Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for enVisionMATH California Common Core Kindergarten partially meet expectations for alignment to the CCSSM. The instructional materials meet expectations for focus and coherence in Gateway 1 as they meet expectations for focus and partially meet expectations for coherence. In Gateway 2, the instructional materials partially meet the expectations for rigor and balance, and they do not meet the expectations for practice-content connections. Since the instructional materials do not meet expectations for both Gateways 1 and 2, evidence was not collected regarding usability in Gateway 3.

See Rating Scale
Understanding Gateways

Alignment

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Partially Meets Expectations

Gateway 1:

Focus & Coherence

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

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
9
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

Usability

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Not Rated

Not Rated

Gateway 3:

Usability

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

Gateway One

Focus & Coherence

Meets Expectations

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Gateway One Details

The instructional materials reviewed for enVisionMATH California Common Core Kindergarten meet expectations for focus on major work and coherence in Gateway 1. For focus, the instructional materials do not assess topics before the grade level in which the topic should be introduced, and they devote the large majority of class time to the major work of the grade. For coherence, the instructional materials partially meet expectations for coherence by including an amount of content designated for one grade level that is viable for one school year and fostering coherence through connections at a single grade.

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 enVisionMATH California Common Core Kindergarten do not assess topics before the grade level in which the topic should be introduced. In the instances where the material is above grade level, the material could easily be omitted or modified by the teacher to address the grade-level standards.

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 enVisionMATH California Common Core Kindergarten meet expectations for assessing grade-level content. Most of the assessments provide material that is appropriate for Kindergarten. In the instances where the material is above grade level, the material could easily be omitted or modified by the teacher to address the grade-level standards. Probability, statistical distributions, similarity, transformations, and congruence are not within these assessments.

The following are examples where the standards are representative of alignment to Kindergarten expectations:

  • Topics 1, 2, 3 and 5 demonstrate a progression of standard K.CC.3.
    • In Topic 1 lesson 1.3, Digital Quick Check, students write numbers 1 to 3 by counting objects and determining the number the objects represent.
    • In Topic 2 lesson 2.7, students practice writing 0.
    • In Topic 3 lesson 3.6, students practice counting objects and determining the number the objects represented for numbers 7-10.
    • In Topic 5 lesson 5.4, students count and write numbers representing 18-20.
  • In Topic 9 lesson 9.1, Digital Quick Check, item 1, students choose the answer that shows a way to make 5. (K.OA.3)
  • In Topic 15 session 15.1, Digital Quick Check, students use directional words in conjunction with the names of shapes in terms such as inside, outside, etc. Item 1 pictures a circle inside a square. (K.G.1)
  • In Topic 3 Performance Task, page 64, students count pictures of apples and bananas and write how many. (K.CC.1, K.CC.3) Students also draw between 6 and 9 oranges and write the number. (K.CC.4) A 3-point rubric is included.
  • In Topic 7 Performance Task, page 144, students draw pictures to match the story of 5 gold coins in one treasure chest and 4 gold coins in the other. Students answer, “How many coins are there altogether?” (K.OA.1)

The assessment items that contain above grade-level content not specifically stated by the standards are noted in the following:

  • In the Topic 6, session 1.1, Digital Quick Check, students count objects above 20 in the End-of-Topic Test: 1) 28 objects, 2) 25 objects, 3) 28 objects, 4) 27 objects, 5) 22 objects, 6) 84 objects, 7) 35 objects, 8) 40 objects, 9) 35 objects. This goes above the K.CC.5 into 1.NBT.1, where students count to 120, read, write numerals, and represent an number of objects with a written numeral.
  • In the Topics 9-12 Benchmark Test, question 7 shows students three objects to sequence from shortest to longest. Question 8 shows four snowmen. Students determine which is tallest. K.MD.2 states, “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.”
  • The Online Topic 12 assessment, questions 9, 10, 14, 15 compare three objects; students place these in order according to length. K.MD.2 involves students comparing two objects to tell more or less of the attribute. In question 11, students compare each of the pencils to the first pencil; because they are not lined up, they would not be able to do a direct comparison. This would necessitate using a third object to indirectly compare the two objects, which is part of Grade 1. (MD.1 standard, compare the length of two objects indirectly by using a third object.)
  • The Online Topic 16 Assessment, question 7 shows a trapezoid. (1.G.2) The students are prompted, “Which of these is part of the shape above?“ The choice students check is a trapezoid.
  • The Topic 14 lesson 14-7, Quick Checks include analyzing flat surfaces of 3D figures beyond using informal language to describe similarities and differences based on their different sizes and orientations. (K.G.4) Students are shown a cone, then students are asked to decide, “Which shape matches the flat surface of the solid figure shown?” There are four choices presented, one of which is a circle and one a rectangle.
  • The Topic 16 Digital Quick Check uses language that is not aligned with Kindergarten standards. Examples are: “1) Which does not slide? 2) Which stacks? or 3) Which rolls?”

