Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for enVisionMATH California Common Core Grade 1 do not meet expectations for alignment to the CCSSM. The instructional materials partially meet expectations for focus and coherence in Gateway 1 as they do not 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

|

Does Not Meet Expectations

Gateway 1:

Focus & Coherence

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

Gateway 2:

Rigor & Mathematical Practices

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

Usability

|

Not Rated

Not Rated

Gateway 3:

Usability

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

Gateway One

Focus & Coherence

Partially Meets Expectations

+
-
Gateway One Details

The instructional materials reviewed for enVisionMATH California Common Core Grade 1 partially meet expectations for focus on major work and coherence in Gateway 1. For focus, the instructional materials assess topics before the grade level in which the topic should be introduced, but they do devote the large majority of class time to the major work of the grade. For coherence, the instructional materials include an amount of content designated for one grade level that is viable for one school year, but they partially meet the expectations for being consistent with the progressions in the Standards 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.
0/2
+
-
Criterion Rating Details

The instructional materials reviewed for enVisionMATH California Common Core Grade 1 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 not 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.
0/2
+
-
Indicator Rating Details

The instructional materials reviewed for enVisionMATH California Common Core Grade 1 do not meet expectations for assessing grade-level content.

The following are examples where the assessment items are representative of alignment to the Grade 1 expectations:

  • Topic 1, Lesson 1.7 - Digital Quick Check: On item 1, students use the commutative property of addition “3 + 4 = 7, 4 + 3 = 7” with pictures of counters. (1.OA.3)
  • In the Topic 1 Assessment, item 13, students use a picture of counters to complete the equation “8 + __ = 9 and __ + 8 = 9.” Counters are used.
  • In the Topic 1 Performance Task, page 38, students draw a picture with 9 boxes (some are big and some are little). A partial word problem is provided, “Susie has 9 boxes. Some are big. The rest are little.” Students determine the quantities of big and little. They write an addition sentence to tell about the boxes and then write a different one (commutative property). (1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions.) A rubric is included.
  • Topic 2, Lesson 2.4 - Digital Quick Check: On item 1, students are provided a picture of a domino face with one side missing and a 4 on the other side. Students determine the subtraction equation that relates to the picture if the domino faces summed to 7. (1.OA.4)
  • In the Topic 5 Performance Task, page 202, students solve a word problem using counters on a ten frame. They write an equation that matches the story problem. In the second part of the problem they subtract using the ten frame and write an equation. 1.OA.A.1, 1.OA.B.3. A 3-point rubric is included.
  • Topic 9, Session 9.1 - Digital Quick Check: On item 3 students find 10 less than 78 in a word problem. (1.NBT.5)
  • Topic 10, Lesson 10.4 - Digital Quick Check: On item 1 students use mental math to add 40 + 49. No pictures or models are present.
  • Topic 11, Lesson 11.4 - Digital Quick Check: On item 1 students mentally solve 50 - 10. (1.NBT.5)

The following are examples where the assessment items are above grade level and cannot be modified or deleted without causing a significant impact on the underlying structure of the materials:

  • In the Topic 9-12 Benchmark Test, item 2 states, “Which string is the longest?” There are 4 strings for students to compare. 1.MD.1 states that students, “Order three objects by length; compare the lengths of two objects indirectly by using a third object.” Item 10 states, “Which is the best estimate for the length of the pencil?” 1.MD.2 states that students, “Express the length of an object as a whole number of length units.” Estimating is 2.MD.3.
  • Online Topic 10 Assessment items 14 - 17 - Students add 2-digit numbers with a 2-digit number (2.NBT.5); e.g., item 14: “26 + 22” and item 15: ”62 + 17”
  • Topic 12 Unit Assessment
    • Item 5: students circle the best unit to measure a pail. This is 2.MD.1; select the appropriate tool.
    • Item 6: students estimate how long a chain is with no benchmark number. This is 2.MD.3.
  • Enhanced Topic 13 Assessment states, “Which tells the time it will be in 30 minutes? Put a circle around the time.” Students use elapsed time in order to solve the problem. (3.MD.1)
  • In Topic 13 Unit Test, items 5 and 6 show a table with four categories; 1.MD.4 states that students compare up to 3 categories.
  • In Topic 13 Performance Task, page 430, item 2, students name the movie that starts a half hour after Dances with Dinosaurs (information is taken from a table). In item 3, students write the names of two movies that start an hour apart. Elapsed time is 3.MD.1.
  • Online Topic 13 Assessment, item 3 states, “Read the clocks. Find the pattern. What comes next?” This is assessing elapsed time. (3.MD.1)
  • Topics 13-16 Benchmark Assessment
    • Item 3 states, “A zoo has different animal shows. Each show comes right after the one before it. Which show lasts for 2 hours?” This goes beyond 1.MD.3 (Tell and write time in hours and half-hours using analog and digital clocks) to 3.MD.1 using elapsed time.
    • Item 13 shows a zoo schedule where students are asked to tell which show lasts for 2 hours. There are 4 shows listed, which is not in 1.MD.4 that limits the categories to 3. This problem also asks students to determine which show lasts for 2 hours.
    • In item 16, students are asked items about a pictograph with four categories. 1.MD.4 states to only compare 3 categories.
  • Topic 14 assessments have items that address standard 2.MD.10.
    • Digital Quick Check items 1 and 2, “4 Favorite Pets” uses four categories rather than three.
    • Online Assessment items 4 through 12 and 18-20 use four categories rather than three.
  • Online Topic 16 Assessment
    • Item 2 states, “How would you cut the sheet of construction paper so 6 people would each get the same amount to use in a craft?” This is a 3.NF.1.
    • Item 4 states, “How would you cut the braiding so 3 people would each get the same amount to use in a craft?” Thirds first appear in 2.G.3. and the rope is not illustrative of either of the specified shapes (rectangles and circles).
    • Item 6 has answer choice B representing a circle partitioned into fifths. Fifths are introduced in 3.NF.

The following example is where the assessment items are not addressed causing a significant impact on the underlying structure for Grade 1 expectations:

  • There are no items that address 1.G.1 [Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes], where students draw shapes that possess defining attributes.

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
+
-
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 77 percent of class time to the major work of Grade 1.

Indicator 1b

Instructional material spends the majority of class time on the major cluster of each grade.
4/4
+
-
Indicator Rating Details

The instructional materials reviewed for enVisionMATH California Common Core Grade 1 meet expectations for spending a majority of instructional time on major work of the grade.

  • Topics 1 through 12 of 16 are devoted to major work of the grade, which is approximately 75 percent.
  • The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is approximately 126 out of 163 lessons, which is approximately 77 percent.
  • The number of weeks devoted to major work (including assessments and supporting work connected to the major work) is approximately 25 out of 34 weeks, which is approximately 73 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 77 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.
4/8

Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
0/2
+
-
Indicator Rating Details

The instructional materials reviewed for enVisionMATH California Common Core Grade 1 do not meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. Several examples of missing opportunities for supporting work to engage students in the major work of the grade include:

  • In Topic 13, five lessons (13-1 through 13-5) have missed opportunities to connect 1.MD.3 to 1.NBT.1. (Count to 120, ... ) For example, in lesson 13-1, page 411: “How many numbers are there?” and “There are 60 minutes in an hour.” Students do not practice oral counting to 60 for minutes, and they do not practice oral counting the hours to enhance their counting to 120.
  • In Topic 14, Lessons 14-6 and 14-7 miss opportunities to connect 1.MD.4 to the major standard 1.OA.1. The majority of the work is making graphs using tally marks then turning those into picture graphs. The lessons each have questions about the graphs; however, one question asks students, “How many more or less are in one category than in another?” (1.MD.4) The majority of the questions center around, “Which activity is the favorite?” or “Which kind of music is the favorite?”
  • Topic 16 consists of students partitioning shapes. There are four lessons included in this topic. The topic is treated separately from major work of the grade. There is a missed opportunity with connecting 1.G.3 to 1.OA.7. (Understanding the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.) For example, in lesson 16-4, page 528, students solve word problems such as, “Pedro made a flag with 4 equal parts. He made 2 parts of his flag yellow. What part of the flag is yellow?” and “Dan drew a flag with 4 equal parts. He made 1 part green. Which picture did Dan draw?” In previous chapters, students examined how 4 = 2 + __ models pictures of fractions of equal sizes, but the materials do not make a connection to equations in this lesson.

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
+
-
Indicator Rating Details

Instructional materials for enVisionMATH California Common Core Grade 1 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 163 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 109 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 Test at the beginning of the year as well as the end of the year, Basic Fact Timed Test, and Benchmark Tests every fourth Topic.

The publisher provides some 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
+
-
Indicator Rating Details

The instructional materials for enVisionMATH California Common Core Grade 1 partially meet expectations for the materials being consistent with the progressions in the standards.

The instructional materials reviewed for Grade 1 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 2nd Grade," where the materials are clearly identified as Grade 2 materials. The Grade 1 materials have several instances where future grade-level content is present and not identified as such. For example:

  • In Lesson 14-2, picture graph is used as a vocabulary word. (2.MD.10)
  • In Lesson 14-3, bar graph is used as a vocabulary word. (2.MD.10)
  • In Lesson 14-6, students decide which graph is the best to use to show the data (picture, bar, or tally marks). The standard, 1.MD.4, states that students are to organize and classify objects to compare and answer questions. Choosing the best graph and the use of tally marks are not part of 1.MD.
  • In Lesson 14-7, Visual Learning, students answer questions about four categories. (2.MD.10)

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, “In lesson 4-1, children added with 0, 1, or 2. In this lesson they solve subtraction problems with 0, 1 or 2.” 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. For example:

  • For Standard 1.OA.7, there is one lesson, 2-10: Connecting Models and Symbols. The standard states, “Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false.” There are two parts to this standard: understanding the equal sign and true/false statements. On pages 78-80, there are four Independent Practice problems using counters to determine true or false statements. Students do not make a statement true or false but “Circle the number sentence that is true. Draw a line through the sentence that is false. Then write another true sentence about the model.” Students complete a related fact to meet the direction given.
  • For Standard 1.OA.8, there is one lesson, 6-6: Subtraction Facts. The standard states, “Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.” This standard is addressed one time in the subtraction Topic but not addressed in the four addition Topics.
  • For Standard 1.NBT.2c, there is one lesson, 8-2: Numbers Made with Tens, page 275. The standard states, “The numbers 10, 20, 30, …, 90, refer to one, two, …, or nine tens (and 0 ones).” From this lesson students understand the value of tens “9 tens is ___.” Using visual models then move to the next lesson putting numerals such as 38 in the correct place of 3 tens and 8 ones in a table and tracing the numeral 38. On page 278, students move to the procedure of identifying numbers in a place value table and do not fully develop conceptual understanding.
  • For Standard 1.NBT.5, there is one lesson, 9-1: 1 More, 1 Less; 10 More, 10 Less. The standard states, “Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.” This is the first time students have encountered 10 more or 10 less. There are no other lessons that engage with the standard.

Indicator 1f

Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for enVisionMATH California Common Core Grade 1 partially meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards.

Below are examples of materials that include learning objectives that are visibly shaped by CCSSM cluster headings.

