Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 2 do 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 appropriately 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
9
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 Everyday Mathematics 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. The instructional materials can easily be adjusted so no future, grade-level content is assessed. 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 Second Grade Everyday Mathematics materials meet the expectations for not assessing topics before the grade level in which they should be introduced. Future, grade-level topics are assessed; however, those assessments could be removed without affecting the progression of learning for students. The number of future grade-level assessments is limited and could easily be removed by the teacher.

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 instructional materials reviewed for Grade 2 meet expectations for assessment because above grade-level assessment items could be modified or omitted without a significant impact on 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 program allows for a Beginning-of-the-Year, Mid-year, End-of-the-Year Assessment, and Unit Assessments, which mostly assess the Grade 2 standards. There are also nine unit assessments/progress checks. The unit assessments/progress checks have portions for self assessment, unit assessment, open response assessment, cumulative assessment, and a challenge. These assessments can be found in the Assessment Handbook. The Individual Profile of Progress for tracking and class progress are present in both paper (pages 100-112 in the Assessment Handbook) and digital formats. A Facts Record Sheet exists to monitor student fluency in the Assessment Handbook on page 98. Most lessons have an Assessment Check-in that can be used as either formative or summative assessment as stated in the implementation guide.

Assessment check-ins are part of most lessons and mostly assess grade-level content. Examples include:

  • Unit 1, Lesson 1-11: 2.NBT.A.4 - Compare values of two and three digit numbers (page 124).
  • Unit 2, Lesson 2-3: 2.OA.B.2 - Develop fact fluency of doubles and facts of ten, with students assessed through individual and/or small group interviews (page 166).
  • Unit 3, Lesson 3-10: 2.OA.B.2 - Develop fact fluency building on student understanding of 10 to decompose numbers strategically to subtract to ten and from ten (page 308).
  • Unit 4, Lesson 4-4: 2.NBT.A.3 - Build and represent two- and three-digit numbers (page 358).
  • Unit 5, Lesson 5-4: 2.MD.C.8 - Use coins to show values and add and subtract with money (page 466).
  • Unit 6, Lesson 6-2: 2.OA.A.1 - Solve comparison word problems (page 542).
  • Unit 8, Lesson 8-6: 2.G.A.2 - Partition a rectangle into rows and columns with equal size squares page 728.

The Unit Assessments, the Middle of the Year Assessment, the End of the Year Assessment and some of the Assessment Check-Ins do have a few off grade-level assessments included. The following off grade-level content is assessed in the Grade 2 Materials:

  • Unit 8 Assessment, page 53 in the Assessment Handbook, problem 3, assesses parallel lines at the Grade 4 level (4.G.A.1).
  • Unit 8 Assessment, page 56 in the Assessment Handbook, problem 1, assesses multiplication at the Grade 3 level (3.OA.A.1).
  • Unit 9 Assessment, page 66 in the Assessment Handbook, problem 11, and page 67 in the Assessment Handbook, problem 2, assesses partitioning shapes at the Grade 3 level (3.G.A.2).
  • Unit 9 Assessment, page 67 in the Assessment Handbook, problems 1b and 1c, assesses multiplication, a Grade 3 standard (3.OA.A.1).
  • The Middle-of-the-Year Assessment in the Assessment Handbook, page 79, problem 6a, and page 80, problem 10, assesses number patterns at the Grade 4 level (4.OA.C.5).
  • The End of the Year Assessment in the Assessment Handbook, page 97, problem 24, assesses partitioning at the Grade 3 level (3.G.A.2).
  • The Assessment Check-In on page 803 has students measuring to the half-inch (3.MD.B.4).
  • The Assessment Check-In for Lesson 9-5, on page 230 of the Math Journal, asks students to write 4-digit numbers in expanded form and compare them. 2.NBT.3 and 2.NBT.4 both specify "numbers to 1000 or two three-digit numbers."
  • The Assessment Check-Ins for Lessons 9-10 and 9-11, on pages 242 and 246 of the Math Journal, ask students to write multiplication models, a Grade 3 expectation (3.OA.A.1).
  • The Assessment Check-Ins for Lessons 8-1, 8-2, and 8-4, on pages 694, 700, and 714, ask students to identify parallel lines and right angles, a Grade 4 expectation (4.G.A.1).

All of the off grade-level assessments could be removed by the teacher without affecting the sequence of learning for students.