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

Students and teachers using the materials as designed devote the large majority of class time to the major work of the grade. The instructional materials devote approximately 67 percent of class time to the major work of Kindergarten.

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 enVisionMATH California Common Core Kindergarten meet expectations for spending a majority of instructional time on major work of the grade.

  • Topics 1 through 11 of 16 are devoted to major work of the grade, which is approximately 68 percent.
  • The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is approximately 110 out of 164 lessons, which is approximately 67 percent.
  • The number of weeks devoted to major work (including assessments and supporting work connected to the major work) is approximately 24 out of 35 weeks, which is approximately 68 percent.

A lesson-level analysis is most representative of the instructional materials as the lessons include major work, supporting work, and the assessments embedded within each topic. As a result, approximately 67 percent 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.
6/8
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Criterion Rating Details

The instructional materials reviewed for enVisionMATH California Common Core Kindergarten partially meet expectations for coherence. The instructional materials include an amount of content designated for one grade level that is viable for one school year and foster coherence through connections at a single grade. However, the instructional materials partially meet expectations for connecting major and supporting work and being consistent with the progressions in the Standards.

Indicator 1c

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

The instructional materials reviewed for enVisionMATH California Common Core Kindergarten partially meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. There are examples where supporting work engages students in the major work of the grade, but there are also multiple instances where supporting work is treated separately and does not engage students in the major work of the grade.

Examples of supporting content connecting to the major work of the grade include:

  • In Lesson 13-6, students “count how many counters of each color there are, and color to show the number of each color counter in the graphs on the right. Then, circle the column that shows which group has fewer objects.” This connects K.MD.3 to the major standard of K.CC.5. (Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.)
  • In the Problem-Based Interactive Learning in lesson 16-1, students determine how to take straws to make specific geometric objects. For example, “What shape was made? How do you know that it is a triangle?” This is a natural connection to K.CC.5. (Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.)

Examples of missed opportunities to connect supporting content to the major work on the grade include:

  • Topic 12 Lessons 1, 3, and 5-8 focus on supporting work of comparing the measurement quantities. (K.MD.A) No connection to major work is established. This is a missed opportunity to make a connection to K.CC.6. For example, in lesson 5, page 230, students make cube trains for the numbers 3, 5, 7 and 10. There is a missed opportunity to have them compare two of these trains at a time to determine whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group. This connection is missed again in lesson 6 page 233 and in the Additional Activity on page 234A.
  • Topic 13 Lesson 3, Pose the Problem: "'There are 6 balls in the grass. You want to sort the balls in two ways. What do you need to know about the balls?' Model: In random order, place 2 big blue circles and 1 small blue circle from the attribute blocks on your left workmat. Then add 1 big yellow circle and 2 small yellow circles. Small group Instruction: Have partners listen to this problem: 'You are sitting on the floor with these 6 marbles. You want to sort the marbles in two ways. Place 1 big and 2 small yellow circles on the right work mat.' Provide prompts, such as: 'Think about different sizes and different colors.' Children sort and then color paper circles yellow and glue them to the right mat.” Students do not have the opportunity to count the number of circles on each side of the sorted mat, which would connect K.MD.3 to major work K.CC.4a.

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

Instructional materials for enVisionMATH California Common Core Kindergarten meet expectations that the amount of content designated for one grade level is viable for one year.

