Alignment: Overall Summary

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

See Rating Scale Understanding Gateways

Alignment

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Meets Expectations

Gateway 1:

Focus & Coherence

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

Gateway 2:

Rigor & Mathematical Practices

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

Usability

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Meets Expectations

Not Rated

Gateway 3:

Usability

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

Gateway One

Focus & Coherence

Meets Expectations

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Gateway One Details

The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet expectations for Gateway 1, focus and coherence. The instructional materials meet the expectations for focusing on the major work of the grade, and they also meet expectations for being coherent and consistent with the standards.

Criterion 1a

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

​The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet expectations for not assessing topics before the grade level in which the topic should be introduced. The materials assess grade-level content and, if applicable, content from earlier grades. In instances where above-level content is assessed, questions could easily be omitted or modified.

Indicator 1a

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

The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet expectations that they assess grade-level content. Above grade-level assessment items are present and all but one assessment could be modified or omitted without a significant impact on the underlying structure of the instructional materials.

The series is divided into topics with an assessment for each topic that can be delivered online and/or paper and pencil, and a topic performance assessment. Additional assessments include a Kindergarten Readiness Test and four Cumulative/Benchmark Assessments addressing Topics 1-4, 1-8, 1-11, and 1-15. Assessments can be found in the Assessment Resource Book online or in print. The materials also include an ExamView Test Generator. Examples of grade-level assessment items include:

  • Topic 2, Topic 2 Assessment, Item 11, students solve an addition word problem, using a ten frame. “Julie has 2 cards. Michael gives her 5 more. How many cards does Julie have in all?” (1.OA.1)
  • Topic 1-8 Cumulative Assessment, Item 8, “Lisa draws 7 pictures. Then she draws 9 more pictures. How many pictures does Lisa draw in all? Solve the problem. Explain the strategy you used.” (1.OA.1)
  • Assessment Sourcebook, Topics 1-8 Cumulative/Benchmark Assessment, Problem 9, “Tell if the equation is True or False. 16 - 6 = 9 + 2. Explain how you know your answer is correct.”  (1.OA.7)
  • Topic 9 Assessment, Item 6, “What number is 10 less than 55? What number is 10 more than 55?” (1.NBT.5)
  • Assessment Sourcebook Topic 11, Topic 11 Assessment, Problem 4, “Solve the problem. Use any strategy. Explain why you picked the strategy. Write an addition equation to check your answer.  90 - 50 = ___” (1.NBT.6)

Criterion 1b

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

​The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet expectations for students and teachers using the materials as designed devoting the large majority of class time to the major work of the grade. The instructional materials devote approximately 81 percent of instructional time to the major clusters of the grade.

Indicator 1b

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

​The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet expectations for spending a majority of instructional time on major work of the grade. The evidence was collected from Topics, Performance Tasks, Topic Assessments, Benchmarks, Centers, and 3-Act activities.

  • The approximate number of topics devoted to major work of the grade (including assessments and supporting work connected to the major work) is 12 out of 15, which is 80%. 
  • The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 87 out of 107, which is approximately 81%.
  • The number of days spent on major work of the grade (including supporting work connected to major work of the grade) is 117 days of 145 days, approximately 81%.

A lesson level analysis is most representative of the instructional materials as the lessons include major work, supporting work connected to major work, and the assessments embedded within each topic. As a result, approximately 81% of the instructional materials focus on major work of the grade. 

Criterion 1c - 1f

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

The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet expectations for being coherent and consistent with the standards. The instructional materials have supporting content that engages students in the major work of the grade and content designated for one grade level that is viable for one school year. The instructional materials are also consistent with the progressions in the standards and foster coherence through connections at a single grade.

Indicator 1c

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

​The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

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

Topic 6 addresses supporting standard 1.MD.4 (represent and interpret data) which connects to major work in 1.OA.1 (use addition and subtraction within 20 to solve word problems) and 1.OA.5 (relate counting to addition and subtraction). 

  • Lesson 6-2, Teacher Edition, Problem Solving, Item 7, students use data from a tally chart to create a picture graph and answer the question related to the graph, “How many students voted in all?” (1.OA.5)
  • Lesson 6-2, Problem Solving Reading Activity,  Teacher Edition, page 260, students answer the questions using data from the given tally chart.  Item 2, “How many more students like toast than eggs?” Item 3 “How many students like bagels or toast?”  Item 6. “How many students were surveyed in all?” (1.OA.5)
  • Lesson 6-3, Independent Practice, page 263, Item 7, students use the information in the picture graph to answer, “2 students changed their vote from blue to red. Use this equation to determine how many fewer students like red than purple. ___ + 6 = 8.” (1.OA.1)
  • Lesson 6-4,  Teacher Edition, Guided Practice, page 266, Item 1, students complete a picture graph as they solve the word problem: “Jim asks 9 members of his family for their favorite fruit. 6 people say they like oranges. The rest say they like apples. How many people say they like apples?” (1.OA.1)
  • Lesson 6-5, Teacher Edition, Solve and Share, page 269, students complete a tally chart as they solve a word problem: “Kelly asks 12 students if they like octopuses, whales, or sharks best. The tally chart shows their responses. How many students would need to change their vote from whales to sharks to make sharks the favorite? Complete the new chart to explain.” (1.OA.1)

Topic 13 addresses supporting standard 1.MD.3 (tell and write time) which connects to major work in standards 1.NBT.1 (Count to 120) and 1.OA.5 (Relate counting to addition and subtraction). 

  • Lesson 13-4, Teacher Edition, Independent Practice, Item 11, students “think about how hands move on the clock to help solve the problem. Mary writes a pattern. Then she erases some of the times. Write the missing times. 6:00, 8:00, _____, 12:00, _____.” (1.OA.5)
  • Lesson 13-5, Solve and Share, page 537, students practice the counting sequence when counting the number of minutes that make up 1 hour. “The minute hand travels all the way around the clock every hour. Each little mark is 1 minute of time. Count how many minutes make up 1 hour. How many marks are there if the minute hand goes only halfway around the clock? Explain your answer.” (1.NBT.1, 1.OA.5)

Topic 14 addresses supporting standard 1.G.1 (reason with shapes and their attributes) which is connected to major work of 1.NBT.1 (Count to 120) and 1.NBT.2 (Understand that the two digits of a two-digit number represent amounts of tens and ones).  