  • In Topic 3 Lesson 3-3, page 99, students solve the word problem, “Andy and Jacklyn want to buy some hats. There are red and yellow hats. They have enough money to buy 10 hats in all. Use the counters on the ten-frame to show how many hats of each color Andy and Jacklyn could buy.” The mathematics aligns to the cluster heading 1.OA.C, Add and subtract within 20.
  • In Topic 7 Counting and Number Patterns to 120, the learning objects align to 1.NBT.1 and 1.NBT.2. The learning objects include lesson 7-3 Counting by 10s, lesson 7-5 Using Counting by 10s, and lesson 7-6 Problem Solving: Look for a Pattern.
  • In Topic 9 Lesson 9-2, Comparing Numbers to 100 Making Numbers on a Hundred Chart are visibly shaped by 1.NBT.4 and 1.NBT.2a.

An example that includes 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 includes:

  • In Lesson 2-1, page 41, students solve a word problem with missing parts. “Imagine that you have 6 coins in all. Some are in the piggy bank, and some are in your hand. Even though you can only see the number of coins in your hand, you know the rest of the 6 coins are in the piggy bank. I have 6 counters in all. There is a part that you can see, and there is a part in the cup. How can you find how many counters are in the cup?” 1.OA.8, Determine the unknown whole number in an addition or subtraction equation…., connects to 1.OA.1, Use addition and subtraction within 20 to solve word problems, and 1.OA.6, Add and subtract within 20, thus connecting clusters 1.OA.A, 1.OA.C, and 1.OA.D.

Examples of missed opportunities include:

  • Lesson 10-6 addresses adding multiples of 10 in word problems. (1.NBT.4) During the lesson, students represent the story problem two ways (draw dots in towers of ten or as the standard algorithm). The opportunity to connect to what students learned and strategies used in 1.OA.1, Use addition and subtraction within 20, is missed. Having students solve problems using the standard algorithm is beyond the expectation of 1.NBT.4.
  • Topic 15 addresses 1.G independently and does not make a connection between any other cluster within Grade 1.

Gateway Two

Rigor & Mathematical Practices

Does Not Meet Expectations

+
-
Gateway Two Details

The instructional materials reviewed for enVisionMATH California Common Core Grade 1 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
+
-
Criterion Rating Details

The instructional materials for enVisionMATH California Common Core Grade 1 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
+
-
Indicator Rating Details

The instructional materials for enVisionMATH California Common Core Grade 1 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 7 Lesson 7-3, the Overview of the PBIL states, “In this activity, children count groups of 10, record the numeral, and write how many 10s.” The Guided Practice directions state, “Count by 10s. Then write the numbers.” There is a picture number line as well as the three different ways to write that number above the Guided Practice problems for the students to reference. The Independent Practice directions state, “Count by 10s. Then write the numbers.” The picture number line continues above the Independent Practice problems for the students to reference. Students do not count independently, write how many 10s, or record the numeral of a given set of objects as they can copy the answers from the reference above.
  • In Topic 9 Lesson 9-3, the Overview of the PBIL states, “In this activity, children will learn how to compare two-digit numbers using concrete materials.” The Independent Practice directions state, “Write the number of cubes. Circle is greater than or is less than.” Students do not compare two-digit numbers independently as the pictures are given for the numbers.
  • In Topic 10 Lesson 101, the Overview of the PBIL states, “In this activity, children will use tens models to find sums of multiples of 10 up to 100.” The Independent Practice directions state, “Write the numbers to complete each number sentence.” Students do not use tens models independently to find sums of multiples of 10 as the pictures are given for the number sentences.

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
+
-
Indicator Rating Details

The instructional materials for enVisionMATH California Common Core Grade 1 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 1.OA.6, Fluently add and subtract within 10.

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

  • In Topic 2 Lesson 2-4, students use a picture to find the difference. The Guided Practice includes opportunities for students to practice subtraction within 10 by using pictures of cubes to represent the given problem.
  • In Topic 3 Lesson 3-4, students use a ten frame to show ways to make 10. The Guided Practice includes opportunities for students to practice using different-colored counters on a ten frame to represent ways to make 10.
  • In Topic 5 Lesson 5-8, students add three single-digit numbers. The Guided Practice includes opportunities for students to practice adding two numbers first and then adding the last number to the sum to find the solution.