As designed, the instructional materials can be completed in 164 days. 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.

The instructional materials consist of 110 lessons that are listed in the Table of Contents. Lessons are structured to contain a Math Background, Problem Based Interactive section, Develop the Concept: Visual section with two or three activities, Guided Practice problems, Independent Practice problems, Close/Assess and Differentiated problems, and Leveled Homework.

The instructional materials consist of 54 reteaching lessons and assessments that are listed in the Table of Contents. These include Reteaching, Topic Tests, Performance Assessments, Placement Tests at the beginning of the year as well as the end of the year, and Benchmark Tests every fourth Topic.

The publisher does provide information about the suggested time to spend on each lesson or the components within a lesson. The Implementation Guide has a chart that suggests time frames of 50-75 minutes per day. Morning Math is recommended but is not incorporated into the daily math block. The Morning Math time incorporates concepts and skills ranging from the Common Core Review to Quick Checks.

Indicator 1e

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

The instructional materials for enVisionMATH California Common Core Kindergarten partially meet expectations for the materials being consistent with the progressions in the standards.

The instructional materials reviewed for Kindergarten are partially consistent with the progressions in the standards. Although students are given extensive grade-level problems and connections to future work are made in the Skills Trace, future grade-level content is not always clearly identified within the lesson or topic for the teacher or student. The exception is the Topic titled, "Step up to 1st Grade," where the materials are clearly identified as Grade 1 materials. The Kindergarten materials have several instances where future grade-level content is present and not identified. For example:

  • In Topic 9, students create a graph. (2.MD.10) In the Practice, Center Activity, Digital Quick Check and Reteaching, students create graphs for their categorical data.
  • In Topic 12, students compare three items, which is a Grade 1 standard. (1.MD.4) Lesson 12-3 introduces the vocabulary of longest/shortest. (1.MD.4) Lesson 12-4 begins with students comparing three pieces of string moving to visually comparing four pieces of string which is beyond Grade 1.
  • Topic 13 Lesson 13-6 references a “real graph” in the visual learning lesson. (2.MD.10) Lesson 13-7 uses picture graphs. (2.MD.10)
  • In Lesson 4-18, students count by 2s and 5s. (2.NBT.2)
  • In Lesson 3-15, students make tens to add three addends. (1.OA.2)

The correlation between the CCSSM and the lessons is found in the Teacher e-text. In the e-text, a menu on the left side appears with Program Resources. Clicking on Program Resources leads to a drop-down menu with Printable Resources where a document called Common Core State Standards Skill Trace resides. Objectives, Essential Understandings, and a Math Background explain connections between prior knowledge and the lesson. Math Background provides a learning arc. For example, in Lesson 4-6, the Math Background states, “This lesson builds on the concepts introduced in Lesson 4-4. Review these concepts by asking children questions such as ‘How do you know if there is one fewer in a group of objects?’” Additionally, each Topic begins with a Progression Overview document. This document connects grade- level concepts to specific standards under the Looking Back Column, and connects grade-level concepts to future standards under the Looking Ahead Column. The Daily Common Core review in each lesson connects to prior knowledge. Materials provide students opportunities to work with grade-level problems. The majority of reteach and center activities provided are on grade level. Extension activities are embedded within lessons and allow students to engage more deeply with grade-level work. Additional extension activities are also provided online, as are reteach items.

The content does not always meet the full depth of the standards. Materials sometimes do not provide extensive work for all students. For example:

  • For K.MD.1, Lesson, 12-1: Describing Objects by More than One Attribute is the one lesson to address “Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.”
  • For K.G.4, there is one lesson involving three-dimensional shapes, Lesson 16-3: Comparing Solid Figures. The standard states, “Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/'corner’) and other attributes (e.g., having sides of equal length).” Students analyze three-dimensional shapes and compare the shapes based on “roll, stack, and slide.” The standard explicitly states that two- and three-dimensional shapes are to be analyzed and compared, but this lesson does not address the relationship between two-dimensional shapes and three-dimensional shapes.
  • For K.G.6, Lesson 16-2: Making Shapes from Other Shapes addresses the standard: “Compose simple shapes to form larger shapes.” Students form larger shapes from simple shapes, but they do not compare what is happening when combining 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 enVisionMATH California Common Core Kindergarten meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards. The connections are natural; using counting of objects to learn to count, read, write and compare numbers.