  • Lesson 14-3, Solve and Share, students solve, “Find square corners and rectangle shapes in the classroom. Tell your partner why a shape you find is a rectangle. Count how many square corners you find. Use the chart to help you keep track.” Students mark the corners on a hundred chart to count and keep track of the total number of square corners they find. (1.NBT.1)
  • Lesson 14-5, Solve and Share, page 573, students solve, “Use exactly 10 pattern blocks to make a picture of a boat. Trace the shapes in the space below to show your boat. Then use what you know about tens. How many pattern blocks would you need to make 6 boats?” (1.NBT.2)

Indicator 1d

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

The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet the expectations for the amount of content designated for one grade-level being viable for one school year in order to foster coherence between grades. 

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

Included are 15 topics for the grade. Each Topic is broken down into lessons which include additional resources for differentiation, additional time, and additional practice activities. Each Topic also includes an assessment (Teacher’s Edition Program Overview, page 22). For example:

  • There are 107 content focused lessons.
  • There are 8 days for 3-Act Math Activities.
  • 30 days of Topic Reviews and Assessments.

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

  • Math Diagnosis and Intervention System
  • 10 Step-Up to Grade 2 Lessons to use after the last topic
  • Readiness Test; Review What You Know; Cumulative/Benchmark Assessment (4 in all); Progress Monitoring Assessment Forms A, B and C (3 in all)

Lessons 13-1 and 13-2 (money) are not included in the above count as they are identified as optional by the publisher in the Table of Contents, in the Teacher’s Edition Page F18.

Indicator 1e

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

​​The instructional materials reviewed for enVision Mathematics 2020 Common Core Grade 1 meet the expectations for being consistent with the progressions in the standards. Content from prior grades is identified and connected to grade-level work, and students are given extensive work with grade-level problems. 

The Teacher Edition contains a Topic Overview Coherence: Look Back and Look Ahead, and a Lesson Overview Coherence: Look Back and Look Ahead, which identify connections to content taught in previous grades, indicating the relevant topics and/or lessons. In addition, the sections include connections to content taught in future grades, topics, or lessons. For example, in Topic 5, the Math Background, Coherence: Look Back includes:

  • “Gr K: “In Topic 4, “students began to develop an understanding of equality when they determined whether two groups of objects are equal in number and when they compared two numbers between 1 and 10.”  “In Topics 6, 7, and 8, students built a foundational understanding of addition as “put together” and “add to” and subtraction as “take apart” and “take from”.”  
  • Earlier in Grade 1: “In Topics 1 and 2, students developed fluency with addition and subtraction within 10.  In Topics 3 and 4, students used strategies, properties, and the relationship between addition and subtraction to add and subtract within 20.” “In Topics 2, 3, and 4, students applied the Commutative Property, as well as doubles, near doubles, and make-10 strategies to help them learn basic addition facts. These strategies go hand-in-hand with the Associative Property to help make addition problems easier.” “In Topic 4, students continued to explore algebraic reasoning by thinking of subtraction as a missing addend problem. Students represented an unknown quantity with a question mark.”

In Topic 5, The Look Ahead, includes: 

  • Later in Grade 1: “In Topic 9, students will use >,<,= to compare numbers. They will apply their understanding of equality and use the equal sign when the values on both sides of an equation are the same.” “In Topics 10 and 11, students will add and subtract within 100. Much of this content will involve working with addition and subtraction equations.”
  • In Grade 2, “students will continue to work with addition and subtraction equations. They will interpret, write and complete equations as they develop fluency with addition and subtraction within 100 and practice strategies for adding and subtracting.”

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

  • Operations and Algebraic Thinking is addressed in Topic 1: Understand Addition and Subtraction, Topic 2: Fluently Add and Subtract Within 10, Topic 3: Addition Facts to 20: Use Strategies, Topic 4 Subtraction Facts to 20: Use Strategies, and Topic 5: Work with Addition and Subtraction Equations
  • Number and Operations in Base Ten is addressed in Topic 7: Extend the Counting Sequence,  Topic 8: Understand Place Value, Topic 9: Compare 2-Digit Numbers, Topic 10: Use Models and Strategies to Add Tens and Ones, and Topic 11: Use Models and Strategies to Subtract Tens
  • Measurement is addressed in Topic 12: Measure Lengths
  • Time and Money is addressed in Topic 13: Time and Money, however the Money concepts do not support the progressions in the standards
  • Geometry is addressed in Topic 14: Reason with Shapes and their Attributes and in Topic 15: Equal Shares of Circles and Rectangles.

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

  • Lesson 1-8, Solve and Share, students solve, “5 pebbles are brown. The other pebbles are black. There are 7 pebbles in all. How many pebbles are black.” (1.OA.1)
  • Lesson 9-4, Problem Solving, Problem 12, students solve, “Mary has 21 red ribbons. She has 12 yellow ribbons. Does Mary have more red ribbons or yellow ribbons? Write >, <, or = to compare the numbers.” (1.NBT.3)
  • Lesson 7-2, Problem Solving, Problem 15, students solve, “Pick a number greater than 99 and less than 112. Write the number in the box. Then write the 3 numbers that come before it and the number that comes after it.” (1.NBT.1)
  • Lesson 10-7, Problem Solving, Problem 10, students solve, “Jon reads 24 pages. Then he reads 27 more pages. How many pages does he read in all? Write an addition equation to show the problem.” (1.NBT.4)

The instructional materials explicitly state connections between prior grades and current grade level work. Each topic contains a Math Background: Coherence document with Look Back narratives that identify connections to what students learned in Kindergarten and previously in Grade 1: 

  • Topic 3, Coherence: Look Back states, Grade K: “In Topics 6 and 7, students were introduced to various meanings of addition and subtraction. Students used objects, drawings, and equations to represent addition and subtraction word problems within 10 and to decompose numbers less than or equal to 10. By the end of Kindergarten, students fluently added and subtracted within 5. In Topic 8, students showed different ways to decompose numbers to 10. Earlier in Grade 1: In Topic 1, students were introduced to ways to think about addition and subtraction. They solved “add to,” “put together,” “take from,” “take apart,” and “compare” problems.”In Topic 2, students solved addition and subtraction problems to 10. They were introduced to strategies including counting on and counting back, using doubles and near doubles, adding within 5, adding to 10, adding in any order, and thinking addition to subtract.”
  • Lesson 7-3, Coherence: Look Back “In Lesson 7-2, students counted by 1s to 120, beginning at any number.”
  • Topic 8, Coherence: Look Back, Grade K: In Topic 9, students were introduced to numbers greater than 10 by counting and writing numbers to 20. In Topic 10, students composed and decomposed numbers between 11 and 19 using ten frames.” Earlier in Grade 1:In Topic 7, students read and wrote numbers to 120. They counted groups of objects by 10s.”
  • Lesson 10-4, Coherence: Look Back: “In Lesson 7-5, students used an open number line to count on by 10s and 1s.”

Indicator 1f

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

The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the Standards.

