Alignment to College and Career Ready Standards: Overall Summary

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

See Rating Scale
Understanding Gateways

Alignment

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Does Not Meet Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
9
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
6
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 Kindergarten enVision Math 2.0 partially meet the expectations for Gateway 1. The materials meet the expectations for focusing on the major work of the grade, but they do not meet the expectations for coherence. Some strengths were found and noted in the coherence criterion as the instructional materials partially met some of the expectations for coherence. Overall, the instructional materials allocate enough time to the major work of the grade for Kindergarten, but the materials do not always meet the full depth of the standards.

Criterion 1a

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

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

Indicator 1a

The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.
2/2
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Indicator Rating Details

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

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

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

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

  • Topic 9, page 562, item 4 asks students to count a set of more than 10 objects in a scattered format. K.CC.5 states, "Count to answer how many questions about as many as 20 things arranged in a line, a rectangular array, or a circle, and as many as 10 things in a scattered configuration, given a number from 1-20, count out that many objects."
  • The materials assess the use of a pan balance. Pan balances are meant to measure mass, a Grade 3 expectation, not weight. To use the pan balance to measure weight, the gram weights would need to be used. Mass is assessed in item 7 on the Topic 14 assessment, page 845-846 TE; item 4 on the Topic 14 Performance Assessment, page 847-848 TE; item 14 on the last cumulative/benchmark assessment; and on page 848B.
  • The assessment for Topic 11 includes off-grade level items. The following examples includes assessment on Grade 1 standards:
    • Page 672, item 4, asks students to color the boxes of numbers that have eight in the ones place. K.NBT.1 involves students working with teen numbers and seeing ten ones and additional ones. This item is more closely aligned to 1.NBT.2.
    • Page 672, item 5, refers to tens and ones place, which is more closely aligned to 1.NBT.2.

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

Criterion 1b

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

The instructional materials reviewed for Kindergarten meet the expectations for focus on the major clusters of each grade. If the materials are used as designed, students and teachers will devote the majority of class time to major clusters of the grade, which include K.CC, K.OA and K.NBT.

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 Kindergarten meet the expectations for focus within major clusters. Overall, the instructional materials spend the majority of class time on the major clusters of each grade.

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

Kindergarten enVision Math 2.0 includes 14 Topics with 106 lessons.

At the topic level, ten of the 14 topics focus on major work. One topic of the 14 focuses on supporting work and is supporting the major work of the grade, and 3 topics of the 14 topics focus on supporting work without supporting the major work. At the topic level approximately 79 percent of the topics are focused on major work and approximately 21 percent are focused on supporting work.

As mentioned above, a lesson-level analysis is more representative of the instructional materials than a topic level analysis because the number of lessons within each topic is inconsistent. At the lesson level, 78 lessons focus on major work, four lessons focus on supporting work and support the major work of the grade, 18 lessons focus on the supporting work without supporting the major work, and six lessons focus on off grade level content. Approximately 17 percent of the lessons focus on supporting work treated separately from major work, and approximately 6 percent of lessons focus on off-grade level materials. At the lesson level, approximately 77 percent of the lessons, 82 out of 106, focus on major work of the grade.

The following are the off grade-level lessons:

  • Topic 9, Lesson 7, page 551: Students count scattered configuration beyond 10.
  • Topic 11, Lessons 2, 3, 4, 5 and 6: Students write numbers beyond 20.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
3/8
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Criterion Rating Details

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

Indicator 1c

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

The instructional materials reviewed for Kindergarten partially meet expectations that supporting content enhances focus and coherence by engaging students in the major work of the grade. Some of the supporting work is treated separately and does not support the major work of the grade.

The following detail supporting work in the instructional materials.

  • Topic 5 consists of four lessons. Lesson 5-1 focuses on classifying objects into categories. There is a missed opportunity here to support major work through a connection of counting the number of objects within each group. Lesson 5-2 focuses on classifying objects and counting the objects in each group, connecting major and supporting work. Lesson 5-3 focuses on classifying objects, counting the objects in each group, and comparing the quantities, connecting major and supporting work. Lesson 5-4 focuses on classifying and counting objects which connects major and supporting work.
  • Topic 12 is focused on identifying and describing shapes. While students are engaged in counting sides and vertices, this work is minimal. This topic is placed at the end of the materials, and the students are engaged in counting numbers beyond ten. If this Topic were moved to closer to the beginning where students are practicing counting with numbers to five then it would be more supportive of major work.
  • Topic 13 is focused on analyzing, comparing, and creating shapes. Again, while students are engaged in counting sides and vertices, this work is minimal. Additionally, the placement of the topic at the end of the materials means the students are engaged in counting numbers beyond ten. If this Topic were moved to closer to the beginning where students are practicing counting with numbers to five, then it would be more supportive of major work.
  • Topic 14 is focused on describing and comparing measurable attributes. This topic is treated separately and does not support the major work of the grade.

Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
0/2
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Indicator Rating Details

The amount of content designated for one grade level is not viable for one school year in order to foster coherence between grades. The pacing guide assumes one lesson per day as stated on page TP-22. The enVison Math 2.0 Kindergarten program consists of 106 lessons, grouped in 14 topics. Assessments are not included in this count; if the 14 days of assessment are added in, this would bring the count to 120 days. This is still below the standard school year of approximately 140-190 days of instruction. Significant modifications by the teacher would need to be made to the program materials to be viable for one school year and for students to learn the grade-level content standards.

Indicator 1e

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

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

Material related to future grade-level content is not clearly identified or related to grade-level work. The exception is the topic titled "Step up to 1st grade" where the materials are clearly identified as Grade 1 materials. The Kindergarten materials have several instances where future grade-level content is present and not identified as such. For example:

  • Topic 11, lessons 2, 3, 4, 6 and 7 have students count groups past 20, 1.NBT.1.
  • Lesson 9-7 asks students to count a set of objects greater than 10 in a scattered format. K.CC.5 states, "Count to answer how many questions about as many as 20 things arranged in a line, a rectangular array, or a circle, and as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects."

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

  • K.CC.2 has one lesson addressing counting on from any number besides 1, lesson 11-5.
  • When looking at K.CC.1 counting to 20 is covered in-depth; however, the full depth of the standard, counting to 100, is not reached.
  • K.G.5 has one lesson on analyzing and comparing shapes.
  • K.G.6 has two lessons, one for two-dimensional shapes and one for three-dimensional shapes, having students compose shapes to make other shapes.
  • Zero is a very difficult concept for students, and there are two lessons focused on zero for K.CC.3.
  • There are some lessons which address K.OA.4; however, there are two lessons which have students finding a number that makes ten when added to a given number. This is a critical idea that is built upon in Grade 1.
  • Lessons in Topic 11 are tagged with K.CC.2; however, it is unclear if the students are actually counting from any number or reading the numbers provided.
  • For K.NBT.1, there are seven lessons which address teen numbers as ten ones and some additional ones, a major focus in Kindergarten. These lessons are consecutive within the text, providing limited opportunity to develop and maintain understanding.

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

  • Students engage in guided and independent practice, problem-solving contexts, and performance tasks. The opportunities for practice are balanced between each of the domains of the standards.
  • Online resources include extra, on-level and advanced-practice materials.
  • Interventions provided with lessons for students most often engage students more deeply in the work of the grade level than the lesson itself. Often, the lessons do not engage students because students are simply following directions instead of being engaged in problems. The following are some examples of lessons where the interventions would engage students more than the lesson: lessons 1-5, 1-6, 2-3, 2-6, 3-6, 3-7, 6-7, 6-9, 7-6, 7-7, 8-5 and 8-7.
  • The numbers of topics addressing Kindergarten domains are as follows: 6 out of 14 topics address Counting and Cardinality; 2 out of 14 topics address Measurement and Data; 1 out of 14 topics addresses Number and Operations in Base Ten; 3 out of 14 Topics address Operations and Algebraic Thinking; and 2 out of 14 topics address Geometry.
  • There are many opportunities for children to count objects within 10 and 20, and there are many opportunities for students to write numbers within 20 as stated in the standards. However, there are not many opportunities for daily counting above 20, which would enable students to more easily master counting to 100 by 1's and counting to 100 by 10's.
  • There is concern that seven lessons address composing and decomposing numbers between 11 and 19 (K.NBT.A) as it pertains to gaining an appropriate understanding of place value for Kindergarten.

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

  • "Math Background: Coherence" includes "Look Back" and "Look Ahead" commentary, connecting to mathematics that came earlier in Kindergarten, explaining connections to the content within the topic, and explaining what will come later in Kindergarten and in Grade 1. An example can be found on pages 1c-1d for Topic 1.
  • Individual lessons also include coherence headings. An example is in lesson 3-5 on page 163 that includes the heading, "Coherence: Engage learners by connecting prior knowledge to new ideas. Students use counters to represent and count a set of 10. This prepares them for the next part of the lesson where they practice representing and counting sets of 10."

