Alignment: Overall Summary

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The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet expectations for alignment to the CCSSM. ​The instructional materials meet expectations for Gateway 1, focus and coherence, by focusing on the major work of the grade and being coherent and consistent with the Standards. The instructional materials meet expectations for Gateway 2, rigor and balance and practice-content connections, by reflecting the balances in the Standards and helping students meet the Standards’ rigorous expectations by giving appropriate attention to the three aspects of rigor and meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

See Rating Scale Understanding Gateways

Alignment

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Meets Expectations

Gateway 1:

Focus & Coherence

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

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
17
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

Usability

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Meets Expectations

Not Rated

Gateway 3:

Usability

0
22
31
38
36
31-38
Meets Expectations
23-30
Partially Meets Expectations
0-22
Does Not Meet Expectations

Gateway One

Focus & Coherence

Meets Expectations

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Gateway One Details

The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet expectations for Gateway 1, focus and coherence. The instructional materials meet the expectations for focusing on the major work of the grade, and they also meet expectations for being coherent and consistent with 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 enVision Mathematics Common Core Kindergarten meet expectations for not assessing topics before the grade level in which the topic should be introduced. The materials assess grade-level content and, if applicable, content from earlier grades. In instances where above-level content is assessed, questions could easily be omitted or modified.

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 enVision Mathematics Common Core Kindergarten meet expectations that they assess grade-level content. Above grade-level assessment items are present but could be modified or omitted without a significant impact on the underlying structure of the instructional materials.

The series is divided into topics with an assessment for each topic that can be delivered online and/or paper and pencil, and a topic performance assessment. Additional assessments include a Kindergarten Readiness Test and four Cumulative/Benchmark Assessments addressing Topics 1-4, 1-8, 1-11, and 1-14. Assessments can be found in the Assessment Resource Book online or in print. The materials also include an ExamView Test Generator. Examples of grade-level assessment items include:

  • Topic 1, Performance Task, Item 1, “Karen’s family sells fruit from a fruit cart. Have students count how many of each kind of fruit, and then write the numbers to tell how many.”  (K.CC.3, K.CC.5)
  • Topic 3, Topic  Assessment, Item 5, students “Read the number (9) and then draw toys to show how many.” (K.CC.4)
  • Topics 1-4, Cumulative  Assessment, Item 13, “Joanie has 2 toy bears and 4 toy lions. Color the cubes to show how many of each type of toy and then draw a circle around the cube train that is greater than the other cube train.”  Students are given a picture with 2 bears and 4 lions. Next to each group of animals is a train of 5 cubes to be colored to match the number of animals. (K.CC.5, K.CC.6)
  • Topic 8, Topic Assessment, Item 2, “Count the fruits, draw counters to show how many more fruits are needed to make 10, and write the number that tells how many.”  (K.OA.4)
  • Topic 9, Topic Assessment, Item 2, students identify which of the 4 pictures shown, has 12 feathers. (K.CC.5)
  • Topic 10, Topic Assessment, Item 5, students view the number 14 and a double ten frame with 10 counters in the top frame. Students “draw counters to make 14, and then complete the equation to match the picture.” (K.NBT.1)

Examples of above grade level assessment items that could be modified or omitted:

  • Topic 11, Topic Assessment, Item 2, students count 78 beads and choose the correct answer from the following choices: 78, 79, 88, and 89.  In K.CC.1, students count to 100, but they do not have to recognize the standard form of the number (1.NBT.1).
  • Topic 14, Topic  Assessment, Item 5 , students are shown a picture of a fishbowl with 1 connecting cube beside it and asked to “find about how many cubes high the fish bowl is.”  (The fishbowl appears to be equivalent in height to 2 cubes.) Students choose the correct answer from the following choices: 1, 2, 4, and 6. (1.MD.2)
  • Topics 1-14 Cumulative/Benchmark Assessment, Item 15, students “Mark all the objects that can be measured with the tool shown.” The tool shown is a measuring cup. In Kindergarten, the focus of standard K.MD.1 focuses on describing measurable attributes such as length or weight, not to identify a tool to use to find an exact measurement.

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 enVision Mathematics Common Core Kindergarten meet expectations for students and teachers using the materials as designed devoting the large majority of class time to the major work of the grade. The instructional materials devote approximately 76 percent of instructional time to the major clusters of the grade.

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 enVision Mathematics Common Core Kindergarten meet expectations for spending a majority of instructional time on major work of the grade. The evidence was collected from Topics, Performance Tasks, Topic Assessments, Benchmarks, Centers, and 3-Act activities.

  • The approximate number of topics devoted to major work of the grade (including assessments and supporting work connected to the major work) is 10 out of 14, which is 71%. 
  • The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 73 out of 96, which is approximately 76%.
  • The number of days devoted to major work (including assessments and supporting work connected to the major work) is 108 out of 145, which is approximately 74%.

A lesson level analysis is most representative of the instructional materials as the lessons include major work, supporting work connected to major work, and the assessments embedded within each topic. As a result, approximately 76% of the instructional materials focus on major work of the grade.

Criterion 1c - 1f

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

The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet expectations for being coherent and consistent with the standards. The instructional materials have supporting content that engages students in the major work of the grade and content designated for one grade level that is viable for one school year. The instructional materials are also consistent with the progressions in the standards and foster coherence through connections at a single grade.

Indicator 1c

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

​The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The publishers identify connections between supporting content and major work in the Topic Planner pages in the Teacher Edition. For example:

Topic 5 addresses supporting standard K.MD.3 (classify objects and count the number of objects in each category) connected to the major work of standards K.CC.5 (count to answer “how many?” questions), K.CC.C (compare numbers).

  • Lesson 5-1, Solve and Share, students solve, “Carlos’s kindergarten class is having a pet fair. The pets need to be put into two tents. One tent is for pets with 4 legs. The other tent is for pets that do NOT have 4 legs. Draw pictures of 5 pets. How many animals are in the 4 legs tent? How many animals are in the NOT 4 legs tent?” Students count the number of animals in each category, and the number of legs on each animal. (K.CC.5)
  • Lesson 5-2, Solve and Share, students are shown a picture of animals on the ground and not on the ground. Students answer, “How many creatures does he see on the ground? How many does he see that are NOT on the ground? Tell how you know you counted all the creatures.”  After counting the creatures in each group, students write the numeral to represent that quantity. (K.CC.5)
  • Lesson 5-3, Independent Practice, Item 5, students look at a picture of pencils of different lengths and “Sort the pencils into pencils that are short and pencils that are NOT short, and then write numbers in the chart to tell how many.” Students then draw a circle around the category that has greater in number of pencils, and tell how they know. (K.CC.C)
  • Lesson 5-4, Share and Solve, students view a picture of blue, yellow, and green cubes and solve, “Carlos says that the number of blue cubes is equal to the number of cubes that are NOT blue. Does his answer make sense?” Using a counting strategy, students decide if the groups are equal and explain their reasoning using numbers, pictures, or words. (K.CC.6)

Topic 13 addresses supporting cluster K.G.B (analyze, compare, create and compose shapes) which is connected to major work of K.CC.B (count to tell the number of objects), K.CC.6 (identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group), and K.CC.3 (represent a number of objects with a written numeral 0 - 20). 

  • Lesson 13-1, Solve and Share, students compare shapes and count the number of sides and vertices of each shape. Students classify the shapes into a group that has 4 vertices and a group that does not have 4 vertices. They count the shapes in each group, write the numbers, and circle the greater number. (K.CC.6, K.CC.3)
  • Lesson 13-5, Guided Practice, Items 2 and 3, “Have students use the pattern block shown to cover the shape, draw the lines, and then write the number tells how many pattern blocks to use”.  Item 4, “Have students use the pattern blocks shown to create the fish, and then write the number that tells how many of each pattern block to use.” (K.CC.5)
  • Lesson 13-6, Teacher Edition, Guided Practice, students use yarn, pipe cleaners, or straws to make a square and a shape that is not a square. They explain why the second shape is not a square. (K.CC.5)

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 enVision Mathematics Common Core Kindergarten 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 amount of time and expectations for teachers and students of the materials are viable for one school year as written and would not require significant modifications. As designed, the instructional materials can be completed in 145 days. Teacher’s Edition Program Overview p.22, “Each core lesson, including differentiation, takes 45-75 minutes.” 

Kindergarten includes 14 topics. Each Topic is broken down into lessons which include additional resources for differentiation, additional time, and additional practice activities. Each Topic also includes an assessment (Teacher’s Edition Program Overview, page 22). For example:

  • There are 96 Content focused lessons. 
  • There are 14 days of Topic Centers 
  • There are 7 days for 3-Act Math activities 
  • There are 28 days of Topic Reviews and Assessments

Additional Resources that are optional and not counted in the program days include:

  • Math Diagnosis and Intervention System
  • 10 Step-Up to Grade 1 Lessons to use after the last topic
  • Readiness Test; Review What You Know; Cumulative/Benchmark Assessment (4 in all); Progress Monitoring Assessment Forms A, B and C (3 in all)

Indicator 1e

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

​The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet the expectations for being consistent with the progressions in the standards. Content from prior grades is identified and connected to grade-level work, and students are given extensive work with grade-level problems.