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

  • Topic 2, Lesson 2-6 and 2-7, Lesson Objectives, ”Count back to solve subtraction problems,” and  “Use addition facts to 10 to solve subtraction problems,” respectively. These objectives are shaped by 1.OA.C, Add and subtract within 20.
  • Topic 5, Lessons 5-1 and 5-2, Lesson Objectives, “Find the unknown number in an equation,” and “Determine if addition and subtraction equations are true or false,” respectively.  These objectives are shaped by 1.OA.D, Work with addition and subtraction equations.
  • Topic 8, Lessons 8-4 and 8-5, Lesson Objectives,  “Count tens and ones to find a two-digit number,” and  “Use drawings to solve problems with tens and ones,” respectively. These objectives are shaped by 1.NBT.B, Understand place value.
  • Topic 12, Lesson 12-3, Lesson Objectives, “Use small same-size objects to measure length” which is shaped by 1.MD.A, Measure lengths indirectly and by iterating length units.

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

  • Topic 1, Lesson 1-2, Guided Practice, Problem 2, connects major clusters, 1.OA.A, Solve addition word problems to 1.OA.D, Write equations to represent the mathematics in the problem.  Students solve “1 white egg and 6 blue eggs. How many eggs in all?”
  • Topic 4, Lesson 4-3, Problem Solving,  Problem 7, connects 1.OA.A, Represent and solve problems involving addition and subtraction to 1.OA.C, Add and subtract within 20, and to 1.OA.B, Understand and apply properties of operations and the relationship between addition and subtraction. Students solve, “Sage has 13 stickers. She gives 7 to her brother. How many stickers does Sage have left? How can you make 10 to solve?”
  • Topic 5, Lesson  5-5, Construct Arguments, connects 1.OA.A Represent and solve problems involving addition and subtraction and 1.OA.B. Understand and apply properties of operations and the relationship between addition and subtraction. The sample classroom conversation states, “Why do you think the numbers are grouped this way? [To use the make- 10 strategy.]”

Gateway Two

Rigor & Mathematical Practices

Meets Expectations

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Gateway Two Details

​The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet expectations for Gateway 2, rigor and balance and practice-content connections. The instructional materials meet expectations for reflecting the balances in the standards and helping students meet the standards’ rigorous expectations by giving appropriate attention to the three aspects of rigor, and they meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

Criterion 2a - 2d

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.
8/8
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Criterion Rating Details

​The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet expectations for reflecting the balances in the standards and helping students meet the standards’ rigorous expectations, by giving appropriate attention to: developing students’ conceptual understanding; procedural skill and fluency; and engaging applications. The instructional materials also do not always treat the aspects of rigor separately or together.

Indicator 2a

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

​The instructional materials for enVision Mathematics Common Core Grade 1 meet the expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. 

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

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

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

  • In Lesson 1-7, Solve and Share, students solve a change unknown problem using addition or subtraction to find the missing addend. “There are five train cars.  More train cars join. Now there are 9 train cars. How many train cars joined?” (1.OA.1)
  • In Lesson 5-4, Solve and Share, students build their understanding of adding three numbers as they use addition to find the total number of books in three stacks and write two different equations to show the addition. “Carlos made stacks of 6 books, 4 books, and 6 books. How can you use addition to find the number of books in all three stacks? Write two different equations to show how many books in all.” (1.OA.3)
  • In Lesson 8-1, Lesson Overview, “Students use models to make the numbers from 11 to 19 and then connect those models with both written numerals and number words. Students are formally introduced to the idea that each of these numbers is made up of 1 ten and some ones.” Solve & Share, students “show different numbers using counters and a ten-frame. They tell how the numbers are alike and different. Their work shows prior and emerging understanding.” (1.NBT.2)
  • In Lesson 8-4, Lesson Overview, students build understanding by “Using models to compose numbers establishes a foundation for place-value concepts with three- and four-digit numbers as well as for addition with greater numbers.” Convince Me!, students “use connecting cubes to represent their numbers” (46 and 64). They then “talk about the similarities and differences between the numbers.” (1.NBT.2)
  • In Lesson 9-1, Lesson Overview, “students use tens rods and one units to model a two-digit number. Then they build upon that model to show a number that is 1 more, 1 less, 10 more, or 10 less than the original number.” During the Visual Learning Bridge, students use place value blocks to model the number 25 and then show 1 more, 1 less, 10 more and 10 less with the blocks and describe the digit that changes. (1.NBT.5)
  • In Lesson 10-1, Solve and Share, students build an understanding of adding multiples of ten as they explore how the sum of 3 + 5 can be used to help add 30 + 50. In the Visual Learning Bridge, students investigate the essential question, “How is adding groups of ten like adding numbers less than 10?” (1.NBT.4)
  • In Lesson 10-9, Guided Practice, Problem 1, “Ellen has 27 stickers. Her brother gives her 26 stickers. How many stickers does Ellen have in all? Use drawings to show and solve the problem. Then write the equation.” (1.NBT.4)

Indicator 2b

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

The instructional materials for enVision Mathematics Common Core Grade 1 meet the expectations that they attend to those standards that set an expectation of procedural skill and fluency. The instructional materials develop procedural skill and fluency throughout the grade-level. 

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

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

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

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

  • In Lesson 2-1, Guided Practice, “Count on to find the sum.”  Item 1, Shows a picture of a bucket with a 3 on it and tray with 2 carrots the equation reads “3+ __= ___”.   (1.OA.5) 
  • Lesson 2-4, Guided Practice, Items 1 and 2, students “Look at the ten-frames. Write an addition fact with 5. Then write an addition fact for 10.” This develops fluency for adding within 10. Item 1, “ 5 + __ = 7. 7 + __ = 10.” (1.OA.6)
  • In Lesson 2-7, Independent Practice, “Think addition to help you subtract. Draw the missing part. Then write the missing numbers.”  Item 1, “6 + __ = 8 so 8 - 6 = ____.” (1.OA.6)
  • In Lesson 3-5, Convince me!, “How would you make 10 to find the sum of 9+4?” as a strategy to add within 20. (1.OA.6)
  • Topic 4, Fluency Practice Activity, students solve addition and subtraction facts within 10, “Color these sums and differences. Leave the rest white.” Students color sums and differences that are equal to 6, 7, or 8, and write the word that they see after the boxes are colored.
  • In Lesson 7-4, Guided Practice, Items 1, 2 and 3, students are directed to “Write the numbers to continue each pattern. Use a number chart to help you.”  Item 1, “Count by 1s: 112, 113, 114, ___, ____, ____, ___, ___,____.” Item 2, “Count by 10s: 22, 32, 42, ___, ___, ___, ___, ___, ___.” Item 3, “Count by 1s: 90, 91, 92, ___, ___, ___, ___, ___, ___.” This works on the development of fluency in counting to 120. (1.NBT.1)
  • In Lesson 10- 7, Guided Practice,“Add. Draw blocks to help.” Item 1,  “Find 36 + 24.” Item 2, “Find 19 + 25.” Students are developing procedural skills to add within 100. (1.NBT.4)

Indicator 2c

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

The instructional materials for enVision Mathematics Common Core Grade 1 meet expectations that the materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied.

