Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 2 did not meet the expectations for alignment to the CCSSM. The instructional materials partially meet the expectations for Gateway 1 as they appropriately focus on the major work of the grade but did not always demonstrate coherence within the grade and across other grades. The instructional materials do not meet the expectations for Gateway 2 as they did not address rigor within the grade-level standards, and there are missed opportunities in the materials when it comes to attending to the full meaning of the standards for mathematical practice.

See Rating Scale
Understanding Gateways

Alignment

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Does Not Meet Expectations

Gateway 1:

Focus & Coherence

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

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
5
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

Usability

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Not Rated

Not Rated

Gateway 3:

Usability

0
22
31
38
0
31-38
Meets Expectations
23-30
Partially Meets Expectations
0-22
Does Not Meet Expectations

Gateway One

Focus & Coherence

Partially Meets Expectations

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Gateway One Details

The instructional materials reviewed for Grade 2 enVision Math 2.0 partially meet the expectations for Gateway 1. The materials meet the expectations for focusing on the major work of the grade, but they do not meet the expectations for coherence. Some strengths were found and noted in the coherence criterion as the instructional materials partially met some of the expectations for coherence. Overall, the instructional materials allocate enough time to the major work of the grade for Grade 2, but the materials do not always meet the full depth of the standards.

Criterion 1a

Materials do not assess topics before the grade level in which the topic should be introduced.
2/2
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Criterion Rating Details

The instructional materials reviewed for Grade 2 meet the expectations for assessing grade-level content. Overall, the instructional materials can be modified without substantially affecting the integrity of the materials so that they do not assess content from future grades within the assessments provided.

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
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Indicator Rating Details

The assessment materials reviewed for Grade 2 meet expectations for focus within assessment. Content from future grades was found to be introduced; however, above grade-level assessment items, and their accompanying lessons, could be modified or omitted without significantly impacting the underlying structure of the instructional materials.

Probability, statistical distributions, and/or similarity, transformations and congruence do not appear in the Grade 2 materials.

The series is divided into topics and each topic has a topic assessment and a topic performance assessment. Additional assessments include a placement test found in Topic 1, four cumulative/benchmark assessments, and a End-of-Year Assessment.

The topic assessments have a few items which assess future grade level standards.

  • Topic 3, Question 1 should say mass instead of weight because balances measure mass, which is a Grade 3 standard 3.MD.1.
  • In Topic 4, page 252A, questions 3 and 4 ask about "regrouping." In lesson 4-3 on page 206, a step-by-step procedure is taught, the standard algorithm; students are not directed to attend to place value, properties of operations and the relationship between addition and subtraction, and this procedure is used throughout the topic.
  • In Topic 4, page 252, item 3, students are directed to use regrouping with a procedure, which is a Grade 4 standard 4.NBT.4; students are not directed to attend to place value, properties of operations and the relationship between addition and subtraction.
  • In Topic 6, pages 383-386, items 1, 2, 5, 6, 7, 8, 9 and 13 all include regrouping which is treated in Topic 6 as a procedure, a Grade 4 standard 4.NBT.4; students are not directed to place value, properties of operations and the relationship between addition and subtraction.
  • In Topic 6, page 386A, items 1, 5, 6, 7, 8, 9 and 13 all include regrouping which is treated in Topic 6 as a procedure, a Grade 4 standard, 4.NBT.4; students are not directed to attend to place value, properties of operations and the relationship between addition and subtraction.
  • Topic 1-8 Cumulative Review, page 502B, item 21, includes regrouping which is treated in Topic 6 as a procedure, a Grade 4 standard, 4.NBT.4; students are not directed to attend to place value, properties of operations and the relationship between addition and subtraction.
  • Topic 10, page 634, item 4, asks students to critique a solution strategy that is using a procedure, a Grade 4 standard, 4.NBT.4; students are not directed to attend to place value, properties of operations and the relationship between addition and subtraction.
  • Topic 10, page 534A, item 4, asks students to critique a solution strategy using a procedure, a Grade 4 standard, 4.NBT.4; students are not directed to attend to place value, properties of operations and the relationship between addition and subtraction.
  • Topic 11, page 684A, item 7, asks students to solve a subtraction problem that is represented as a procedure, a Grade 4 standard, 4.NBT.4; students are not directed to attend to place value, properties of operations and the relationship between addition and subtraction.
  • Topic 8 Topic Assessment item 2 and Topic 8 Performance Assessment item 4b assess adding minutes to time; this is a Grade 3 standard, 3.MD.1.

The off-grade level items could be removed without affecting the sequence of learning for the students.

Note:

  • In Topic 12, item 2, the student is expected to answer that the scarf is 1 yard and the shoe is 1 foot. In the picture, the scarf and shoe are the same size.

Criterion 1b

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

The instructional materials reviewed for Grade 2 meet the expectations for focus on the major clusters of each grade. Students and teachers using the materials as designated will devote the majority of class time to major clusters of the grade which include 2.OA.A, 2.OA.B, 2.NBT, 2.MD.A and 2.MD.B.

Indicator 1b

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

The instructional materials reviewed for Grade 2 meet the expectations for focus within major clusters. Overall, the instructional materials spend the majority of class time on the major clusters of each grade which includes 2.OA.A, 2.OA.B, 2.NBT, 2.MD.A and 2.MD.B.

To determine this, three perspectives were evaluated: 1) the number of topics devoted to major work, 2) the number of lessons devoted to major work, and 3) the number of days devoted to major work. The number of days is the same as the number of lessons. A lesson level analysis is more representative of the instructional materials than a topic level analysis because the number of lessons within each topic is inconsistent, and we drew our conclusion based on that data.

Grade 2 enVision Math 2.0 includes 15 Topics with 116 lessons.

