Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 3 partially meet the expectation for alignment to the CCSSM. The materials meet expectations in the areas of focus and coherence, but 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 are above grade-level topics included in the assessment, but they do 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 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 does 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. 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
7
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 3 meet expectations for major work and coherence. Stepping Stones does assess future grade level content on some Grade 3 test items. However, 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 CCSSM Supporting Work and Major Work Mathematics Standards 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 content designated for one grade level is viable for one school year in order to foster coherence between grades. The instructional materials identify and connect prior or future grade-level work to current grade-level work. Additionally, students are consistently provided extensive work with Grade 3 work and connections are made to prior knowledge from earlier grades. The materials include learning objectives that are visibly shaped by CCSSM cluster headings. 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.

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 3 meet expectations for assessing grade-level content. For this indicator, the review team examined all summative assessments. There are several test items that would need to be modified or omitted because of their alignment to above grade-level standards. 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 3 meet the expectations for assessing grade-level content. For this indicator, the review team examined all summative assessments. There are several test items that would need to be modified or omitted because of their alignment to above grade-level standards. 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 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).
  • Module 1, Interview 2, assesses 4.MD.A.1 (students use pints, quarts and gallons to estimate and measure liquid volume). This assessment could be replaced by one of the other assessment options.
  • Module 10, Check-Up 2, Question 3, assesses 4.MD.C.5 (measure and compare angles using nonstandard units). This item could be omitted, or the assessment could be replaced by one of the other assessment options.
  • The following items assess 4.NBT.B.4 (standard algorithm for addition) and the teacher could change the directions to allow students to use any strategy:
    • Module 8, Check-up 2, Item 2
    • Module 8, Performance Task 1, Items 1 and 2
    • Quarterly Test 3, Items 11 and 12 (labeled)
    • Module 11, Check-Up 1, Items 1 and 2 (labeled)
    • Quarterly Test 4, Items 4 and 5
    • Module 11, Performance Task 1
  • The following items assess 4.NBT.B.5 (multiplication) and these items or assessments could be omitted:
    • Module 3, Interview 1
    • Quarterly Test 1, Item 5
    • Module 9, Performance Task 1
    • Quarterly Test 2, Item 7

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 3 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 144 lessons, 96 are devoted to major work of third grade. Overall, the instructional materials allocate adequate instructional time to clusters of standards that are major work of Grade 3.

Indicator 1b

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

The instructional materials reviewed for Grade 3 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, approximately 67 percent, is aligned with this indicator because it specifically addresses the amount of standards instruction devoted to major work.

  • Grade 3 instruction is divided into 12 modules with 12 lessons in each module. Of the 144 lessons, 96 are aligned to major work of Grade 3. Therefore, approximately 67 percent of instruction would be focused on major work.
  • Grade 3 instruction is divided into 12 modules. 10 of the 12 modules have instruction in half or more of the module that is focused on major work of Grade 3. Therefore, approximately 83 percent of instruction would be focused on major work.
  • Grade 3 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 3. Therefore, approximately 53 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 3 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, 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 content designated for one grade level is viable for one school year in order to foster coherence between grades. 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. The materials include learning objectives that are visibly shaped by CCSSM cluster headings. 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.

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 3 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 perimeter (3.MD.8) is addressed in lessons 12.9, 12.10, 12.11 and 12.12 and is connected to major work of area (3.MD.C).
  • Representing data sets (3.MD.3) is addressed in lessons 7.10, 7.11 and 7.12. Students are asked to identify and label fractions/mixed numbers on the number line (3.NF.2).
  • Representing bar graphs (3.MD.3) is addressed in lesson 7.11. Using the bar graphs to answer addition and subtraction problems supports part of the major work of 3.OA.8.
  • Shading parts with equal areas (3.G.2) is addressed in lessons 4.9, 4.10, 4.11 and 4.12. Students are asked to focus on the area of the parts, which are equal (3.NF.1), and not count the number of parts.

Missed connections between supporting and major work:

  • Working with shapes and their attributes (3.G.A) is addressed in lessons 5.9, 5.10, 5.11 and 5.12. In this supporting cluster, students are not asked to determine area measurements (3.MD.C).
  • Representing data sets (3.MD.3) is addressed in lessons 7.10, 7.11 and 7.12. However, students are not asked to multiply or divide to solve problems (3.OA.8).