Each topic is structured by a specific domain and the learning objectives within the lessons are clearly shaped by CCSSM cluster headings. For example:

  • Topics 10 (Composing Numbers 11-19) and 11 (Decomposing Numbers 11-19) are shaped by K.NBT.A, “Work with numbers 11-29 to gain foundations for place value.” In these two topics, students explore composing and decomposing the teen values 11-19 using ten frames. Students fill one ten frame, and more objects are placed in another ten frame.
  • In Topic 16 (Analyzing, Comparing, and Composing Shapes), page 303, K.G.B, students create 2D shapes. “Lin has 2 triangles. She thinks she can use them to make a shape she has learned - a circle, triangle, square, or rectangle. Try to make one of these shapes with your triangles. Tell what shape you made.”

Materials include problems and activities that sometimes serve to connect two or more clusters in a domain, or in two or more domains, where connections are natural and important.

  • Lessons 1-3 and 1-6 connect two clusters, K.CC.A and K.CC.B. Lesson 1-3 is connected to Lessons 1-1 and 1-2 as students count objects. On page 7, students are shown a number card and practice writing the number 1. In lesson 1-6 page 14, students count objects up to 5 and write the numeral.
  • Lesson 13-5 connects K.MD.B and K.G.A as students classify objects and count the number of objects in each category by identifying and describing shapes (squares, circles, triangles, rectangles, hexagons, cubes, cylinders, and spheres).

Gateway Two

Rigor & Mathematical Practices

Does Not Meet Expectations

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Gateway Two Details

The instructional materials reviewed for enVisionMATH California Common Core Kindergarten do meet expectations for rigor and mathematical practices. The instructional materials partially meet expectations for rigor by meeting expectations on giving attention to the development of procedural skill and fluency and balancing the three aspects of rigor. The instructional materials do not meet the expectations for practice-content connections by meeting expectations on explicitly attending to the specialized language of mathematics and partially or not meeting expectations for the remainder of the indicators in the criterion.

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.
6/8
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Criterion Rating Details

The instructional materials for enVisionMATH California Common Core Kindergarten partially meet expectations for rigor and balance. The instructional materials meet expectations for giving attention to the development of procedural skill and fluency and balancing the three aspects of rigor. However, the instructional materials partially meet expectations for giving attention to conceptual understanding and applications.

Indicator 2a

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
1/2
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Indicator Rating Details

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

The instructional materials present a Problem-Based Interactive Learning activity (PBIL) and a Visual Learning Bridge (VLB) within each lesson to develop conceptual understanding. However, the PBIL and VLB are teacher-directed and do not offer students the opportunity to practice conceptual understanding independently through the use of pictures, manipulatives, and models.

Overall, the instructional materials do not consistently provide students opportunities to independently demonstrate conceptual understanding throughout the grade level.