At the topic level, 9 of the 15 topics focus on major work. 2.5 of the 15 topics focus on supporting work and connect to the major work of the grade, 1.5 of the 15 topics focus on supporting work without connecting to the major work, and 2 topics focus on the off-grade level work of 4.NBT.4 using procedures to solve addition and subtraction instead of attending to place value, order of operations and the relationship between addition and subtraction. Approximately 77 percent of the topics are focused on major work (counting the 2.5 topics which somewhat supports major work), approximately 10 percent of the topics are focused on supporting clusters and do not support the major work of the grade, and approximately 13 percent of the topics are focused on off-grade level topics.

A lesson level analysis is more representative of the instructional materials than a topic level analysis because the number of lessons within each topic is inconsistent. At the lesson level 70 lessons focus on major work, 17 lessons focus on supporting work and the major work of the grade, 10 lessons focus on the supporting work without connecting to the major work, and 20 lessons focus on off-grade level work that consists of having students use procedures to solve addition and subtraction problems. At the lesson level approximately 59 percent of the lessons focus solely on major work, approximately 15 percent of the lessons focus on supporting work connected to major work, approximately 9 percent of the lessons focus on supporting work which does not support the major work, and approximately 17 percent focus on off-grade level work. At the lesson level, approximately 74 percent of the lessons focus on major work of the grade.

Criterion 1c - 1f

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

The instructional materials reviewed for Grade 2 do not meet the expectations for being coherent and consistent with CCSSM. The instructional materials do not have enough materials to be viable for a school year and do not always meet the depth of the standards. The majority of instructional materials do not have supporting content enhancing focus and coherence simultaneously but do have objectives which are clearly shaped by the CCSSM. Overall, the instructional materials for Grade 2 do not exhibit the characteristics of coherence.

Indicator 1c

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

The instructional materials reviewed for Grade 2 partially meet expectations that supporting content enhances focus and coherence by engaging students in the major work of the grade. Some of the supporting work is treated separately and does not support the major work of the grade, and many natural connections are missed.

The following details supporting work in the instructional materials.

  • Topic 2 is focused on working with equal groups. It supports the major work of the grade. The lessons each have questions about adding and subtracting within 20.
  • Topic 8 is focused on time and money. The money lessons support the major work of the grade by adding and subtracting within 100. For example, lessons 8-1 through 8-4 focus on solving problems with money. Students count coin and dollar values to find sums. At times directions ask students to "count on" to find the total value. There is a missed opportunity here to support major work through a connection to addition and subtraction; this connection isn't introduced until 8-4. Lesson 8-5 focuses on reasoning and has students showing values in different ways. There is a missed opportunity to make connections to place value as the coin values could also be seen as distinct units. For example a dime is a ten, composed of 10 ones, or pennies. There could also be a connection to composing any given number in multiple ways. The lessons on time are treated separately from the major work of the grade. There are missed opportunities to connect time to counting by fives 2.NBT.2.
  • Topic 14 is focused on graphs and data. This topic minimally supports the major work of the grade. Students could be answering compare, put-together, and take-apart problems with graphs. The majority of the questions associated with the graphs do not ask these types of questions but instead simply ask how many.
  • Topic 15 is focused on equal shares of circles and rectangles. This topic is treated separately with the exception of one lesson; 15-5 supports adding within 100.

Indicator 1d

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

The amount of content designated for one grade level is not viable for one school year in order to foster coherence between grades. The pacing guide assumes one lesson per day as stated on page TP-23A. The enVision Math 2.0 Grade 2 program consists of 116 lessons, grouped in 15 topics. Assessments are not included in this count; if the 15 days of assessment are added in this would bring the count to 131 days. This is still below the standard school year of approximately 140-190 days of instruction. Significant modifications by the teacher would need to be made to the program materials to be viable for one school year and for the students to meet the expectations of the grade-level standards.

Indicator 1e

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

The instructional materials reviewed for Grade 2 partially meet the expectations for being consistent with the progressions in the standards. Overall, the materials give students extensive work with grade-level problems and relate grade-level concepts explicitly to prior knowledge from earlier grades, but the materials do not reach the full depth of the standards and do not always clearly identify work that is off grade level.

Material related to future grade-level content is not clearly identified or related to grade level work. The exception is the topic titled "Step up to 3rd grade" where the materials are clearly identified as Grade 3 materials. The Grade 2 materials have some instances where future grade-level content is present and not identified as such. For example, lesson 4-4 teaches students to add without attending to strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

The content does not always meet the full depth of the standards. This occurs due to a lack of lessons addressing the full depth of standards. For example:

  • There are six lessons which address 2.NBT.1, all of which fall in Topic 9. This standard, understanding the values of 3-digit numbers, is the foundation for students to understand numbers from 100-999 and "use place value and properties of operations ...," and this standard supports the development of "level 3 strategies" as explained on page 6 of the Operations and Algebraic Thinking progression document.
  • A second example is 2.OA.C, work with equal groups of objects to gain foundations for multiplication. There are five lessons that address this standard, all in Topic 2.
  • A third example is major clusters 2.MD.A and 2.MD.B, for which there are two lessons addressing 2.MD.2, two lessons addressing 2.MD.4, and 2 lessons addressing 2.MD.6.

The materials extensively work with grade-level problems, for example:

  • All students complete grade-level materials, and suggestions for re-teaching and intervention are included with each lesson and at the end of each topic.
  • Online resources include extra, on-level and advanced-practice materials.
  • Interventions provided with lessons for students most often engage students more deeply in the work of the grade level than the lesson itself. Often, students are simply following directions instead of being engaged in problems.
  • The numbers of topics addressing Grade 2 domains are as follows: 7 out of 15 topics address numbers in base ten; 3 out of 15 topics address operations and algebraic thinking; 4 out of 15 topics address measurement and data; and 1 out of 15 topics address geometry.