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

  • In Topic 2 Lesson 2-9, students use a picture to find sums and differences. The Independent Practice includes opportunities for students to demonstrate addition and subtraction independently within 10 by writing addition and subtraction number sentences for a given model.
  • In Topic 4 Lesson 4-4, students use a ten frame to find sums within 10. The Independent Practice includes opportunities for students to demonstrate addition within 10 independently by writing addition number sentences for a given model.
  • In Topic 6 Lesson 6-6, students find the difference. The Independent Practice includes opportunities for students to demonstrate subtraction independently when finding the difference of several subtraction problems within 20.

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
+
-
Indicator Rating Details

The instructional materials for enVisionMATH California Common Core Grade 1 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 4-10, students write a number sentence using addition or subtraction. Independent Practice problem 3 states, “Twan picks 9 berries. Then he picks 3 more. How many berries does Twan pick?”
  • In Topic 6 Lesson 6-7, students write a number sentence using addition or subtraction. Independent Practice problem 4 states, “Dana won 12 spinning tops at the fair. She gave 6 of them to her friend. How many spinning tops does Dana have left?”
  • In Topic 11 Lesson 11-5, students draw a picture to solve and write a subtraction sentence. Independent Practice problem 5 states, “A store had 70 toy cars. It sold 40 cars. How many cars does the store have left?” The problem has a blank subtraction number sentence below the story problem. The students fill in the blanks with the numbers.

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
+
-
Indicator Rating Details

The instructional materials for enVisionMATH California Common Core Grade 1 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 4:

  • In Lesson 4-1, students develop conceptual understanding of addition when using pictures of object to represent an addition equation.
  • In Lesson 4-3, students practice fluency of addition within 10 when solving addition problems.
  • In Lesson 4-9, students apply knowledge of subtraction when 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 8 Lesson 8-1, students develop conceptual understanding of place value by drawing a picture while applying that knowledge to solve the story problem.
  • In Topic 6 Lesson 6-2, students develop conceptual understanding of subtraction when working with a ten frame to represent the problem, while practicing the procedural skill of subtraction when writing the number sentence to solve.
  • In Topic 5 Lesson 6-9, students practice procedural skill of adding three addends while writing a number sentence to solve a story problem.

Criterion 2e - 2g.iii

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

Indicator 2e

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

The instructional materials reviewed for enVisionMATH California Common Core Grade 1 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 (no 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)
  • In Math Background (page 1D) for Topic 1, the teachers note states, “Mathematical Practices Attend to Precision: To learn how to represent addition, children need many experiences moving among real-world addition stories, counters or pictures, and the symbols for addition.” This explanation is MP2 Reason Abstractly and Quantitatively, not MP6 Attend to Precision.
  • In Lesson 10-3, there is a discussion and activity built around MP2 when adding 10, yet that MP is not identified. In the Visual Learning section, students answer, “How do you add 3 tens to 28 without seeing 28 cubes?” Followed by, “Why does the tens digit change? What digit stays the same? Explain.”
  • In Lesson 12-3, MPs 2, 6, and 8 are identified. Within the lesson, there is a discussion and activity built around MP5."Should teacher steps be used to measure a pencil? What should the teacher use?" Yet that MP is not identified.