  • In Topic 5 Lesson 1, the Overview of the PBIL states, “Children will read and write the numbers 11 and 12 and identify or make matching sets of objects.” The Guided Practice section of the lesson states, “Remind children that there is a special symbol for the number eleven and for the number twelve.” Students then count a given set of pictures and trace over the given numbers of eleven and twelve. The directions for the Independent Practice state, “Children count 11 and 12 pictures and write the number that tells how many there are in each group.” Students do not demonstrate conceptual understanding of writing the numbers 11 and 12 independently. Within the Independent Practice, students count a given set of pictures and trace over the given numbers of 11 and 12.
  • In Topic 7 Lesson 6, the Overview of the PBIL states, “Children will join groups of connecting cubes to show a number story. They will write numbers to record each group and how many there are altogether.” In the teacher-directed PBIL activity, students use cubes to represent the number of boats from a given problem. The Guided Practice section of the lesson states, “Guide children to use cubes to show each group of boats and place them on the appropriate pictures. Then have them connect the cubes to find out how many boats there are altogether.” The directions for the Independent Practice state, “Children use cubes to show each group of boats. They connect the cubes to find out how many there are altogether. Children record each number sentence.” Students do not independently demonstrate conceptual understanding of adding groups as the boat pictures are given within the Independent Practice and is the same exercise as in the Guided Practice.
  • In Topic 8 Lesson 6, the Overview of the PBIL states, “Children will act out a subtraction story with counters. Then they will complete a subtraction sentence to show the story.” In the teacher-directed PBIL activity, students use counters to represent the number of puppets in all from a given problem. The Guided Practice section of the lesson states, “Have children cross out the puppets in each exercise and read each subtraction sentence with you.” On the student page, some puppets have a dotted X printed on top of them so the students can see how many are to be subtracted. The directions for the Independent Practice state, “Children write how many puppets there are in all. They cross out three puppets in exercise 3 and one puppet in exercise 4 and write the subtraction sentences. Ask children to read the completed subtraction sentences aloud.” Students do not independently demonstrate conceptual understanding of subtraction as the puppets already have a dotted X printed on top of them that the students can see. This exercise within the Independent Practice is the same exercise as in the Guided Practice.

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 enVisionMATH California Common Core Kindergarten meet expectations for attending to those standards that set an expectation of procedural skill and fluency.

The instructional materials provide regular opportunities for students to attend to the standard K.OA.5, Fluently add and subtract within 5.

The instructional materials develop procedural skill and fluency throughout the grade level.

  • In Topic 7 Lesson 1, students use counters to act out number stories and complete addition sentences in the PBIL activity. The Guided Practice includes opportunities for students to practice addition within five by using counters to represent the given problem.
  • In Topic 8 Lesson 2, students use counters to act out subtraction stories and to find how many are left in the PBIL activity. The Guided Practice includes opportunities for students to practice subtraction within five by using counters to represent the given problem.
  • In Topic 11 Lesson 3, the Develop the Concept: Visual section of the lesson models the use of ten frames to decompose teen numbers. The materials develop procedural skill when showing how to use two ten frames to represent the teen number in two groups.

The instructional materials provide opportunities to independently demonstrate procedural skill and fluency throughout the grade level.

  • In Topic 7 Lesson 3, the Independent Practice section of the lesson provides addition practice problems for students to demonstrate knowledge of procedural skill. Students practice joining two groups of pictures to find how many altogether.
  • In Topic 8 Lesson 5, the Common Core Review includes subtraction problems. Question 3 states, “6 take away 4 is 2.” Students choose which picture models the subtraction problem.
  • In Topic 11 Lesson 4, the Independent Practice section of the lesson provides practice decomposing teen numbers. Students decompose the numbers seventeen and eighteen into two groups with one group being a group of 10.

Indicator 2c

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

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

Each topic includes at least one Problem Solving lesson that can be found at the end of the topic. These lessons offer students opportunities to integrate and apply concepts and skills learned from earlier lessons. Within each individual lesson, there is a section titled, Problem Solving, where students practice the application of the mathematical concept of the lesson.

However, the instructional materials provide opportunities for working with the applications of mathematics through routine problems within the Problem Solving lessons and the Problem Solving section within all lessons.

The instructional materials have few opportunities for students to engage in non-routine application throughout the grade level. Examples of routine applications, where a solution path is readily available, are:

  • In Topic 4 Lesson 10, students count on two more from a given number. Independent Practice problem 5 states, “Jacob sees birds in a tree. Then he sees 2 more. How many birds are there now?” All four of the practice problems have this same format.
  • In Topic 11 Lesson 5, students decompose a teen number into a ten and some ones. Independent Practice problem 3 states, “Write the numbers that complete the number sentence.” There are two ten frames shown with counters already in them.
  • In Topic 9 Lesson 6, students write two different number sentences that describe a given picture. Independent Practice problem 3 presents two yellow counters and seven red counters to students.

Indicator 2d

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

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

Lessons included components such as Daily Common Core Review, Problem-Based Interactive Learning, Develop the Concept: Visual, Guided and Independent Practice, and Problem Solving. These components are designed to develop conceptual understanding, procedural skills, and application skills.