The materials develop according to the grade-by-grade progressions in the standards. The Teacher Edition contains a Topic Overview Coherence: Look Back and Look Ahead, and a Lesson Overview Coherence: Look Back and Look Ahead, which identify connections to content taught in previous grades, indicating the relevant topics and/or lessons. In addition, the sections include connections to content taught in future grades, topics, or lessons. For example: 

The Topic 3, Numbers 6 to 10 Topic, Overview, Coherence:

  • Look Back, “In Topic 1, students counted quantities of 1 to 5 objects in different arrangements.  They recognized that each successive number name is one greater, and learned that the last number name in the counting sequence answers the “how many” question.”
  • In Topic 3, “The numbers 6-10 are introduced in order, thus reinforcing the understanding students acquired previously that each successive number name refers to a quantity that is one greater.”
  • Look Ahead - Later in Kindergarten, “In Topics 9 and 11, students will extend the counting sequence and count to 20 and then 100 using most of the same principles and processes that were incorporated in Topic 3.”
  • Look Ahead - Grade 1, students will “relate counting to addition. In Topics 2, 3 and 4, students will use counting on and counting back as strategies for adding and subtracting within 20.”

The lessons support the progression of Kindergarten standards by explicitly stating in the Lesson Overview connections between prior lessons, the current lesson, and future lessons. For example: 

  • In Lesson 4-2, the Lesson Overview Look Back, This Lesson, and Look Ahead, “In Lesson 4-1, students used a matching strategy to compare groups of up to 10 objects.” In this lesson, “Students continue to match objects, then also compare the corresponding numbers. In the next lesson, students compare groups of objects by counting.”
  • In Lesson 7-1, the Lesson Overview Look Back, This Lesson, and Look Ahead, “Students learned the foundations of addition in Topic 6. In this lesson, students explore various ways to represent subtraction. Later in this Topic, students will use subtraction sentences and equations to represent subtraction.”
  • In Lesson 13-2, the Lesson Overview Look Back, This Lesson, and Look Ahead, “In Topic 12, students learned to identify spheres, cylinders, cones, and cubes, and to find objects that have those shapes in the environment. In this lesson, students learn that some attributes of solid figures give objects the ability to roll, stack, or slide. In Lesson 13-3, students will compare 2-D and 3-D shapes.”

The instructional materials support the progressions of grade-level standards, as evidenced by the sequencing of the topics in the curriculum. For example, in developing number concepts:

  • Counting and Cardinality clusters are addressed in Topic 1: Numbers 0 to 5; Topic 2: Compare Numbers 0 to 5; Topic 3: Numbers 6 to 10; Topic 4: Compare Numbers 0 to 10;  Topic 9: Count Numbers to 20; and Topic 11: Count Numbers to 100. These concepts are also supported in Topic 5: Classify and Count Data.
  • Operations and Algebraic Thinking is addressed in Topic 6: Understand Addition; Topic 7: Understand Subtraction; and Topic 8: More Addition and Subtraction.
  • Number & Operations in Base Ten is addressed in Topic 9: Count Numbers to 20 and Topic 10: Compose and Decompose Numbers 11-19.

The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. All Topics include a topic project, and every other topic incorporates a 3-Act Mathematical Modeling Task. During the Solve and Share, Visual Learning Bridge, and Convince Me!, students explore ways to solve problems using multiple representations and prompts to reason and explain their thinking. Guided Practice provides students the opportunity to solve problems and check for understanding before moving on to the Independent Practice. During Independent Practice, students work with problems in a variety of formats to integrate and extend concepts and skills. The Problem Solving section includes additional practice problems for each of the lessons. For example:

  • Lesson 2-4, Solve and Share, students solve, “Maria builds a tower with red and blue blocks. Count how many red blocks and how many blue blocks she uses. Write the numbers to show how many. Then draw a circle around the number that is less than the other.” (K.CC.6, K.CC.3, K.CC.5)
  • Lesson 4-3, Solve and Share, students solve, “The class aquarium has two kinds of fish, goldfish and tetras. Place counters on the fish as you count how many of each kind. Write numbers to tell how many of each kind. Draw a circle around the fish that has a number greater than the other. Tell how you know you are right.” (K.CC.6,  K.CC.2, K.CC.7)
  • Lesson 6-6, Solve and Share, students solve, “Daniel’s teacher is making name tags for her students. She makes 3 name tags for boys. She makes 2 more for girls. Now she has 5 name tags. How does Daniel’s teacher know that she has made 5 name tags? Explain and then show how you know.” (K.OA.2, K.OA.1)
  • Lesson 10-1, Guided Practice, Problem 2, students find, “How many?” Students have 11 cubes and use ten frames to find 10 + 1. (K.NBT.1, K.CC.5)

There are two instances where the materials engage students with above grade level work:

  • Lesson 14-1, Guided Practice, Problem 6, students compare the lengths of two rulers with the first ruler shown vertically and the second ruler shown on a diagonal. Students are unable to do direct comparison because the objects are not lined up beside each other. This exercise goes beyond directly comparing two objects (K.MD.2) and aligns to 1.MD.1, order three objects by length; compare the lengths of two objects indirectly by using a third object.
  • Lesson 14-4, Solve and Share, students see two trays. One has a measuring cup on it, and the other has a train of 6 connecting cubes. Students think about the measuring cup and the train of connecting cubes, as they answer the questions, “What can you measure with the cup? What can you measure with the cube train?” Choosing appropriate tools aligns to 2.MD.1. In kindergarten, students “directly compare two objects with a measurable attribute in common, to see which object has "more of"/"less of" the attribute, and describe the difference.” (K.MD.2)

The Topics and Lessons support the progression of Kindergarten standards by explicitly stating connections between prior grades and current grade level work. Each topic contains a Math Background: Coherence document with Look Back narratives that identify connections to what students learned before entering school and concepts previously learned in Kindergarten. 

  • Topic 3, Numbers 6-10, Coherence: Look Back, “Earlier in Kindergarten, Count 1 to 5 in Topic 1, students counted quantities of 1 to 5 objects in different arrangements. They recognized that each successive number name is one greater, and learned that the last number name in the counting sequence answers the “how many” question.”
  • Lesson 4-3, Coherence: Look Back: “In Lesson 4-2 students wrote numbers to compare groups of up to 10 objects that are aligned.”
  • Topic 5, Coherence: Look Back section explains that before entering school most “students have been finding similarities and differences in objects and classifying objects from a very young age.” It also relates to earlier in Kindergarten lessons on counting and comparing 0 - 10.
  • Lesson 12-7, Coherence: Look Back, “Previously in this topic, students learned shape and positions words for naming and describing two- and three-dimensional shapes.”

Indicator 1f

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

​The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the Standards.

Examples of learning objectives visibly shaped by CCSSM cluster headings include:

  • Topic 2, Lessons 2-2, 2-3, and 2-5, Lesson Objectives, “Tell whether one group is greater in number than another group,” “Tell whether one group is less in number than another group,”  and “Use objects, drawings and numbers to compare numbers” respectively. These objectives are shaped by K.CC.C Compare Numbers.
  • Topic 6, Lessons 6-2 and 6-3, Lesson Objectives, “Represent addition as adding to a number” and “Represent addition as putting two or more numbers together,” respectively. These objectives are shaped by K.OA.A, “Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.”
  • Topic 12, Lessons 12-2 and 12-5, Lesson Objectives, “Identify and describe circles, and triangles” and “Describe and identify solid figures,” respectively.  These objectives are shaped by K.G.A, Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres.)

Materials include problems and activities connecting two or more clusters in a domain, or two or more domains in a grade, in cases where the connections are natural and important. For example:

  • Topic 3, Lesson 3-2, Guided Practice, Problem 5, connects K.CC.B, “Count to tell number of objects” to K.CC.A, “Know number names and the count sequence”. Students view a picture of seven sailboats. They “count the objects, and then practice writing the number that tells how many.”
  • Topic 4, Lesson 4-2, Independent Practice, Problem 4, connects K.CC.A, “Know number names and the count sequence”, to K.CC.B, “Count to tell the number of objects”, and to K.CC.C, “Compare numbers.” Students view a picture of ten corn seed packets and seven tomato seed packets. They count the number of objects in each group, write the corresponding numbers to tell how many, and identify the number that is less than the other number by crossing it out.
  • Topic 10, Lesson 10-3, Guided Practice, Problem 4, connects K.NBT.A, “Work with numbers 11-19 to gain foundations for place value” to K.CC.A, “Know number names and the count sequence.” Students view a picture of a group of ten connected cubes and a group of seven unconnected cubes. They “write an equation to match the counters” and “tell how the picture and equation show 10 ones and some more ones.

Gateway Two

Rigor & Mathematical Practices

Meets Expectations

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Gateway Two Details

​The instructional materials reviewed for enVision Mathematics Common Core Grade Kindergarten meet expectations for Gateway 2, rigor and balance and practice-content connections. The instructional materials meet expectations for reflecting the balances in the standards and helping students meet the standards’ rigorous expectations by giving appropriate attention to the three aspects of rigor, and they meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

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 enVision Mathematics Common Core Kindergarten meet expectations for reflecting the balances in the standards and helping students meet the standards’ rigorous expectations, by giving appropriate attention to: developing students’ conceptual understanding; procedural skill and fluency; and engaging applications. The instructional materials also do not always treat the aspects of rigor separately or together.

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 instructional materials for enVision Mathematics Common Core Kindergarten meet the expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

The structure of the lessons include several opportunities that address conceptual understanding. For example:

  • Math Background: Rigor page contains information about where conceptual understanding is built within the topic.
  • The Lesson Overview includes a narrative on how conceptual understanding is included in the lesson.
  • The Solve & Share activity’s purpose is “to elicit productive struggle that builds understanding by connecting prior knowledge to new ideas.”
  • Lessons are introduced via video, Visual Learning Animation Plus, at PearsonRealize.com building on conceptual understanding.
  • Students have the opportunity to independently demonstrate conceptual understanding through Independent Practice and Problem Solving pages within lessons.