In the Teacher Edition, each Topic begins with Math Background: Rigor, where applications for the topic are outlined for teachers. Math Background: Rigor for Topic 4, Applications states, “Addition and Subtraction Situations Lesson 4-8 specifically introduces “take from” and “compare” subtraction situations. These situations allow students to apply their understanding of subtraction in context. Students solve problems with unknowns in all positions. In Lesson 4-9, students apply what they know about addition and subtraction to write word problems for addition or subtraction situations.” Each Topic also includes a variety of application tasks, for example:

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

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

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

  • In Lesson 3-8, Guided Practice, Item 1, students solve, “Tim writes 9 stories. He writes 3 fewer stories than Daisy. How many stories did Daisy write?” (1.OA.6)
  • In the Topic 4 Performance Task, Item 1, students use information from a graph to solve, “How many more moon stickers than sun stickers does Maria have?” (1.MD.4)
  • In Lesson 6-3, Convince Me!, students are presented with a picture graph displaying data on what students like to drink for lunch. In addition to typical routine statements about the data, students answer, “What other information do you know about what students like to drink at lunch?” with a sample answer of “The students like juice and milk more than water.” (1.MD.4)
  • In Lesson 1-9, Solve and Share, students solve, “7 rabbits, 3 turtles. How many more rabbits than turtles? Do you add or subtract to solve the problem? Tell why. Show how to solve.” (1.OA.1, 1.OA.4)
  • In Topic 1, 3-Act Math Task, students determine how many apples were taken from the fruit bowl. In Act Two, they are given the number of red and green apples before and after some were taken out of the bowl. Students draw models to determine the solution. (1.OA.1)
  • In Topic 10, Pick a Project - Octopuses, students write and draw an octopus story. “Write an octopus story about octopuses that are seen on a reef and those that are hidden. Draw a picture that relates to your number story. You can draw counters to show the octopuses that are seen. Then write an equation with an unknown for the number story. Have a classmate solve it. They should use the equation and counters to help them solve.” (1.NBT.4, 1.NBT.5)
  • In Topic 5, Performance Task, Item 5, students see a picture that includes 5 daisies and 8 lilies. They solve, “Terry says that if there were 2 fewer lilies, then the number of lilies would be equal to the number of daisies. He writes the equation below. Is this equation true or false? Explain how you know. 8 - 2 = 5” (1.OA.7, 1.OA.1)

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

  • In Lesson 1-6, Independent Practice, Item 4, students solve  “Beth writes on 3 cards. Joe writes on 9 cards. How many fewer cards does Beth write on than Joe?”  (1.OA.1)
  • In Lesson 5-6, Independent Practice, Item 4, students solve, “Harry has 5 fewer buttons than Tina. Harry has 7 buttons. How many buttons does Tina have?” (1.OA.1, 1.OA.4)
  • In Lesson 10-9, Independent Practice, Item 4, students solve, “There are 16 apples in the bowl. George buys 15 more apples. How many apples are there in all?”  (1.NBT.4)

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 enVision Mathematics  Common Core Grade 1 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. 

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

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

  • In Lesson 3-4, Solve and Share, students develop conceptual understanding as they solve, “Carlos and I each pick 5 strawberries. What doubles fact shows how many strawberries we have in all? If I pick 1 more strawberry, how could you find how many strawberries in all?” (1.OA.6)
  • In Lesson 2-6, Lesson Overview, “As students use the strategy of counting back to solve subtraction problems, they begin to develop fluency for subtraction facts within 10.” In the Visual Learning Bridge, students “count back” 2 on a number line in order to model subtracting 2 from 7. (1.OA.5)
  • In Lesson 10-8, Independent Practice, Items 3-4, students find each sum, solve any way they choose, and draw or explain what they did: “27 + 9 = ___, and 50 + 23 = ___.” (1.NBT.4, 1.NBT.5)
  • In Lesson 5-5, Solve and Share, students engage with application as they solve, “I have 6 oranges, Alex has 2 pears, and Jada has 4 apples. How many pieces of fruit do we have in all? Write 2 different addition equations to solve the problem.” (1.OA.2, 1.OA.3)

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

  • In Lesson 2-7, Lesson Overview, “Conceptual Understanding: Bar models help deepen student understanding of the relationship between wholes and parts and addition and subtraction. Fluency: By recognizing the addition-subtraction relationship, students further develop fluency as they use previously learned addition facts to solve subtraction facts.” Students demonstrate both aspects of rigor in the Additional Practice, Item 1, as students view a picture of a row of 4 counters and beneath it a row of 3 counters. Students write an addition fact that will help them write and solve the subtraction problem. (1.OA.4)
  • In Lesson 6-3, Lesson Overview, “Conceptual Understanding: Students go deeper to analyze how problems can be solved using data presented in graphs. Procedural Skill: Students continue to develop skills of building graphs. Application: Students apply their knowledge of addition and subtraction to solve problems.” Students demonstrate all three aspects of rigor in the Guided Practice, Item 5, as they interpret data shown in a tally chart applying what they know about addition and subtraction to 10 to solve, “How many more students like purple than red?”  (1.MD.4)
  • In Topic 6, Topic Assessment, Item 3, students are given a tally chart titled Favorite Winter Activity: Skating 5, Skiing 3, Sledding 7. Students “use the tally chart to solve” the following problems, “Which is the favorite winter activity of most students?” and “How many more tally marks does skating need to have the most tally marks?” They use an equation to explain their answer. (1.MD.4)
  • In Lesson 9-3, Lesson Overview, “Conceptual Understanding: Students use their understanding of using place value to compare 2 two-digit numbers.  Procedural Skill: Students compare 2 two - digit numbers by comparing the tens and then, if necessary, by comparing the ones.” Students demonstrate both aspects of rigor in the Solve & Share when they are presented with the numbers 37 and 73, and answer, “How can place-value blocks help you decide which number is larger?”  (1.NBT.3)

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
9/10
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Criterion Rating Details

The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs). The MPs are identified and used to enrich mathematics content, and the instructional materials support the standards’ emphasis on mathematical reasoning.