All three aspects of rigor are present independently throughout each topic in the materials. For example, in Topic 8:

  • In Lesson 1, students develop conceptual understanding of subtraction when using counters to represent a subtraction story problem.
  • In Lesson 3, students practice the procedural skill of subtracting when solving a story problem.
  • In Lesson 7, students apply knowledge of subtraction when drawing pictures and writing number sentences to solve story problems.

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

  • In Topic 7 Lesson 2, students develop conceptual understanding of addition by using pictures to write number sentences while applying that knowledge to represent a given picture set as a number sentence.
  • In Topic 9 Lesson 2, students develop conceptual understanding of addition within five when drawing a picture to represent the problem, while practicing the procedural skill of addition when writing the number sentence to solve.
  • In Topic 5 Lesson 5, students practice procedural skill of counting objects while finding the group that has the correct number of objects that matches the given number.

Criterion 2e - 2g.iii

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

The instructional materials reviewed for enVisionMATH California Common Core Kindergarten do not meet expectations for practice-content connections. The instructional materials explicitly attend to the specialized language of mathematics, but they do not meet expectations for any other indicators in this criterion. The instructional materials partially meet expectations for identifying and using the mathematical practices to enrich mathematics content within and throughout the grade and assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others.

Indicator 2e

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

The instructional materials reviewed for enVisionMATH California Common Core Kindergarten partially meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade level. Overall, the MPs are identified and used in connection to the content standards, but the materials do not always use the MPs to enrich the mathematics content. In the materials, the connections between the MPs and the content standards are not always clear.

  • There are multiple places for finding the MPs in the materials: Content Guide in the Program Resources Tab, the beginning of each Topic, sometimes in the Math Background section within each Topic, and at the beginning of each lesson.
  • Within each lesson there is a check list of MPs, but not all of the checked MPs are explicitly labeled within the lesson itself.
  • In the Content Guide and the check lists, the MPs are labeled and addressed. Within enVisionMATH California Common Core Grade 1 lessons, the MP is abbreviated.
    • MP1 - Make Sense of Problems (not perseverance)
    • MP2 - Reason Quantitatively or Reason Abstractly (treated separately)
    • MP3 - Communicate or Critique the Reasoning of Others (treated separately)
    • MP4 - Model with Mathematics
    • MP5 - Use Appropriate Tools
    • MP6 - Attend to Precision
    • MP7 - Use Structure
    • MP8 - Check for Reasonableness or Make Generalizations (treated separately)
  • Lesson 16-3, page 307A, identifies MPs 1, 4, 5, 6 and 7. The Problem-Based Interactive Learning on page 307 is labeled with “MP7 Use Structure: Remind children to use attributes such as curved or flat surfaces to determine which three-dimensional (solid) figures can roll, stack and slide.” In this example, students are not engaged in MP7 because the teacher rolls the sphere and the cone before students have had a chance to search for themselves.
  • Each Topic has a list of MPs checked off if done within the Topic. Each of the lessons within the Topic has a list of MPs checked off if done within the lesson. If an MP is checked, there is not necessarily explicit instruction for teachers as how to use the MP effectively when teaching the lesson. In lesson 3-1, MP3 is one of six MPs checked, but MP4 has explicit directions for teachers within the lesson.

Indicator 2f

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

The instructional materials reviewed for enVisionMATH California Common Core Kindergarten do not meet expectations that the instructional materials carefully attend to the full meaning of each practice standard.