Note:

  • Assessment Check-in on page 153 of the teacher manual refers to bill combinations on page 19 of Math Journal 1. However, the bills are on page 17, and page 19 is an addition number story.
  • Unit 5 Assessment question 9 has a question mark on the blank, this could be a typo.

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 Grade 2 Everyday Mathematics materials do meet expectations for devoting the large majority of class time to the major work of the grade level. In Grade 2, the materials should engage students in the major work of the grade 65-85 percent of the time. The Second Grade Everyday Mathematics engages students in the major work of the grade about 72 percent of the time.

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 by spending the majority of the time on the major clusters of the grade. This includes all the clusters in 2.NBT and clusters 2.OA.A, 2.OA.B, 2.MD.A and 2.MD.B.

The Grade 2 materials do spend the majority of class time on the major clusters of the grade. Work was not calculated by units since the units spiral and are not clustered by groups of standards. At the lesson level, the lessons are divided into Daily Routines, Core Activities, and Practice. Each day consists of 15-20 minutes on routines, 30-45 minutes of a core activity, and 15-20 minutes of practice. Assessment days were not included in these calculations. Additionally, the Open Response Lessons were counted as two lessons.

There are nine units with 10-13 lessons per unit. Each unit has a 2-day open response lesson. There are also two days provided for a progress check at the end of each lesson. Including the two days for open response lessons, there are 107 days (98 lessons total) and another 18 days allowed for assessment, making 125 days worth of materials.

The following calculations were derived from the core activities of the lesson.

  • Seventy-eight lessons out of the 108 are focused on the major work. This represents approximately 72 percent of the lessons.
  • Twenty-seven lessons out of the 108 are focused on the supporting work of the grade. This work was treated separately from the major work of the grade. This represents approximately 25 percent of the lessons.
  • Three lessons out of the 108 are focused on off-grade level work. This represents approximately 3 percent of the lessons. This includes: lesson 9-4, page 799, on measuring to the 1/2 inch, a Grade 4 standard; lesson 1-10, "Skip Counting with a Calculator", counting by 3's, 4's, 6's and 9's, which would be a Grade 3 standard; and Lesson 8-9 concentrates on changing arrays and repeated addition to multiplication problems, with no mention of preparing students for the Grade 3 standard.

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 did not meet the expectations for being coherent and consistent with CCSSM. The instructional materials do have enough materials to be viable for a school year, but they 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 they do have objectives which are clearly shaped by the CCSSM. Overall, the instructional materials for Grade 2 do not exhibit enough 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 enhancing 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.

At times supporting content does enhance focus and coherence by engaging students in the major work of the grade. Examples of the connections between supporting work and major work include the following:

  • Lesson 4-2 is focused on students telling time to the nearest five minutes (2.MD.7) and connects telling time to counting by 5's (2.NBT.2).
  • Lessons 7-7 and 7-8 focus on students collecting data and plotting the data on line plots (2.MD.9) and connects with calculating the difference between the different data sets (2.NBT.5).

At times, supporting work does not enhance and support the major work of the grade. At times, standards listed at the beginning of each unit are logically connected to each other; however, when the specific work of the unit and lessons is examined, some connections are missed or not specifically noted for teacher or students. Also, many lessons address supporting work in isolation from major work of the grade. Examples of units and lessons without connections between supporting and major work include the following:

  • Lesson 1-9 is focused on odd and even numbers using 10-frames. Supporting work is treated separately from the major work of the grade in the focus lesson. A natural connection for students in Grade 2 would be to apply their work with doubles to the concept of odd and even numbers. Students could explore the concept that if a number can be decomposed (broken apart) into two equal addends or doubles addition facts (e.g., 10 = 5 +5), then that number (10 in this case) is an even number. This connection is not made.
  • Lesson 2-1 introduces place value through 100 using money. On page 153 of the Teacher’s Lesson Guide, the following suggestion is provided: “You might have them draw symbols for bills or write number sentences to record different ways to make the same total.” Writing number sentences is not required in this lesson, so an opportunity to link to major work of 2.OA.1 is missed.
  • Lessons 4-1 and 4-3 focus on supporting work of the grade. As the focus lesson, supporting work is treated separately from the major work of the grade.
  • Lesson 5-5 focuses on arrays and repeated addition which is supporting work of the grade. Supporting work in the focus lesson is treated separately from the major work.
  • Lesson 7-9 is focused on supporting work of the grade, 2.G.A.1 and 2.G.A.2, and is not connected to major work of the grade.
  • Lessons 8-1, 8-2, 8-3, 8-4, 8-5, 8-6, 8-7, and 8-11 focus on supporting work of the grade. These focus lessons are treated separate from the major work of the grade level.
  • Lessons 9-1 and 9-3 focus on supporting work of the grade with no connection to the major work of the grade presented.