The materials relate grade-level concepts to prior knowledge within the introduction of each topic, for example:

  • "Math Background: Coherence" includes "Look Back" and "Look Ahead" commentary, connecting to mathematics that came earlier in Grade 2, explaining connections to the content within the topic, and explaining what will come later in Grades 2 and 3. An example can be found on pages 389c-389d for Topic 7.
  • Individual lessons also include coherence headings. An example is in lesson 5-6 on page 285A that includes the heading, "Coherence: In lesson 5-5, students broke apart a 1-digit subtrahend to make it easier to subtract mentally. In this lesson, students subtract a 2-digit number from a 2-digit number by breaking apart the lesser number..."

Indicator 1f

Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.
1/2
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Indicator Rating Details

The instructional materials reviewed for Grade 2 partially meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards. Overall, the materials include learning objectives that are visibly shaped by CCSSM cluster headings, but the materials lack problems and activities that connect two or more clusters in a domain or two more domains in the grade.

The materials are designed at the cluster level, and this design feature is represented throughout the material in the form of a color-coded wheel identifying the cluster focus of each unit. The materials include learning objectives which are visibly shaped by CCSSM cluster headings, and the Topic Planner at the beginning of each topic has an example of this.

  • The focus of Topic 3 is 2.NBT.5 and 2.NBT.9: Add within 100 using strategies. Lesson objectives in Topic 3 include: L1 - Add tens and ones on a hundreds chart, L2 - Add tens and ones on an open number line, and L4 - Break apart numbers to add.
  • A similar example for Topic 10 can be found on pages 583I - 583J.

The materials for Grade 2 enVision Math 2.0 do not foster coherence through grade-level connections. Most lessons in the Grade 2 program focus within a single domain and cluster. Of 116 lessons, 85 lessons focus within a single cluster and domain.

  • In Topic 1, lessons 1-9 and 1-10 are identified as addressing standards within two clusters 2.OA.1 and 2.OA.2.
  • In Topic 2, all five lessons address standards in two clusters (2.OA.A, 2.OA.B, 2.OA.C), all within the same domain.
  • Topic 3 includes one of nine lessons that addresses more than one domain, all other lessons are within a single cluster.
  • Topic 4 includes one of nine lessons that addresses more than one domain, all other lessons are within a single cluster.
  • Topic 5 includes one of nine lessons that addresses more than one domain, all other lessons are within a single cluster.
  • Topic 6 includes one of nine lessons that addresses more than one domain, all other lessons are within a single cluster.
  • All lessons within Topic 7 are within a single cluster and domain.
  • In Topic 8, all eight lessons address standards in two domains.
  • Topic 9 includes two lessons that address two clusters.The remaining lessons focus on one cluster, all within the same domain.
  • All lessons within Topic 10 are within a single cluster and domain.
  • All lessons within Topic 11 are within a single cluster and domain.
  • Topic 12 includes one lesson that addresses two clusters within a single domain.
  • In Topic 13, three of five lessons (13-2, 13-3, and 13-5) address standards within two domains.
  • In Topic 14, two of six lessons (14-1, 14-2) address standards within two clusters and the same domain, and two of six lessons (14-5, 14-6) address standards from two domains.
  • In Topic 15, two of eight lessons (15-5, 15-8) address standards within two domains.

Further analysis of Topics 8 and 12, which address supporting work, provided the following examples:

  • In Topic 8, as students work with time and money, they sometimes connect the use of operations to telling time and finding values. Lessons 8-1 through 8-3 do not connect counting coin and dollar values to operations or place value, missing opportunities to make connections across domains.
  • In Topic 12, as students work with measuring lengths, the lessons focus on the procedure of measuring. There are missed opportunities for students to make connections to fluency (2.OA.1) by comparing lengths or comparing estimates and lengths.

Gateway Two

Rigor & Mathematical Practices

Does Not Meet Expectations

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Gateway Two Details

The instructional materials reviewed for Grade 2 do not meet the expectations for rigor and practice-content connections. The instructional materials partially meet the expectations for spending sufficient time with engaging applications, but the materials do not meet expectations for any of the other indicators in rigor and balance. The instructional materials do identify the MPs and give students opportunities to construct viable arguments, but they do not always use the MPs to enrich the mathematics content and rarely have students critique the reasoning of other students. The materials do not attend to the full meaning of each MP and do not assist teachers in engaging students in constructing viable arguments and analyzing the arguments of other students. The materials meet the expectations for attending 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.
1/8
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Criterion Rating Details

The instructional materials reviewed for Grade 2 do not meet the expectations for rigor and practice-content connections. The instructional materials partially meet the expectations for spending sufficient time with engaging applications, but the materials do not meet expectations for any of the other indicators in rigor and balance. The instructional materials do identify the MPs and give students opportunities to construct viable arguments, but they do not always use the MPs to enrich the mathematics content and rarely have students critique the reasoning of other students. The materials do not attend to the full meaning of each MP and do not assist teachers in engaging students in constructing viable arguments and analyzing the arguments of other students. The materials meet the expectations for attending to the specialized language of mathematics.

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.
0/2
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Indicator Rating Details

The instructional materials reviewed for Grade 2 enVision Math 2.0 do not meet the expectations for giving attention to conceptual understanding. The materials rarely develop conceptual understanding of key mathematical concepts where called for in specific content standards or cluster headings.

Most all of the lessons in the materials have students filling out student pages in a very procedural manner. For example, in Lesson 3-4 has students using place value to solve addition problems; however, instead of truly using place value properties, students are given a procedure to use. In Lesson 5-2 students are asked to use an open number line to solve a subtraction problem; again students are quickly led to a procedure instead of exploring the conceptual understanding needed.

Rarely do the materials feature high quality conceptual problems or conceptual discussion questions. Some of the lessons start with a problem which could develop conceptual understanding; however, the lessons quickly transition to simply filling out pages in the student book.