Materials include problems and questions developing conceptual understanding throughout the grade-level and provide opportunities for students to independently demonstrate conceptual understanding throughout the grade. For example:

  • Lesson 4-1, Lesson Overview, “Students further their understanding of comparison as they compare larger groups to determine which is greater or less in number.” In the Visual Learning Bridge, students compare groups of yellow and black chicks, “draw a line from each chick in the top group to a chick in the bottom group, and then draw a circle around the group that is greater in number than the other group.” (K.CC.6)
  • In Lesson 6-3, Solve and Share, students build understanding of Put Together addition situations as they add 2 green tomatoes and 3 red tomatoes by putting counters on pictures of plants. In the Visual Learning Bridge, students investigate the essential question, “How can you solve addition problems?” as they look at a picture of tomatoes and create a word problem for it. (K.OA.1)
  • In Lesson 7-1, Lesson Overview, “By utilizing multiple representations, students conceptualize problems in order to solve them.” In the Visual Learning Bridge, students “listen to the story, and then do all of the following to find out how many are left: give an explanation of a mental image, use objects to act it out, and hold up fingers.” (K.OA.1)
  • In Lesson 7-3, Solve and Share, students build understanding of subtraction as take from as they solve a take from situation: “Marta is watching bugs. She sees 4 ladybugs in a group. Look at the picture and decide how many are left.” (K.OA.1)
  • In Lesson 10-4, Solve and Share, students build conceptual understanding that the number 13 can be decomposed into two parts by solving the task, “13 students wait for the train. There are only 10 seats in each train car. How many students will have to ride in a second car?” (K.NBT.1)
  • In Lesson 10-6, Guided Practice, students create 18 with cubes using 10 of one color and 8 of another color. They then color to match the cubes in ten frames and complete the equation __ = __ + __. (K.NBT.1)

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 for enVision Mathematics Common Core Kindergarten meet the expectations that they attend to those standards that set an expectation of procedural skill and fluency. The instructional materials develop procedural skill and fluency throughout the grade-level. 

In the Teacher Edition, each Topic begins with Math Background: Rigor, where procedural skill and fluency for the topic is outlined for teachers. The structure of the lessons include several opportunities to develop procedural skills and fluency, including:

  • Math Background: Rigor page contains information about where procedural skill and fluency is built within the topic.
  • The Lesson Overview includes a narrative on how procedural skills are addressed in the lesson, when applicable. 
  • A Steps to Fluency Success chart details steps to move students to fluency and provides resources to use for practice, intervention, and enrichment. 

Later Topics include Additional Practice and Fluency worksheets, Math Diagnosis and Intervention Systems, and My Fluency Progress Forms. Additional practice is located online at PearsonRealize.com. 

Materials include Items and questions intended to develop procedural skill and fluency throughout the grade-level and provide opportunities for students to independently demonstrate procedural skill and fluency throughout the grade. For example:

  • In Lesson 3-6, Guided Practice, Items 1-3, “Have students count the boats and write the number to tell how many.” Students practice counting and writing the numbers 10 and 8. (K.CC.3, K.CC.5)
  • In Lesson 5-2, Guided Practice, Item 2, “Have students draw lines in the chart as they count the animals that have 8 legs and the animals that do NOT have 8 legs, and then write the numbers to tell how many are in each category on another chart.” Item 3, “Have students draw lines in the chart as they count birds that are in the trees and birds that are NOT in the trees, and then write the numbers to tell how many are in each category in another chart.” (K.CC.5)
  • In Lesson 6-7, Guided Practice, Items 2-5, “Have students color the boxes to complete the pattern of ways to make 4 started on the previous page, and then write an equation to match the boxes.” Item 3, “__ + 3 = 4”, students color 1 box to represent the missing addend and write the number 1. (K.OA.5, K.OA.1)
  • In Lesson 8-2, Guided Practice, guidance for Items 2-3, “Have students use cubes for these facts with 4. Have them decide whether the cubes show addition or subtraction. Encourage students to make up their own stories to match the cubes. Then have them write equations to tell the related facts.” (K.OA.5)
  • In Lesson 10-2, Guided Practice, Item 4, “Draw counters to match the equation.  Then have them tell how the picture and equation show 10 ones and some more ones.”  (K.CC.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
2/2
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Indicator Rating Details

The instructional materials for enVision Mathematics Common Core Kindergarten meet expectations that the materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step Items, routine and non-routine, presented in a context in which the mathematics is applied.

In the Teacher Edition, each Topic begins with Math Background: Rigor, where application for the topic is outlined for teachers. Math Background: Rigor for Topic 6, Applications states, “Addition Situations Real-world addition situations are used throughout this topic to illustrate the “put together” and “add to” meanings of addition.” Each Topic also includes a variety of application tasks, for example:

  • A Topic Opener, containing a contextual STEM problem designed to spark interest in the content of the topic,
  • Topic Centers with application problems, 
  • 3-Act Math activities where students engage in application problems, and
  • Performance Tasks, where students apply mathematics of the topic in multi-step, real-world situations. 

The structure of the lessons includes several opportunities for students to engage in routine and non-routine application problems. Practice & Problem Solving sections provide students with a variety of problem types to apply what they have learned. The way in which application is incorporated into specific lessons is stated in the Rigor section of the Lesson Overview of those lessons. 

Examples of opportunities for students to engage in routine application problems include:

  • In Lesson 2-2, Solve and Share, students solve “Marta’s class goes to the park.  Mr. Leeman brings 4 soccer balls and 3 basketballs. Which group of balls has more? How do you know? Use counters to show your work.” (K.CC.6)
  • In Lesson 10-5, Solve and Share, students solve “14 students go to the zoo. The first bus takes 10 students. The rest of the students go on the second bus. Use counters to describe this situation. Then complete the equation to match the counters and tell how the counters and equation show 10 ones and some more ones.” (K.NBT.1, K.CC.5)
  • In the Topic 2 STEM Project, Severe Weather, students identify different types of severe weather. Then they make a poster that includes up to “5 items people might need to be safe in a snowstorm” and “5 items people might need to be safe during a drought”. Students “write the number of objects in each group, compare them, and then draw a circle around the number that is greater than the other number.” (K.CC.6)
  • In Lesson 8-3, Solve and Share, students are presented with the problem “4 - 3 = 1.” Students tell a story to match the equation and illustrate it with a drawing. As they solve the problem, students are asked to think about “What do the numbers stand for?” (K.OA.2)
  • In Lesson 1-10, Guided Practice, Item 1, students are given a picture of 4 blue birds and a 4 to trace. “Students make a math argument about how many birds are in each row, and then write the number.” They “use objects, words or a method of their choice to explain their arguments and tell why they are correct.” (K.CC.4a)

Examples of where the instructional materials provide opportunities for students to independently demonstrate the use of mathematics flexibly in a variety of contexts include:

  • In Lesson 6-6, Independent Practice, Item 7, students draw a picture to show what is happening and write an equation to solve, “Kris eats 2 grapes at lunch and 6 grapes for her snack. How many grapes does she eat in all?” (K.OA.2)
  • In Topic 7, enVision STEM Project: Animal Needs, students find out about the basic needs of humans and animals such as food, water, nutrients, shelter and then complete a project. Students “make a poster and draw as many as 5 pictures of a human’s needs and then as many as 5 pictures of an animal’s needs. They cross out the needs that are the same for humans and animals, and then write how many are left.” (K.OA.2)
  • In Topic 8, Problem Solving Performance Task, Item 4, students are presented with the problem: 4 + _ = 5 and asked, “What story can you tell to help solve the problem?” (K.OA.1)

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.
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Indicator Rating Details

​The instructional materials for enVision Mathematics Common Core Kindergarten meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. 

Each Topic Overview contains Math Background: Rigor, where the components of Rigor are addressed. Every lesson within a topic contains opportunities for students to build conceptual understanding, procedural skill and fluency, and/or application. During Solve and Share and Guided Practice, students explore alternative solution pathways to master procedural fluency and develop conceptual understanding. During Independent Practice, students apply the content in real-world applications, use procedural skills and/or conceptual understanding to solve problems with multiple solutions, and explain/compare their solutions.

The three aspects of Rigor are present independently throughout the instructional materials. For example:

  • In Lesson 1-9, Independent Practice, Item 4, students are given pictures of boxes with 0, 1, 2, 3, 4, and 5 toys. Students count the toys in each box, write the corresponding numbers, “and draw a circle around the number that comes just after 4 when counting how many.” Students develop fluency with counting to five.  (K.CC.4c)
  • In Topic 2, Topic Centers, “Watch them Grow,” students plant beans and watch them grow in a cup.  Each cup is assigned a number from 1 to 5, and that number of beans is planted in the cup. As the plants grow, “students count the number of sprouts and compare them with the number of seeds in each cup.  Which has more? Which has fewer?” This activity allows students to apply their knowledge of counting and comparing. (K.CC.5; K.CC.6)
  • In Lesson 6-4, Solve and Share, students are provided an opportunity to represent an addition situation in any way they want to solve. “Daniel counts 4 drums in a parade. Then he sees 1 more drum. What numbers do you add to find how many drums he sees in all? How can you show the adding?” Allowing students to solve problems in different ways deepens conceptual understanding. (K.OA.2)
  • In Lesson 11-4, Solve and Share, procedural skill and fluency are the focus as students count forward beginning at 48, 75, and 95. On a hundred chart, students “count forward from the yellow number. (48, 75, 95) Stop at the red number. (54, 86, 100) Tell how many numbers you counted aloud. Color the boxes of the numbers you counted aloud to show your work.” (K.CC.1, K.CC.2)

Multiple aspects of Rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials. For example:

  • Lesson 3-4, Lesson Overview, “Conceptual Understanding: Students see that 8 and 9 can be made in different ways. They learn the unique symbol for each of these numbers. Procedural Skill: Students practice how to write 8 and 9 to tell how many are in a group.” Students demonstrate both aspects of rigor in the Independent Practice, Item 10, as they look at a picture of sea creatures, “count each group of animals, and then write the numbers that tell how many.” (K.CC.3)
  • Lesson 4-1, Lesson Overview,  “Conceptual Understanding: Students further their understanding of comparison as they compare larger groups to determine which is greater or less in number.” Procedural Skill: “Students use a 1 to 1 matching strategy to compare groups.” Students demonstrate both aspects of rigor in the Guided Practice, Item 1, as they compare groups of yellow and black chicks and by drawing a line from each chick in the top group to a chick in the bottom group. Then they draw a circle around the group that is greater in number than the other group. (K.CC.6;  K.CC.5)
  • Lesson 6-5, Lesson Overview, “Conceptual Understanding: Students build upon their understanding of addition as they work more closely with interpreting, representing, and solving addition word problems. Application: Students apply what they have learned in this topic as they solve Add To Result Unknown problem types in real-world situations.” Students demonstrate both aspects of rigor in the Guided Practice, Item 5, as they solve, “2 turtles swim in the water. 5 more join them. How many turtles are swimming in all?” (K.OA.2)
  • In Lesson 8-2, Lesson Overview, “Conceptual Understanding: Students deepen their understanding of addition and subtraction as individual operations as they see how the two related to one another. Fluency: The connection between the two operations aids in the development of students’ ability to fluently solve both addition and subtraction basic facts.” Students demonstrate both aspects of rigor in the Visual Learning Bridge, as they “listen to a story and use connecting cubes to help act out each story to choose an operation.” Then students complete the equations to tell the related facts. (K.OA.5)

Criterion 2e - 2g.iii

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

The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs). The MPs are identified and used to enrich mathematics content, and the instructional materials support the standards’ emphasis on mathematical reasoning.

Indicator 2e

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

The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet expectations that the Standards for Mathematical Practice (MPs) are identified and used to enrich mathematics content within and throughout the grade level, and are not treated separately.

The math practices are identified throughout the materials. For example: 

  • Every Topic includes a Math Practices and ETP (Effective Teaching Practices) page with an explanation of how students engage with the MPs throughout the topic.
  • Every lesson includes a Lesson Overview where an explanation of how students engage with the math practice during the lesson.  
  • Special Item Solving lessons in each topic focus on specific math practices. 
  • Specifically flagged comments and Items in all lessons focus on specific math practices. 
  • Math Practice Animation videos for each MP provide a student-friendly explanation with demonstration Items. These can be found in the Digital Resources in Pearson Realize. 
  • The Math Practices and Item Solving Handbook contains a detailed explanation for each MP, identifies “Thinking Habits” unique to each MP, connections to content and other MPs, and student behavior look-fors to monitor progress toward proficiency.

Examples of the MPs identified within individual lessons:

  • MP.1: Lesson 12-6, Lesson Overview, “Students make sense of the meaning of position words in different contexts as they follow directions to name and describe shapes and objects.” 
  • MP.2: Lesson 9-7 Lesson, Overview, “Students identify possible answers to word Items that have more than one potential answer.” 
  • MP.4: Lesson 2-5, Lesson Overview, “Mathematical Practices MP4 Model with Mathematics: Students compare groups of objects, using models to show how they know those which are greater in number, less in number, and equal in number.” 
  • MP.5: Topic 4, Math Practices and ETP, “Students use a variety of tools to represent and compare quantities, including counters, color tiles, and connecting cubes (e.g., p.160, Item 7).” 
  • MP.6: Lesson 6-4, Lesson Overview, “Students use the symbols for plus and equals consistently as they begin to use equations to represent addition.”
  • MP.7: Lesson 6-7, Lesson Overview, “Students use structure as they see patterns in addition equations to help solve Items.”
  • MP.8: Lesson 1-5, Lesson Overview, “Students build on their understanding that the arrangement of objects does not change the total number. They see this as a concept relatable to other numbers.”

Examples of where MPs are identified and used to enrich the content:

  • In Lesson 2-5, Independent Practice, Item 4, students engage with MP1 as they are asked to identify the information they know from the problem: “Marta has 2 stickers. Emily has a greater number of stickers than Marta. How many stickers could Emily have?” and “So, is it possible for Emily to have 1 sticker?” (K.CC.6)
  • In Lesson 4-2, Lesson Overview, students engage in MP2 as they “represent quantities with written numerals and use those numerals to show which is greater or lesser.”  In Independent Practice, Item 4, “Have students count the seed packets in each group, write the number to tell how many, draw a line from each seed packet in the top group to a seed packet in the bottom group, and then mark an X on the number that is less than the other number.” (K.CC.6,  K.CC.7)
  • In Lesson 8-5, Lesson Overview, students engage in MP4 as they “use equations, cubes, and pictures to model and help solve word Items with 6 and 7 where both addends are unknown.” In Guided Practice, Items 2-4, students listen to this story: “Carlos has 7 flowers. He wants to put some in a red vase and some in a blue vase. How many flowers can he put in each vase?” Given pictures of 7 cubes, students “use and color cubes to show 3 different ways you can break apart the flowers and put them in the vases, and then complete the equations to match each way.”  (K.OA.2, K.OA.3)
  • In Lesson 6-2, Solve and Share, students engage with MP5 as they solve, “Daniel sees 2 boats on the water. Then 2 more boats go out on the water. Use red and blue cubes to show how many boats are in each group.” (K.OA.1)
  • In Lesson 9-2, Solve and Share, students engage with MP6 as they use a ten frame and a picture of 14 leaves to solve, “Carlos collected leaves to put in a scrapbook. How can Carlos show the number of leaves he collected? Use counters, and then draw them to show one way.” (K.CC.3)
  • In Lesson 7-6, Lesson Overview, students engage with MP7 as they “see patterns in subtraction equations to help solve Items.” Students work with subtraction patterns in Guided Practice, Item 2, as they observe three rows of three butterflies. In the first row, one butterfly is crossed out. In the second row, two butterflies are crossed out, and in the third row, three butterflies are crossed out. Students explain the pattern they see and write an equation for each row of insects.
  • In Lesson 8-10, Independent Practice, Item 7, students draw counters in the ten-frame to show the part that they know, and then draw yellow counters in the empty spaces in the ten-frame and count to find the missing part of 10. Then  students write the missing number in the equation. 3+__=10” (K.OA.4)

Indicator 2f

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

The instructional materials reviewed for enVision Mathematics Common Core Kindergarten partially meet expectations for carefully attending to the full meaning of each practice standard. 

The materials do not attend to the full meaning of MP4 and MP5. Students have limited opportunity to model with mathematics or choose tools strategically. 

The materials often provide students with models, including problems that have no real-world context. Examples of the materials not attending to the full meaning of MP.4 include:

  • Lesson 10-2, Independent Practice, Item 7, students are given double 10 frames. “Draw counters and write an equation to show how to make 14. Then have them tell how the picture and equation show 10 ones and some more ones.”  This is an example of making a model not modeling with mathematics. (K.NBT.1, K.CC.5)
  • Lesson 4-1, Lesson Overview, MP4 is identified as “Students match objects one-to-one to model comparisons of up to 10 objects.” In the Convince Me!, “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? Show me how you know.” (K.CC.6)
  • Topic 7, Lesson 7-3, Independent Practice, Item 7, students are provided with pictures to solve, “Jerome sees 8 snails on the sidewalk. 3 slink away. How many snails are left?”  A model is already provided showing 8 snails separated into groups of 5 and 3.” (K.OA.1, K.OA.2)

The materials present few opportunities for students to choose tools strategically. In most instances, tools are chosen for students, or teachers are given guidance on what tools students should use. Examples of the materials not attending to the full meaning of MP5 include:

  • Lesson 8-1, Solve and Share, students are given 5 two-color counters and a red and yellow crayon. “Alex plants 5 daisies in a flowerpot. Some are yellow. Some are red. Use counters to show one way to break apart a group of 5 daisies. Draw the counters on the flowerpot. Color the daisies. Complete the equation to show how many red and how many yellow daisies.” (K.OA.2, K.OA.3)
  • Lesson 11-4 Lesson Overview, identifies MP5: “Students use a hundred chart to count by ones, coloring each of the numbers to show the sequence they have counted.” In the Independent Practice Item 9, on the hundred chart, the numbers 12 and 33 are colored in. “Students color the boxes of the numbers as they count aloud”, starting at 12 and ending at 33. (K.CC.2)

Examples of the materials attending to the full meaning of the MPs include:

  • MP.1: Lesson 5-3, Convince Me!, students make sense of problems and persevere in solving them as they determine whether there are more teddy bears than other stuffed animals. “Make Sense and Persevere: 2 more teddy bears were added. Use counters to find the new totals for each category. Which category is greater now? )The new totals are 8 teddy bears and 9 NOT teddy bears, so the Not teddy bears category is still greater in number.)” (K.MD.2)
  • MP.2: Lesson 10-1, Visual Learning Bridge, students use reasoning to determine how an equation (10 + 3 = 13) represents a given ten-frame model of a cube in 1 ten frame and 3 more cubes. In the equation, “What does the 10 represent? What does the 3 mean?” (K.NBT.1)
  • MP.6:  Lesson 5-1, Lesson Overview, “Students classify objects into two categories, analyzing to find those which have a given attribute and those which do not.” Independent Practice, Item 7, “Draw a circle around the animals that have tails, and then mark an X on the animals that do NOT have tails.”  (K.MD.3)
  • MP.7: Lesson 8-8 Guided Practice, Items 2 - 4, students listen to the story, “10 children are going on a field trip. Each child will wear either a red or yellow shirt. How many of each color shirt will there be?” Then using an empty ten frame, students “use and color counters to show three different ways to break apart 10 and tell how many of each color shirt, and then complete the equations to match their answers.” (K.OA.2, K.OA.3)
  • MP.8: Lesson 9-3. Independent Practice, Item 8, “Students use counters to make the number and use ten-frames or draw circles to show how many.” (K.CC.3, K.CC.5)

Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
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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.
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Indicator Rating Details

The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. 