The materials do not attend to the full meaning of three or more MPs. Examples include:

  • MP1: In Lesson 7-1, students solve the problem: “Danny is sitting on a bench in the park. Three friends join him. How can you find out how many friends are sitting on the bench in all?” Students do not make sense of the problem because the numbers are presented to them. Students trace the numbers to complete the problem. On the Enrichment Master, students record the two addends based on the picture given. The solution is given, so students do not need to attend to the equation, only count the objects.
  • MP2: In Lesson 10-1 page 194B, the teacher note states, “MP2 Reason Quantitatively: Children should write the number sentence and fill in the drawing to show how to make 13.” Students do not reason quantitatively because there is no context for students in which to interpret the number 13.
  • MP4: In Lesson 9-1, the teacher note states, “MP4 Model with Mathematics: Ask children how using red and yellow counters helps show different ways to make 4 and 5.” Students do not create equations that represent the arrangements of counters.
  • MP5: In Lesson 5-1 page 93, the teacher note states, “MP5 Use Appropriate Tools: Emphasize the importance of the ten frame as an appropriate model to think about the numbers 11 and 12 as 1 ten and 1 or 2 extra ones.” Students do not choose the tool to use in this lesson.

Indicator 2g

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

Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
0/2
+
-
Indicator Rating Details

The instructional materials reviewed for enVisionMATH California Common Core Kindergarten do not meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Materials have few, if any, prompts for students to both construct viable arguments and/or analyze the arguments of others. Students are not given problems that are conducive to public explanations of their solutions. Students are given guided practice to follow steps and then given individual work that imitates the guided-practice problems. On occasion, there is a whole-group discussion, but students do not critique the reasoning of others during the discussion. Examples include:

  • In Lesson 3-6, MP3 is identified, and the materials state: “Tell the story about Rosie again. Have pairs of children work together to practice writing the number 10 on the right side of the page. As they work, have the children ask each other questions about what they are doing. 'How many counters did you show? What number will you write?'”
  • In Lesson 3-1 page 48C, students turn over a card and count dots aloud. If the card matches a tag that the students have, he or she keeps the card. If the card matches the partner’s card, he or she gives it to the partner. Cards that do not match are put aside. Students do not have to justify how they know how many are on the card or decide if they agree or disagree with each other’s reasoning.
  • In Lesson 5-1, MP3 is identified, and students ask each other questions about their thinking. They are not asked to critique each other’s thinking. “Have pairs of children work together to complete the student page. Have children ask each other questions about what they are doing. 'How many counters did you show? What number will you write?'”
  • In Lesson 7-3 Problem-Based Interactive Learning, page 131A, the problem is modeled for the students so there is no opportunity for students to justify any conclusions they may have made, nor do they communicate with other students or respond to the arguments of others. In Whole Group Discussion, students label each group of boats with cubes. Direct instruction is used throughout the discussion. Students do get the opportunity to work with a partner, but they complete the page as the teacher tells number stories about boats on a dock. This is a missed opportunity to have students compare answers, explain them to their partner, and to critique each other’s reasoning.
  • In Lesson 13-4 Pose the Problem, page 251, there is a direction given to have students share their ideas about how they problem sort the blocks, but there are no questions for students to reason about other’s thinking during the activity. In the Extend section of this lesson, students are asked, “If there were a small yellow shape on the rug, would it belong to your group of yellow shapes? Why or why not?” The teacher is to look for the answer, “No, because it is not the same size as the other shapes.”
  • In Lesson 13-5 Problem Solving: Use Logical Reasoning, students examine four shapes, determine how they are alike, and think about a sorting rule. Guided directions lead students through a series of instructions, including coloring the shapes as students walk through the questions. Students do not discuss initial ideas for a sorting rule before completing the guided instructions.

Indicator 2g.ii

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

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

The Teacher Edition contains a Mathematical Practice Handbook which defines each math practice and includes question stems for each MP to help the teacher engage students. MP3 offers the following questions stems: “How can I use math to explain why my work is right?” “How can I use math to explain why other people’s work is right or wrong?” and “What questions can I ask to understand other people’s thinking?”

The materials label multiple questions throughout the material as MP3 or parts of MP3; however, those labeled have little information assisting teachers to engage students in constructing viable arguments or to critique the reasoning of others. The information that the materials provide is not specific and are often hints or reminders to give students while they are solving a problem.

Materials provide little assistance to teachers in engaging students in both constructing viable arguments and analyzing the arguments of others.