Clusters 2.NBT.A and 2.NBT.B focus on understanding place value and using place value understanding and properties of operations to add and subtract.

  • Lessons 8-1, 8-2, 8-3, 8-6, 8-7 and 8-8 focus on MD.C and work with time and money, but an additional alignment to 2.NBT.2 is included. Skip-counting by 5s, 10s, and 100s based on place value is not addressed until Topic 9, so these six lessons are not truly developing conceptual understanding of skip-counting. These lessons focus on a procedure for figuring out the value of a group of coins or bills or telling time. For example, Lesson 8-1 is the first lesson focused on coins. The lesson begins with a word problem about cents; although the teacher directions on page 443 of the teacher’s edition state that “(y)ou may want to give students coins…to use during this activity” and “(e)ncourage students to use coins or drawings of coins,” students are not required to use manipulatives in this first problem. The example of correct student work for this problem features addition equations, not skip-counting. On page 444, students are introduced to coins and counting-on to find total values. The coins are drawn, and students are told the value of each coin. As students begin solving problems, they are using pictures of coins and the defined value of the coins to solve problems; no manipulatives are required in the lesson, including actual coins. Lesson 8-3 is the first lesson focused on dollar bills and students are provided limited opportunities to skip-count, again focused on procedure.
  • Lesson 9-1 is designed to build student understanding of hundreds, but often the lesson focuses more on procedures than conceptual understanding. The first problem on page 511 of the teacher’s edition tells teachers that “(y)ou may want to give students place-value blocks to use during this activity.” Many students in Grade 2 still need the support of concrete models in building conceptual understanding. On page 512 of the teacher’s edition, the Essential Question is “How can you find the value of a group of hundreds?” The sample answer is “I can count by hundreds to find the total.” This focus on counting impedes conceptual understanding of hundreds and place value.
  • Lesson 9-2 begins with students using place-value blocks to model 125, 259, and 395. Then the lesson transitions into pictures of place value blocks. The directions for the guided practice and independent practice problems say to “(u)se models and your workmat if needed.”
  • In Lesson 9-3, students are identifying the value of the digits in 3-digit numbers. Although a place-value chart is provided for the first problem, the instructions on page 523 of the teacher’s edition state to “(p)rovide place-value blocks…for students to use, as needed.” Place-value blocks are drawn for two problems on page 524, but the emphasis is on using the place-value chart. The Essential Question asks “How does the position of a digit help you name its value?” The sample answer is “Each place has a value. In a 3-digit number, the first digit tells the number of hundreds, the second digit tells the number of tens, and the third digit tells the number of ones.” The lesson focuses more on a procedure of using the chart more than conceptual understanding of amounts of hundreds, tens, and ones.
  • In Lesson 9-4, students are reading and writing 3-digit numbers. The directions on page 529 of the teacher’s edition say to “(m)ake available place-value blocks…for students to use throughout the lesson, as needed.” The pages in the student book focus more on correct procedures for writing numbers than conceptual understanding of place value. For example, the higher order thinking problem on the bottom of page 531 has students write a number in standard form and expanded form based on the following: “It has 5 hundreds. The tens digit is 1 less than the hundreds digit. The one digit is 2 more than the hundreds digit.” This problem does not emphasize the amount of hundreds, tens, or ones or conceptual understanding of place value.
  • Lesson 9-5 cites 2.NBT.3 and 2.NBT.1a; however, in this lesson students are simply writing 3-digit numbers in different ways. For example, on page 536 the sample problem at the top of the page shows 123 written as 100+20+3, 120+3, and 100+10+13. This lesson is not focused on developing conceptual understanding of place value.
  • In Lesson 9-8, students are comparing two 3-digit numbers. Although the lesson starts with students comparing numbers using place-value blocks, the lesson quickly transitions to writing the numbers in a place value chart vertically in order to compare digits. The lesson emphasizes the procedure of using the place value chart more than comparing the two 3-digit numbers based on the meanings of the hundreds, tens, and ones digits.
  • In Lesson 9-9, students are completing a comparison of two three-digit numbers using a number line. The focus of the lesson is on understanding that numbers that are less than another number are found to the left on the number line and numbers that are more than another number are found to the right on the number line, not comparing the two 3-digit numbers based on the meanings of the hundreds, tens, and ones digits. Students complete the page from the student book by providing a sample number that is greater than or less than a given number with no explanation or model to show their thinking.
  • Although 2.NBT.6 is cited in three lessons, Lessons 3-7, 4-5, and 4-6, this standard is only the focus of one of the lessons, Lesson 4-5. Lesson 3-7 focuses on strategies and procedures to add two 2-digit numbers, and Lesson 4-6 focuses on procedures and strategies to add numbers. In Lesson 4-5, although students are adding up to four two-digit numbers, the lesson focuses mostly on procedures. On page 218 in the teacher’s edition, the Essential Questions is “How can you add more than two 2-digit numbers?” The sample answer is “I can use the same method as adding two 2-digit numbers. I can write the numbers in two columns to align the tens and the ones. Add the ones, then add the tens. Regroup 10 ones as one ten, if needed.” The directions at the top of page 217 state that the opening activity “prepares them for the next part of the lesson, where they add up to four 2-digit numbers using the standard algorithm.” This is the only lesson focused on 2.NBT.6, and all of the pages from the student book are expected to be completed using the standard algorithm.
  • Standard 2.NBT.7 is the focus of Topics 10 and 11. In Topic 10 students are adding within 1,000, and in Topic 11 students are subtracting within 1,000. The lessons begin with using open number lines, then mental math, then partial sums, and then models. Models are used “to reinforce conceptual understanding of the standard addition algorithm” and the standard subtraction algorithm (pages 609A and 661A), not to build conceptual understanding of using place value to add and subtract within 1,000.
  • Although standard 2.NBT.8 is cited in four lessons--Lesson 9-6, Lesson 9-10, Lesson 10-1, and Lesson 11-1--this standard is only the focus of two lessons, Lesson 10-1 and 11-1. Lessons 9-6 and 9-10 focus more on patterns than using place value understanding to mentally add or subtract 10 or 100 to a given number. Lesson 10-1 focuses on adding 10 and 100, and Lesson 10-2 focuses on subtracting 10 and 100. The first problem states that the teacher should “if possible, distribute place-value blocks” (pages 585 and 637), so students may not use concrete models to develop their conceptual understanding of adding and subtracting 10 or 100. Place value drawings are provided for a few problems in both lessons, but the emphasis of the lesson is on developing procedures for finding the answers. For example, the Essential Question on page 638 of the teacher’s edition is as follows: “How can you use mental math to subtract 10 (or 100) from a 3-digit number?” The sample answer is as follows: “To subtract 10, I take away 1 from the tens digit of the 3-digit number. To subtract 100, I take away 1 from the hundreds digit of the 3-digit number. To subtract 10 from a number that has 0 in the tens place, I regroup 1 hundred as 10 tens before I subtract.”
  • Although 2.NBT.9 is cited in many lessons, the only lesson that lists this standard as the main standard is Lesson 10-6, “Explain Addition Strategies;” however, although it is not listed as the main standard, Lesson 11-6 is titled “Explain Subtraction Strategies.” In these two lessons, students are provided opportunities to choose and explain any strategy to add and subtract. Often the other lessons aligned to 2.NBT.9 include a small number of problems that require students to explain an answer based on the procedure taught in the lesson.

