional materials spending the majority of class time on the major clusters of the grade. The materials devote approximately 71 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 4. Overall, the instructional materials allocate adequate instructional time to clusters of standards that are major work of Grade 4.

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 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 71 percent, is aligned with this indicator because it specifically addresses the amount of instruction devoted to major work of the grade.

  • Grade 4 instruction is divided into 12 modules with 12 lessons in each module. Of the 144 lessons, 102 are aligned to major work of Grade 4. Therefore, approximately 71 percent of student instruction would be focused on major work.
  • Of the 12 modules, 11 have instruction focused on major work of Grade 4 in half of the module or more. Therefore, approximately 92 percent of student instruction would be focused on major work.
  • Grade 4 instruction is designed to be taught over 180 days (15 days per module). Of the 180 days, 96 days of instruction focus on major work of Grade 4. Therefore, approximately 56 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.
7/8
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 4 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. The instructional materials identify and connect prior or future grade-level work to grade-level work. Additionally, students are consistently provided extensive work with Grade 4-level work and connections are made to prior knowledge from earlier grades. Materials develop according to the grade-by-grade progressions. The materials include learning objectives that are visibly shaped by CCSSM cluster headings. They 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, and they connect two or more clusters within the grade.

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 4 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:

  • Finding factors (4.OA.4) is addressed in lessons 5.4 and 5.5 and is connected to major work of understanding fraction equivalance (4.NF.1).
  • Several lessons in module 9 have students using the area model (4.MD.A) to multiply common fractions (4.NF.4).
  • Measuring angles (4.MD.C) in lesson 5.9 is connected to fractions (4.NF) by having students use angle testers to measure fractions of a full turn.
  • Finding factors (4.OA.4) in lessons 3.1 and 3.4 has some connections to finding numbers that are "evenly divisible" or to remainder work in division (4.NBT.B).
  • Work with factors and multiples (4.OA.4) in Lessons 3.9 – 3.12 is connected with comparing fractions, using number lines and ordering common fractions (4.NF.A).
  • Fractions on a number line (4.NF.A) in lessons 5.7, 5.8, 6.10, 6.11, 6.12, 7.9, 9.6 and 12.1 is connected to making line plots (4.MD.4).
  • Using the standard formula for area and perimeter (4.MD.3) in lessons 9.1, 9.4 and 9.7 is connected to grade-level work with multiplication (4.NBT.4), and this work is continued with mixed numbers and multiplication with fractions/whole numbers (4.NF.B).

Missed connections between supporting and major work:

  • Finding factor pairs (4.OA.4) is not connected to the major work of using place value understanding and properties of operations to perform multi-digit arithmetic (4.NBT.B).
  • Creating line plots displaying data in fractions of units (4.MD.4) is not connected to the major work of adding and subtracting fractions (4.NBT.B & 4.NBT.A).
  • Understanding relative sizes of units with a system and converting larger to smaller units (4.MD.1) is covered in 21 lessons. There are more lessons focused on this standard than any other standard. Although some connections are made to multiplication and place value patterns (Lessons 8.10, 8.11 and 12.11), line plots (Lesson 9.10), and multiplicative comparison (Lesson 9.10), few of these are explicit, and they are inconsistent across very similar lessons.
  • Work with arrays in Lessons 3.4 makes a strong connection to Grade 3 multiplication work and finding factor pairs (4.OA.4). However, none of the lessons on factors and multiplies (4.OA.4) makes a connection to the properties of multiplication or how to use them as a strategy from multiplying larger numbers (4.NBT.B).

Indicator evidence revised September 2016.  

Indicator 1d

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

The instructional materials reviewed for Grade 4 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.

  • 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.

Indicator 1e

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

The instructional materials reviewed for Grade 4 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-level work. Additionally, students are consistently provided extensive work with grade-level work and connections are made to prior knowledge from earlier grades.

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 1.8 working with whole number lengths (2.MD.6), Lesson 2.10 reviewing time measurement (3.MD.1), and Lesson 8.4 locating 6-digit numbers on a number line (2.MD.6).
  • Future grade level topics are not taught.