  • In Lesson 1-3, there is no supporting commentary or questioning to assist teachers in helping students form or develop an explanation. For example, the question, “How can you use numbers to tell about groups of objects?” is an open question. Yet there is no guidance for the teacher for how to continue the line of questioning and launch a conversation about student thinking. “Peer Questioning: Have pairs of children complete the right side of the student page as you continue with stories about Tess. Have children ask each other questions about what they did. “How many counters did you show?” “What number is this?”
  • In Topic 8 Small Group Interaction, page 149, students repeat the steps that were presented in the Whole Group Instruction. There are no instructions for students to have dialogue in the lesson.
  • On page 150, the teacher is given directions for “Error Intervention.” “If children are unsure why they mark Xs, then explain that marking an X means taking away.” This is a missed opportunity to have students discuss the way that they would show taking away and critique each other’s reasoning.
  • In Topic 11 page 211, “Note about MP3: Communicate. Ask children to explain what the numbers in each number sentence represent.” This question does not have students construct an argument. The students discuss how to fill in a ten frame when making 14, 15 and 16. There is no explanation or justification needed, and students do not analyze the arguments of others.

Indicator 2g.iii

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

The instructional materials reviewed for enVisionMATH California Common Core Kindergarten meet expectations for explicitly attending to the specialized language of mathematics.

  • Each lesson includes a list of vocabulary in the Lesson Overview at the beginning of each lesson. The identified vocabulary words appear at times within the blue script that teachers may use, and the words are highlighted in the student edition.
  • Each Topic includes two-sided vocabulary cards in the Teacher Edition in the Printable Resources section. Each card has a word on one side and its definition and/or representation on the other. The Teacher Edition includes vocabulary activities at the start of each topic. For example, in Topic 1 Math Background Vocabulary, page 1F, “Number Match: Attend to Precision - give each child number cards for 1-5. Then call out a number 1-5. Have children hold up the number card for the number you called.”
  • Each Topic opener has a vocabulary review activity, and each Topic ends with a vocabulary review activity. In Topic 9 (More Addition and Subtraction), the Topic Opener on page 167 lists “My New Math Words as whole, part,and graph, with illustrations of what the words represent. On page 168 in Topic 9, the Vocabulary Cards activity directions state, “Cards can always be used as flash cards. Have children create large vocabulary cards with visuals to add to the classroom word wall.”
  • There are instances in the materials where the definition may be unclear for kindergarten students. For example, on page 267, “Find the square. How do you know it’s a rectangle?" Since the questions before and after this question address squares, there is no support for teachers on discussing the difference between squares and rectangles with their students. The Closing on page 268B states, “A square has four sides that are the same length and four corners. Remember that rectangles have opposite sides that are the same length, but squares have all four sides that are the same length.” This language indicates that squares are not rectangles.
  • Correct vocabulary is sometimes not used. Examples include: Same number as is used instead of equal, and lessons about Real Graphs are defined as a graph with real objects on it. (page 255)

Gateway Three

Usability

Not Rated

Criterion 3a - 3e

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

Indicator 3a

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

Indicator 3b

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

Indicator 3c

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

Indicator 3d

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

Indicator 3e

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

Criterion 3f - 3l

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

Indicator 3f

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

Indicator 3g

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

Indicator 3h

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

Indicator 3i

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

Indicator 3j

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

Indicator 3k

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

Indicator 3l

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

Criterion 3m - 3q

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

Indicator 3m

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

Indicator 3n

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

Indicator 3o

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

Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

Indicator 3p.i

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

Indicator 3p.ii

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

Indicator 3q

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

Criterion 3r - 3y

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

Indicator 3r

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

Indicator 3s

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

Indicator 3t

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

Indicator 3u

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

Indicator 3v

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

Indicator 3w

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

Indicator 3x

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

Indicator 3y

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

Criterion 3aa - 3z

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

Indicator 3aa

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

Indicator 3ab

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

Indicator 3ac

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

Indicator 3ad

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

Indicator 3z

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

Additional Publication Details

Report Published Date: Wed Oct 24 00:00:00 UTC 2018

Report Edition: 2015

Title ISBN Edition Publisher Year
enVisionMATH California Common Core - Kindergarten 9780328792672 Pearson 2015

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Math K-8 Rubric and Evidence Guides

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

For math, our rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

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

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