Cluster 2.MD.A focuses on measuring and estimating lengths in standard units.

  • Lesson 12-1 is the first lesson addressing 2.MD.A, and the standard cited is 2.MD.3. In this lesson students are using the length of objects to estimate the length of other objects before they have measured anything. On page 14 of the K-5 Progression on Measurement and Data (measurement part), the last paragraph states that “(a)fter experience with measuring, second graders learn to estimate lengths.” The progression document continues to say that “(s)killed estimators move fluently back and forth between written or verbal length measurements and representations of their corresponding magnitudes on a mental ruler.” This conceptual understanding is not possible because students have no experience with a ruler at this point.
  • In Lesson 12-5, students begin using rulers to measure objects in centimeters. An initial activity uses centimeter cubes to measure an object. However, instruction on how to use rulers and the concepts behind measuring length are not included in the lesson. Students continue estimating and measuring objects in Lessons 12-6 and 12-7 without instruction on how to use and understand the measuring tools.

There are some interventions that encourage the development of conceptual understanding; however, these interventions are not meant for all students- only those not meeting the standard.

  • For example, in Lesson 1-3 students in the intervention activity are actually connecting cubes to combine them instead of just counting cubes such as on the page from the student book from in the lesson.
  • In the Lesson 1-6 intervention kids are using post-its to show the relationship between adding and subtraction.
  • In the interventions for Lessons 2-3 and 2-4 interventions students are using counters to make arrays to find totals.

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.
0/2
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Indicator Rating Details

The materials do not give enough opportunities for students to develop fluency and procedural skill throughout the text and especially where it is specifically called for in the standards.

Standard 2.OA.2 is fluently adding and subtracting within 20 using mental strategies. By the end of Grade 2, students should know from memory all sums of two one-digit numbers.

  • The teacher's edition program overview indicates 14 lessons address this standard, and all of these lessons are in Topics 1 and 2 which would fall within the first month of school. There are fluency practice activities at the end of each of topics 1-5, 7-8, and 11. If these are used, students would have an additional eight days of fluency instruction which is likely not enough to ensure all students achieve fluency adding and subtracting to 20.
  • In Lesson 1-1 students are counting on and changing the order of addends; the sums are all within 14, not 20.
  • In Lesson 1-3, only six out of the 18 problems have sums larger than 15, and three of the six problems are in the Math Practices and Problem Solving section at the end of the lesson.
  • In Lesson 1-5, students are counting to subtract. All of the subtraction is within 16.
  • In Lesson 1-6, students only subtract from numbers larger than 15 in 6 of the 20 problems.
  • In Lesson 1-7, students only subtract from numbers larger than 15 in 5 of the 19 problems.
  • Fluency practice activities aligned to 2.OA.2 are found at the end of Topics 1-5, 7-8, and 11. These activities are all either "Point & Tally," “Follow the Path,” or "Find a Match" activities. These eight pages are found at the end of each topic, not within a lesson, so teachers would have to intentionally incorporate these activities into the lessons. Also, in some of these activities more problems are devoted to addition and subtraction within 15. For example, on page 111 only has three problems have numbers over 15, and only two sums are over 15. On page 177 every difference is less than 10, and only three problems include numbers greater than 15. On page 309, only four problems have numbers over 15, and all sums and differences are within 15. On page 679 only 7 problems out of 50 have sums over 15, and all differences are within 10.
  • Six Fluency Practice/Assessment pages from the student book aligned to 2.OA.2 are included in the instructional materials. These pages from the student book can be seen on page TP-71 of the teacher's edition. These pages from the student book each have 19 problems. There are a total of 114 problems on these pages from the student book. Only 13 problems have sums or differences from 15 to 20; most of the problems focus on addition and subtraction within 20.