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 3 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 3 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 current 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:
    • Lesson 10.11 and 10.12 reasoning with shapes and their attributes (2.G.1).
    • Lessons 1.1 and 1.2 working with 3-digit numbers (2.NBT.3).
    • Lesson 1.3 comparing 3-digit numbers (2.NBT.4).
    • Lesson 1.4 rounding 3-digit numbers (2.NBT.1).
    • Lessons 4.1-4.7 working with 4-digit numbers (2.NBT.3).
    • Lesson 4.6 comparing 4-digit numbers (2.NBT.4).
    • These lessons are used to build prior knowledge to introduce the addition and subtraction of larger numbers.
  • Future grade level topics taught are identified:
    • Lesson 1.10 introduces gallons (4.MD.1) and has students make liquid comparisons, not conversions.
    • Lesson 10.9 introduces angle measurement (4.MD.5) and has students making comparisons using pattern blocks, not protractors, for measurement.
    • Lessons 8.2-8.5 specifically ask students to use the standard algorithm for subtraction (4.NBT.4).

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 provide practice to reinforce concepts and computational skills at grade level.
  • Reviewer Note: Represent and interpret data (3.MD.B) is only addressed in three lessons: picture graphs lesson 7.10, bar graphs lesson 7.11 and line plots lesson 7.12. 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 relate grade-level concepts explicitly to prior knowledge from earlier grades.

  • 3.OA.5, in lesson 3.3, has students develop their multiplication knowledge by using place-value understandings from prior grades to double quantities.
  • Strong connections are made between the array models and the concept of equal groups learned in Grade 2 to the multiplication learning in Grade 3.
  • Work with subtraction strategies begins with a review of the count-back and count-on strategies as well as work to subtract across key benchmarks such as 100.

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 3 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. 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.

  • Working with liquid volume (3.MD.2) is connected to problem solving (3.OA.8) in lesson 1.12.
  • Partitioning shapes (3.G.2) is related to fraction work (3.NF.1) in lessons 4.9-4.12.
  • Using distributive property (3.OA.5) is used to calculate area (3.MD.7) in lesson 10.6.

Gateway Two

Rigor & Mathematical Practices

Does Not Meet Expectations

+
-
Gateway Two Details

The instructional materials reviewed for Grade 3 Stepping Stones do not meet expectations for rigor and the MPs. The instructional materials give attention to all three aspects of rigor, but there is not equal emphasis given to the three aspects. Materials do not consistently offer opportunities for conceptual understanding, which under-emphasizes that aspect of rigor. The lesson and assessment materials do not consistently provide opportunities for students to work with all three aspects of rigor in a balanced way. 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. Sometimes the materials prompt students to construct viable arguments, but they do not consistently prompt them to analyze other students' arguments. They do not assist teachers in engaging students in constructing viable arguments or analyzing the arguments of others. 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.
6/8
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 3 Stepping Stones partially meet expectations for rigor and balance. The instructional materials give attention to all three aspects of rigor, but there is not equal emphasis given to the three aspects. Materials do not consistently offer opportunities for conceptual understanding, which under-emphasizes that aspect of rigor. The lesson and assessment materials do not consistently provide opportunities for students to work with all three aspects of rigor in a balanced way. 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 3 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 1.6, 3.1, 3.2, 3.6, 5.1, 5.2, 5.3, 6.7, 9.5, 9.7 and 9.8 specifically address standards which are explicitly outlined as conceptual standards (3.OA.1 and 3.OA.2).
  • Lessons 4.8-4.12, 6.8-6.12, 11.1-11.5 and 12.1-12.8 specifically address standards which are explicitly outlined as conceptual standards (3.NF.A).
  • The “Number Case” channel provides resources for students to use models.
  • Students are given opportunities to develop multiplication concepts when asked to represent multiplication with cubes and other manipulatives in groups and arrays.
  • Lesson 1.6 addresses multiplication concepts (3.OA.1) and includes visual models, discussions of equality of arrays, interpretations of array rows, and equations associated with visuals models.
  • Lesson 3.1 develops the concept of multiplication (3.OA.1). Students model multiplication problems with number blocks, write multiplication equations and word problems, and draw a picture to match the story. However, sufficient time is not allowed for students to develop the concept of multiplication as defined by the standards. There is little opportunity for students to explain their thinking/reasoning. Opportunities for student explanations is not addressed in the following sections of the program: observation, discussion, journal, portfolio, or the interview.
  • Lesson 3.6 addresses multiplication concepts (3.OA.1) using engaging problems with recipes and groups of guests. Students are asked to interpret multiplication using doubling and quadrupling.
  • Lessons 9.5 and 9.7 develop multiplication concepts (3.OA.1). However, the major focus of these lessons is fluency, and therefore does not support the full intent of the standard. Less emphasis is placed on using manipulatives as tools to conceptualize.
  • Lessons 5.1, 5.2 and 5.3 develop division concepts (3.OA.2). These lessons introduce the concept of whole-number quotients. There is some use of visual representations to help students understand the concept, but there is little opportunity for students to verbalize their thoughts or understanding and is not provided in the following sections of the program: observation, discussion, journal, portfolio, or the interview.
  • Lesson 4.9 addresses fraction concepts (3.NF.A) by using paper squares folded in equal parts to model the same fraction in different ways. Squares are marked with dashed lines for folding or are represented in the student journal. Students are not asked to take squares and partition them into equal parts independently.
  • Lesson 6.8 addresses fraction concepts (3.NF.A) by using fractions strips to model how folding certain fractions creates other fractions. Students are provided fraction strips and must individually partition them to show fractions with the denominators 2, 3, 4 and 6.
  • Lesson 11.1 addresses fraction concepts (3.NF.A) through the use of area models to identify equivalent fractions. Students are not required to partition shapes on their own. The partitioning is always provided and students do not create the models themselves.
  • Lesson 12.1 addresses fraction concepts (3.NF.A) through the use of number line models to identify equivalent fractions. Number lines are provided for students with the partitioning already done. Students do not have to create number lines and then identify fractions.