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
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Indicator Rating Details

The instructional materials reviewed for Grade 2 meet the expectations for the amount of content designated for one grade level being viable for one school year in order to foster coherence between grades. The suggested pacing includes 109 days of lessons (100 lessons total) and another 24 days allowed for assessment, making 133 days of materials. According to the Teacher Guide on page xxxvi, each lesson is expected to last between 60-70 minutes. The online curriculum states to use Friday's as a Flex Day for games and intervention work. With Fridays being included as Flex Days, this curriculum allows for approximately 33 to 34 weeks of instruction.

Indicator 1e

Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
0/2
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Indicator Rating Details

The instructional materials reviewed for Grade 2 do not meet the expectation for being consistent with the progressions in the standards. Content from prior grades is not clearly identified or connected to grade-level work, and students are not given extensive work with grade-level problems.

Material related to future, grade-level content is not clearly identified or related to grade-level work. The second grade materials have three instances where future grade-level content is present and not identified as such. This includes: lesson 9-4 on page 799, on measuring to the 1/2 inch, a third grade standard (3.MD.B.4); lesson 1-10 "Skip Counting with a Calculator", counting by 3's, 4's, 6's and 9's which would be a Grade 3 standard (3.OA.D.9); and Lesson 8-9 on changing arrays and repeated addition to multiplication problems, with no mention of preparing students for the third grade standard (3.OA.A.3).

The content does not always meet the full depth of standards. This mainly occurs because of a lack of lessons addressing the full depth. For example, there are seven lessons which address 2.OA.1; however, only three of them are subtraction. The others are addition. Additionally, the majority of the subtraction problems use friendly numbers and do not have students using place value understanding to prepare for use of the standard algorithm. Another example is 2.NBT.6 which has only two lessons with students adding up to four digits. A third example is 2.MD.5 which has only three lessons relating addition and subtraction to length.

Everyday Mathematics Second grade materials do not provide extensive work with grade-level standards. For example, the instructional materials do not provide extensive work with the following standards:

  • 2.NBT.1b: The online spiral tracker indicates that there are 17 exposures to Standard 2.NBT.1b in the instructional materials, and two of these exposures are Focus activities.  As noted on page xxxix of the Teacher’s Guide, Focus activities are “(t)wo to four main instructional activities, including games, in which children explore and engage in new content (skills, concepts, applications).” In Lesson 4-4, students use number cards, base-10 blocks, and expanded form to represent 3-digit numbers in the Focus portion of the lesson. The Lesson 4-4 Focus activity is 30-40 minutes of the 60-80 minute lesson. This standard is also included in the Focus portion of Lesson 9-6. The Lesson 9-6 Focus activity is 35-40 minutes of the 60-75 minute lesson. In Lesson 9-6 students use base-10 blocks to subtract. There are limited opportunities for students to work with hundreds in this lesson; most problems focus on subtracting 2-digit numbers. For example, on the Math Journal worksheet on page 232, which is an Assessment Check-in, one of four problems has a 3-digit number. The rest of the exposures occur in Practice, Warm Up, or Assess portions of lessons. For example, the Practice Math Journal page 86 in Lesson 4-9 and the Practice Math Journal page 118 in Lesson 5-7 each include a problem aligned to 2.NBT.1b.
  • 2.NBT.A.2: There is only one lesson that works with counting to 1000. Unit 1 provides one lesson where children create a math scroll to 1000, and then 1000 is not discussed again until lesson 9-5 where the thousand cube is introduced. Other lessons throughout the units occasionally include a math warm up with skip counting within 1000.  There are also opportunities to count in math warm ups, math journals, and home-link work.
  • 2.NBT.A.3: Expanded form is taught in 6-8 and reviewed in lesson 9-5. There is not a lesson teaching writing numbers to 1000 in word form, although it is stated in the standard. Students are only asked to put numbers in word form on eight questions in the series in either Math Journals or Home-links. 1000 is not introduced until lesson 9-5.
  • 2.NBT.B.9: There are few problems where students are to explain how and why strategies work.