Standard 2.NBT.5 is adding and subtracting within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

  • Page 83 of the teacher's edition program overview indicates 29 lessons address this standard, and all of these lessons are in Topics 3 through 6 which would fall within the half of the school year. Without continued, ongoing opportunities to practice and continue strategy instruction, it is not evident that all students will achieve fluency to 100.
  • Topic 4, which specifically references fluency in the topic title, uses partial sums and algorithms to teach procedural skill but has no specific activities designed to increase student fluency other than these procedures. Topic 6, which also specifically references fluency in the title, uses algorithms for subtraction to teach procedural skill but does not specifically address fluency either.
  • Fluency practice activities aligned to 2.NBT.5 are found at the end of Topics 9, 10, and 12-15. These activities are all either "Point & Tally," “Follow the Path,” or "Find a Match" activities. These six pages are found at the end of each topic, not within a lesson, so teachers would have to intentionally incorporate these activities into the lessons. Some of these activities provide a limited number of problems. For example, pages 747 and 839 each only have 8 two-digit addition and subtraction problems.

There are online mathematics games provided to help build fluency. Although these games are listed in the Math Background pages, they are never actually mentioned in the lesson to suggest to teachers when they may be beneficial. The "Flying Cow Incident" game is good for building fluency and the concept of using a number line to add and subtract. The "Launch the Sheep" game is focusing on multiplying and dividing and function tables which are not second grade skills. The "Robo Launch" game is confusing and above grade level as it using function tables. "Gobbling Globs "uses numbers larger than 1,000. It is a good game for students in Grade 3, but not Grade 2. The "Fluency Games" are good games for building fluency at a Grade 2 level. The "Add It" game focuses on using a procedure and not on the conceptual understanding that second graders need. The "Space Jump" game would be better used at a higher level; it would be difficult for most second graders to maneuver and understand.

There is minimal time spent on counting within 1,000 in the instructional materials. Although standard 2.NBT.2 is cited for Lessons 8-1, 8-2, 8-3, 8-6, 8-7, 8-8, and 9-7 these lessons focus on the second part of the standard, skip-count by 5s, 10s, and 100s.,

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 materials reviewed in Grade 2 for this indicator partially meet the expectations for being designed so that teachers and students spend sufficient time working on engaging the applications of the mathematics. In general, some lessons designed to emphasize application do not always provide opportunities for students to apply mathematical knowledge and skills in a real-world or non-routine context.

In the materials application is limited to word problems, which is appropriate for Grade 2. However, many of the problems do not require the context; the numbers can simply be pulled out of the problem and solved by using key words, a strategy included in the instructional materials.

Most topics have at least one lesson designated to application. However, the emphasis of these lessons is on the standard or procedures addressed in the rest of the topic and not necessarily application. For example, Lesson 1-10 is designated as an application lesson. Of the three independent practice problems on page 61, 2 are one-step word problems, and one simply requires students to complete an explanation for how to find 8+9 in order to reinforce doubles facts. Some of these lessons do not provide opportunities for students to apply mathematical knowledge and skills in a real-world or non-routine contexts. For example, Lesson 9-10 is designated as an application lesson. In this lesson students look for patterns, sort numbers, and order numbers.

  • Standard 2.OA.1 is using addition and subtraction within 100 to solve one- and two-step problems.
  • Lessons 2-5 and 4-8 are application lessons targeting 2.OA.1. Although the lessons do include word problems, most of the word problems in each lesson are the same type, so the problems become routine.
  • Application Lesson 5-9 includes both one- and two-step equations; however, the focus of the lesson is on MP3, not application of 2.OA.1.
  • Application Lesson 6-9 targets 2.OA.1. The inclusion of fill-in-the-blank equations make the problems more routine than if students had the opportunity to read the problems and represent them with equations without blanks.
  • An analysis of lessons in Topic 7, which addresses 2.OA.1, identified a variety of problem types and experiences. However, only two lessons specifically target two-step word problems.
  • In Lesson 7-1, while students are solving real world problems, there's limited connection to grade level mathematic concepts that could be developed or reinforced through solving problems. For example, in the change-unknown problems students are asked to show two equations. There is a missed opportunity within the lesson to reinforce the relationship between addition and subtraction and how that can be used to solve problems.
  • Lesson 7-6 is the lesson designated to application in Topic 7. This problem does not provide students with word problems. Students are provided with equations or pictures and must write number stories to match. This lesson does not require students to use addition and subtraction to solve word problems. Students can solve the equations first and then write a word problem. Also, most of the problems require addition and subtraction within 50. Only 1 problem requires students to subtract two numbers larger than 50, and one sum is larger than 50.
  • Some lessons that list 2.OA.1 as a standard even though it is not the main standard targeted in the lesson do not really address 2.OA.1 to the full depth. For example, Lesson 14-5 targets 2.MD.10 but also lists 2.OA.1. Although students use bar graphs and picture graphs to answer one-step word problems, most of the problems require addition and subtraction within 20.
  • Additionally, some lessons are mislabeled as application. For example, Lesson 8-2, page 449 is labeled application. In this lesson students are solving problems with coins, but there is no context provided for most of the problems other than stating that someone has coins.

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.
0/2
+
-
Indicator Rating Details

The instructional materials do not meet the expectations for balance. The majority of the lessons are very procedural. However, the fluency of facts is underdeveloped, and additional problems focusing on addition and subtraction from 15-20 are needed. There is a lack of conceptual understanding in the materials; most of the materials labeled as conceptual understanding miss opportunities to develop understanding and instead teach a procedure. Many lessons only focus on one aspect of rigor at a time. Often when more than one aspect of rigor is the focus of a lesson, the aspects are conceptual understanding and procedural skills. For example, in Topic 3, of the 10 lessons, five target conceptual understanding and procedural skills, three target conceptual understanding, and two target application. In Topic 7, of the seven lessons, two target procedural skill and conceptual understanding, four target conceptual understanding, and one targets application. There are many missed opportunities to connect the different aspects of rigor.