Specific features of the materials engage students in constructing viable arguments and/or analyzing the mathematical reasoning of others. Examples include:

  • Convince Me! prompts provide the opportunity for students to share their thinking and to analyze the reasoning of others.
  • Three-Act Math - Students critique other’s reasoning as solution methods for the task are shared with the class. 
  • Solve and Share - Students share and justify solutions with the class, and they critique the reasoning of others as teachers select which solutions to share.
  • In the Visual Learning Bridge, there are opportunities for students to construct viable arguments.
  • “I Can” bubbles prompt students, i.e., “I Can...compare groups of numbers by counting.” 
  • The Math Practices and Problem Solving Handbook.

The materials consistently provide opportunities for students to construct viable arguments. Examples include:

  • Lesson 2-3, Independent Practice, Item 8, students are given a picture with 4 train engines and 3 dump trucks. “Have students draw lines to match the objects from one group to the other group. Have them mark an X on the group that is less in number than the other group, and then explain why they are correct.” (K.CC.6, K.CC.5)
  • Lesson 6-5, Convince Me!, “There are 5 birds in the fountain and 3 more came and joined them. How many birds are there in all? Explain how you know you are correct.” (K.OA.2)
  • Lesson 10-7, Problem Solving Performance Task, Item 8, after solving word problems in Items 6-8, students are asked to, “Tell a friend why your answers are correct. Then tell the friend about the pattern you see in the  number chart and how the equations show 10 ones and some more ones.” (K.NBT.1)

The materials consistently provide opportunities for students to analyze the reasoning of others. Examples include:

  • Lesson 5-4, Solve & Share, students solve, “Carlos says that the number of blue cubes is equal to the number of cubes that are NOT blue. Does his answer make sense? Use numbers, pictures, or words to explain your answer.” (K.MD.3, K.CC.6, K.CC.7)
  • Lesson 8-4, Convince Me!, “Daniel says 2 -1 = 3 because he starts with 2 counters, adds 1 more, and has 3 in all. Is he correct? Explain.”  (K.OA.5)
  • Lesson 11-3, Convince Me!, “Mike counts the decade numbers to count by 10s to 40. He counts: 10, 20, 30, 35, 40. Which number should he not have counted. Why?” (K.CC.1)

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.
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Indicator Rating Details

The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

There are multiple locations in the materials where teachers are provided with prompts to elicit student thinking. For example:

  • The Math Practices and Problem Solving Handbook provides guidance on implementing MP3 and questions that students might ask themselves as they reflect on MP3. The Problem Solving Lessons which focus on MP3 are identified, such as Lessons 1-10 and 5-4.
  • In the teacher’s notes for each lesson, MP3 is identified in red print as “Construct Arguments” or “Analyze Reasoning”. Questions to elicit student thinking are included below the prompts. 
  • In the teacher notes for Solve & Share activities, questions to prompt students thinking are included in Share Solution Strategies and Key Ideas.
  • The Convince Me! activity, when connected to MP3, provides prompts to assist students in constructing arguments and analyzing the reasoning of others.
  • Three Act Math Tasks includes Construct Arguments which provides prompts for the teacher to help students construct arguments.

The materials provide guidance to support teachers in engaging students in constructing viable arguments. Examples include:

  • Lesson 1-10, Solve & Share, Construct Arguments: “How can you use math to explain why your counting is correct?” (K.CC.4a)
  • Lesson 5-1, in the Visual Learning Bridge, animals were classified in Hair and No Hair categories. In Convince Me!, teachers are prompted to “have students classify the animals in a different way: Brown and Not Brown.” “The cat is white and the frog is green, but they are both in the same category. Is this correct? Explain.” (K.MD.3, K.CC.5)
  • Lesson 14-2, Convince Me!, “Hold up 2 glasses of different sizes. Which glass holds more than the other? [Answers will vary.] Encourage students to justify their response. How do you know?” (K.MD.2, K.MD.1)

The materials provide guidance to support teachers in engaging students in analyzing the reasoning of others. Examples include:

  • Lesson 2-3, Independent Practice, “Provide students with an opportunity to critique the answer of a fictional classmate: Carly draws 3 counters in the bottom five-frame. Is her answer correct? [No] Why not?” (K.CC.6, K.CC.5)
  • In Lesson 5-4, Visual Learning Bridge, students view a picture of vehicles. In Convince Me!, the teacher asks, ”What do you see? [Cars and trucks] Tucker and Olivia counted 6 cars and 5 vehicles that are not cars.  How can you check whether their answers make sense?” The teacher is prompted to say, “Emily says the number of cars is equal to the number of vehicles that are not cars. Does this make sense? Explain.” (K.MD.3)
  • Lesson 12-6, Convince Me!, to encourage the critiquing of reasoning, the teacher is prompted to “place 5 different objects on a desk. Stack 2 of the objects. Point to an object and have students name the object and describe its position. Other students tell if they agree and explain why. Have students suggest another way to describe the object’s position.” (K.G.1)

The materials provide guidance to support teachers in both the construction of viable arguments and analyzing/critiquing the arguments/reasoning of others. Examples include:

  • Lesson 1-10, Solve & Share, while observing students at work, the teacher is directed to ask the guiding question, “Can you explain how you counted or checked your work to explain why your number is right?” Guidance is also provided during whole class discussion: “Based on your observations, choose which solutions to have students share and in what order. Focus on the explanation of ways to tell there are 5. If needed, show and discuss the student work at the right.” (K.CC.4a)
  • Lesson 5-4, Solve & Share, teachers are prompted to note how students explain their answers and if needed, ask “What does it mean if the number of cubes in each category is equal? How can you tell or show what you found?” Then, after the sharing of strategies, teacher presents Tim’s Work and asks, “What mistake did Tim make? Why might this mistake make him think Carlos was correct?” (K.MD.3, K.CC.6, K.CC.7)

Topic 9, 3-Act Math, students make predictions for the question, “What is missing  from the box?” (comparing the contents of a box of vegetables with what was ordered). In Act 1, Construct Arguments, guiding questions are provided for the teacher: “What cannot be missing from the box? Why do you think your prediction is the answer to the Main Question? Who has a similar prediction? Who has a different prediction?” In Act 2, Share Solution Strategies Critique Reasoning, teachers are prompted to “have students share their solution methods. If needed, teachers are told to use the Analyze Student Work screen. For Carlos’s Work, teachers are provided this prompt: “Carlos says he drew a picture and then counted the missing items.  What mistakes did he make?” (K.CC.5)

Indicator 2g.iii

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

The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet the expectations of attending to the specialized language of mathematics.

The materials provide explicit instruction on the use of mathematical language including words, diagrams, symbols, and conventions. Each topic includes:

  • My Word Cards are available online. In the Teacher Edition, Build Mathematical Literacy, page 1J, explains how My Word Cards are used: “Students use the example on the front of the card to write the definition on the back” 
  • Vocabulary Activities at the beginning of Topics
  • Vocabulary Review at the end of each Topic
  • Glossary in the Student Edition
  • Animated glossary is available online.
  • Online vocabulary game in the Games Center

For each topic, the Topic Planner includes a list of the new vocabulary words for each lesson. The vocabulary words are also included in the Teacher Edition, Lesson Overview page for each lesson. For example, (Teacher Edition, page 57A)

  • In Lesson 2-1: compare, equal, group, and same number are identified.
  • In Lesson 2-2: greater than is identified.
  • In Lesson 2-3: less than is identified.

In the Vocabulary Review at the end of each Topic, teachers are provided several activities to help students review the vocabulary. For example, In Topic 8, teachers are provided with suggestions including: 

  • “Have students define the terms in their own words.” 
  • “Have students say math sentences or math questions that use the words.”
  • Play a “What’s My Word?” guessing game in which you or a student thinks about one of the words and says a clue that others listen to before they guess the word.
  • Play a “Right or Wrong?” game in which you or a student says a sentence that uses one of the words correctly or incorrectly. Then others say “right” or “wrong.”

The materials use precise and accurate terminology and definitions when describing mathematics, and they provide support for students to use them correctly. Examples include:

  • Topic 2, Vocabulary Review, Items 1-4, students review the terms less than, equal, and compare as they “draw 5 counters in group; write the number that is less than” 1; draw a group of counters that is equal in number to the group of counters shown;” and “compare red and yellow counters using matching to find which group is less in number than the other, and then mark an X on that group.” Vocabulary words being reviewed  are equal and less in number.
  • Topic 7, Vocabulary Review, Items 1-4, students review the terms minus sign, left, subtraction sentence, and separate as they “write the minus sign to show subtraction; draw a circle around the number that tells how many are left; complete the subtraction sentence; and separate the tower into 2 parts, draw each part, and then write the numbers to tell the parts.”  The vocabulary words being reviewed are minus sign, left, subtraction sentence, and separate.
  • Lesson 12-4, Visual Learning Bridge, “Emily is tracing a shape called a hexagon. How many sides does a hexagon have? [6 sides] How many vertices does a hexagon have? [6 vertices]”

Gateway Three

Usability

Meets Expectations

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
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Criterion Rating Details

​The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet expectations for being well-designed and taking into account effective lesson structure and pacing. The instructional materials include an underlying design that distinguishes between problems and exercises, assignments that are not haphazard with exercises given in intentional sequences, variety in what students are asked to produce, and manipulatives that are faithful representations of the mathematical objects they represent.