In lessons where prior knowledge is needed, the instructional materials do not state that prior knowledge is being used. When future, grade-level concepts are introduced, there is no mention that the concept will be used in future grades. If the teacher uses the spiral trace at the beginning of the lesson or unit, the teacher will know where prior knowledge is used based on the spiral trace and when the student will use the skill/concept again in the future. The spiral tracker is listed by lessons and not connecting standards. At the beginning of each unit, the spiral trace provides an explanation of what will occur by the end of the unit, but the spiral trace does not explain any further and does not connect to the next standard.

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 when the standards require. Overall, materials include learning objectives that are visibly shaped by CCSSM cluster headings, but there are missed opportunities to provide problems and activities that connect two or more clusters in a domain or two or more domains when these connections are natural and important.The materials do include learning objectives which are visibly shaped by CCSSM cluster headings. In the teacher's lesson guide on page EM3, the materials show the Goals for Mathematical Content for Everyday Math and how they align to the CCSSM. From this alignment, it is apparent the goals are shaped by the CCSSM cluster headings. Instructional materials shaped by cluster headings include the following examples:

  • Lesson 4-5, "Using Place Value to Compare Numbers," is shaped by 2.NBT.A.
  • Lesson 5-6, "Mentally Adding and Subtracting 10 and 100," is shaped by 2.NBT.B.
  • Lesson 7-4, "Measuring with Yards," is shaped by 2.MD.A.
  • Lesson 9-5, "Reviewing Place Value," is shaped by 2.NBT.A.

While the materials have many instances where two or more domains are connected, often the connections are only surface-level connections. Generally the lessons are divided into parts, and the parts only truly address one standard at a time. Additionally, 46 of the lessons are only aligned to one domain.

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 MPs. The instructional materials partially meet the expectations for the indicators on rigor and balance, but they do not meet the expectations of the indicators on practice-content connections. Overall, the instructional materials are strongest in regards to procedural skill and fluency and identifying MPs, although improvements are still needed for identifying MPs to fully meet expectations as well.

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.
5/8
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Criterion Rating Details

The instructional materials reviewed for 2nd Grade partially meet expectations for rigor and balance. The instructional materials give appropriate attention to procedural skill and fluency but partially meet the expectations for application. The materials do give attention to conceptual understanding; however, the full meaning of conceptual understanding is still not met. Overall, because of not fully meeting expectations for application and conceptual understanding, the instructional materials do not reflect the balances in the CCSSM.

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
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Indicator Rating Details

Materials partially meet the expectation for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings. There are good conceptual discussion pieces located throughout the work. Some good conceptual Home-Link and practice problems exist; however, these come before the focus lessons, which, without the lesson to understand the concept, could present possible issues for the students.

Below are lessons where the full depth of conceptual understanding is addressed.

  • Unit 1: 1-2 Number Line Squeeze Game; 1-5 Open Response: Number-Grid Puzzles.
  • Unit 2: 2-4 The Making-10 Strategy; 2-7 Open Response: Subtraction and the Turn-Around Rule; 2-8 Exploring Addition Tools, Odd and Even and Patterns and Shapes; 2-10 Name-Collection Boxes; 2-11 Playing Name that Number.
  • Unit 3: 3-1 Open Response: Using Addition Strategies; 3-2 Subtraction from Addition: Think Addition; 3-6 -0 and -1 Fact Strategies and Subtraction Top-It; Unit 3 Open Response Assessment (which allows students to represent mathematical thinking with representations and verbalization).
  • Unit 4: 4-4 Numeration and Place Value; 4-5 Using Place Value to Compare Numbers; 4-6 Open Response using Base-10 Blocks to Show a Number; 4-7 Playing Target; 4-11 Explorations Matching Facts with Strategies and Exploring Arrays.
  • Unit 5: 5-5 Explorations Exploring Arrays: Time, and Shapes; 5-6 Mentally Adding and Subtracting 10 and 100; 5-11 Open Response Adding Multi-digit Numbers.
  • Unit 6: 6-7 and 6-8 Partial sums addition; 6-9 Open Response Subtracting with Base-10 Blocks; 6-10 Explorations Exploring Arrays.
  • Unit 7: 7-1 Playing Hit the Target; 7-2 Open Response Four or More Addends; 7-3 Playing Basketball Addition; 7-4 Measuring with Yards; 7-5 Measuring with Meters.
  • Unit 9: 9-5 Reviewing Place Value; 9-6 and 9-7 Expand and Trade Subtraction.

