Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 1 partially 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 partially meet the expectations for Gateway 2 as they did partially address rigor within the grade-level standards, but there are missed opportunities in the materials when it comes to attending to the full meaning of the MPs.

See Rating Scale
Understanding Gateways

Alignment

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Partially Meets 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
12
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 1 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. 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 1, 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 Grade 1 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 above 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 1 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 1 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 1 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. Each grade level's standards are broken down into 45 to 80 Goals for Mathematical Content that are listed in the back of the Teacher's Lesson Guide and also in the online Teacher Center. 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 101-112 in the Assessment Handbook) and digital formats. 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:

  • Lesson 2-11, (page 201), students solve word problems with unknowns in different positions (1.OA.1).
  • Lesson 3-9, (page 277), students count forward and backward and add or subtract 10 from given numbers (1.OA.5, 1.NBT.1, 1.NBT.5).
  • Lesson 4-1, (page 312), students directly compare lengths of objects indirectly by using a third object (1.MD.1).
  • Lesson 4-11, (page 374), students find 10 more or 10 less than a given number (1.NBT.5).
  • Lesson 5-4, (page 417), students compare numbers and use symbols <, >, = to express the relationship (1.NBT.3).
  • Lesson 6-10, (page 566), students build numbers with base-ten blocks, identify the tens and ones within a two-digit number and exchange ten ones for a ten stick. (1.NBT.2)
  • Lesson 7-3, (page 610), students use addition and subtraction to find missing addends. (1.OA.4, 1.OA.6)
  • Lesson 8-2, (page 693), students partition shapes to make two equal shares (1.G.3).
  • Lesson 9-1 (page 780), students measure objects using multiple copies of a smaller object (1.MD.2).

The Unit Assessments, the End of the Year Assessment and some of the Assessment Check-Ins do have a few off grade-level problems included. The following off grade-level content is assessed in the Grade 1 Materials:

  • In Unit 1 Open response assessment, students count buttons. In the rubric for this assessment, students must group buttons together in consistent groups, which leads to skip-counting, a second-grade skill (2.NBT.A.2), in order to meet or exceed expectations.
  • Unit Assessment 3, page 21 in the Assessment Handbook, problem 5 assesses counting by 5's which is a Grade 2 expectation (2.NBT.A.2). Question 7 is skip counting by 2's using odd numbers, which is finding a pattern, Grade 4 standard (4.OA.C.5).
  • Unit Assessment 4, page 29 in the Assessment Handbook, problem 3 assesses counting by 5's which is a Grade 2 expectation (2.NBT.A.2).
  • Unit Assessment 9, problems 5 and 6, and page 68, problem 7, assess money which is a Grade 2 expectation (2.MD.C.8).
  • In the End of the Year Assessment in the Assessment Handbook, page 89, problem 1 and page 90, problem 5, assess counting by 5's which is a Grade 2 expectation (2.NBT.A.2). Page 99, problem 26, assesses defining a larger category of shapes, i.e., polygons, which is a Grade 3 expectation (3.G.A.1).
  • The Assessment Check-In for Unit 3, lesson 3-9, page 277, assesses counting by 5's which is a Grade 2 expectation (2.NBT.A.2).
  • The Assessment Check-In for Unit 7, lesson 7-7, page 634, assesses defining larger categories of shapes which is a Grade 3 expectation (3.G.A.1).
  • Four Assessment Check-Ins for Unit 9 assess money, which is a Grade 2 expectation (2.MD.C.8). Lesson 9-2, page 786, lesson 9-3, page 794, lesson 9-6, page 813, and lesson 9-8, page 824, all assess money (2.MD.C.8).

Most of the off grade-level assessments could be removed by the teacher without affecting the sequence of learning for students. The assessments of money would need to be modified since those assessments are also assessing addition and subtraction. In Units 1, 3, 6 and 9, the teacher will need to supplement in order to assess all skills and concepts.

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 1 Everyday Mathematics materials meet expectations for devoting the large majority of class time to the major work of the grade level. The Grade 1 Everyday Mathematics engages students in the major work of the grade about 65 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 1 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 1.OA and 1.NBT and cluster 1.MD.A.