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.”
  • Fundamental games reinforce and practice computational skills.
  • "Extra help" assignments are typically created to provide a tool or scaffold to help make grade level content more accessible (i.e., Lesson 2.11 uses a number line to help with elapsed time problems, Lesson 8.7 provides an "expander tool" to help students see place value patterns when making unit conversion and Lesson 5.5 provides practice with a Venn diagram to help connect to common factors).
  • Reviewer Note: Make a line plot to display a data set of measurements in fractions of a unit (4.MD.4) is not addressed. Adding whole numbers (4.NBT.4) is only addressed in Module 2, Lessons 1, 4, 5, 6, 7, 8 and 9. Subtracting whole numbers (4.NBT.4) is only addressed in Module 2, Lessons 2 - 3, and Module 4, Lessons 1 – 7. Subtracting fractions (4.NF.B) is only addressed in four lessons. Recognizing angle measure as additive (4.MD.7) is only addressed in Lesson 5.12. Classifying 2-dimensional figures (4.G.2) is only addressed in Lessons 5.11 and 10.10. Recognizing lines of symmetry (4.G.3) is only addressed in lessons 10.11 and 10.12. These lessons MAY NOT be enough to cover the true depth of the standard and supplemental material may need to be provided.

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

  • 2.MD.6, in lesson 1.8, has students extend their number line knowledge by rounding 5-digit numbers to the tens, hundreds and thousands.
  • 2.MD.6, in lesson 8.4, has students extend their number line knowledge by focusing on the thousands place and their place value understanding.
  • Module 2 begins with a review of the addition and subtraction computation strategies that were studied in Grade 3. The module also focuses on formalizing the standard algorithm by reviewing the steps studied in Grade 3.
  • Work in measurement reviews and builds on concepts of time intervals learned in Grade 3 - hours, minutes, and seconds.
  • Related ideas associated with multiplication are developed. Students apply their understanding of area of rectangles to help establish and reinforce the connection between factors and multiples.
  • Students build on their understanding of the properties of multiplication to solve more complex problems by breaking one number into a product of two smaller factors.
  • The area model and number lines are used to review and reinforce the concepts of fractions.
  • Base-10 blocks and pictures are used to review and extend work with the standard algorithm.
  • Grade 3 work with the area model is used to demonstrate how place value can be used to break the factors into parts to multiply.
  • Each lesson has clear icons at the top of the screen that identify the larger theme the lesson fits into with easily accessible links to both prior grade content to help with differentiation and making connections to content. There are several examples of strong progressions from prior grade (i.e., use of arrays and area models with multiplication work).

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 s tandards. The standards are referred to throughout the materials. Overall, 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 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.

  • Solving multistep word problems (4.OA.3) is connected to multiplying whole numbers (4.NBT.5) in lesson 3.7.
  • Solving multistep word problems (4.OA.3) is connected to subtracting whole numbers (4.NBT.3) in lesson 4.7.
  • Working with factors and multiples (4.OA.4) is connected to finding equivalent fractions with same denominators (4.NF.1) in lessons 5.4 and 5.5.
  • Identifying angles (4.G.2) is connected to measuring angles with a protractor (4.MD.6) in lesson 5.11.
  • Finding area (4.MD.3) is connected to multiplication (4.NBT.5) in lessons 9.1 and 9.2
  • There are missed connections between number patterns and creating tables to explore number patterns (4.OA.5).
  • There is not consistent work in reinforcing multiplicative comparison (4.OA.1) or to place value understanding with work in the metric system (4.NBT.1).

Gateway Two

Rigor & Mathematical Practices

Does Not Meet Expectations

+
-
Gateway Two Details

The instructional materials reviewed for Grade 4 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. There are many missed opportunities to address aspects of rigor in a balanced way. The lesson and assessment materials do not consistently provide opportunities for students to work in all three areas of rigor. Overall, the instructional materials do not 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 Standards’ emphasis on mathematical reasoning. The students are given very limited opportunities to justify or explain their thinking, and there are no 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 4 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. There are many missed opportunities to address aspects of rigor in a balanced way. The lesson and assessment materials do not consistently provide opportunities for students to work in all three areas of rigor. Overall, the instructional materials do not 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 4 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.