Indicator 2e

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

The instructional  materials reviewed for enVision Mathematics Common Core Grade 1 meet expectations that the Standards for Mathematical Practice (MPs) are identified and used to enrich mathematics content within and throughout the grade level, and are not treated separately.

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

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

Examples of the MPs identified within individual lessons:

  • MP.1: Topic 1, Math Practices and ETP,  “Students make sense of Items by using addition or subtraction to help find the missing addend.. (e.g., p. 34, Visual Learning Bridge).”
  • MP.2: Lesson 4-1, Lesson Overview, “Mathematical Practices MP2 Reason Abstractly and Quantitatively Students discuss how number lines can be used in different ways to subtract.”
  • MP.4: Lesson 10-9, Lesson Overview, “Students use blocks, drawings, or number lines to model Items.”
  • MP.5: Lesson 4-2, Lesson Overview, “Students use ten-frames to facilitate their thinking and modeling of making 10 to help subtract.”
  • MP.6: Lesson 12-1, Lesson Overview, “Students use appropriate mathematical language in making accurate comparisons of the lengths of objects.”
  • MP.7: Topic 5, Math Practices and ETP,  “Students look for structure when they look for compatible numbers or make 10 to add three addends in a strategic way.  (e.g., p. 226, Visual Learning Bridge.)”
  • MP.8: Lesson 8-2, Lesson Overview, “Students use repeated reasoning when they see that 10 ones is the same as 1 ten and connect that they can count objects by grouping into tens.”

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

  • In Lesson 3-8, Lesson Overview, students engage with MP1 as they “make sense as they compare quantities to determine the larger, unknown amount in Item situations.”  In Guided Practice, Item 1, students solve: “Tim writes 9 stories. He writes 3 fewer stories than Daisy. How many stories did Daisy write?” (1.OA.1, 1.OA.6)
  • In Lesson 8-2, Problem Solving, Item 9, students engage with MP2 as they solve “George has 3 boxes of pens. 10 pens are in each box. How many pens does George have?” (1.NBT.2c)
  • In Lesson 10-9, Independent Practice, Item 2, students use drawings to show and solve the Item. Then write the equation. “Barry has 12 red cars. He has 14 blue cars. How many cars does Barry have in all?” (1.NBT.4)
  • In Lesson 7-3, Problem Solving, Item 16, students use a 120 number chart to solve, “Sasha counts forward to 115. What are the next 5 numbers she counts? Write the numbers. 115, ___, ___, ___, ___, ___” (1.NBT.1)
  • In Lesson 15-1, Problem Solving, Item 17,students engage with MP6 when they are given pictures of two flags, both sectioned into two pieces, one in two equal pieces and the other in two unequal pieces, students solve, “Ruth picks a flag with equal shares. Which flag did she pick? Circle the correct flag.” (1.G.3)
  • In Lesson 2-5, Lesson Overview, students engage with MP7 as they “look for patterns and make use of structure when they discover and discuss how changing the order of any two addends does not change the sum.” In Solve and Share, page 73, students are shown one cube tower of 5 green and 2 yellow cubes and another with 2 yellow and 5 green cubes. They “Write an addition equation for the green and yellow cubes in each cube tower.” 5 + 2 = 7 and 2 + 5 = 7 “How are the addition equations  the same? How are they different?” (1.OA.3)
  • In Lesson 1-6, Lesson Overview, students engage with MP8 as they “generalize that like with finding ‘how many more’ from the past lesson finding ‘how many fewer’ involves a comparison to find the difference in amount.”  In Independent Practice, Item 3, students use cubes or draw a picture and write an equation to solve, “Emma buys 10 red apples. She buys 5 green apples. How many fewer green apples than red apples does Emma buy?” (1.OA.1)

Indicator 2f

Materials carefully attend to the full meaning of each practice standard
1/2
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Indicator Rating Details

The instructional materials reviewed for enVision Mathematics Common Core Grade 1 partially meet expectations for carefully attending to the full meaning of each practice standard. 

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

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

  • Lesson 3-6, Visual Learning Bridge, “Make 10 to help you add. Find the sum. 9 + 7 = ? You can use a number line to help you make 10.”  A number line is shown and teachers are directed to ask, “What number do you add to 9 to make 10? Why do you add 6 to 10? What are the two addition problems shown on the number line? Does this number line show 9 + 7? How do you know?”  (1.OA.6)
  • Lesson 5-1, Visual Learning Bridge, students are presented with the problem: 12 - __ = 3. The teacher is directed to ask, “How could you use counters to solve this problem?” (1.OA.8)
  • Lesson 9-1 Guided Practice, Items 1-2, students “use place-value blocks to show each number and to help complete each sentence.” For the numbers 45 and 17, students find the numbers that are 1 more, 1 less, 10 more, and 10 less. (1.NBT.5) 
  • Lesson 9-5 Independent Practice, Items 7-9 students “write the correct number or symbol >, <, or = to make each correct. Draw a numberline to help if needed. ___ < 26, 75 > ___, and 33 > ___.” (1.NBT.3)

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

  • MP.1: Lesson 6-5, Guided Practice, Item 1, students are provided data in a tally chart that shows that baseball is the favorite sport of 7 people and football is the favorite sport of 8 people. Students solve, “3 more students take the survey. Now, football and baseball have the same number of votes. How many votes does each have? Use pictures, words, or equations to explain.”  (1.MD.4)
  • MP.2: Lesson 10-7 Solve and Share, “Grace is solving 35 + 8. First she adds 35 + 5 = 40. What should she do next to find the answer? Draw a model to explain.” (1.NBT.4)
  • MP.4: Lesson 11-4, Problem Solving, states ‘Solve each problem. You can use models to help. Show your work. Item 6, Model: Jeff has 517 baseball cards. He has 263 football cards. How many more baseball cards than football cards does he have?”
  • MP.6: Lesson 13-3, Independent Practice, Items 4 - 11, students are shown blank analog clocks, and they “draw the hour and minute hands to show the time” that is shown in words, i.e. 10 o’clock. (1.MD.3)
  • MP.7: Lesson 4-4, Lesson Overview, students engage with MP7 as they “look for and use patterns between wholes and parts to write related facts.” In the Convince Me!, students answer “How are 15 - 6 = 9 and 15 - 9 = 6 related?” In the Guided Practice, Item 2, students are presented with a model of 9 red and 7 yellow dots (total of 16) and asked to “Write the fact family for each model.”  (1.OA.4, 1.OA.6)
  • MP.8:  Lesson 10-1, Convince Me!, “How is adding 6 + 3 like adding 60 + 30?”   (1.NBT.4)

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.
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Indicator Rating Details

​The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. 