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.
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Indicator Rating Details

The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet expectations that the underlying design of the materials distinguishes between problems and exercises for each lesson. It is clear when the students are solving problems to learn and when they are completing exercises to apply what they have learned.

Lessons include: Solve & Share, Look Back, Visual Learning Bridge, Convince Me!, Guided Practice, Independent Practice, Problem Solving, and Assessment Practice. Additional Practice is in a separate section of the instructional materials, distinguishing between problems students complete and exercises in the lessons. The Solve & Share section serves to either connect prior learning or engage students with a problem in which new math ideas are embedded. Students learn and practice new mathematics in Guided Practice. 

In the Independent Practice and Problem Solving sections, students have opportunities to build on their understanding of the new concept. Each activity lesson ends with an Assessment Practice in which students have opportunities to apply what they have learned from the activities in the lesson and can be used to help differentiate instruction.

Additional Practice problems are consistently found in the Additional Practice Workbook accompanying each lesson. These sets of problems include problems that support students in developing mastery of the current lesson and topic concepts.

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
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Indicator Rating Details

The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet expectations for not being haphazard; exercises are given in intentional sequences.

Overall, activities within lessons within topics are intentionally sequenced. Students have the opportunity to develop understanding leading to mastery of the content. The structure of the lesson provides students with the opportunity to activate prior learning and build procedural skill and fluency. Students also engage with multiple activities that are sequenced from concrete to abstract and increase in complexity.

Students are introduced to concepts and procedures through a problem-based situation in the Solve & Share, and then connect that problem to the content of the lesson during the Visual Learning Bridge. The Convince Me! portion of the lesson serves to solidify understanding of mathematical concepts through the MPs, followed by teachers and students working together through Guided Practice. Students engage in problems independently in the Independent Practice section. Lessons close with Problem Solving, where students apply learning from the lesson, and Assessment Practice, where students engage with two questions aligned to the daily lesson objective.

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.
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Indicator Rating Details

The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet expectations for having variety in what students are asked to produce.

The instructional materials prompt students to produce written answers and solutions within Solve & Share, Guided Practice, Independent Practice, Problem Solving, and 3-Act Math. Students produce oral arguments and explanations through discussions that occur in whole group, small group, or partner settings. Students also produce written critiques of fictional students’ work including models, drawings, and calculations.

In the materials, students use a digital platform (Visual Learning Animation Plus) and paper-pencil activities to conduct and present their work. The materials prompt students to use appropriate mathematical language in their written and oral responses, and students frequently use various mathematical representations in their work even though the representation is often provided for students. For example:

  • In Lesson 2-1, students solve using counters to show work and critical reasoning skills to describe the answer. 
  • In Lesson 7-1, students listen to the story, and then complete all of the following to find how many are left: give an explanation of the mental image, use objects to act it out, and hold up fingers.
  • In Lesson 10-1, students work in pairs, use their fingers to represent teen numbers, and say the equation that represents the addition situation. 

Indicator 3d

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

​The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet expectations that manipulatives are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

There are few hands-on manipulatives used in the materials. In general, the manipulatives are visual manipulatives printed in the materials or virtual manipulatives found in the online materials. Occasionally, students will be prompted to use tools such as counters, cubes, place value blocks, ten frames, ruler, protractor, or grid paper. When they are used, they are used appropriately. If manipulatives are used in lessons, students are usually directed as to when and which manipulatives to use.


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
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Indicator Rating Details

The instructional materials for enVision Mathematics Common Core Kindergarten are not distracting or chaotic and support students in engaging thoughtfully with the subject. 

The page layout in the materials is user-friendly, and the pages are not overcrowded or hard to read. Graphics promote understanding of the mathematics being learned. The digital format is easy to navigate and is engaging for students. There is ample white space for students to write answers in the student book.

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
7/8
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Criterion Rating Details

​The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet expectations for supporting teacher learning and understanding of the CCSSM. The instructional materials include: quality questions to support teachers in planning and providing effective learning experiences, a teacher edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials, a teacher edition that partially contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons, and explanations of the role of the specific grade-level mathematics in the context of the overall mathematics curriculum.

Indicator 3f

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

The instructional materials reviewed for enVision enVision Mathematics Common Core Kindergarten meet the expectation for supporting teachers in planning and providing effective learning experiences by providing quality questions to help guide students’ mathematical development.

Each lesson contains a narrative for the teacher including the Lesson Overview, suggested questions for discussion, and guiding questions designed to increase classroom discourse, support the teacher in knowing what to look for, and ensure understanding of the concepts. For example:

  • In Lesson 1-5, Visual Learning, Model with Math, teachers ask, “How does this picture go with the bees? Why are all the boxes covered with counters?”
  • In Lesson 3-5, Visual Learning, Convince Me!, teachers ask, “How can you use a ten-frame and counters to count 10 objects? What is another tool you can use?”
  • In Lesson 8-1, Visual Learning, Use Structure, teachers ask, “What whole do you

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.
2/2
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Indicator Rating Details

The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet the expectation for containing a teacher 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 also include teacher guidance on the use of embedded technology to support and enhance student learning.

  • Each Topic has a Topic Planner that gives an overview of every lesson, the Objective of the lesson, Essential Understanding, Vocabulary, Materials needed, Technology and Activity Centers, along with the Standards. 
  • The Topic Planner also includes Lesson Resources such as the Digital Student Edition, Additional Practice Workbook, print material available, and what can be found in the Digital Lesson Courseware and Lesson Support for teachers.
  • Each lesson opens with a Lesson Overview including: an Objective, an Essential Understanding, Look Back, Look Ahead, Cross-Cluster Connections, aspect(s) of rigor addressed, support for English Language Learners, and any possible Daily Review pages with Today’s Challenge to be implemented. Within the lesson, technology resources or places to print PDF work pages are embedded. 
  • Lessons include detailed guidance for teachers for the Warm-Up, Activities and the Lesson Synthesis.
  • Each lesson activity contains an overview, guidance for teachers and student facing materials, anticipated misconceptions, extensions, differentiation support based on formative assessments called “Quick Checks,” and opportunities for further practice in the online materials. Included within the lessons are guiding questions and additional supports for students.
  • The teacher materials that correspond to the student lessons provide annotations and suggestions on how to present the content within the lesson structure: Step 1 (Engage and Explore), Step 2 (Explain, Elaborate, and Evaluate) and Step 3 (Assess and Differentiate). A “Launch” section follows which explains how to set up the activity and what to tell students. During the Visual Learning Bridge in Step 2, supporting questions and narratives for students are provided.
  • The materials are available in both print and digital forms. Additional online resources support the material. These opportunities are noted within the lessons. For example, each lesson has a Visual Learning Animation Plus video in Step 2, an Interactive Practice Buddy noted in Step 2 and Step 3, as well as Another Look Video found in Step 3.

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.
1/2
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Indicator Rating Details

​The instructional materials for enVision Mathematics Common Core Kindergarten partially meet the expectations that materials contain adult-level explanations so that teachers can improve their own knowledge. 

The Teacher Edition Program Overview includes resources to help teachers understand the mathematical content within a topic and a lesson. The Program Overview includes the overarching philosophy of the program, a user’s guide, and a content guide. Each Topic has a Professional Development Video presenting full adult-level explanations of the mathematics concepts in the lessons. The Professional Development Video includes clearly explained examples. A section titled, Math Background, is included for each Topic and Lesson identifying the connections between previous grade, grade-level, and future grade mathematics. However, these are not presented in ways supporting teachers to understand the underlying mathematical progressions.

The Assessment Source Book, Teacher Edition, and Mathematical Practices and Problem Solving Handbooks provide answers and sample answers to problems and exercises presented to students; however, there are no adult-level explanations to build understanding of the mathematics in the tasks.

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.
2/2
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Indicator Rating Details

The instructional materials for enVision Mathematics Common Core Kindergarten meet the expectations for explaining the role of the grade-level mathematics in the context of the overall mathematics curriculum.

  • Each topic opens with a Topic Overview including a Math Background for the Topic.
  • The Coherence section has three parts: Look Back, Topic, and Look Ahead. Each section gives a clear, specific explanation of how the topic is connected across grades. 
  • Each topic includes an Objective, Essential Understanding, (critical area for grade level), Look Back, This Lesson, Look Ahead, Cross-Cluster Connection, Conceptual Understanding, Procedural Skill, and Lesson Resources.
  • The Teacher Edition Program Overview Materials contain an overview of mathematics for K-12.

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
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Indicator Rating Details

​The instructional materials for enVision Mathematics Common Core Kindergarten cross-reference the standards addressed with an estimated instructional time for each unit and lesson.

The standards are cross-referenced in multiple places in the Teacher Edition, including in the Topic Planner at the beginning of each topic showing the lesson names, vocabulary, objectives, standards, mathematical practices, and essential understandings for the topic. The Topic Planner also includes a suggested pacing for each lesson. The Program Overview includes a Pacing Guide providing an overview of the number of days expected per Topic.

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
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Indicator Rating Details

The instructional materials for enVision Mathematics Common Core Kindergarten contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement. 

The Teacher’s Resource Masters have Home School Connection Letters, in English and Spanish, for each Topic. The letters include information on the mathematical content, activities parents can use with their child, and a Focus on Mathematical Practices section encouraging parents to support their child with the mathematics presented in each Topic. For example, Topic 7:

  • Sample Family Letter Introduction: “Dear Family, Your child is learning about subtraction. He or she will learn to understand subtraction as taking apart a quantity of objects and…”
  • Sample Family Letter Activity: “Gather 8 to 10 small objects. Count the objects as you place them in a paper bag, basket, or box. Take out 4 objects...”
  • Sample Family Letter Focus on Mathematical Practices: “Observe Your Child: During one of your turns use the sentence stem: ____ take away ____ is ____. Then have your child write a matching equation.”