The Grade 1 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. Grade 1 Everyday Math includes 109 lessons, 100 of which are expected to be completed within one day. Each of the nine units includes an Open Response and Reengagement lesson which is designed to be done over two days. Progress checks are also allotted two days worth of instructional time at the end of each unit. 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.

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

  • Sixty-eight lessons out of the 109 are focused on the major work. This represents approximately 62 percent of the lessons. Additionally, another three lessons, or approximately 3 percent, are supporting work which truly supported the major work of the grade bringing the time spent on major work to approximately 65 percent.
  • Thirty-one lessons out of the 109 are focused solely on the supporting work of the grade. This work was treated separately from the major work of the grade. This represents approximately 27 percent of the lessons.
  • Ten lessons out of the 109 are focused on off grade-level work. This represents approximately 8 percent of the lessons. This includes: lessons 3-5 and 3-8, on counting by 5's, a Grade 2 standard; lesson 3-9, page 275, on counting by 2's, a Grade 2 expectation; lesson 3-11 on counting by 2's and 5's, a Grade 2 expectation; lesson 6-11 on exchanging money, a Grade 2 standard; and lessons 9-2, page 784, 9-3, page 788, 9-5, page 802, 9-6, page 808, and 9-8, page 823, on money, which is a Grade 2 standard.

Notes: Lesson 2-5 includes finding the missing day of the week which is not a mathematics standard. Lesson 5-3, focusing on exchanging ones for tens, comes very close to the Grade 2 standard of exchanging money. Lesson 6-7 is on the reference book; however, it is not introduced until the 6th chapter, or almost the end of the year.

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 1 do not meet the expectations for being coherent and consistent with CCSSM. The instructional materials 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 1 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 materials partially meet the expectations for having the supporting content enhance focus and coherence by engaging students in the major work of the grade. The majority of supporting work is mostly treated separately and does not always support the major work of the grade. The following details the lessons and practices with supporting work.

  • Unit one has three lessons and five practices which are supporting work, and only one lesson, 1-8, supports major work. Lesson 1-8 connects supporting work with tally charts (1.MD.4) with addition and subtraction and counting. In Lesson 1-7, tally marks for data, tally marks are treated mainly as a means to represent data with little support for using tally marks as a counting tool. In Lesson 1-9, Building with base 10 blocks, blocks are used to build structures with no support for the base-10 numbering system which they represent.
  • Unit two has two lessons and two practices which are supporting work, and only one practice, 2-2, supports major work.
  • Unit three has one lesson which is supporting work, and it does not support the major work.
  • Unit four has two lessons which are supporting work, and both lessons, 4-5 and 4-6, support major work. Lesson 4-5 connects supporting work with tally charts (1.MD.4) with addition and subtraction and counting. Lesson 4-6 connects supporting work with bar graphs (1.MD.4) with addition and subtraction and counting.
  • Unit six has two lessons and one practice which are supporting work, and they do not support the major work. In lesson 6-7. My Reference Book is introduced as a tool and sections are discussed, but the book is not used in a real problem-solving or classroom mathematics situation until this lesson. Connections to a tool that could be helpful for students should be made earlier in the year.
  • Unit seven has four lessons which are supporting work, and they do not support major work.
  • Unit eight has nine lessons and six practices which are supporting work, and no lessons or practices support major work.
  • Unit nine has two lessons and five practices which are supporting work, and no lessons or practices support major work.

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 1 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 1 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 Grade 1 materials have several instances where future grade-level content is present and not identified as such. For example, unit 3, lesson 5 is on skip counting by two's and five's, which is a Grade 2 standard, 2.NBT.A.2, and does not state it is future grade-level work or how it would relate to work of Grade 1. The same is true of unit 9 lesson 2, which is on solving money problems, a Grade 2 standard, 2.MD.C.8. This is true of all of the instances of off grade-level work.

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 three lessons which address 1.OA.2; however, only one of them, 4-10, is a full lesson. The other two are a very small part of the core lesson. Another example is 1.NBT.5; only four lessons have students mentally finding 10 more or 10 less than a number. A third example is 1.OA.1; only 2 lessons out of 17 have students solving addition and subtraction to 20. Three of the seventeen reach sums of 12, and the rest all only use within 10. Two lessons, 4-8 and 4-10, are the only lessons for properties of operations. Geometry is given slightly more attention than place value throughout the materials, and Geometry is given significantly more attention than measuring and iterating length units.