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

  • Convince Me! prompts provide the opportunity for students to share their thinking and to analyze the reasoning of others.
  • Three-Act Math - Students critique other’s reasoning as solution methods for the task are shared with the class. 
  • Solve and Share - Students share and justify solutions with the class, and they critique the reasoning of others as teachers select which solutions to share.
  • In the Visual Learning Bridge, there are opportunities for students to construct viable arguments.
  • “I Can” bubbles prompt students.  Lesson 3-9, “I Can...critique the thinking of others by using pictures, words, or equations.”  
  • Thinking Habits thought bubbles prompt students to critique reasoning and/or construct arguments. Lesson 3-9, Solve & Share, Thinking Habits, “Can I improve on Lidia’s thinking? Are there mistakes in Lidia’s thinking?” 
  • The Math Practices and Problem Solving Handbook.  

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

  • Lesson 1-9, Solve & Share, students solve, “7 rabbits. 3 turtles. How many more rabbits than turtles?” They are asked, “Do you add or subtract to solve the problem? Tell why? Show how to solve. Use pictures, numbers, or words.”  In the Thinking Habits thought bubble on the page: “How can I use math to explain my work? Is my explanation clear?” (1.OA.1)
  • Lesson 5-7, Convince Me!, “Is the equation below true or false? How do you know?  10 + 8 = 9 + 3 + 3” (1.OA.7)
  • Lesson 9-4, Convince Me!, “How do you know that 48 is greater than 40?” (1.NBT.3)

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

  • Lesson 3-3, Convince Me!, “Becca shows 6 + 7 with cubes and says it is not a doubles fact. Is she correct? How do you know?” (1.OA.6)
  • Lesson 3-9, Solve & Share, “ A pet store has 9 frogs. 5 of the frogs are green and the rest are brown. Lidia adds 5 + 9 and says that the store has 14 brown frogs. Circle if you agree or do not agree with Lidia. Use pictures, words, or equation to explain.” (1.OA.1)
  • Lesson 8-6, Problem Solving, Item 6, “Nate says 5 tens and 3 ones shows the same number as 3 tens and 13 ones. Do you agree? Explain.” (1.NBT.2)
  • Lesson 13-3, Solve & Share, “Look at the clock. Ria says the clock says 12 o’clock. Pat says the clock shows 3 o’clock. Do you agree with Ria or Pat? Tell why.” (1.MD.3)

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.
2/2
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Indicator Rating Details

The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

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

  • The Math Practices and Problem Solving Handbook provides guidance on implementing MP3 and questions that students might ask themselves as they reflect on MP3. The Problem Solving Lessons which focus on MP3 are identified for example, Lessons 1-9 and 3-9.
  • In the teacher’s notes for each lesson, MP3 is identified in red print as “Construct Arguments” or “Analyze Reasoning”. Questions to elicit student thinking are included below the prompts. 
  • In the teacher notes for Solve and Share activities, questions to prompt students thinking are included in Share Solution Strategies and Key Ideas.
  • The Convince Me! activity, when connected to MP3, provides prompts to assist students in constructing arguments and analyzing the reasoning of others.
  • Three Act Math Tasks includes Construct Arguments which provides prompts for the teacher to help students construct arguments.

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

  • Lesson 1-9, Visual Learning Bridge, during the Classroom Conversation narrative, teachers are prompted to ask, “How did Jada use cubes and counting to show the number of red crayons? How does the model help show Jada’s addition equation 6 + 3 = 9 is correct?” and  “How did Marta use cubes and counting to show the number of red crayons? How does the model help show Marta’s subtraction equation 9 - 6 = 3 is correct?” (1.OA.1)
  • Lesson 2-5, Visual Learning Bridge, page 74, students observe two equations, 4 + 2 = 6 and 2 + 4 = 6. The teacher is prompted to say, “Look at the sentences and the addition facts. Do they show the same addends and sum?” The teacher helps “students see how the cubes and equations create a strong argument that when you change the order of the addends, the sum remains the same.” (1.OA.3)
  • Lesson 8-6, Convince Me!, students answer the question, “How could you break apart 24 using only 1 ten? Explain.” In order to support students in constructing an argument, teachers are prompted to “Have students use connecting cubes, as needed, to model their method. Ask them to back their claim by counting to prove their method shows 24.” (1.NBT.2)

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

  • Lesson 1-5, Solve & Share, Analyze Student Work, the teacher is prompted to share Mariyah’s Work and asks: “How did Mariyah show the red and blue cars? How was her way of finding how many more alike and different from Charles’s way?” (1.OA.1)
  • Lesson 3-9, in the Visual Learning Bridge students listen to the story, “5 dogs are playing. Some more dogs join. Now 8 dogs are playing.” In Convince Me!, the teacher is prompted to say, “Sharon wrote the equation 8 - 5 = 3 to solve the problem and said that 3 more dogs came to play. Do you agree or not agree with her thinking?” (1.OA.1) 
  • Lesson 14-2, Solve & Share, Analyze Student Work, the teacher is prompted to share Juan’s Work and ask students, “Choose one of the ways Juan describes the shapes. Do you agree? Explain.”  Also, the teacher shares Erin’s work and asks, “Erin says the shapes are different and cannot be alike. Do you agree? Explain.” (1.G.1, 1.MD.2)

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

  • Lesson 1-9, Solve and Share, students are presented with a problem “Do you add or subtract to solve the problem? Tell why? Show how to solve. Use pictures, numbers, or words.”  While observing students’ work, teachers are prompted to support if needed and ask “How can you use objects or drawings to help explain why you added or subtracted?” Teachers are provided two pieces of work to share: Rita’s Work and Bill’s Work with the following questioning prompts:  “Does Rita argue that you add or subtract for the problem? How does her work support her argument you can subtract?” and “Does Bill argue that you add or subtract for the problem? How does Bill support his argument you can add?” (1.OA.1)
  • In Topic 5, 3-ACT MATH: Weighted Down, students are presented with the main question, “ How can you balance the two sides?” In Act 1, Prediction, teachers engage students in their predictions by asking “What is a number of erasers too small to be the number of erasers to balance the scale? What number is too many erasers? Why do you think your prediction is the answer to the Main Question? Who has a similar prediction? Who has a different prediction?” Then in Act 2, students share their work and teachers are provided with Luis’s and Lin’s Work for students to analyze. “Luis says he added the number of erasers on each side. How is his answer unclear?”  Lin says there are 4 too many erasers on the right. How did drawing a picture help her find her answer?” (1.OA.8)
  • Lesson 5-1, Solve & Share, students are presented with a problem “Find the missing number in this equation. 7 + __ = 13. Explain how you found the missing number.” After students share their work, teachers are provided two pieces of work to share: Darnell’s Work and Lucy’s Work with the following prompts:  “How did Darnell find the missing number? How do the counters and his writing show his thinking?” How did Lucy find the missing number? Is Lucy correct? Are the two equations related? Do they have the same parts and whole?” (1.OA.8, 1.OA.6, 1.OA.5)

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 enVision Mathematics Common Core Grade 1 meet the expectations of attending to the specialized language of mathematics.