In addition, the following routine also builds conceptual understanding.

  • Routine 1: Students represent the number of the day on a class number line, count the days using straws or craft sticks bundled in tens and hundreds, record the number in expanded form, and represent and count the number using coins. There are also additional add-ons that build upon place value understanding including adding and subtracting 10s or 100s. The ongoing assessment of this routine (TE page 9) also includes questions addressing 2.NBT.A and 2.NBT.B including, "Can children use the number line to represent and read the number of the day? Can children identify the value of the ones, tens, and hundreds digits? Do children understand the structure of expanded form and use it to write the number of the day?"

Lessons which partially meets the requirements for conceptual understanding are listed below.

  • 1-12 Exploring Base-10 Blocks, Area, and Dominoes: The base-10 building activity with the recommended sentence frame does not encourage open-ended conceptual conversation between students to explain the whys or hows of their mathematical representations. Unit 1 Assessment provides students some opportunity to verbalize their understanding but only in the challenge, which is optional. The Challenge provides opportunity for students to create their own visual representations with showing how much money is spent.
  • 2-1 Grouping by 10's- Playing the Exchange game: The game involves students in hands-on activities but misses opportunities for students to have conversations about the exchanges being made. The Unit 2 Assessment provides one opportunity for students to verbalize their mathematical thinking and no opportunities for students to create concrete or visual mathematical representations.
  • The Unit 3 Assessment allows the student to verbalize their mathematical thinking but does not provide opportunity for concrete or visual representation.
  • 4-8 How Big is a Foot, 4-9 The Inch, 4-10 The Centimeter and 4-11 Exploration for measuring a path: These lessons do not get to the full depth of the standard which calls for students to measure and estimate lengths in standard units. Unit 4 assessment gives students opportunities to verbalize their mathematical thinking but no opportunities for students to demonstrate their understanding through concrete or visual representations.
  • The Unit 5 Assessment provides students some opportunity to verbalize their understanding, but only the Open Response Assessment provides opportunity for students to create their own visual representations with showing how much money spent.
  • 6-10: Exploring lengths does not meet the full depth of the standard to measure and estimate lengths. Unit 6 assessment gives students opportunities to verbalize their mathematical thinking but no opportunities for students to demonstrate their understanding through concrete or visual representations.
  • The Unit 7 Assessment provides students some opportunity to verbalize their understanding, but only the Open Response Assessment provides opportunity for students to alter a visual representations of base-10 blocks.
  • In Unit 9, only the Open Response Assessment provided opportunity for students to verbalize their understanding of place value concepts.

Lessons which miss opportunities to develop conceptual understanding are listed below.

  • 1-11 Comparing Numbers: The lesson does not employ visual representations of numbers to illustrate the difference in amounts when comparing numbers. Students should be able to see the difference using base-10 blocks or other groups of objects.
  • Lesson 1-3 does not work on building conceptual knowledge. Although labeled with 2.NBT.A, students are not developing understanding of place value. In this lesson students are learning to use various math tools.
  • 5-2 through 5-4, using and calculating with coins: These activities are more about measuring value with money and do not clearly connect to learning about the concepts of place value using coins as visual representations of numbers.

A lack of instructional time devoted to some topics and the late introduction of some topics lead to a lack of development of conceptual understanding for students. For example, students may not be given enough time to build a conceptual understanding of a yard and a meter based on the lessons provided. Students also only spend lesson 7-9 exploration (10 minutes) measuring the same object in two different units. In the lessons for length measurement, there is no time spent determining how much longer one object is than another. One thousand is not introduced conceptually with base ten blocks until lesson 9-5. Addition strategies based on models are not introduced until focus lessons 6-7 and 6-8. Finally, conceptual subtraction strategies for multi-digit numbers are not shown until lessons 9-6 and 9-7

Indicator 2b

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

The instructional materials reviewed for Grade 2 meet the expectation for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

According to the spiral tracker, there are 232 exposures to 2.OA.2 in the instructional materials. Approximately twenty-nine different lessons address 2.OA.2 in the Focus portion of the lesson. However, many of the provided problems focus on adding and subtracting within 15. For example, in Lesson 3-2 on Math Journal page 47, students are using dominoes to write addition and subtraction facts, so addition and subtraction is within 12. The Lesson 7-1 Math Message includes three problems that require students to find missing addends to find a sum of 10.