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

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

  • The focus of topic 1 is K.CC.A, Knowing number names and the count sequence, and K.CC.B, Count to tell the number of objects. Lesson objectives in Topic 1 include: L1 - Count 1, 2, and 3 objects, L2 - Count groups of 1, 2, and 3 objects in different ways, L3 - Read and write the numbers 1, 2, and 3, and L11 - Use math to explain what you know about counting.
  • A similar example for Topic 2 can be found on pages 85I - 85J.

The materials for Kindergarten enVision Math 2.0 do not foster coherence through grade-level connections. Most lessons in the kindergarten program focus within a single domain and cluster. Of 106 lessons, 83 lessons focus within a single cluster and domain.

  • In Topic 1, only one lesson, lesson 1-9, is identified as addressing standards within two domains K.CC.4 and K.OA.3.
  • All lessons within Topic 2 are within a single cluster and domain.
  • Five of eight lessons in topic 3 (3-2, 3-4, 3-6, 3-7, 3-8) address standards in two clusters, with two of those within different domains.
  • Topic 4 includes two of six lessons that address two clusters, both within the same domain.
  • In Topic 5, addressing supporting work, three of the four lessons address two clusters and domains, Measurement and Data and Counting and Cardinality.
  • Of the 10 lessons in Topic 6, one lesson addresses standards within two clusters and domains, K.CC.2 and K.OA.1.
  • All lessons within Topic 7 are within a single cluster and domain.
  • All lessons within Topic 8 are within a single cluster and domain.
  • Although six of the seven lessons in Topic 9 address two clusters, both clusters are within the same domain.
  • All lessons within Topic 10 are within a single cluster and domain.
  • All lessons within Topic 11 are within a single cluster and domain.
  • Although four of the eight lessons in Topic 12 address two clusters, both clusters are within the same domain.
  • Although one lesson focuses on supporting work, of the seven lessons in Topic 13 that address two clusters, both clusters are within the same domain.
  • All lessons within Topic 14 are within a single cluster and domain.

Further analysis of Topics 5 and 13, both of which address supporting work, and Topic 10, which addresses major work of number and operations in base ten, provided the following examples:

  • In Topic 5, as students classify objects, they also count how many objects are in different categories (5-2), use counting to compare how many objects are in categories (5-3), and tell whether the way objects have been sorted, counted, and compared makes sense (5-4). There is a missed opportunity in lesson 1 to count the number of objects in each sorted group.
  • In Topic 10, as students work with teen numbers, they write two-digit numbers (K.CC.3), although this standard is not tagged within the unit. There are missed opportunities within this unit for students to further develop counting skills, such as counting teen numbers and forward and backward from any number. Counting is mentioned as an extension for early finishers but is not part of the main lesson (10-2).
  • In Topic 13, as students work with shapes, there are many opportunities for students to count and compare numbers; however, counting is limited within the topic to finding a shape with a given number of sides or vertices. There are missed opportunities for students to count the number of shapes within given sets. For example, in lesson 13-3 after identifying solid figures with flat surfaces, students could count the number of shapes they identified or the number of shapes that did not fit that criteria. This same context would also allow for students to compare the number of items within each group.

Gateway Two

Rigor & Mathematical Practices

Does Not Meet Expectations

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Gateway Two Details

The instructional materials reviewed for Kindergarten do not meet the expectations for rigor and practice-content connections. The instructional materials partially meet the expectations for developing conceptual understanding, spending sufficient time with engaging applications, and having an appropriate balance of the three aspects of rigor. The instructional materials do identify the MPs and give students opportunities to construct viable arguments, but they do not always use the MPs to enrich the mathematics content and rarely have students critique the reasoning of other students. The materials do not attend to the full meaning of each MP and do not assist teachers in engaging students in constructing viable arguments and analyzing the arguments of other students.

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.
3/8
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Criterion Rating Details

The instructional materials reviewed for Kindergarten do not meet the expectations for rigor and practice-content connections. The instructional materials partially meet the expectations for developing conceptual understanding, spending sufficient time with engaging applications, and having an appropriate balance of the three aspects of rigor. The instructional materials do identify the MPs and give students opportunities to construct viable arguments, but they do not always use the MPs to enrich the mathematics content and rarely have students critique the reasoning of other students. The materials do not attend to the full meaning of each MP and do not assist teachers in engaging students in constructing viable arguments and analyzing the arguments of other students.