  • Modules 1-9 and 11-12 contain lessons that specifically address standards which are explicitly outlined as standards developing conceptual understanding. (4.NF.A, 4.NBT.A and 4.NBT.B).
  • “Number Case” and “Fundamentals” provide resources for students to use models.
  • Lesson 3.3 addresses multiplying whole numbers (4.NBT.5). Students use a rectangular array to demonstrate the double and half strategy for multiplication when multiplying a one-digit factor by a two-digit factor. Students also draw on place value understanding to use the distributive property. This opportunity is provided in both whole group instruction and independent practice.
  • Lesson 3.6 addresses multiplication properties (4.NBT.5). Students construct and multiply the cubes on rectangular prisms to demonstrate understanding of the associative and commutative properties. Students are prompted to discuss the efficiency of strategies and are gradually released from models to equations.
  • Lesson 3.7 addresses multiplication properties (4.NBT.5). Students reason about the most efficient way to decompose numbers in a rectangular prism to make multiplication calculations easier. Students are encouraged to describe their strategies in selecting the order to multiply the numbers. Emphasis is placed on manipulating numbers for easier computations.
  • Lesson 3.8 addresses multiplication strategies (4.NBT.5). Students use strategies based on place value to solve problems involving multiplication.
  • Module 3, Check-Up 2, Problems 1a-d encourage the use of the associative and commutative properties (4.NBT.5) and place value understanding to solve multiplication problems.
  • Lessons comparing fractions (4.NF.2) focus on developing procedural fluency with creating common denominators. There is only one lesson (3.11) focused on using unit fractions and number line strategies for comparing fractions. Very few problems focused on this standard further student conceptual understanding of the size of fractions by using reasoning skills related to benchmark fractions, visual fraction models or the number line.
  • Lessons addressing equivalent fractions (4.NF.1) use the area model to help connect and develop the concept of equivalent fractions and why the algorithm for creating equivalent fractions works. However, in these lessons the student practice pages focus on using the standard algorithm without more lengthy practice and exploration on why it works.
  • Lessons addressing multiplication and division (4.NBT.A and 4.NBT.B) offer opportunities at the beginning of the lessons to use arrays and other visual models (3.3 and 10.8), and the rest of the lesson focuses on procedural fluency with a given strategy. Students are not asked to justify or explain their answers 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
+
-
Indicator Rating Details

The Grade 4 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.
  • Some lessons have ongoing practice that primarily address procedural skill and fluency (e.g., 3.2, 5.8 and 6.2).
  • Several lessons offer opportunities to develop fluency to "add and subtract multi-digit whole numbers within 1 million" (4.NBT.4). (Modules 2 and 4.)
    • The lessons on using the standard algorithm for addition and subtraction (Lessons 2.4-2.8 for addition; Lessons 4.1-4.7 for subtraction) have student work that primarily addresses developing procedural skill and fluency for the aspect of rigor stated in the standard. Some lessons include a generic application context (e.g., making change with money to connect to needing to rename numbers (Lesson 4.1); and a few lessons also include Justification/Explanation type problems where student must catch and explain an error (Lesson 2.5, Lesson 4.2).
    • However, unlike Grade 3, there is little indication that the expectation of fluency is consistently addressed throughout the year. Of the interview assessments, none address fluency with the standard algorithm for addition/subtraction.

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 4 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.

  • Modules 2 and 4-12 contain lessons that address solving real-world problems.
  • Several lessons specifically address standards that involve application (4.OA.3, 4.NF.3.D and 4.NF.4.C).
  • "Stepping Into Financial Literacy" offers lessons on Financial Literacy.
  • Each module contains three investigations that require application.
  • Some lessons have ongoing practice available that focuses on application (e.g., 3.2, 4.10 and 5.6).
  • Lessons aligned to the 4.OA.3 do not reach the full intent of the standard. Few word problems in these lessons are 2-step and rarely do students encounter multi-step problems.
  • Most problem-solving lessons focus on measurement and do not offer opportunities to solve 2-step problems.
  • Students are not consistently exposed to non-routine problems. There are missed opportunities in each module's problem-solving lesson to expose students to non-routine problems.
  • Students are rarely asked to use a letter to represent the unknown when solving problems (Lesson 2.9, 4.7 and 6.12).
  • Lessons addressing word problems with multiplying fractions (4.NF.4.C) primarily focus on the development of conceptual understanding or procedural skill rather than application.
  • Students do not have opportunities to solve application problems in each lesson. Additionally, students are not exposed to application problems on each type of assessment.

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 4 partially meet the expectations for balance. Overall, the three aspects of rigor are neither always treated together nor always treated separately within the materials, and a balance of the three aspects of rigor within the grade is lacking.

  • 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 conceptual understanding and application work compared to the emphasis given to fluency.
  • There are almost no lessons that bring multiple aspects of rigor together. For example, lesson 4.9 only requires students to use application to find whole-number quotients. There is a missed opportunity to show conceptual understanding.
  • Conceptual development related problems are included in the curriculum, but typically as introductory questions where the majority of time spent is on student independent work on procedural responses.
  • Each module contains lessons addressing procedural skill (4.1) conceptual understanding (4.4) and application (4.7).
  • Assessments do not include a balance of questions from all three aspects of rigor. Fluency and application questions are often missing from assessments. For example, summative assessment 1 (checkup, interview and performance task) do not contain questions that address fluency or 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 4 do not meet the expectation for supporting the Standards’ emphasis on mathematical reasoning. The students are given very limited opportunities to justify or explain their thinking, and there are no 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 4 partially meet the expectations for identifying the MPs and using them to enrich mathematics content within and throughout Grade 4. Overall, the instructional materials identify the MPs but do not consistently use them to enrich the content. Also, some MPs are over identified, and some are under identified.