Indicator 3l

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

​The instructional materials reviewed for enVision Mathematics Common Core Kindergarten contain explanations of the program's instructional approaches and identification of the research-based strategies.

The Teacher Edition Program Overview describes the organization of the curriculum and why the structure was chosen. The core instructional model for enVision Common Core is a two-step approach including Problem-Based Learning and Visual Learning. The two steps are described, with references in the teacher materials. 

Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
9/10
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Criterion Rating Details

The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet expectations for offering teachers resources and tools to collect ongoing data about student progress on the CCSSM. The instructional materials provide strategies for gathering information about students’ prior knowledge, strategies for teachers to identify and address common student errors and misconceptions, opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills, and assessments that clearly denote which standards are being emphasized.

Indicator 3m

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

​The instructional materials for enVision Mathematics Common Core  Kindergarten meet the expectations for providing strategies to gather information about students’ prior knowledge within and across grade levels.

The Assessment Sourcebook and the Teacher’s Program Overview provide information about the use of assessments to gather information about students’ prior knowledge. Every grade level includes a Grade-Level Readiness test. The Topic Readiness Assessment in each Topic helps teachers gather information about students’ prior knowledge within and across grade levels. Topic Readiness assessments can also be taken online, where they are auto-scored and interventions are auto-assigned. 

The Topic Opener assignment located at the beginning of each Topic helps students activate prior knowledge and prepare for the skills needed in the Topic. Each of these assignments has questioning strategies for the teacher. Each lesson also provides information for the teacher about prior, current grade level, and future math that is used.

Indicator 3n

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

​The instructional materials for enVision Mathematics Common Core Kindergarten meet the expectations for providing strategies for teachers to identify and address common student errors and misconceptions.

Each lesson identifies common errors and misconceptions for the teacher to address in the Guided Practice. The misconception/error is followed with prompts that the teacher can ask to help students understand their mistakes. For example:

  • In Lesson 2-5, Error Intervention, “If students are unsure how to solve the problem, then refer them to the cube trains. Remind students that the number of cubes in the shorter cube train is less in number than the other cube train.” 
  • In Lesson 9-1, Error Intervention Item 2, “If students have difficulty writing the number 12, then have them practice by using a finger to trace over the numbers on their number cards or in the air.”
  • In Lesson 12-1, Error Intervention Item 1, “If students identify the circle or triangle as solid, then discuss the examples in the Visual Learning Bridge again. Read the words flat and solid and ask students where the circle and triangle fit.”
  • In Lesson 14-6, Error Intervention Item 2, “If students’ comparisons are incorrect, then help them use the dashed lines as guides to compare the ends of the pictured object.”

Indicator 3o

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

The instructional materials for enVision Mathematics Common Core Kindergarten meet the expectations for providing opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

The lesson structure, consisting of Solve & Share, Visual Learning Bridge, Guided Practice, Independent Practice, Problem Solving, and Assessment Practice, provide students with opportunities to connect prior knowledge to new learning, engage with content, and synthesize their learning. Throughout the lesson, students have opportunities to work independently, with partners and in groups where review, practice, and feedback are embedded into the instructional routine. In addition, practice problems for each lesson activity reinforce learning concepts and skills and enable them to engage with the content and receive timely feedback. Discussion prompts in the Teacher Guide provide opportunities for students to engage in timely discussion on the mathematics of the lesson.

Each Topic includes a “Review what you know/Concept and Skills Review” containing a vocabulary review and practice problems. This section also includes review and practice on concepts related to the new Topic. 

The Cumulative/Benchmark Assessments found at the end of Topics 4, 8, 11, and 14 provide review of prior topics as an assessment. Students can take the assessment online, with differentiated intervention automatically assigned to students based on their scores. 

Different games online at Pearson Realize support students in practice and review of procedural skills and fluency.

Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
2/2
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Indicator Rating Details

The instructional materials for enVision Mathematics Common Core Kindergarten meet the expectations for assessments clearly denoting which standards are being emphasized. 

Assessments are located in a separate book, or the online portion of the program, and can be accessed at any time. For each topic, a Practice Assessment, an End-Unit Assessment, and a Performance task are included. Assessments in the Teacher Edition provide a scoring guide and standards alignment for each question.

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.
1/2
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Indicator Rating Details

​The instructional materials reviewed for enVision Mathematics Common Core  Kindergarten partially meet expectations that assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up. For example:

  • There are “scoring guidelines” to assist the teacher in interpreting student performance; however, these are an answer key or sample student answers.
  • A general rubric is provided to interpret student written responses, but it is not topic specific. 
  • Topic Readiness and End of Topic Assessments have Item Analysis for Diagnosis and Intervention, which include standards being assessed and depth of knowledge levels.
  • Assessments can be taken online where they are automatically scored, and students are assigned appropriate practice, enrichment, or remediation based on their results.
  • Teachers interpret the results of print assessments and determine materials for follow up on their own.

Indicator 3q

Materials encourage students to monitor their own progress.
0/0
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Indicator Rating Details

​The instructional materials for enVision Mathematics Common Core  Kindergarten do not include opportunities for students to monitor their own progress. There are no specific materials for students encouraging them to monitor their own progress.

Criterion 3r - 3y

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

​The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet expectations for supporting teachers in differentiating instruction for diverse learners within and across grades. The instructional materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners and strategies for meeting the needs of a range of learners. The materials embed tasks with multiple entry points that can be solved using a variety of solution strategies or representations, and they provide opportunities for advanced students to investigate mathematics content at greater depth. The instructional materials also suggest support, accommodations, and modifications for English Language Learners and other special populations and provide a balanced portrayal of various demographic and personal characteristics.

Indicator 3r

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

The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet expectations for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

The materials include a detailed Scope and Sequence of the course, including pacing. The Topic Overview in the Teacher Edition includes Coherence which enhances scaffolding instruction by identifying prerequisite skills that students should have. Each lesson is designed with a Daily Review and a Solve & Share Activity reviewing prior knowledge and/or preparing all students for the following activities.

In lessons, the following explicit instructional supports are available for sequencing and scaffolding: the Lesson Overview, questions and extensions for the Solve & Share, Prevent Misconceptions in Visual Learning Bridge, Revisit the Essential Question in Convince Me!, Error Intervention during Guided Practice, and item-related support during Independent Practice and Problem Solving. This information assists the teacher in making the content accessible to all learners.

Lesson narratives often include guidance on where to focus questions in all lesson activities, sample student work, and guidance on what to look for. Optional activities are often included in Step 3 (Assess and Differentiate) and can be used for additional practice or support before moving on to the next activity or lesson.

Indicator 3s

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

The instructional materials for enVision Mathematics Common Core Kindergarten meet the expectations for providing teachers with strategies for meeting the needs of a range of learners.

  • The Additional Practice Materials include a lesson for each topic including specific questions for the leveled assignment for all learning ranges. These three levels of problems are I (Intervention), O (On-Level), and A (Advanced) and include verbal, visual, and symbolic representations.
  • Response to Intervention strategies are included in each lesson. Teachers identify “Look Fors” and suggestions to address the needs of students who are struggling. Questions for the teacher to ask are also included.
  • Each lesson has at least one Additional Example. These help students cement or extend their understanding of the concept being taught. It includes an extra problem for the teacher to use.
  • Each lesson has Differentiated Interventions for a wide-range of learners, which include Reteach to Build Understanding (provides scaffolding to reteach) and Enrichment (extends concepts from the lesson).

Indicator 3t

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

The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet expectations for embedding tasks with multiple entry­-points that can be solved using a variety of solution strategies or representations.

The Solve & Share, Explore It, Visual Learning Bridge, Guided and Independent Practice, 3-Act Math Tasks, and Quick Check/Assessment Practice provide opportunities for students to apply mathematics from multiple entry-points. Though there may be times when the material asks a student to use a specific strategy, there are still questions within the same lesson that allow for students to use a variety of strategies. 

The lesson and task narratives provided for teachers offer possible solution paths and presentation strategies from various levels. For example:

  • In Lesson 6-1, Solve & Share, “Students determine the number of flowers in all and represent the total in different ways.” The Student Work examples show students using counters, fingers, and numbers to represent the groupings of flowers.
  • In Lesson 11-1, Solve & Share, “Count forward from 1 to 30. Count aloud and point to each numbers as you say it. What patterns do you see or hear when you count to 30 using the numbers on the chart? Color the boxes that show a pattern you find.” The example shows the different patterns that students heard and colored. 

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).
2/2
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Indicator Rating Details

The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet expectations for suggesting support, accommodations, and modifications for English Language Learners (ELL) and other special populations that will support their regular and active participation in learning mathematics.

The ELL Design is highlighted in the Teacher Edition Program Overview and describes support based on the student’s level of language proficiency. An ELL Toolkit provides additional support for English Language Learners.

ELL suggestions are provided for every lesson, in the Lesson Overview, Solve & Share, and in the Visual Learning Bridge. Guidance includes ELL learners at the entering, developing, expanding, and bridging levels of language acquisition. Visual Learning support is embedded in every lesson to support ELL learners. This includes a Visual Learning Animation Plus online, Visual Learning Bridge for each lesson, and the Animated Glossary. These use motion and sound to reduce language barriers. Questions are read aloud, visual models are provided, and motion and sound definitions of mathematical terms are provided.

Additionally, a multilingual handbook is included with a mathematics glossary in multiple languages, and an English Language Learners Toolkit is a resource providing professional development and resources for supporting English Language Learners. 