Everyday Mathematics Grade 1 materials do not provide extensive work with grade-level standards. For example, the instructional materials do not provide extensive work with the following standards:

  • 1.OA.A.1: Much of the work in this series focuses on addition and subtraction within 10, not 20.
  • 1.NBT.A.1: Most of the lessons in this series focus on numbers under 100, not 120. Lessons where students either work with or at least see numbers over 100 occur in 1-11, 3-8, 5-6 (only in the homework); 5-12 (using the number grid to subtract); and lesson 9-9 (homework to 107). The Number of the Day Routine does give the student work with numbers larger than 100.
  • 1.OA.A.2: Word problems with 3 addends are fully attended to in two lessons, 4-10 and 6-6. Lessons 6-2 and 9-2 are identified with this standard and dedicate a small portion of the lesson to this standard.  Other focus lessons labeled with this standard 9-5 and 9-6 are misidentified.  
  • 1.NBT.B.2: Only lessons 5-1, 5-2 and 5-3 address this standard with a few more questions in math journal and/or homework.

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. For example, in lesson 3-9 on page 272, the spiral snapshot shows how the lessons progress through the materials. 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 1 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 3-7: "More Counting to Add and Subtract," is shaped by 1.OA.C.
  • Lesson 5-2: "Digits and Place Value," is shaped by 1.NBT.B.
  • Lesson 7-7: "Exploring Attributes, Fractions, and Salute!" is shaped by 1.NBT.A.
  • Lesson 8-8: "Time to the Half Hour," is shaped by 1.MD.B.

While the materials have many instances where two or more domains are connected, often the connections are only surface-level connections. For example, Lesson 2-3 shows a connection between 1.OA.6 and 1.NBT.1 The lesson has students adding within 10 but does not truly have them counting within 120. Lesson 5-4 shows a connection between 1.OA.6, 1.OA.7 and 1NBT.3. The lesson has students comparing numbers using the symbols for less than, greater than, and equal to, but it does not have students adding and subtracting. The connection between place value and adding or subtracting is very rare, and no explicitly stated connections could be found. Other times, lessons provide more than one standard or cluster that will be worked on, but these standards are mostly worked on separately in the different portions of the lesson, such as warm-ups, daily routines, focus lesson, and practice. Additionally, 60 of the lessons are only aligned to one domain.

A few lessons were found to have connections among domains. Lesson 1-8 includes students collecting, organizing, and interpreting data (1.MD.4) and using that data as a context for solving comparison word problems (1.OA.1). Lesson 5-10 includes students solving comparison word problems (1.OA.1) and understanding the relationship of addition and subtraction (1.OA.4) as they use either or both operations to solve (page 451).

Gateway Two

Rigor & Mathematical Practices

Partially Meets Expectations

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Gateway Two Details

The instructional materials reviewed for Grade 1 partially meet the expectations for rigor and MPs. The instructional materials meet the expectations for the criterion on rigor and balance but do not meet the expectations of the criterion on practice-content connections. Overall, the instructional materials are stronger in regards to conceptual understanding and application.

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.
8/8
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Criterion Rating Details

The instructional materials reviewed for Grade 1 meet the expectations for rigor. The instructional materials meet the expectations for the criterion for conceptual, fluency and procedure and application. Conceptual understanding gets much more emphasis than the other two aspects of rigor. Overall, the instructional materials are stronger in regards to conceptual understanding and application.

Indicator 2a

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
2/2
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Indicator Rating Details

The materials 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 materials. 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.

  • Lesson 4-11: Students begin to compare numbers on a 100 chart in columns and rows and discuss what the numbers have in common.
  • Lesson 5-1 and Lesson 5-2: Students use concrete representations (base-10 blocks) along with number grids, 100's charts, and calculators to explore place value for 10's and 1's.
  • Lesson 5-6: Students fill in a 100's chart while the teacher asks about digits in the 10's and 1's places and relates this to ordering and comparing numbers.
  • Lesson 6-6: Page 535 has students using double ten frames to make ten as a strategy.
  • Lesson 7-1: Students explore fact families using dominoes.
  • Lesson 8-2: Students explore halves by partitioning pancakes and crackers.
  • Lesson 9-5: Students are asked to share their strategies and solutions for adding 55 and 35 including possible use of concrete models such as base-10 blocks, mentally counting up from the larger number, and changing to an easier number by making 10's. Students are similarly encouraged to use a strategy to subtract.
  • Most lessons in the materials have a "Math Message" which targets conceptual understanding.
  • Most lessons call for students to use concrete and/or visual representations when solving problems. For example, in lesson 7-5, students are introduced to the meter and are estimating and measuring lengths.