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

The instructional materials reviewed for Kindergarten enVision Math 2.0 partially meet the expectations for giving attention to conceptual understanding. The materials rarely develop conceptual understanding of key mathematical concepts where called for in specific content standards or cluster headings. The lessons do not devote a lot of time to hands-on learning which would lend itself to building the conceptual understanding of a student in Kindergarten.

Rarely are students asked to work with manipulatives when the materials would lend themselves to it. Most of the regular grade-level work consists of pages in the Student book.

Also, these lessons are sometimes clustered in a way that may be problematic if students don't grasp the concepts within the specific topic. For example, students work with place value (K.NBT) in Topic 10. There are seven lessons devoted to K.NBT.1. The remaining lessons after Topic 10 focus on other domains such as counting and cardinality, geometry, and measurement and data. Students are not provided the opportunity to apply or further develop understanding of number and base ten within the lessons.

Standard K.OA.1 focuses on representing addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.

  • Topics 6, 7 and 8 specifically address K.OA.1.
  • Lesson 6-1 is the first lesson that addresses K.OA.1. The whole class portion of this lesson begins with a page from the student book showing pictures of flowers and pictures of hands. Although the directions on page 288 state that students should “do all of the following to show each part to find how many in all: clap and knock, hold up fingers, and give an explanation of a mental image,” the students are doing these things in order to complete pages from the student book. Although crayons, erasers, and blocks are all pictured on the pages from the student book, students are not building their understanding through hands-on work with any of these objects mentioned in the lesson.
  • On page 293, Lesson 6-2 begins with a hands-on activity that allows students to represent addition using connecting cubes. Although the rest of the lesson includes directions to use connecting cubes or counters to model the problems and write addition sentences, students are shown pictures and given a sentence with blanks to fill beneath the groups of pictures.
  • Lesson 6-3 begins with a page from the student book. The page from the student book has a picture of two tomato plants with tomatoes on them, and students fill in blanks in a sentence. From the beginning the lesson focuses on completing pages from the student book and lacks hand-on activities to build conceptual understanding of addition. Although the directions in the lesson state to use connecting cubes or counters to model the problems and write addition sentences, students are shown pictures and given a sentence with blanks to fill beneath the groups of pictures.
  • Lesson 6-4 focuses on the idea that the plus sign means “and.” Students complete pages from the student book recopying numbers and replacing “and” with a “+” sign.
  • Lesson 7-1 is the first lesson focused on subtraction. The lesson begins with five problems with pictures, and then students begin solving problems on pages from the student book. Page 367 of the Teacher Edition does state that for items 3-6, teachers should “(g)ive each student 10 connecting cubes so that they can act out each problem using objects.” The lesson and the directions do not require hands-on activities in order to complete the pages from the student book until the independent practice portion of the lesson. The lesson is developed using pages from the student book.
  • On page 371, Lesson 7-2 begins with a hands-on activity that allows students to represent subtraction using connecting cubes. In problems 1-8 students are shown pictures and given blanks to fill beneath the pictures. Problems 9 and 10 suggest that student “draw counters to show a group,” not actually use physical counters.
  • Lesson 7-3 begins with a page from the student book. The page from the student book has a picture of four ladybugs, and students fill in blanks in a sentence. From the beginning, the lesson focuses on completing pages from the student book and lacks hand-on activities to build conceptual understanding of addition and subtraction. Students are shown pictures and given a sentence with blanks to fill beneath the groups of pictures throughout the lesson.
  • Lesson 7-4 focuses on the idea that the minus sign means “take away.” Students complete pages from the student book recopying numbers and replacing “take away” with a “-” sign.
  • Lesson 7-5 focus on subtraction with equations. Although the directions state that students should use counters to solve the problems, the page from the student book includes drawings of objects. For all but one of the problems, the equations are written by recopying the numbers and filling in blanks beneath the words “take away” and “is” with the “-“ and “=” signs. Students are following this procedure as they complete nine problems.
  • In Lesson 8-3, students draw their own pictures to represent addition and subtraction equations and then write the corresponding equations. This lesson allows students to show their understanding of addition and subtraction.

Cluster K.NBT.A focuses on working with numbers 11-19 to gain foundations for place value.