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

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

For each topic, the Topic Planner includes a list of the new vocabulary words for each lesson. The vocabulary words are also included in the Teacher Edition, Lesson Overview page for each lesson. For example, in Topic 2:

  • Lesson 2-1, identifies number line 
  • Lesson 2-2: identifies doubles fact
  • Lesson 2-3: identifies near doubles fact

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

  • Topic 1, Vocabulary Review,  Oral Language, using the vocabulary words in the word bank, students “define the terms in their own words, say math sentences or questions that use the words,” and play a matching game with the class where one partner is the word and the other partner is the definition or example of the word. (equation, difference, part, plus)
  • Topic 5, Vocabulary Review, Item 6, Use Vocabulary in Writing,  “Write a story problem with a true equation. Use at least two words from the Word List.” (add, equation, more, subtract)
  • Topic 9, Vocabulary Review, Item 4, “Write a problem using the terms from the Word List. Use place-value blocks to help solve your problem.”  (compare, greater than >, less, less than <, more)

Gateway Three

Usability

Meets Expectations

Criterion 3a - 3e

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

​The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet expectations for being well-designed and taking into account effective lesson structure and pacing. The instructional materials include an underlying design that distinguishes between problems and exercises, assignments that are not haphazard with exercises given in intentional sequences, variety in what students are asked to produce, and manipulatives that are faithful representations of the mathematical objects they represent.

Indicator 3a

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

The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet expectations that the underlying design of the materials distinguishes between problems and exercises for each lesson. It is clear when the students are solving problems to learn and when they are completing exercises to apply what they have learned.

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

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

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

Indicator 3b

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

The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet expectations for not being haphazard; exercises are given in intentional sequences.

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

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

Indicator 3c

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

​The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet expectations for having variety in what students are asked to produce.

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

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

  • In Lesson 2-1, students use a number line to count on to find the sum for addition facts. 
  • In Lesson 6-3, students make, read, and analyze a tally chart or picture graph.
  • In Lesson 7-6, students use place-value blocks to count by both 10s and 1s in order to determine the number of objects in a group. 
  • In Lesson 14-5, students compose two-dimensional shapes to make pictures of real-world items.

Indicator 3d

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

​The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet expectations that manipulatives are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

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

Indicator 3e

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

The instructional materials for enVision Mathematics Common Core Grade 1 are not distracting or chaotic and support students in engaging thoughtfully with the subject. 

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

Criterion 3f - 3l

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

​The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet expectations for supporting teacher learning and understanding of the CCSSM. The instructional materials include: quality questions to support teachers in planning and providing effective learning experiences, a teacher edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials, a teacher edition that partially contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons, and explanations of the role of the specific grade-level mathematics in the context of the overall mathematics curriculum.

Indicator 3f

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

​The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet the expectation for supporting teachers in planning and providing effective learning experiences by providing quality questions to help guide students’ mathematical development.

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

  • In Lesson 2-2, Solve & Share, teachers ask, “How can you show Emily’s and her friend’s toys? How can you make sure each friend has the same number?”
  • In Lesson 6-4, Solve & Share, teachers ask, “What are you asked to find about the animals at the park? What do you already know? How are you supposed to show your work?”
  • In Lesson 14-5, Solve & Share, teachers ask, “What shapes would you see on a boat?  How can you use those shapes to make a boat?”

Indicator 3g

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

The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet the expectation for containing a teacher edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials also include teacher guidance on the use of embedded technology to support and enhance student learning.

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

Indicator 3h

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.
1/2
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Indicator Rating Details

​The instructional materials for enVision Mathematics Common Core Grade 1 partially meet the expectations that materials contain adult-level explanations so that teachers can improve their own knowledge. 

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

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

Indicator 3i

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

The instructional materials for enVision Mathematics Common Core Grade 1 meet the expectations for explaining the role of the grade-level mathematics in the context of the overall mathematics curriculum.

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

Indicator 3j

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

​The instructional materials for enVision Mathematics Common Core Grade 1 cross-reference the standards addressed with an estimated instructional time for each unit and lesson.

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

Indicator 3k

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

The instructional materials for enVision Mathematics Common Core Grade 1 contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement. 

The Teacher Resource Masters have Home School Connection Letters, in English and Spanish, for each Topic. The letters include information on the mathematical content, activities parents can use with their child, and a Focus on Mathematical Practices section encouraging parents to support their child with the mathematics presented in each Topic. For example, Topic 1:

  • Sample Family Letter Introduction: “Dear Family, Your child is learning about addition and subtraction. In this topic, your child will learn to solve problems by adding or subtracting and writing addition and subtraction equations…”
  • Sample Family Letter Activity: “Take 5 small objects as paper clips or buttons, and divide them into 2 groups. Have you child write 2 addition equations for the objects. Then allow your child to divide the objects into 2 different groups…”
  • Sample Family Letter Focus on Mathematical Practices: “Observe Your Child: Discuss how the objects are good tools to model the equations. Then discuss other ways to model the equations.”

Indicator 3l

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

​The instructional materials reviewed for enVision Mathematics Common Core Grade 1 contain explanations of the program's instructional approaches and identification of the research-based strategies.

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

Criterion 3m - 3q

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

The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet expectations for offering teachers resources and tools to collect ongoing data about student progress on the CCSSM. The instructional materials provide strategies for gathering information about students’ prior knowledge, strategies for teachers to identify and address common student errors and misconceptions, opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills, and assessments that clearly denote which standards are being emphasized.

Indicator 3m

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

​The instructional materials for enVision Mathematics Common Core Grade 1 meet the expectations for providing strategies to gather information about students’ prior knowledge within and across grade levels.

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

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

Indicator 3n

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

​The instructional materials for enVision Mathematics Common Core Grade 1 meet the expectations for providing strategies for teachers to identify and address common student errors and misconceptions.

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

  • In Lesson 1-1, Error Intervention Item 2, “If students cannot write an addition equation directly  from the story or picture, then have them act out the story using connecting cubes.”
  • In Lesson 4-1, Error Intervention Item 2, “If students have difficulty keeping track of how many spaces they are counting on or counting back, then have them label each jump on the number line as they count: 1, 2, 3, ...6.”

In Lesson 8-1, Error Intervention Item 2, “If students do not recognize the word fourteen as the number 14, then remind them that words that end in “teen” always have 1 ten, and the “four” in fourteen means that there are 4 ones.” 