Here are some places where fluency is given attention in the materials.

  • Most lessons in the materials have a "Mental Math and Fluency" piece which allows students to practice fluencies required in Grade 2.
  • Several online games help students with the expectation of fluency, including Top It, Basketball Addition, Beat the Computer, Name that Number, and Two-Fisted Addition.
  • Most lessons have a "Practice" section which has students practicing fluency and skills. For example, lesson 7-5, page 647, is "Practicing with Fact Triangles."
  • Online is a reference sheet called "Do Anytime Activities" with suggestions to help students practice fluencies at home.
  • There is a fact check in the assessment book for teachers to mark when mastery of facts is accomplished.

Indicator 2c

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade
1/2
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Indicator Rating Details

The materials partially meet the expectation for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade.

Each unit contains a two-day "Open Response" lesson which engages students in application of mathematics. For example, lesson 9-3 has students engaging in application of the mathematics where students are asked to find a way to fairly share four muffins with five people. Online in the resource section, several projects are available to help students with application of mathematics.

Word-problem contexts are generally familiar to Grade 2 students including children playing, pencil cups, markers, stickers, and books. Add to and take from result unknown problems are the most frequently presented. There are limited opportunities for students to solve take-from, start-unknown, and change-unknown problems. Compare problems are frequently represented within the curriculum, sometimes connected to a graph (Student journal, page 149). However, there is not enough instruction for application for two-step addition (only one lesson directly focuses on this) and no instruction for application for two-step subtraction. Examples of application in number stories include:

  • 2-2 Addition Number Stories
  • 2-7 Subtraction and the Turn Around Rule (writing number stories and number models)
  • 3-2 Subtraction from Addition
  • 3-9 (Practice) Solving Subtraction Stories
  • 5-8 Change to More Number Stories
  • 5-9 Parts-and-Total Number Stories
  • 6-2 Comparison Number Stories
  • 6-3 Interpreting Number Stories
  • 6-4 Animal Number Stories
  • 6-9 Subtracting with Base-10 Blocks
  • 8-8 Equal-Groups and Array Number Stories
  • 8-9 More Equal Groups and Arrays
  • 9-10 Connecting Doubles Facts, Even Numbers, and Equal Groups

Examples of 2-step application number stories include:

  • 6-5 Two-Step Number Stories including home-link page.
  • These lessons provide some instruction and focus on multi-step addition: 6-7 Finding partial sums involving multi-step addition strategies for adding 2-digit numbers, 7-2 Four or More Addends, 9-9 Estimating Costs in which students must choose at least three items from a market to mentally estimate which items they can purchase for $100.

Indicator 2d

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

The Grade 2 Everyday Mathematics instructional materials partially meet the expectations for balance. Overall, the three aspects of rigor are neither always treated together nor always treated separately within the materials. However, the lack of lessons on application do not allow for a balance of the three aspects.

  • 36 lessons focus on or partially address conceptual understanding.
  • "Daily Warm Ups," including "Mental Math and Fluency," and "The Number of the Day Routine" directly focus on math fact fluency.
  • Seventeen lessons focus on Application with only one lesson directly focused on two-step addition and no lessons directly focused on two-step subtraction.

In terms of balance, the lessons do not provide as much instruction for application as they do for conceptual understanding. Conceptual understanding gets much more emphasis than the other two aspects of rigor.

One cluster where you can see the expectations for balance handled appropriately is 2.MD.A, measure and estimate lengths in standard units.