  • Topic 10 specifically addresses K.NBT.A.
  • In Lesson 10-1 students compose the numbers 11, 12 and 13. Students begin with a hands-on activity using 13 counters using a ten-frame. However, after that activity students are completing pages from the student book. Some questions provide students with pictures of 10-frames filled in with additional ones drawn underneath, and students fill-in the equations in the blanks beneath. Some questions provide students equations and ask them to draw the pictures to represent the equations. A couple of problems give students equations with a missing addend and ask students to fill in the missing number and draw the pictures to represent the equation. For two problems students are given a number and have to draw counters and write an equation to show how to make the number. The last problem of the independent practice asks students to decompose the number 13; this is the only time that a number is decomposed in the lesson.
  • In Lesson 10-2 students compose the numbers 14, 15, and 16, and in Lesson 12-3 students compose the numbers 17, 18 and 19. Students begin these lessons with a hands-on activity using counters and a 10-frame. However, after that activity students are completing pages from the student book by either drawing counters or filling in blanks to write equations. The last independent practice problem in Lesson 10-2 asks students to decompose the number 16; this is the only time that a number is decomposed in the lesson. The last independent practice problem in Lesson 10-3 asks students to decompose the number 19; this is the only time that a number is decomposed in the lesson.
  • In Lessons 10-4 thru 10-6, students are decomposing the numbers 11-19. These lessons begin with a hands-on activity using 10-frames and counters. However, after that activity, students are completing pages from the student book by either drawing counters or filling in blanks to write equations, although occasionally students are prompted to use counters before drawing the counters.

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

  • Lessons 6-3, page 303A, and 6-10, page 345A, have interventions developing conceptual understanding for K.OA.A.
  • Lesson 8-5 on page 463A, Lesson 8-7 on page 475A and Lesson 8-9 on page 487A have interventions developing conceptual understanding for K.OA.A.
  • Lesson 10-4 on page 589A and Lesson 10-6 on page 601A have interventions developing conceptual understanding for K.NBT.

Indicator 2b

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
0/2
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Indicator Rating Details

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

In the instructional materials, daily opportunities to develop fluency and procedural skill with counting are not found (K.CC.1). There are many opportunities for children to count objects within 10 and 20. There are also many opportunities for students to write numbers within 20 as stated in the standards. However, there are not many opportunities for daily counting above 20. Frequent practice with rote counting is needed in order to master counting to 100 by 1's and counting to 100 by 10's and to build fluency.

Standard K.OA.5 focuses on fluently adding and subtracting within 5.

  • Five lessons address this standard: 6-9, 7-8, 8-2, 8-3 and 8-4.
  • In Lesson 6-9, although students explore addition within 5 for eight of the problems on the page from the student book, the last problem is 200+100=?. The teacher’s edition says the following: “Some students may be confused as they are dealing with 3-digit numbers. Have students look at what is similar and what is different between the two equations. Remind students about the patterns in items 6 and 7.” Although students are adding within 5, the lesson is more focused on using patterns than fluency.
  • Lesson 7-8 focuses on using patterns to subtract. All of the items on the pages from the student book include two or more equations. Students are supposed to fill in the blanks based on patterns, not fluency with subtraction.
  • In Lesson 8-2, students are writing equations to represent both addition and subtraction situations that are presented to them in picture form. Although the addition and subtraction equations for each item are related facts, the lesson focuses more on interpreting the pictures and writing equations than fluently adding and subtracting within 5.
  • Lesson 8-3 cites both K.OA.1 and K.OA.5. The lesson requires students to write a story to match an equation. Although students must fill in the blanks to complete the addition and subtraction equations, the focus of the lesson is on telling stories to represent situations, not fluently adding and subtracting within 5.
  • Lesson 8-4 is the last lesson that addresses K.OA.5. The page from the student book for this lesson provides 14 questions for students to complete. Students can solve the addition and subtraction equations any way that they choose. Although all of the addition and subtraction equations are within 5, none of them require students to subtract 3 or 4 from a number. Additional problems are needed to ensure that students can fluently add and subtract within 5.
  • Fluency Practice Activities aligned to K.OA.5 are found at the end of Topics 8-14. These activities are all either "Show the Letter" or "Find a Match" activities. These seven pages are found at the end of each topic, not within a lesson, so teachers would have to intentionally incorporate these activities into the lessons.
  • Six Fluency Practice/Assessment pages from the student book aligned to K.OA.5 are included in the instructional materials. These pages from the student book can be seen on page 431H of the teacher's edition. These pages from the student book each have 10 problems.
  • Two games are available online to practice fluency within 5.

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

Most topics have at least one lesson designated to application. However, the emphasis of these lessons is on the standards addressed in the rest of the topic and not necessarily application. Some of these lessons do not provide opportunities for students to apply mathematical knowledge and skills in a real-world or non-routine contexts. For example, Lesson 1-11 is designated as an application lesson. In this lesson, students are shown five circles on the page, and the teacher says “Alex needs to count the group of shapes. How can you count these shapes? Use objects or words to help. Write the number to tell how many shapes. Tell why your number is correct.” Although the problem includes a person’s name, students are simply counting circles on the page. Another example is lesson 11-7. The objective of this lesson is to count on from any number counting by tens and by ones. The lesson emphasizes patterns using a hundreds chart and does not include real-world or non-routine contexts.