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
4/10
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 2 do not meet the expectations for practice-content connections. The materials meet the expectations for attending to the specialized language of mathematics. The materials partially meet the expectations for attending to indicators 2e and 2gi, but they do not meet expectations for 2f and 2gii. Overall, in order to meet the expectations for meaningfully connecting the Standards for Mathematical Content and the MPs, the instructional materials should carefully attend to the full meaning of each MP, especially MP3 in regards to students critiquing the reasoning of other students and give teachers more guidance for implementing MP3.

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 materials partially meet the expectations for identifying the MPs and using them to enrich the mathematics content within the grade. Overall, the MPs are identified and used in connection to the content standards, but the materials do not always use the MPs to enrich the mathematics content. In the materials, the MPs are over-identified, and the connections between the MPs and the content standards are not clear.

According to the teacher overview, the MPs are identified as follows:

  • MP 1: approximately 60 lessons.
  • MP 2: approximately 80 lessons.
  • MP 3: approximately 60 lessons.
  • MP 4: approximately 85 lessons.
  • MP 5: approximately 60 lessons.
  • MP 6: approximately 60 lessons.
  • MP 7: approximately 50 lessons.
  • MP 8: approximately 40 lessons.

The total number of lessons identified for the eigt MPs is approximately 495, with about 115 lessons total in the materials, so this would lead to approximately 4 to 5 MPs per lesson. With this many practices identified in each lesson, there are many times when the entire meaning of the MP is not evident in the lesson, which leads to students not being able to develop a complete understanding of the MP and its connection to the grade-level content. For example, items 2-5 on page 423 in lesson 7-6 is labeled "MP7 Look for Patterns What is the same about the items? What is different about the items?" In this example, the answers provided to the questions do not indicate what structure students should be seeing or how the items directly connect to MP7. In some instances, more guidance to teachers could enrich the content, and in other instances, the connection is limited or the MP may be misidentified. Additional examples include:

  • In Topic 3 on page 143, item 9 is labeled "MP5: Use Appropriate Tools Strategically. Encourage students to solve the problem mentally... If needed, allow students to choose and use a tool to solve the problem." In this example students are encouraged to not use a tool.
  • In Topic 4 on page 217, the "Solve & Share" item is labeled "MP6: Be Precise. In this problem, students calculate the sum of three 2-digit numbers and provide a clear explanation of the steps they took." The directions in the student edition state, after making three 2-digit numbers, "How can you add your three numbers? Explain." In this example, neither teachers nor students are supported on how they might be precise or what this might mean. These words are, however, bolded in the teacher edition.
  • In Topic 6 on page 355, item 3 is labeled " MP4: Model with Math. Guide students to model the regrouping by writing the regrouped numbers above the subtraction problem. Make sure students understand the relationship between the three numbers in the subtraction problem and the three numbers in the addition problem." Students follow teacher directions and do not create their own mathematical model.

The Math Practices and Problem Solving Handbook in the front of the teacher's edition is a resource for understanding the MPs and knowing what to look for in student behaviors. For example, page F23A lists 10 indicators to assess MP1, "Listen and look for the following behaviors to monitor students' ongoing development of proficiency with MP1." A proficiency rubric is also included.

Indicator 2f

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

The instructional materials reviewed for Grade 2 do not meet the expectations for carefully attending to the full meaning of each practice standard. Overall, the materials do not treat each MP in a complete, accurate, and meaningful way.

The lessons give teachers very little guidance on how to implement the MPs, and many of the MPs are misidentified in the materials. Also, the materials often do not attend to the full meaning of some of the MPs.

  • MP1: Lesson 9-2 cites MP1; however, there isn't a rich problem attached. Students don't have an opportunity to persevere or make sense of a problem; students are putting numbers into a chart. Lesson 12-7 cites MP 1; but, there is not a rich problem attached. Students are asked to decide how to measure objects. Although Lesson 14-5 cites MP1, students are filling out sentence frames about a graph, which is not having students persevere or make sense of a problem.
  • MP4: Lesson 9-3 cites MP4 for items 2 through 6; however, students are not asked to provide a mathematical model as they are identifying the value of an underlined digit. Lesson 10-2 cites MP4; however, students are told to use an open number line as the model. Lesson 13-1 cites MP 4; however, students are told how to model the problem.
  • MP5: Lesson 9-1 cites MP 5; however, students are told to use place value blocks instead of being allowed to choose their own tools. In Lesson 10-4, students are told to use place-value blocks, and MP5 is cited. Although Lesson 12-3 cites MP5, students are told to use rulers.
  • MP7: Lesson 9-4 cites MP 7; however, students are not using structure to solve the problem. Lesson 12-5 cites MP7; however, students are not using structure to solve the simple addition problem. Lesson 15-2 cites MP7; however, telling students what to look for is not having students look for structure.
  • MP8: Lesson 2-4 cites MP8; however, it tells the students to draw the array first. Lesson 10-1 cites MP8; however, with only one problem present, it is impossible for students to generalize. Lesson 11-7 cites MP8; however, with only one problem present, it is impossible for students to generalize.

Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
0/0

Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
1/2
+
-
Indicator Rating Details

The materials partially meet the expectation for prompting students to construct viable arguments and analyze the arguments of others. Although the materials at times prompt students to construct viable arguments, the materials miss opportunities for students to analyze the arguments of others, and the materials rarely have students do both together.

There are some questions that do ask students to explain their thinking in the materials. MP3 is identified 60 times in the student edition. In many of the places where MP3 is identified, the students are not attending to the full meaning of the MP. For example, lessons 1-3 and 3-1 cite MP3; however, students are not asked to either create an argument or analyze the arguments of others. Additional examples of this can be found in the following lessons: 2-5, 3-9, 4-3, 5-5, 6-4, 7-6, 8-2, 9-8, 10-4, 12-7, 13-3, 14-5 and 15-1.