  • Lesson 4-8, students learn about the importance of using consistent measurement lengths and measure classroom objects by iterating units without overlaps or gaps. In this lesson, students engage in all of the aspects of rigor.
  • Lesson 5-8, students look for objects in the room that are about an inch, centimeter, 10 inches, and 10 centimeters and measure the objects. In this practice lesson, students engage in two aspects of rigor, procedural skills and application.
  • Lesson 6-4, students understand length versus height and use lengths (in inches and feet) to compare length and/or height of animals. Students also write and solve comparison problems using the same context. In this lesson, students engage in all of the aspects of rigor.
  • Lesson 6-10, students measure four different objects and compare their lengths, engaging in one of the aspects of rigor, procedural skill.
  • Lesson 7-4, students estimate lengths, explore standard and non-standard units, compare measuring tools such as a yard stick and tape measure, select and measure familiar objects and measure distances. In this lesson, students engage in all of the 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 only partially meet the expectations for attending to all of the indicators 2e through 2g, except for 2f which did not meet expectations. Overall, in order to meet the expectations for meaningfully connecting the Standards for Mathematical Content and the MPs, the instructional materials should carefully pay attention to the full meaning of every practice standard, especially MP3, in regards to students critiquing the reasoning of other students, and the use of correct vocabulary throughout the materials.

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 2 partially meet the expectations for identifying the MPs and using them to enrich the mathematics content. Each of the standards is identified in the Grade 2 materials. The practices are not over-identified or under-identified. For example, Unit 1, page 55 discusses how MP2 and MP5 unfold within the unit and lesson. Within the lesson are spots where the MPs are identified. However, within the lessons, limited teacher guidance is given on how to help students with the MPs. Because there is limited guidance on implementation, it is difficult to determine how meaningful connections are made. MP3, MP4 and MP8 are the least identified in the Grade 2 materials.

The Assessment Handbook includes "Mathematical Practices for Unit(s) Individual Profile of Progress" that can be used to assess practice standards. Unit Assessments do not identify content or practice standards being assessed. The Beginning of Year assessments identifies MP1 and MP7 for assessment, and the Middle of Year assessment identifies MP1, MP2, MP3, MP4, MP6 and MP7 for assessment. The End of Year assessment identifies MP1, MP2, MP3, MP4 and MP6 for assessment. MP5 is not identified with any formal assessment.

Indicator 2f

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

The Grade 2 Everyday Mathematics do not meet the expectation for carefully attending to the full meaning of each practice standard. They do not treat each MP in a complete, accurate, and meaningful way. The lessons give teachers limited guidance on how to implement the standards. Some lessons are attached to standards without having students actually attending to them.

Below are examples of where the full intent of the MPs is not met.

  • MP1: Lesson 2-5 cites MP1; simply recording strategies is not having student making sense of problems or persevering in solving them. In lesson 3-4, MP1 is identified; however, there is not a rich problem attached for students to make sense of or persevere in solving. In lesson 5-2, MP1 is identified; however, expecting students to be successful with problems 1 and 2 on a worksheet is not having students persevere or make sense of problems.
  • MP4: In lesson 3-2, MP4 is identified; however, students are told how to make their mathematical models. Lesson 4-3 cites MP4; however, students are using a tool not making a mathematical model. Additionally, they are being told which tool to use. In lesson 5-8, MP4 is identified; however, students are told how to make thier mathematical models.
  • MP 5: Lesson 1-1 cites MP5; however, students are told to work with thermometers. Lesson 2-8 cites MP5, but again students are told which tools to use. In lesson 5-1, MP5 is identified; however, students are only given calculators to work with. They are not asked to choose a tool, and for the depth of MP5 to be met, students must be choosing their own tools.
  • MP 6: Lesson 2-1 cites MP6; however, telling students how to count is not the students attending to precision. In lesson 3-5, MP6 is identified; however, having students notice it is more efficient to count up because they have to make fewer hops is not having students attend to precision. Lesson 4-8 cites MP6, but simply having the students discuss why the bed in the story didn't turn out to be the right size is not having the students attend to precision.
  • MP 7: Lesson 1-9 cites MP7; however, simply asking the students how many shoes in a pair and what other things comes in pairs is not having students look for structure to solve problems. The materials state lesson 2-3 is connected to MP7 where students are supposed to look for structure such as categories, patterns, or properties. However, within the lesson there isn't any indication of where or how MP7 plays out. Lesson 3-7 cites MP7; however, expecting most students to solve the problems on a worksheet with manipulatives is not attending to MP7.

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 evidence of others. MP3 is not explicitly called out in the student material. 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 on assessments and in the materials. Sometimes there are questions asking them to look at other's work and tell whether the student is correct or incorrect and explain. Little direction is provided to make sure students are showing their critical thinking, process or procedure, or explaining their results. Many questions that prompt students to critique the reasoning of others tell the student if the reasoning was originally correct and incorrect. It should be noted, though, that student materials never explicitly call out entire MPs at once; MP3 is broken into GMP3.1 and GMP3.2 in the materials.