Standard K.OA.2 is focused on solving addition and subtraction word problems and adding and subtracting within 10.

  • Only seven lessons specifically target K.OA.2.
  • Lessons 6-7, 6-8 and 6-10 include addition stories. 6-7 includes ten add-to result-unknown problems and one add-to change-unknown problem within the problem based learning, guided practice, and independent practice sections. Lesson 6-8 includes nine put-together problems and one add-to result-unknown problem within the problem-based learning, guided practice, and independent practice sections. Lesson 6-10 includes ten word problems with a variety of add-to and put-together problems. In Lesson 6-10, most of the word problems are accompanied by pictures of the objects. Once students learn the procedure needed to solve the problem, the context of the word problem is irrelevant.
  • Lessons 7-3, 7-7, and 7-9 include subtraction stories. 7-3 includes thirteen take-from result-unknown problems within the problem based learning, guided practice, and independent practice sections. The problems in Lesson 7-3 are accompanied by pictures of the objects. Once students learn the procedure needed to solve the problem, the context of the word problem is irrelevant. Lesson 7-7 includes ten take-from result-unknown problems within the problem based learning, guided practice, and independent practice sections. Lesson 7-9 includes four take-from and three add-to problems within the problem based learning, guided practice, and independent practice sections. Lesson 7-9 is the only lesson in which students have to listen to the story problem and consider which operation to use. Other lessons focus solely on addition or solely on subtraction problems.
  • Lesson 8-8 includes both-addends-unknown story problems. Most of the word problems are accompanied by pictures of the objects. Once students learn the procedure needed to solve the problem, the context of the word problem is irrelevant. The last problem does not include pictures, but it is not a both addends unknown problem.

Real world situations are often found in the solve-and-share and visual learning components of lessons, but the contexts are not always relevant or familiar to Kindergarten age students. For example, the solve-and-share for Lesson 4-1 is about a chicken farm. Another example is the use of shells in the Lesson 3-2 visual learning component. Word problem contexts may also not be familiar to some kindergarten students including flamingos and food bars and baby alligators in the marsh in Lesson 7-9.

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 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, but most lessons focus on one aspect of rigor at a time. Procedural skill is treated separately from fluency with a small number of activities dedicated to fluency, and the lack of lessons on fluency does not allow for a balance of the three aspects.

In Topic 11, of the 7 lessons, four target conceptual understanding, one targets procedural skills, one targets application, and one targets both conceptual understanding and procedural skills. Often when more than one aspect of rigor is the focus of a lesson, the aspects are conceptual understanding and procedural skills. For example, in Topic 1, of the 11 lessons, eight target conceptual understanding and procedural skills, two target conceptual understanding, and one targets application. There are many missed opportunities to connect the different aspects of rigor.

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
3/10
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Criterion Rating Details

The instructional materials reviewed for Kindergarten do not meet the expectations for practice-content connections. The materials partially meet the expectations for attending to indicators 2e through 2giii, except for 2f and 2gii which do 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 each MP, especially MP3 in regards to students critiquing the reasoning of other students and giving teachers more guidance for implementing MP3.

Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
1/2
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Indicator Rating Details

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

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

  • MP 1: approximately 40 lessons.
  • MP 2: approximately 70 lessons.
  • MP 3: approximately 50 lessons.
  • MP 4: approximately 60 lessons.
  • MP 5: approximately 50 lessons.
  • MP 6: approximately 60 lessons.
  • MP 7: approximately 40 lessons.
  • MP 8: approximately 30 lessons.

Since each MP is identified in so many lessons, each lesson has 3-5 practices identified in it. With this many practices identified in each lesson, there are many times when the entire meaning of the MP is not evident in the lesson, which leads to the MP not enriching a student's opportunity to learn the content of the lesson. For example, the "Do You Understand? Show Me!" item on page 202 in lesson 4-1 is labeled "MP4 Model with Math: Show students a row of 8 counters and a row of 7 counters. Is a group of 8 counters greater or less in number than a group of 7 counters? How can you tell?" In this example, students are not modeling with math because they are simply answering questions about something the teacher is showing them.

In some instances, more guidance to teachers could enrich the content, and in other instances, the connection is limited or the MP may be misidentified.