Indicator 3o

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

​The instructional materials for enVision Mathematics Common Core Grade 1 meet the expectations for providing opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

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

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

The Cumulative/Benchmark Assessments found at the end of Topics 4, 8, 12, and 15 provide review of prior topics as an assessment. Students can take the assessment online, with differentiated intervention automatically assigned to students based on their scores. 

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

Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

Indicator 3p.i

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

The instructional materials for enVision Mathematics Common Core Grade 1 meet the expectations for assessments clearly denoting which standards are being emphasized. 

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

Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
1/2
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Indicator Rating Details

​The instructional materials reviewed for enVision Mathematics Common Core Grade 1 partially meet expectations that assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up. For example:

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

Indicator 3q

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

​The instructional materials for enVision Mathematics Common Core Grade 1 do not include opportunities for students to monitor their own progress. There are no specific materials for students encouraging them to monitor their own progress.

Criterion 3r - 3y

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

​The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet expectations for supporting teachers in differentiating instruction for diverse learners within and across grades. The instructional materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners and strategies for meeting the needs of a range of learners. The materials embed tasks with multiple entry points that can be solved using a variety of solution strategies or representations, and they provide opportunities for advanced students to investigate mathematics content at greater depth. The instructional materials also suggest support, accommodations, and modifications for English Language Learners and other special populations and provide a balanced portrayal of various demographic and personal characteristics.

Indicator 3r

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

The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet expectations for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

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

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

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

Indicator 3s

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

The instructional materials for enVision Mathematics Common Core Grade 1 meet the expectations for providing teachers with strategies for meeting the needs of a range of learners.

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

Indicator 3t

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

​The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet expectations for embedding tasks with multiple entry­ points that can be solved using a variety of solution strategies or representations.

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

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

  • In Lesson 3-1, Solve & Share, “Students solve an addition problem with a sum of more than 10.” During Small Group work, students can use “counters, cubes, the number line, or their own method” to solve the problem. 
  • In Lesson 5-3, Solve & Share, “Students find a missing number to make an equation true.” During Small Group work, “students might use counters, drawings, or equations” to solve the problem.

Indicator 3u

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

The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet expectations for suggesting support, accommodations, and modifications for English Language Learners (ELL) and other special populations that will support their regular and active participation in learning mathematics.

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

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

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

An example of ELL supports within the instructional materials:

  • In Lesson 6-4, Lesson Overview, English Language Learners, “Speaking: Read the Solve & Share problem. Ask students to think about the best way to solve the problem.
    • Emerging: Reread the problem. Ask: How could you use addition to count on from 9 to solve the problem? Have students discuss with a partner. Ask: How could you subtract the birds to solve the problem? Have students discuss with a partner. 
    • Developing: Reread the problem. Ask: How could you add to solve the problem? Have students discuss with a partner. Ask: How could you subtract to solve the problem? Have students discuss with a partner. 
    • Bridging: Reread the problem. Ask students to think about the best way to solve the problem, then turn and discuss with a partner.”

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

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

Indicator 3v

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

The instructional materials for enVision Mathematics Common Core Grade 1 meet the expectations for providing opportunities for advanced students to investigate mathematics content at greater depth.

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

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

Indicator 3w

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

​The instructional materials for enVision Mathematics Common Core Grade 1 meet the expectations for providing a balanced portrayal of various demographic and personal characteristics.

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

Indicator 3x

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

​The instructional materials reviewed for enVision Mathematics Common Core Grade 1 provide opportunities for teachers to use a variety of grouping strategies. The materials include teacher-led instruction presenting options for whole-group, small-group, partner, and/or individual work. When suggestions are made for students to work in small groups, no specific roles are suggested for group members, but teachers are given suggestions and questions to move learning forward.

Indicator 3y

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

​The instructional materials for enVision Mathematics Common Core Grade 1 encourage teachers to draw upon home language and culture to facilitate learning.

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

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

Criterion 3z - 3ad

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

​The instructional materials reviewed for enVision Mathematics Common Core Grade 1: integrate technology in ways that engage students in the Mathematical Practices; are web-­based and compatible with multiple internet browsers; include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology; can be easily customized for individual learners; and include or reference technology that provides opportunities for teachers and/or students to collaborate with each other.

Indicator 3z

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

​The instructional materials reviewed for enVision Mathematics Common Core Grade 1 integrate technology including interactive tools, virtual manipulatives/objects, and dynamic mathematics software in ways that engage students in the Mathematical Practices.

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

Indicator 3aa

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

​The instructional materials for enVision Mathematics Common Core Grade 1 include digital materials that are web-based and compatible with multiple internet browsers. 

Digital materials (either included as part of the core materials or as part of a digital curriculum) are web-­based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, Safari, etc.). In addition, materials are platform neutral (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow for the use of tablets and mobile devices including iPads, laptops, Chromebooks, MacBooks, and other devices that connect to the internet with an applicable browser.

Indicator 3ab

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

​The instructional materials for enVision Mathematics Common Core for Grade 1 include opportunities to assess students' mathematical understandings and knowledge of procedural skills using technology.

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

Indicator 3ac

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

The instructional materials for enVision Mathematics Common Core Grade 1 include digital materials with opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. Teachers can select and assign individual practice items for student remediation based on the Topic Readiness assessment. Teachers can create and assign classes online for students. An online Accessible Student Edition can be assigned to students. Closed Captioning is included in STEM and 3-Act Math videos.

The instructional materials reviewed for enVision Mathematics Common Core Grade 1 can be easily customized for local use. Digital materials provide the same lessons to draw from on a topic as the print materials. Teachers can create and upload files, attach links, and attach documents from Google Drive and assign them to students. Teachers can also create assessments using a bank of items or using self-written questions that can also be assigned to students.

Indicator 3ad

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

The instructional materials for Envision Mathematics Common Core Grade 1 include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.). There is a “Discuss” tab to assign discussion prompts to students in the “Classes” tab, and a file can also be attached.

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Additional Publication Details

Report Published Date: 01/07/2020

Report Edition: 2020

Title ISBN Edition Publisher Year
enVision Mathematics Common Core Grade 1 9780134959009 Digital Pearson Education 2020

About Publishers Responses

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

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

The publisher has not submitted a response.

Educator-Led Review Teams

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

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

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

Rubric Design

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

Advancing Through Gateways

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

Key Terms Used throughout Review Rubric and Reports

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

Math K-8 Rubric and Evidence Guides

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

For math, our rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

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

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

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

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

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

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

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

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

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

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

Math K-8

Math High School

ELA K-2

ELA 3-5

ELA 6-8


ELA High School

Science Middle School

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