The open response lessons could be opportunities for students to construct arguments for or against a mathematical question. However, besides just working in groups, there is little prompting from the teacher for students to discuss the answers of other groups or students.

The following are examples of MP3 in the assessments:

  • Unit Assessment 1: questions 4b and 7e, "Explain how you knew."
  • Unit 1 Open Response Assessment: question 3, "Explain what you did to solve problem 2."
  • Unit 2 Challenge: "Explain how she can use to double to solve."
  • Unit 3 Assessment: question 2, "How do you know? Explain your thinking." question 4c, "Explain how you solved one of the facts above." question 6, "Explain Martin's thinking."
  • Unit 3 Challenge: "Write an argument to explain why you agree or disagree with Zoe."
  • Unit 3 Open Response: "Show and explain how to use Grace's strategy."

The following are examples of opportunities to construct viable arguments:

  • Student Math Journal Volume 1 and 2: Most Math Boxes pages ask "what do you notice" and "explain" and other how and why questions.
  • The Student Math Journals include at least 50 items that ask students to explain their solution, their strategy, how they know, etc.

The following are examples of opportunities to analyze the arguments of others found in Student Math Journal Volume 1:

  • page 74, item 7: Student has to critique and explain student with wrong answer.
  • page 79, item 8: Do you agree with Marta? Explain your answer.
  • page 81, item 6: Why were your measures and your partner's measures the same for each object?
  • page 91, item 5: For Problem 1, suppose your teacher asked your class to write the number in expanded form. Your friend Cassie wrote 700+2+5. Do you agree? Why or why not?

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.
1/2
+
-
Indicator Rating Details

The materials partially meet the expectation for assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards. In the materials, usually only one right answer is available, and there is limited teacher guidance on how to lead the discussion given besides a question to ask. Many missed opportunities to guide students in analyzing the arguments of others exist. Students spend time explaining their thinking but not always justifying their reasoning and creating an argument.

The following are examples of lessons aligned to MP3 that have missed opportunities to assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others:

  • In Routine number 4, the teacher is asked to have children support their arguments about weather trends based on data from the weather bar graph. No further direction.
  • In Lesson 2-6 on page 183 TE, teachers are given the question to ask, but there is no follow-up on how to direct the discussion.
  • In the summarize section of lesson 1-2, children discuss how sharing strategies with a partner can help with learning mathematics. There is no further direction for the teacher.
  • Lesson 1-9 directs the teacher to call students up and for children to make predictions, but it does not guide the teacher in asking students to explain their thinking.
  • Lesson 2-5 explains how to use nearby doubles and then apply the strategy. Not enough information is provided to the teacher.

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 2 partially meet the expectations for explicitly attending to the specialized language of mathematics. Overall, the materials for both students and teachers have multiple ways for students to engage with the vocabulary of mathematics; however, often the correct vocabulary is not used.

  • Each unit includes a list of important vocabulary in the unit organizer which can be found at the beginning of each unit.
  • Vocabulary terms are bolded in the teacher guide as they are introduced and defined but are not bolded or stressed again in discussions where students might use the term in discussions or writing.
  • Each regular lesson includes an online tool, "Differentiating Lesson Activities." This tool includes a component, "Meeting Language Demands," that includes vocabulary, general and specialized, as well as strategies for supporting beginning, intermediate, and advanced ELLs. An example of this from Lesson 1-4 includes "For beginning ELLs use ... Visual aids, gestures, modeling, and guided practice to teach the meanings of words and phrases."
  • Everyday Math comes with a reference book that uses words, graphics, and symbols to support students in developing language.
  • Correct vocabulary is often not used. For example, turn-around fact is used rather than the term commutative property, number sentence is used instead of equation, name-collection box instead of equivalent equations or equivalent expressions.

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: Mon Apr 11 00:00:00 UTC 2016

Report Edition: 2016

Title ISBN Edition Publisher Year
null 978-0-02-138323-8 null null null
null 978-0-02-138351-1 null null null
null 978-0-02-140924-2 null null null
null 978-0-02-140937-2 null null null
null 978-0-02-140991-4 " null null null
null 978-0-02-140995-2 null null null
null 978-0-02-143082-6 null null null
null 978-0-02-143086-4 null null null
null 978-0-02-36608-8 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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