  • In Topic 4 on page 204, item 8 is labeled "MP8: Generalize The first step is for students to draw a group that is the same in number. Once the two groups match, then students can add more to their drawing to make a group that is greater in number. How many are in the group? How can you draw a group that has more?" This item does not have students express regularity in repeated reasoning as there is only one step in the problem.
  • In Topic 6 on page 330, part of the "Guided Practice" is labeled "MP5: Use Appropriate Tools Strategically What could you use to solve the problem? How did you use the cubes? How does the picture of the cubes help you find the answers?" In this example, students aren't using any tools; they are responding to questions about a picture that shows cubes being used.

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

Indicator 2f

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

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

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

  • MP 1: In Topic 1, on page 15, items 3-8 cite MP1; however, persisting through a set of mathematical skills does not attend to the full meaning of this practice standard. Lesson 4-2 cites MP1, asking students to plan their work and how they will defend it; however, there is not a rich problem attached, only a page from the student book where students are matching. This does not provide the opportunity to makes sense of a problem or persevere in solving it. Lesson 7-6 cites MP1; however, there is only a page from the student book problem with little opportunity for students to persevere in problem solving.
  • MP4: Lesson 1-1 cites MP4; however, giving the students the materials to model with and then telling them how to model it is not meeting the intention of the MP. Lesson 1-4 asks students to draw oranges to represent a number; telling the students what to draw does not meet the intent of MP4. Lesson 4-1 cites MP4, but the problem is already being modeled on the page from the student book. This does not meet the intention of the MP because students are not actually modeling the problem.
  • MP5: Lesson 1-3 cites MP5, but giving students counters to use does not meet the intent of using appropriate tools strategically. To meet the intention students should be choosing and using their own mathematical tools. In Lesson 3-1, students use counters to represent and count a group of six (page 139). Students are not selecting tools; they are given a specific tool. Lesson 3-2 on page 147 cites MP5. The items that are tagged include a set of sea creatures, and students are directed to "count the objects and then practice writing the number that tells how many." Tools are not used. Lesson 4-3 cites MP5; however, telling the students to use the number sequence at the top of the page does not meet the intent of the standard. Lesson 6-2 cites MP5; giving students the tools to use does not meet the intent of the standard.
  • MP 6: Lesson 6-4 cites MP6; simply having students complete the page from the student book with the addition sign is not meeting the intention of the standard. Lesson 6-5 cites MP6; again, filling in the page from the student book with the addition sign and the equal sign does not meet the intention of the standard.
  • MP7: Lesson 3-7 is connected to MP7; students are supposed to look for structure such as categories, patterns, or properties. However, within the lesson (page 177), three items are tagged, and the explanation states, "If students are having trouble, have them place two-color counters on the bugs and turn some of the counters over. Then have students color the bugs with red counters red and the ones with yellow counters yellow. Instruct students to turn over one additional counter the next time. This will begin a pattern that they can continue throughout the page. Point out that the numbers they write also follow a pattern." This explanation directs students in what to do; students themselves are not engaging in MP7. Lesson 6-6 cites MP7; having students explain a problem already modeled for them where they are only filling in the numbers does not have students looking for structure. Lesson 6-9 cites MP7; however, simply saying that students generating a list of equations with the sum of 2 will lead to a search for patterns to add numbers does not get students to see the patterns. Lesson 7-4 cites MP7; however, reminding students that there is a structure to each expression is not having students looking for and using structure to solve problems.

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
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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 in the materials. MP3 is identified 52 times in the student edition. In many of the places where MP3 is identified, the students are not attending to the full meaning of the MP. For example, in lesson 11-4, MP3 is cited; however, in the student materials students are not asked to construct an argument or analyze the arguments of others. Additional examples of this can be found in the following lessons: 1-3, 2-4, 3-2, 4-3, 6-1, 7-3, 9-2, 10-7, 12-8, 13-4 and 14-2.

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

  • Topic 1, page 8. Show students a group of three objects, such as buttons. Say: Tell how you know how many objects are in this group.
  • Topic 1, page 61. Marta is thinking of two numbers - one is the number that comes just before 4 when counting, and the other is the number that comes just after 4 when counting. Write the two numbers Marta is thinking of. Show how you know you are correct.
  • Topic 1, page 67. Alex needs to count the group of shapes. How can you count these shapes? Use objects and words to help. Write the number to tell how many shapes. Tell why your number is correct.
  • Topic 2, page 99. Have them draw a circle around the group that is greater in number than the other group, and then explain why they are correct.
  • Topic 4, page 202. Let's count the chicks together. Point to each chick as you count aloud with students. Is a group of 7 chicks greater in number or less in number than a group of 10 chicks? How do you know?
  • Topic 6, page 329. Give pairs of students three connecting cubes of one color and two of another color. Have them place the cubes on the workman in groups arranged by color. Say: Daniel's teacher is making name tags for her students. She makes 3 name tags for boys. She makes 2 name tags for girls. Now she has 5 name tags. How does Daniel's teacher know that she has 5 name tags? Explain and then show how you know.