Examples of opportunities to construct viable arguments but not analyze the arguments of others:

  • Topic 1, page 22. Blanca wants to add 5+8. Describe how she can make a 10 to solve.
  • Topic 1, page 42. Do you prefer to add first to get to 10 or subtract first to get to 10? Explain.
  • Topic 1, page 50. Glen counts on to solve 9+_=14. Explain how he can do this. What is the missing addend?
  • Topic 3, page 123. How can you use the hundred chart to help you find 32+43? Explain.
  • Topic 4, page 200. Ken adds 43+27. His sum is 60. Is he correct? Explain.
  • Topic 5, page 257. Have students explain how they found the differences using the hundred chart. Tell students to practice using the word difference when they talk about their work.

Examples of opportunities to analyze the arguments of others is far less frequent.

  • Topic 5, page 263. Jada drew this number line to find 79-40. She circled her answer. Did Jada get the correct answer? Explain.
  • Topic 5, page 287. Encourage students to actually solve the problem Tina's way, to see if it works, before they respond. If students need prompting to come up with another way, encourage them to think about the value of the digits in each number in the problem.
  • Topic 5, page 303. Bill collects and sells seashells. He has 45 shells, finds 29 shells, and sells 20 shells. How many seashells does Bill have now? Tara says you have to subtract 45-29 and then add 20 to solve the problem. Do you agree with Tara's thinking? Circle your answer. Use pictures, words, or equations to explain.

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 materials do not meet the expectation for assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others. Usually questions have one correct answer, and there is not a lot of teacher guidance on how to lead discussions beyond the provided questions. There are many missed opportunities to guide students in analyzing the arguments of others.

  • In Lesson 1-3, the leveled assignment on page 22 includes an item that is tagged with MP3. "Blanca wants to add 5+8. Describe how she can make a 10 to solve." There is no supporting commentary or questioning to assist teachers in helping students form or develop an explanation. This is the first place MP3 is tagged in the second grade curriculum, and support is not provided.
  • In Lesson 1-7 on page 42, the teacher commentary states: "MP3 Construct Arguments. Students explain and justify whether they prefer to use addition or subtraction to make a 10." This is followed by a discussion of the mathematics that's being built upon, but no information for teachers on how to support students to construct an argument is provided. This is the second time MP3 is tagged at this grade level, again with no support or guidelines. Later in the same lesson, on page 43, teachers are provided with some support. Item 15 states, "Remind students to provide reasons why Carol was correct or incorrect. Suggest that they make a 10 to find 15-6 on their own to check Carol's work and find possible reasons she may be correct."
  • In Lesson 1-8 on page 50, the teacher commentary states "MP3 Construct Arguments. Make sure students understand that the gray box represents the missing addend. Encourage students to use words and sentences to explain their thinking." While teachers are directed to tell students what to do, the materials don't provide guidance on how to do this. Teachers could be provided with examples of good explanations or components that they can support students to develop.
  • In Lesson 5-2, students are asked "Why should you place the greater number in the problem on the far right side of the line?" Although a sample answer is provided, teachers are not provided assistance in helping students construct their answer.
  • In Lesson 6-4 of the Teacher's Edition, the teacher is prompted to have students explain why they need to regroup. Although a suggestion for follow-up is provided, the teacher is not given assistance to help students construct their explanations.
  • In Lesson 8-7, students are asked "What is the greatest number of minutes that a digital clock can show to the right of the colon? How do you know?" Although a sample answer is provided, the teacher is not provided any assistance in helping students construct viable arguments or analyze the arguments of others.
  • In Lesson 10-1, students share their explanations for how they used mental math to add 100 and 10 to a 3 digit number and explain why their strategy works. Teachers are not provided with sample explanations or guidance.

Indicator 2g.iii

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

The Grade 2 instructional materials explicitly attend to the specialized language of mathematics. The vocabulary words are taught and worked with at the beginning of each topic and, again, at the very end of the topic. The assumption is that Grade 2 students will remember all words from the beginning of the topic and will not need them reintroduced before they are used in a lesson.

  • Each lesson includes a list of important vocabulary in the topic organizer which can be found at the beginning of each topic.
  • Each topic opener has a vocabulary review activity, and each topic ends with a vocabulary review activity. However, there isn't any direction on how or when to use the activities.
  • There is an online game for vocabulary, Save the Word.
  • Student edition contains a mathematical vocabulary glossary.
  • Online animated glossary in Spanish and English.
  • “My Word Cards” is a set of mathematical language flash cards available for each topic in the student edition.
  • Reteach pages from the student book contain a vocabulary section of questions (i.e 3-7, 7-2, and 11-4).
  • Vocabulary questions are in the independent practice.

Gateway Three

Usability

Not Rated

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
0/8

Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
0/2

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
0/2

Indicator 3c

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
0/2

Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
0/2

Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
0/0

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
0/8

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
0/2

Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
0/2

Indicator 3h

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.
0/2

Indicator 3i

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.
0/2

Indicator 3j

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
0/0

Indicator 3k

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
0/0

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
0/0

Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
0/10

Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
0/2

Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
0/2

Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
0/2

Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
0/2

Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
0/2

Indicator 3q

Materials encourage students to monitor their own progress.
0/0

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
0/12

Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
0/2

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
0/2

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
0/2

Indicator 3u

Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
0/2

Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
0/2

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
0/2

Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
0/0

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
0/0

Criterion 3aa - 3z

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
0/0

Indicator 3aa

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
0/0

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
0/0

Indicator 3ac

Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
0/0

Indicator 3ad

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
0/0

Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
0/0

Additional Publication Details

Report Published Date: Wed Apr 20 00:00:00 UTC 2016

Report Edition: 2017

Title ISBN Edition Publisher Year
null 978-0-328-82737-4 null null null
null 978-0-328-82743-5 null null null
null 978-0-328-82779-4 null null null
null 978-0-328-82785-5 null null null
null 978-0-328-82792-3 null null null

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Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

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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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