Indicator 2f

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

The instructional materials reviewed for enVisionMATH California Common Core Grade 1 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 2-11, students solve the problem: “There are 9 children playing inside. Three of them go outside. How many children are left inside?” The teacher note states, “MP1 Make Sense of Problems: Ask children what they know about the story problem. What type of number sentence do you need to use to solve the problem? Why?” No perseverance is required by students in this lesson as part of MP1. In Lesson 11-1, the teacher note states, “MP1 Make Sense of Problems: Remind children to make sure that they understand what is happening in the problem. What does it mean for the teddy bears to be sold? Does this mean more bears are added or bears are taken away?” No perseverance is required by students in this lesson as part of MP1.
  • MP4: In Lesson 11-2 page 359, the teacher note states, “MP4 Model with Mathematics: Have children tell which direction they would move on a hundred chart to subtract 30 from 50.” Students do not create equations that represent the subtraction problem. Also, there is no context in which modeling with mathematics can be used.
  • MP5: In Lesson 3-2, the teacher note states, “MP5 Use Appropriate Tools: Look for children to use a ten frame to represent numbers up to 10. Ask children how they can recognize a number on a ten frame without counting every counter.” Students do not get to choose which tool to use. In lesson 15-2, the teacher notes states, “Ask children how they can use an organized list to find out all the ways pattern blocks are used to make a shape.” Students are told which to tool to use.
  • MP7: In Lesson 8-6 exercise 6, the teacher note states, “Encourage children to gather information from the table. 'Look at the Tens column. Do you see a pattern? How can it help you find the missing number of tens?'” The teacher is instructed to repeat for finding the missing number of 1s. Rather than students looking for and making use of patterns in the table, they are led step-by-step through the exercise.

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 Grade 1 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 Topic 2, MP3 is listed in Lesson 2-4, but there is no evidence that student materials include questions or problems where students evaluate someone else’s explanation, work, or thinking.
  • The Lesson 2-7 Communicate says, “Read the problem aloud. Ask children to explain what number they are supposed to find. [The number of blue fish.] Model solving the problem on a part-part-whole mat with connecting cubes.” Students are not constructing a viable argument or critiquing the reasoning of others.
  • In the Visual Learning Lesson 14-1, page 434, students are asked, “Do you think we could arrange the counters differently to make counting them easier?” It is followed with a direction to consider all responses. The students do not critique each other’s reasoning.
  • In Lesson 2-4 Quick Check, MP3 is cited for the following example: “Write a story about the ladybugs. Use words and numbers. Then write a subtraction sentence to show how many are left.” Students do not analyze the arguments of others; they explain their own thinking. In Lesson 5-1: " Encourage children to use examples as they discuss why some numbers are doubles and some are not.” In Lesson 5-3: “Ask children to explain how they used the strategy of adding two to a doubles fact to solve the equations.” MP3 is cited; however, in both lessons, students do not create an argument or critique the arguments of others.
  • In Lesson 4-10 page 154, teachers are instructed how to prevent errors in Error Intervention. "If students add 7 and 4 instead of subtracting 4 from 7, ... ask them what they would find if they added. Would that help find how many more stars Charlie drew than Luz? What kind of number sentence should you write? Why?” An opportunity to use MP3 to critique the reasoning of others is missed.
  • In Topic 7 page 259, Problem Solving: Looking for a Pattern. In the Pose the Problem section, the following problem is given: “There are 6 people. Each person is wearing 2 shoes. How could you find how many shoes they are wearing in all? You may use your counters to help you solve.” The next direction is for the teacher to allow time for the students to solve. This is a missed opportunity to have children share their thoughts before solving the problem or asking children once they’ve solved the problem, how they did so, then critique each other’s reasoning.
  • In Lesson 16-3 page 521, students are given a square and asked, “How could a square be folded in halves or fourths? Give children time to look at their squares and discuss in pairs.” The lesson continues to have students fold exactly how the teacher folds. This is a missed opportunity to have students fold their own paper into halves and discuss what they did, then critique what others did with their squares.