Indicator 2b

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

The Grade 3 materials meet the expectations for procedural skill and fluency. Fluency is strategically developed, interwoven throughout the curriculum, and connected to conceptual development. In addition, it is very clear that this curriculum expects the development of fluency as described in the grade levels standards.

  • “Fundamental Games” provides opportunities for students to practice fluency through games.
  • Multiplication/division facts are taught in a designed sequence (e.g., 5s and 10s in Module 1; 2s and 4s facts in Module 3; connection of 5s, 10s, 2s, and 4s facts to division facts in Module 5; etc.) that show a focus on supporting development of fact fluency for multiplication and division.
  • Several lessons offer opportunities to fluently multiply and divide within 100. (Modules 2, 3, 5, 7, 8 and 9)
  • Fluency is built upon a series of steps in the materials. Students are introduced to a strategy with pictorial support. They then build fluency based on facts related to strategies they have been using.
  • Every module includes interview-based assessments which include assessment of student fact fluency and often include recording of student strategy use.

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
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 3 meet the expectations for students to spend sufficient time working with engaging applications of the mathematics. Overall, the instructional materials consistently offer opportunities for students to engage in application of learning to real-world situations.

  • Lessons 3.6, 5.1, 5.4, 5.5, 6.7, 7.5, 8.9, 9.7 and 10.5 specifically address standards which are explicitly outlined as application standards (3.OA.3).
  • Lessons 1.12, 2.12, 3.6, 6.7, 7.5, 8.6, 9.7, 9.10-9.12, 11.12 and 12.3 specifically address standards which are explicitly outlined as application standards (3.OA.8).
  • Students are exposed to single and multi-step contextual problems and non-routine problems.
  • Each module contains one lesson focused on “Solving Real World Problems.”
  • "Stepping Into Financial Literacy" offers lessons in financial literacy.
  • Each module contains three investigations that require application of learning.
  • A variety of one- and two-step story problems are presented in the lessons and assessments.
  • Lesson 3.6 extends student exploration with standard equal groups and rows using word problems that introduce the concept of making multiples of a recipe.
  • Lessons 9.5 and 9.6 provide abstract, interesting game contexts to help students explore sets of factors that create the same product and the order of operations and its effect on the size of a total.

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 3 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 conceptual understanding compared to the emphasis given to procedural skill and fluency.
  • Students assessments do not offer a balance of rigor and are often missing questions requiring application.
  • Each module contains one lesson focused on “Solving Real World Problems” and three investigations that require application.
  • There are a few areas where the three aspects of rigor are well balanced. For example, in lesson 3.6, students develop conceptual understanding of interpreting contexts where a recipe needs to be multiplied by a factor, work through a range of more difficult application problems and develop fluency with creating multiplication equations to model more familiar multiplication contexts, and work with strategies (double a double when multiplying by 4).

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 3 do not meet the expectation for supporting the Standards’ emphasis on mathematical reasoning. Sometimes the materials prompt students to construct viable arguments, but they do not consistently prompt them to analyze other students' arguments. They do not assist teachers in engaging students in constructing viable arguments or analyzing the arguments of others. 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 3 partially meet the expectations for identifying the MPs and using them to enrich mathematics content within and throughout Grade 3. Overall, the instructional materials identify the MPs 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 throughout all 144 lessons. Each lesson has 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.
  • MP2 was over-identified in the materials with 70 lessons out of 144 addressing this practice.
  • MP5 was greatly under-identified with only 6 lessons out of 144 and was found in 3 of the 12 modules.
  • Module 4 does not address MP1, MP3, or MP5.
  • 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.