Examples of opportunities to analyze the arguments of others:

  • Page 133, item 2. David says that his group of toy cars is greater than his group of alphabet blocks. Do you agree with him? Have students draw a circle around yes or no, and then have them draw a picture to explain their answer.
  • Page 271, item 1. Jared says that the category of green crayons is greater than the category that is NOT green. Does his answer make sense?

Most of the time when students are asked to critique the reasoning of others it is on paper, not with a partner.

Indicator 2g.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.
0/2
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Indicator Rating Details

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

  • In Lesson 1-1 on page 8, teachers show students three objects and say, "Tell how you know how many objects are in this group." There is no background knowledge for teachers to take this beyond a single student response or explanation of how this is a beginning step to teaching students to construct viable arguments.
  • In Lesson 3-1 on page 140, teachers are given the following question to ask: "How can you tell that there's 6 objects in a group?" but there is no follow up on how to direct the discussion. In lesson 3-3, page 152 includes a parallel example.
  • Lesson 3-2 states "use pictures, counters, and symbols.....These representations are the proof students know their counting is correct". No prompts are given for the teacher to lead the class in a rich discussion for the students to either construct their own arguments or critique the reasoning of others.
  • Lesson 6-2 asks students "how can you use the cubes to find out how many boats there are in all?" Simply asking an open ended question is not getting students to have rich discussions about the mathematics in which they are engaged.
  • Lesson 6-4 asks students "how does the plus sign help you solve the problem?" This question does not give students the opportunities to construct their own argument or critique the reasoning of others.

Indicator 2g.iii

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

The instructional materials reviewed for Kindergarten partially meet the expectations for explicitly attending to the specialized language of mathematics.

  • Each lesson includes a list of important vocabulary in the topic organizer which can be found at the beginning of each topic. These vocabulary words are also noted in the "Lesson Overview" at the beginning of each lesson. While the identified vocabulary words appear within the blue script that teachers may use, the words are not highlighted or identified in any way.
  • Each unit includes two-sided vocabulary cards in the student edition with a word on one side and definition and/or representation on the other. The teacher's edition includes vocabulary activities at the start of each topic.
  • Each topic opener has a vocabulary review activity, and each topic ends with a vocabulary review activity.
  • There is an online game for vocabulary, Save the Word.
  • There are instances in the materials that the definition may be vague or unclear for kindergarten age students. For example, on page 312, "Point out to students that the number of circles on either side of the is and the + is the same. Say: This word and symbol are the balance points in the equation."
  • Correct vocabulary is sometimes not used. For example, "addition sentence" and "subtraction sentence" are used instead of "equation" and "same number as" is used instead of "equal."

Gateway Three

Usability

Not Rated

Criterion 3a - 3e

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

Indicator 3a

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

Indicator 3b

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

Indicator 3c

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

Indicator 3d

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

Indicator 3e

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

Criterion 3f - 3l

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

Indicator 3f

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

Indicator 3g

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

Indicator 3h

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

Indicator 3i

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

Indicator 3j

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

Indicator 3k

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

Indicator 3l

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

Criterion 3m - 3q

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

Indicator 3m

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

Indicator 3n

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

Indicator 3o

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

Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

Indicator 3p.i

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

Indicator 3p.ii

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

Indicator 3q

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

Criterion 3r - 3y

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

Indicator 3r

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

Indicator 3s

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

Indicator 3t

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

Indicator 3u

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

Indicator 3v

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

Indicator 3w

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

Indicator 3x

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

Indicator 3y

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

Criterion 3aa - 3z

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

Indicator 3aa

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

Indicator 3ab

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

Indicator 3ac

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

Indicator 3ad

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

Indicator 3z

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

Additional Publication Details

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

Report Edition: 2017

Title ISBN Edition Publisher Year
null 978-0-328-82734-3 null null null
null 978-0-328-82735-0 null null null
null 978-0-328-82776-3 null null null
null 978-0-328-82777-0 null null null
null 978-0-328-82790-9 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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