Indicator 2g.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for enVisionMATH California Common Core Grade 1 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 1-5 there is little supporting commentary or questioning to assist teachers in helping students form or develop an explanation. For example, the prompt states, “As children say the sentences, have children ask their partner to check and see if they agree. If there is not agreement, have children discuss their opinions, talking about the workmat, the cubes, and the sentences to support their view.” This tag is in the Problem-Based Interactive Learning section. How students engage in deep mathematical conversation if they do agree is not explained further. When students disagree, only then critiquing others is encouraged.
  • In Lesson 2-6 Extend, students explore the classroom looking for items to compare, “such as board erasers and erasable markers for the board or doors and windows. Encourage discussion.” Teachers are not given further direction as to whether students talk to each other or bring back their findings for a whole-group debrief.
  • Topic 5 Communicate, page 163, states, "Encourage children to use examples as they discuss why some numbers are doubles and some are not.” There is no explicit mention of having children make sense of one another’s argument.
  • In Lesson 6-2 Prevent Misconceptions, page 211, the teacher note says, "Children may think that the number they subtract to make 10 is the answer. Emphasize that they have to subtract a total of 6 counters, not 4, to find the answer to the problem.” This is a missed opportunity to get students in a discussion about subtraction strategies and critiquing others' reasoning when solving subtraction problems.
  • In Lesson 11-5, pages 373-74, students are to solve the problem: “Jack took 50 berries from the basket. There are 40 berries left in the basket. How many berries were in the basket to begin with?” Teacher is directed that the “Drawing should show 8 boxes with 6 10-boxes underneath.” The teacher note for Constructing Arguments exercise 6, says: "Have children explain how they knew where to write the numbers in the subtraction sentence. Compare children’s drawings and have them explain how their drawing represents the problem.” This is a missed opportunity for students to share strategies used and for their classmates to critique their reasoning.
  • In Topic 12 Math Background, the following explanation on how to use MP3 within the topic is provided: “Mathematical Practices: Communicate - Use language such as ‘This football is 2 straws long’ to emphasize that measurement is approximate.” The Topic 14 Math Background states, “Mathematical Practices: Communicate - To help children understand the meaning of graphs, emphasize making a class graph of favorite shoe colors shows which colors the class likes more or likes less. It is not about which color ‘wins’ or ‘loses.’” Critiquing others' arguments is not mentioned in either topic.

Indicator 2g.iii

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

The instructional materials reviewed for enVisionMATH California Common Core Grade 1 meet the 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 5 in Math Background Vocabulary Activities, page 161D, “Double Up: Write an addition fact on each of three index cards. Include a doubles fact, a doubles-plus-1 fact, and a doubles-plus-2 fact. Put the cards on a table along with vocabulary cards for doubles, doubles-plus-1, and doubles-plus-2. Have children find an addition fact to go with each vocabulary card. Repeat the activity on a different day with a different set of addition facts.”
  • Each Topic Opener has My New Math Word followed by a Vocabulary Cards activity. In Topic 4 Addition and Subtraction Facts to 12, the Topic Opener on page 115 lists My New Math Words as near double and 1 less than along their definitions. On page 238 in Topic 4, the Vocabulary Cards activity directions state, “Cards can always be used as flashcards. Have children create large vocabulary cards with visuals to add to the classroom word wall.”
  • In Lesson 15-3 page 476, enVisions California Edition uses the combination of straight sides and curved shapes to ask if both have straight sides. There is a call to prevent misconceptions: “Some children may mistake a curve for a side. Tell children that side means straight side.” There is another misconception in the line of questioning about the blue shape. “How do you know it’s a square?” Expected student response is “It has 4 sides.” “The pink shape has 4 sides also. Why is that a square?” Expected student response is, “All four sides of a square are the same.” This leaves a possibility for a misconception because a non-square rhombus also has all four sides the same. A more precise response attends to the corners of a square all being the same as well.
  • In Lesson 15-4, students use pattern blocks to compose shapes. The shapes are referred to by their color rather than their specific name. In Grade 1, students are to learn about trapezoids. This is a missed opportunity to take students away from “non-defining attributes (e.g., color)” and work on precise vocabulary.

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 - Grade 1 9780328792689 Pearson 2015

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.

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.

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.

X