An example of ELL supports within the instructional materials:

  • In Lesson 12-1, Lesson Overview, English Language Learners, “Speaking: Write and read different. Remind students they have used this word before. Ask students to tell you what they think the word different means. Show a square and a cube. Say: These are both shapes. Rotate the shapes so that students can see the dimensions. Ask: How are these shapes different? 
    • Entering: Have students tell what is different with one or two words. Show another 2-D shape and another 3-D shape and repeat. 
    • Developing: Have students explain with the sentence stem: “The shapes are different because ____.” Show another 2-D shape and another 3-D shape and repeat. 
    • Expanding: Have students explain the difference in their own words. Show another 2-D shape and another 3-D shape and repeat.”

Support for other special populations noted in the Teacher Edition Program Overview include:

  • Resources are provided on for Ongoing Intervention (during a lesson), Strategic Information (at the end of the lesson), and Intensive Intervention (as needed anytime). 
  • The Math Diagnosis and Intervention System (MDIS) supports teachers in diagnosing students’ needs and providing more effective instruction for on- or below-grade-level students. Diagnosis, Intervention Lessons, and Teacher Support is provided through teachers notes to conduct a short lesson where vocabulary, concept development, and practice can be supported. 
  • Online Auto Design Differentiation is included, and the supports within this part of the program include: Differentiation After a Lesson (based on an Online Quick Check where the Interactive Practice Buddy can be utilized), Differentiation after a Topic (based on the online topic assessments where Visual Learning Animations Plus are then assigned), and Differentiation after a Group of Topics (based on the online cumulative benchmark assessments where students can then receive remediation or enrichment). The teacher can track progress using Assignment Reports and analyze Usage Data.

Indicator 3v

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

The instructional materials for enVision Mathematics Common Core Kindergarten meet the expectations for providing opportunities for advanced students to investigate mathematics content at greater depth.

Each lesson offers differentiated instruction to extend the concepts in the lesson and provides opportunities to challenge advanced students:

  • Extensions are found at the end of every Solve & Share;
  • Higher Order Thinking items within the Independent Practice and Problem Solving section;
  • Enrichment pages as a result of the Quick Checks in every lesson;
  • Opportunities to engage in STEM activities during the activity centers;
  • Noted advanced problems to complete during the Additional Practice portions of each lesson; and 
  • Differentiation after a group of Topics based on the online cumulative benchmark assessments where students can then receive enrichment.

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
2/2
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Indicator Rating Details

​The instructional materials for enVision Mathematics Common Core Kindergarten meet the expectations for providing a balanced portrayal of various demographic and personal characteristics.

  • The lessons contain tasks including various demographic and personal characteristics. All names and wording are chosen with diversity in mind and the materials do not contain gender biases.
  • The materials mostly contain pictures of objects or cartoonish drawings instead of photos or drawings of people.
  • The materials reference roles instead of pronouns (e.g., the players, book fair, sailboats, collection of toy cars, piggy banks, carton of eggs).
  • The materials include a set number of names used throughout the problems and examples (e.g., Carlos, Jada, Martha, Carl, Benito, Drake, Daniel, Yasmin, Jonathan). These names are presented repeatedly and in a way that does not stereotype characters by gender, race, or ethnicity.

Indicator 3x

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

​The instructional materials reviewed for enVision Mathematics Common Core Kindergarten provide opportunities for teachers to use a variety of grouping strategies. The materials include teacher-led instruction presenting options for whole-group, small-group, partner, and/or individual work. When suggestions are made for students to work in small groups, no specific roles are suggested for group members, but teachers are given suggestions and questions to move learning forward.

Indicator 3y

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

​The instructional materials for enVision Mathematics Common Core Kindergarten encourage teachers to draw upon home language and culture to facilitate learning.

The Teacher Edition Program Overview includes Supporting English Language Learners, which contains ELL Instruction and Visual Learning. The Teacher Edition Program Overview states, “Levels of English language proficiency are indicated, and they align with the following level identified in WIDA (World-Class Instructional Design and Assessment): Entering, Emerging, Developing, Expanding, and Bridging.” 

English Language Learners support for each lesson is provided for the teacher throughout lessons to provide scaffolding for reading, as well as differentiated support based on the students’ language proficiency level (emerging, developing, expanding, or bridging). The Home-School Connection letters for each topic are available in both English and Spanish. An English Language Learners Toolkit is available consisting of many Professional Development Articles and Graphic Organizers. A few of the examples of the Professional Development Articles that can help teachers support ELL learners include: English Language Learners in the Math Classroom, Strategies for Teaching English Language Learners, Welcoming Newcomers to the Mainstream Classroom, Multilingual Thinking Words, and Teaching Math to Culturally and Linguistically Diverse Students.

Criterion 3z - 3ad

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

​The instructional materials reviewed for enVision Mathematics Common Core Kindergarten: integrate technology in ways that engage students in the Mathematical Practices; are web-­based and compatible with multiple internet browsers; include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology; can be easily customized for individual learners; and include or reference technology that provides opportunities for teachers and/or students to collaborate with each other.

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
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Indicator Rating Details

​The instructional materials reviewed for enVision Mathematics Common Core Kindergarten integrate technology including interactive tools, virtual manipulatives/objects, and dynamic mathematics software in ways that engage students in the Mathematical Practices.

Teachers and students have access to tools and virtual manipulatives within a given activity or task, when appropriate. Pearson Realize provides additional components online such as games, practice, instructional videos, links to other websites, differentiation, etc. For each Mathematical Practice, there is a detailed interactive video included in the online materials. However, in the teacher print materials, online resources are referenced generically without specific guidance. On the website, there is not an explicit link to activity directions for the online tools; they are not clearly labeled or connected to specific lessons.

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
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Indicator Rating Details

​The instructional materials for enVision Mathematics Common Core Kindergarten include digital materials that are web-based and compatible with multiple internet browsers. 

Digital materials (either included as part of the core materials or as part of a digital curriculum) are web-­based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, Safari, 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 for the use of tablets and mobile devices including iPads, laptops, Chromebooks, MacBooks, and other devices that connect to the internet with an applicable browser.

Indicator 3ab

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

​The instructional materials for enVision Mathematics Common Core for Kindergarten include opportunities to assess students' mathematical understandings and knowledge of procedural skills using technology.

  • Online games enhance fluency and include games where students use procedural skills to solve problems.
  • Virtual Nerd offers tutorials on procedural skills, but no assessment or opportunity to practice the procedures is included with the tutorials.
  • The online Readiness Assessment tab for each topic includes a Remediation link including tutorials and opportunities for students to practice procedural skills using technology.

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
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Indicator Rating Details

The instructional materials for enVision Mathematics Common Core Kindergarten include digital materials with opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. Teachers can select and assign individual practice items for student remediation based on the Topic Readiness assessment. Teachers can create and assign classes online for students. An online Accessible Student Edition can be assigned to students. Closed Captioning is included in STEM and 3-Act Math videos.

The instructional materials reviewed for enVision Mathematics Common Core Kindergarten can be easily customized for local use. Digital materials provide the same lessons to draw from on a topic as the print materials. Teachers can create and upload files, attach links, and attach documents from Google Drive and assign them to students. Teachers can also create assessments using a bank of items or using self-written questions that can also be assigned to students.

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
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Indicator Rating Details

The instructional materials for Envision Mathematics Common Core Kindergarten include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.). There is a “Discuss” tab to assign discussion prompts to students in the “Classes” tab, and a file can also be attached.

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Additional Publication Details

Report Published Date: 01/07/2020

Report Edition: 2020

Title ISBN Edition Publisher Year
enVision Mathematics Common Core Kindergarten 9780134958996 Digital Pearson Education 2020

About Publishers Responses

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

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

About Technology Information

EdReports requested that publishers fill out The Instructional Materials Technology Information document about each of their products that met our alignment criteria. This document does not evaluate the quality or desirability of any product functionality, but documents features in order to empower local schools and districts with information to select materials that will work best for them given their technological capabilities and instructional vision.

Please note: Beginning in spring 2020, reports developed by EdReports.org will be using an updated version of our review tools. View draft versions of our revised review criteria here.

Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

Rubric Design

The EdReports.org’s rubric supports a sequential review process through three gateways. These gateways reflect the importance of standards alignment to the fundamental design elements of the materials and considers other attributes of high-quality curriculum as recommended by educators.

Advancing Through Gateways

  • Materials must meet or partially meet expectations for the first set of indicators to move along the process. Gateways 1 and 2 focus on questions of alignment. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?
  • Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom. In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Key Terms Used throughout Review Rubric and Reports

  • Indicator Specific item that reviewers look for in materials.
  • Criterion Combination of all of the individual indicators for a single focus area.
  • Gateway Organizing feature of the evaluation rubric that combines criteria and prioritizes order for sequential review.
  • Alignment Rating Degree to which materials meet expectations for alignment, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.
  • Usability Degree to which materials are consistent with effective practices for use and design, teacher planning and learning, assessment, and differentiated instruction.

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.

The EdReports rubric supports a sequential review process through three gateways. These gateways reflect the importance of alignment to college and career ready standards and considers other attributes of high-quality curriculum, such as usability and design, as recommended by educators.

Materials must meet or partially meet expectations for the first set of indicators (gateway 1) to move to the other gateways. 

Gateways 1 and 2 focus on questions of alignment to the standards. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?

Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom. 

In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

For ELA and math, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to college- and career-ready standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For science, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to the Next Generation Science Standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For all content areas, usability ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for effective practices (as outlined in the evaluation tool) for use and design, teacher planning and learning, assessment, differentiated instruction, and effective technology use.

Math K-8

Math High School

ELA K-2

ELA 3-5

ELA 6-8


ELA High School

Science Middle School

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