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Report Overview
Summary of Alignment & Usability: Envision 2.0 | Math
Math K-2
The instructional materials reviewed for K-2 do not meet the expectation for alignment to the CCSSM. K-2 materials spend sufficient time on major work but do not meet expectations for coherence, scoring partial in Gateway 1. Grades K-2 were reviewed for rigor and mathematical practices in Gateway 2 and did not meet expectations.
Kindergarten
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
1st Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
2nd Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
Math 3-5
The instructional materials reviewed for 3-5 do not meet the expectation for alignment to the CCSSM. Third grade materials spend sufficient time on major work but do not meet expectations for coherence, scoring partial in Gateway 1. Grades 4 and 5 did not meet expectations for focus and coherence. Grade 3 was reviewed for rigor and mathematical practices in Gateway 2 and did not meet expectations.
3rd Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
4th Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
5th Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
Report for 3rd Grade
Alignment Summary
The instructional materials reviewed for Grade 3 did not meet the expectations for alignment to the CCSSM. The instructional materials partially meet the expectations for Gateway 1 as they appropriately focus on the major work of the grade but did not always demonstrate coherence within the grade and across other grades. The instructional materials do not meet the expectations for Gateway 2 as they did not fully address rigor within the grade-level standards, and there are missed opportunities in the materials when it comes to attending to the full meaning of the standards for mathematical practice.
3rd Grade
Alignment (Gateway 1 & 2)
Usability (Gateway 3)
Overview of Gateway 1
Focus & Coherence
The instructional materials reviewed for Grade 3 enVisions Math 2.0 partially meet the expectations for Gateway 1. The materials meet the expectations for focusing on the major work of the grade, but they do not meet the expectations for coherence. Some strengths were found and noted in the coherence criterion as the instructional materials partially met some of the expectations for coherence. Overall, the instructional materials allocate enough time to the major work of the grade for Grade 3, but the materials do not always meet the full depth of the standards.
Gateway 1
v1.0
Criterion 1.1: Focus
The instructional materials reviewed for Grade 3 meet the expectations for assessing grade-level content. Overall, the instructional materials can be modified without substantially affecting the integrity of the materials so that they do not assess content from future grades within the assessments provided.
Indicator 1A
The assessment materials reviewed for Grade 3 meet expectations for focus within assessment. Content from future grades was found to be introduced; however, above grade-level assessment items, and their accompanying lessons, could be modified or omitted without significantly impacting the underlying structure of the instructional materials.
Probability, statistical distributions, and/or similarity, transformations and congruence do not appear in the Grade 3 materials.
The series is divided into topics and each topic has a topic assessment and a topic performance assessment. Additional assessments include a placement test found in Topic 1, four cumulative/benchmark assessments, and a End-of-Year Assessment.
The assessments have items which assess future grade-level standards.
- Topic 1 topic assessment question 7 requires interpreting remainders (4.OA.3).
- In Topic 2 topic assessment, problems 4 and 11 have students identifying multiples of a number, a Grade 4 grade standard (4.OA.4), and question 13 requires interpreting remainders (4.OA.3).
- Topic 4 topic assessment questions 3 and 10 require interpreting remainders (4.OA.3).
- Topics 1-4 cumulative benchmark assessment problem 2 assesses multiples of a number, a Grade 4 standard (4.OA.4) and problem 22 assesses factors at the Grade 4 level (4.OA.4).
- Topics 1-8 cumulative benchmark assessment problem 6 assesses multiples of a number, a Grade 4 standard (4.OA.4).
- Topic 12 topic assessment question 5 includes improper fractions which is a Grade 4 standard.
- Topic 14 topic assessment problems 10, 11, 12, 13, 14 and 15 and performance assessment problems 1 and 3 assess knowing relative sizes within a measurement system, a Grade 4 standard (4.MD.1).
- Topic 15 topic assessment problem 4 and performance assessment problems 2, 3, 4 and 7 assess parallel lines, a Grade 4 standard (4.G.1).
- Topics 1-16 cumulative benchmark assessment problem 7 assesses the fraction 1/5, a Grade 4 fraction; problems 12 and 26 assess parallel lines, 4.G.1; and problem 21 assesses knowing relative sizes within a measurement system (4.MD.1).