Indicator 2f

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

The instructional materials reviewed for Grade 3 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: Often routine problems are given and are quoted as MP1. MP1 is not fully addressed in lessons 3.10 and 5.1. Students are not asked to make meaning of problems and are asked to work in small groups, not independently. This MP is typically assigned in this curriculum when a problem type is being used in the whole class discussion or in a game that is more difficult due to being slightly out of the range/focus of the grade (i.e., rate contexts with multiplication/division or has multiple steps) or requires generating multiple answers. There is little evidence this MP is addressed regularly on student independent work or on assessments.
  • MP2: Students are asked to reason abstractly when introducing vocabulary as part of lessons in Module 2, but they are not asked to use the same skills during the lesson or ongoing practice. In lessons 5.2 and 8.1, students are asked to represent their thinking symbolically but not required to manipulate the symbols.
  • MP4: Modeling is not always tied to a real-life context. For example, in lesson 3.1, there is no real-life context provided when using multiplication or addition equations. Also, when creating mathematical models, students are told which models to use and are not provided opportunities to select for themselves. For example, in lesson 9.6, students are taught adding fractions using number lines and fraction models, but during independent practice, they are instructed to use number lines.
  • MP5: The tools are usually chosen for the student and the teacher rather than allowing the student to choose the tool. For example, in lesson 1.3 students are told to use a number line and in lesson 2.1 students are told to use a pan balance.
  • MP6: Students are given multiple opportunities to use a variety of mathematical symbols including the equal sign. However, students are often provided with equations and do not get to state the meaning of the symbols that they choose.

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 3 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 materials sometimes prompt students to construct viable arguments, but they do not consistently prompt them to analyze other students' arguments.

  • There are some occasions where students are asked to present an argument when prompted by a teacher to tell how they know; however, opportunities for constructing arguments are rarely found in the student journal.
    • An example where this is done well: Module 2, Lesson 5, where students explain their thinking. Student pages include these questions: “Which strategy on this page do you like the best? Why?” These questions prompt the critique of others’ thinking.
  • There are many missed opportunities including:
    • Module 1, Lesson 2: Students are not prompted by the materials to construct an argument or explain their thinking.
    • Module 7, Lesson 5: Students explain why the letter t is chosen as the variable and create questions and number sentences relating to a menu, but there is no opportunity to analyze the thinking of others.
    • MP3 is not identified in Modules 3, 4 or 5 and minimally so in the other Modules. Students occasionally construct viable arguments, but rarely critique the reasoning of others (i.e., lesson 1.7 and 2.3). Students are often encouraged to share their strategies, but are not provided guidance on critiquing others (i.e., lesson 7.5 and 11.6).
  • No opportunity for students to reconsider their own argument in response to the critique of others.
  • No opportunity for students to construct an argument and/or analyze the thinking of others on assessments.

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 3 do not meet the expectation for assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others.

  • Teacher materials sometimes prompt students to have discussions, but do not provide true opportunities for students to construct arguments or analyze the arguments of others. For example, in Module 8, Lesson 2, students are only prompted to discuss “How is the recording of the steps the same or different from other methods we have used?”
  • The materials do not provide ample open-ended questions that allow students to grapple with concepts.
  • Many questions are low depth of knowledge and do not promote deep understanding of the concepts. (e.g., Module 3, Lesson 1, "What amount do we have in each place value? What will we write in each place so we know the amount when we do not have base-10 blocks?")
  • There are many missed opportunities for teachers to prompt students to analyze 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 3 do not meet the expectation for attending to the specialized language of mathematics.

  • There is little to no explicit instruction on how to use the language of mathematics.
  • There are instances where using precise and accurate mathematical language is avoided.
    • The commutative property is referred to as the "turn-around facts."
    • In Module 1, lesson 6, the introduction of the array is not supported with precise language. “Introduce or remind students of the term array which is used to describe this type of arrangement of objects.” (rows of/groups of.)
    • In Module 6, lesson 10, numerator and denominator are referred to without being defined for students. Fold is used instead of partition in reference to fractions. Students are not prompted to use the precise language of numerator and denominator when referring to numbers in a fraction.
    • In Module 5, lesson 9, no specific definitions are used to introduce vertices. The Student Journal page refers to the vertices as corners. Students sort shapes into “shapes with dents” and “shapes without dents.”
    • Students are not always prompted to use precise language when writing and speaking about mathematics.

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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