In addition, the following routines also build conceptual understanding:

  • Routine 1, Number of the Day, engages students in counting concrete objects by ones, bundling and making 10's, and bundling to make 100.
  • Routine 2 ,Calendar Routine, references 1.NBT.C and asks if students can "mentally find 10 less or 10 more than a date on the calendar."

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

  • Lesson 2-2 introduces 10-frames and 10-frame Top-It, which introduces students to the idea of grouping counters (dots) in groups of 10. The lesson still does not explicitly link the 10-frames to place value.
  • In Lesson 5-8, students exchange base-10 blocks, exchanging 1's for 10's but are still referring to these blocks as flats, longs, and cubes, missing the connections with hundreds, tens, and ones.
  • In Lesson 6-10, students work with base-10 blocks and place-value mats to solve riddles such as "show 4 longs and 6 cubes. Is this number larger or smaller than 64? How do you know?" This lesson is using the terms longs and cubes rather then 10's and one's.

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

  • Lesson 1-3 references 1.NBT.B in the Penny-Dice game. The game, if played as described in this lesson, misses an opportunity for students to group 10 counters (pennies) to show a "bundle" of 10. The "Observe" question asks "What strategies do children use to count their total pennies?" but strategies have not been explicitly taught in or before this lesson or in the game.
  • Lesson 1-5 references 1.NBT.B in the Top-It Game, but it asks if students use a number line to compare numbers rather than using place value.
  • In Lesson 4-5 on page 338, Building with base 10 blocks, "Children compose shapes with base-10 blocks and gain familiarity with the names, shapes, and sizes of these manipulatives." In this activity, children refer to base-10 blocks as flats, longs, and cubes rather than 100's, 10's, and 1's.

A concern does exist concerning the lack of lessons for some of the standards. Students may not be able to develop a deep conceptual understanding of the following standards:

  • 1.OA.A.1: "Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem." Much of the work in this series focuses on addition and subtraction within 10.
  • 1.NBT.B.2: "Understand the two digits of two-digit numbers represent 10's and 1's." Only lessons 5-1, 5-2 and 5-3 address this standard with a few more questions in math journal and/or homework.

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 1 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 399 exposures to 1.OA.6 in the instructional materials. Approximately fifty-six different lessons address 1.OA.6 in the Focus portion of the lesson.

 

There 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 for students to practice fluencies required in first grade.
  • Several online games help students with the expectation of fluency, including Top It, Plus or Minus, Beat the Computer, and Bingo.
  • Most lessons have a "Practice" section which has students practicing skills and building fluency. For example, lesson 7-3, page 635 is "Drawing a Picture Graph."
  • Online is a reference sheet called "Do Anytime Activities" with suggestions to help students build fluencies at home.

 

Note: On page 157 lesson 2-4 states “Tell children that they should subtract the smaller number from the larger number to find the difference.” This procedure will set students up for procedural misconceptions later in mathematics.

Indicator 2c

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

The materials 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 4-4 has students engaging in application of the mathematics by measuring markers. Online in the resource section, several "Projects" are available to help students with application of mathematics.

Word-problem contexts are generally familiar to first grade students including children playing, classroom materials, books, fish and dogs. In addition to word problems provided within some of the daily warm ups (24 warm ups include word problems) and focus lessons, the student journals provide many opportunities to engage students in working with word problems. Add-to, take-from, and result unknown problems are the most frequently presented.

Home-links and math journal problems focus on one-step story problems. The number of one-step story problem lessons create a good sense of application, but only for numbers under 10. This is an area of concern.

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.
2/2
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Indicator Rating Details

The Grade 1 Everyday Mathematics instructional materials meet the expectations for balance. Overall, the three aspects of rigor are neither always treated together nor always treated separately within the materials.