  • MPs are identified in the “Steps” portion of each module lesson.
  • MPs are identified in 123 of the 144 lessons. These lessons have 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 explains 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 64 lessons, whereas MP4 is only identified in 5 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 4 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: In Module 1 students are asked which strategy they used, however the student doesn’t have to persevere to solve these problems. The problems in ongoing practice are routine. In lesson 2.3, students are shown several musical instruments with price tags. The students are told to use estimation to see if they have enough money to buy them instead of being asked how they could determine if they had enough money to buy the instruments. This MP is typically assigned to problems used in whole class discussion or games that are more difficult due to being slightly out of the range/focus of the grade (i.e., rate contexts with multiplication/division or multiple steps) or require students generate multiple answers. There is little evidence this MP is addressed regularly on student independent work or on assessments.
  • MP2: Module 3 asks students to think about fractions quantitatively, but rarely asks them to think abstractly. In lesson 1.4 students are asked to represent numbers in terms of different place value groupings. However, they are told how 20 groups of one hundred is the same as 200 groups of 10 instead of being asked to contextualize the numbers for themselves.
  • MP4: Few real world problems are available in the program except in “Stepping into Financial Literacy.” Students rarely choose their own models to help solve a problem or reason about a real-life situation. Models, when used, are provided for the student (i.e., tables and extending patterns). Lessons 10.12 does involve parts of the modeling process by extending growing shape patterns, using tables to model pattern situations, and creating equations, but students are explicitly directed to finish a pattern. Lesson 9.10 provides conversion tables and line plots rather than allowing students to select a modeling tool. In lesson 11.1 students are creating fraction models with a partner, but not real-world context is provided.
  • MP5: Tools are chosen for the students rather than allowing students to choose the tools themselves (lesson 12.8). Lessons usually focus on using a particular mathematical tool. In Lesson 1.1 and 1.8 students are prompted to use the number line. In lesson 3.8 students are prompted to use a number line and visual fraction models. In lesson 8.8 students are given rulers and prompted to use cm or mm.

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
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 4 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 very limited opportunities to justify or explain their thinking. There are not opportunities for evaluating the thinking of others.

  • The materials rarely prompt students to explain and justify their thinking, and, opportunities for constructing arguments are not found in the student journal.
  • There are no opportunities for students to reconsider their own argument in response to the critique of others.
  • There were only 18 lessons that specifically addressed MP3. Four Modules did not address MP3 at all.
  • There are many missed opportunities including:
    • Module 2 Lesson 1-Students compare strategies and discuss efficiency.
    • Students considered a conjecture made by the teacher in Module 3 Lesson 3. However, they did not make a conjecture on their own. This does not fully support MP3.
    • In lesson 3.9, students are asked to write in their reflection journal about fraction concepts, but not justify their fractional shading of a whole. Also, while working in pairs they are only asked to share their shadings, not justify their shadings with a partner and explain why theirs is correct. Students are sometimes asked to construct viable arguments, but are rarely asked 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 4 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 student 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 3, Lesson 9, students are only prompted to share their fractional shadings with a partner, but are not asked to justify their shadings to their partner or ask their partner to justify their shadings. Students are strictly "showing" their work.
  • There is no evidence of teachers engaging students in both constructing viable arguments and analyzing the arguments of others.
  • There is no evidence of supporting teachers in helping students create viable arguments. There are instances in lessons (especially at the beginning) that do ask questions where arguments/responses would be created and discussed, but there is no guidance for the teacher on how to assist students in creating clear arguments.
  • There is no support for teachers in supporting students critiquing each other.

Indicator 2g.iii

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

The materials reviewed for Grade 4 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.
  • The materials use precise and accurate mathematical language some of the time.
  • For example, definitions are provided for teachers and students in Module 10, Lesson 9. Line segment, angle, and ray are explicitly defined. Students work with geometric vocabulary and symbols to distinguish line segments, lines and rays.
  • There are instances where using precise and accurate mathematical language is avoided.
    • Multiple is defined as the numbers that you say when counting in steps of the same number.
    • Module 10, Lesson 9 - Any line can be split into two parts by a point. Each part is called a “half-line” or “ray”

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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