While some lessons target each individual aspect of rigor, some lessons focus on more than one aspect of rigor. For example, some lessons blend application and conceptual understanding, and some lessons use conceptual knowledge to help build procedural skill and fluency.

Criterion 2e - 2g.iii

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

The instructional materials reviewed for Grade 1 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
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Indicator Rating Details

The instructional materials reviewed for Grade 1 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 1 materials. The practices are not under-identified. For example, Unit 5, page 393 discusses how MP2 and MP6 unfold within the unit and lesson. Within the lesson are spots where the MPs are identified. However, within the lessons, it does not give teachers guidance 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 1 materials. MP1 and MP6 are over-identified.

The Assessment Handbook includes "Mathematical Practices for Unit(s) Individual Profile of Progress" that can be used to assess practice standards. The Beginning-of-Year assessments do not identify any practice standards for assessment, and the Middle-of-Year assessment identifies MP1, MP2, MP3, MP4, MP5, MP6 and MP7 for assessment. The End Of Year assessment identifies MP1, MP2, MP3, MP4, MP6 and MP7 for assessment. MP8 is identified with only on unit assessment while MP1 is assessed in six unit assessments.

Indicator 2f

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

The First Grade 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 where the full intent of the MPs is not met.

  • MP1: Lesson 1-2 cites MP1; however, simply having students know a faster way to count their fingers is not having students persevere in a problem. Lesson 2-3 cites MP1; however, simply having students count and model tally marks is not having students make sense of problems or persevere in problem solving. Lesson 3-6 cites MP1; however, telling students to make jumps on a number line does not have students making sense of problems or persevering in solving them. Lesson 6-3 cites MP1; however, simply having students determine if a equation is true or false does not have them making sense of problems or persevering in solving them.
  • MP4: Lesson 1-8 cites MP4; however, telling students to use tally marks is not having students choose an appropriate mathematical model, which is the intent of the MP. Lesson 2-2 cites MP4; however, again students are told to use tally marks. Lesson 3-3 cites MP4, and again the lesson tells the students how to model the mathematics.
  • MP5: Lesson 1-3 cites MP5; however, telling the students to use the pattern block template is not having students choose an appropriate tool, which is the intent of the MP. Lesson 2-7 cites MP5; however, telling students to use their calculators is not having students choose an appropriate tool. Lesson 3-5 cites MP5 but tells students to use number lines instead of having students choose an appropriate tool. Lesson 3-11 tells students to use calculators instead of letting students choose an appropriate tool. Lesson 6-7 cites MP5; however, telling students to use the Table of Contents is not having students choosing an appropriate tool.
  • MP6: Lesson 1-9 cites MP6; however, simply asking students "how many of each type of base 10 blocks were used and how many in all" is not having students attend to precision. Lesson 2-4 cites MP6; however, simply asking students "which problems were the easiest to solve, which problems were hardest to solve, and can you think of any other strategies that might have helped with the hardest problems?" is not having students attending to precision. Lesson 7-2 cites MP6; however, having students race to find the answer on calculators is not having them attend to precision.
  • MP8: Lesson 2-6 cites MP8; however, telling students to restate the turn-around rule and counting strategy in their own words is not having students look for and express regularity in repeated reasoning. Lesson 6-4, cites MP8, but telling students that a strategy is called near doubles is not having them look for and express regularity in repeated reasoning.

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. 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.

The following are examples of MP

3 in the assessments:

  • Unit 1 Assessment: Students explain their thinking in items 3 and 6, or two of the eight problems.
  • Unit 2 Assessment: Students explain their thinking in items 1, 2, 4 and 6, or four of the six problems. They explain their thinking in both problems on the Unit Challenge and items 10 and 11, two of the 11 problems on the Cumulative Assessment.
  • Unit 3 Assessment: Students explain their thinking in items 1, 3, and 5, or three of the seven problems, in one of two problems in the unit challenge and in the open response problem.
  • Unit 4 Assessment: Students explain their thinking in one of six problems, in one problem on the unit challenge, and three of seven problems on the cumulative assessment.
  • Unit 5 Assessment: Students explain their thinking on items 8, 12 and 13, or three of 14 problems and on one of two problems on the unit challenge and on one of three problems on the open response assessment.
  • Unit 6 Assessment: Students explain their thinking on items 3, 4 and 10, or three of 11 problems, and on two of 12 problems on the cumulative assessment.
  • Unit 7 Assessment: Students explain their thinking on items 3 and 4, or two of 12 problems, and on one of two problems on the open response assessment.
  • Unit 8 Assessment: Students explain their thinking or critique another person's thinking on item 9, one of 17 problems and items 3, 4, 7 and 8, four of eight problems on the cumulative assessment.
  • Unit 9 Assessment: Students explain their thinking on items 4, 6, 7 and 9, four of nine problems, and on the open response assessment.
  • The mid-year assessment includes 6 of 14 problems that ask students to justify, explain, show their thinking or critique reasoning of others.
  • The end-of-year assessment includes 8 of 28 problems that ask students to justify, explain, show their thinking or critique reasoning of others.

Examples of opportunities to construct viable arguments: (All pages reference Student Journals)

  • Lesson 2-2, page 4: "How did you figure out how many more?"
  • Lesson 2-5, page 8: "Tell your partner how you know."
  • Lesson 3-2, page 23: "How does solving 3+5 help you solve 5+3?"
  • Lesson 3-9, page 36: "How did you know what numbers to write?"
  • Lesson 4-1, page 43: "Tell your partner how you know;" page 45: "Can you count up to find the answer? How?"
  • Lesson 4-4, page 52: "Explain how you can tell how many without counting."
  • Lesson 7-7, page 147: "How do you know what to label the name-collection box?"
  • Lesson 7-8, page 149: "How are these pictures alike?"
  • Lesson 7-10, page 153: "Raoul wants to show [10's] in the box. Is that right or wrong? Explain."
  • Lesson 8-1, page 159: "How do you know that they both show the same number?"
  • Lesson 8-2, page 161: "How can you find the rule in problem 4?"
  • Lesson 8-4, page 165: "Explain how you know;" page 166: "How can knowing 7+7 help you solve 8+6?"

Examples of opportunities to analyze the arguments of others:

  • Lesson 7-6, page 145 of the Student Journal has students explaining if both Dan's and Pam's strategy will get the same answer.
  • Lesson 7-10, page 153 of the Student Journal has students explaining if Raoul's mathematical model is right or wrong and why.
  • Lesson 9-6, page 201 of the Student Journal has students sharing their answers with a partner and checking answers.

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 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 is given.
  • Lesson 1-8 cites MP3, but it only gives the teachers questions with right and wrong answers. Additionally, there is no direction for the teacher to help with facilitating a discussion.
  • In lesson 4-1, there is a question for teachers to ask, and there is a little direction for the teacher. Additionally, there is no direction on how to get students to analyze the arguments of others.
  • Lesson 4-2 does a good job providing questions so that teachers can help students guide constructing their own arguments; however, it has a missed opportunity for students to analyze the arguments of others.
  • Lessons 4-7, 4-11, 5-1, and 5-4 cite MP3; however, they do not give the teacher enough direction.
  • Lesson 6-7 cites MP3; however, simply asking students to tell what they find interesting about the reference book is not participating in constructing arguments or analyzing the arguments of others.

MP3 is well represented in Lesson 5-8. The teacher directions say to "have children work in groups to make arguments about which object is taller, citing evidence that goes beyond just looking at the objects" (page 439) and includes a sentence frame to help students prepare their arguments.

Indicator 2g.iii

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

The instructional materials reviewed for Grade 1 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.
  • The units do not have lessons or activities dedicated to developing mathematics vocabulary.
  • Terms are introduced in the text of the lessons. For instance, when the term "vertices" first appears, the instructions to students are to put their finger on the shape that has exactly four vertices, or corners (1-3, page 65).
  • 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, and big cube instead of base-ten block.

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 978-0-02-114463-1 null null null
null 978-0-02-134826-8 null null null
null 978-0-02-136607-1 null null null
null 978-0-02-138323-8 null null null
null 978-0-02-138351-1 null null null
null 978-0-02-138365-8 null null null
null 978-0-02-140936-5 null null null
null 978-0-02-143078-9 null null null
null 978-0-02-143081-9 null null null

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Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

The K-8 Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

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