- The end-of-year assessment problem 12 assesses knowing relative sizes within a measurement system (4.MD.1).
The off-grade level items could be removed without affecting the sequence of learning for the students or the mathematical integrity of the materials.
Notes:
- Topic 1 topic assessment question 3 does not require students to do any mathematics.
- Topic 1 includes basic facts timed tests but do not include directions on how or when to use them. Additionally, the addition and subtraction set do not go beyond 20, which is the Grade 2 fluency 2.OA.2.
Criterion 1.2: Coherence
The instructional materials reviewed for Grade 3 meet the expectations for focus on the major clusters of each grade. Students and teachers using the materials as designated will devote the majority of class time to major clusters of the grade.
Indicator 1B
The instructional materials reviewed for Grade 3 meet the expectations for focus within major clusters. Overall, the instructional materials spend the majority of class time on the major clusters of each grade.
To determine this, three perspectives were evaluated: 1) the number of topics devoted to major work, 2) the number of lessons devoted to major work, and 3) the number of days devoted to major work. The number of days is the same as the number of lessons. A lesson level analysis is more representative of the instructional materials than a topic level analysis because the number of lessons within each topic is inconsistent. and we drew our conclusion based on that data.
Grade 3 enVison Math 2.0 includes 16 topics with 110 lessons. At the topic level, ten of the 16 focus on major work. Two of the 16 focus on supporting work and are supporting the major work of the grade, and four of the 16 topics focus on supporting work without supporting the major work. Approximately 75 percent of the topics are focused on major work. As mentioned above, a lesson level analysis is more representative of the instructional materials than a topic level analysis because the number of lessons within each topic is inconsistent. At the lesson level 69 lessons focus on major work, 12 lessons focus on supporting work and continue major work of the grade, 20 lessons focus on the supporting work without connecting to the major work, and 9 lessons focus on off grade level topics. At the lesson level approximately 73 percent of the lessons focus on major work, approximately 18 percent of the lessons focus on supporting work, and approximately 8 percent of the lessons focus on off grade-level topics.
Criterion 1.3: Coherence
The instructional materials reviewed for Grade 3 do not meet the expectations for being coherent and consistent with CCSSM. The instructional materials do not have enough materials to be viable for a school year and do not always meet the depth of the standards. The majority of instructional materials do not have supporting content enhancing focus and coherence simultaneously but do have objectives which are clearly shaped by the CCSSM. Overall, the instructional materials for Grade 3 do not exhibit enough characteristics of coherence.
Indicator 1C
The instructional materials reviewed for Grade 3 partially meet expectations that supporting content enhances focus and coherence by engaging students in the major work of the grade. Some of the supporting work is treated separately and does not support the major work of the grade, and many natural connections are missed. The following details supporting work in the instructional materials.
- Topic 7 is focused on classifying data and somewhat supports the major work of the grade in multiplication.
- Topics 8 and 9 are focused on addition and subtraction within 1000 and are treated separately from the major work of the grade.
- Topic 10 is focused on multiplying by 10s and does support the major work of the grade.
- Topic 15 is focused on describing and comparing measurable attributes. This topic is treated separately and does not support the major work of the grade. In these supporting cluster lessons, students are not asked to partition shapes (3.NF.1).
- Topic 16 is focused on perimeter. About half the lessons are treated separately from major work, and about half support major work with area. Lessons 16.4, 16.5 and 16.6 connect to the major work of the grade (3.MD.C).
Indicator 1D
The amount of content designated for one grade level is not viable for one school year in order to foster coherence between grades. The pacing guide assumes one lesson per day as stated on page TP-23A. The enVison Math 2.0 Grade 3 program consists of 110 lessons, grouped in 16 topics. Assessments are not included in this count; if the 16 days of assessment are added in this would bring the count to 127 days. This is still below the standard school year of approximately 140-190 days of instruction. Significant modifications by the teacher would need to be made to the program materials to be viable for one school year.
Indicator 1E
The instructional materials reviewed for Grade 3 partially meet the expectations for being consistent with the progressions in the standards. Overall, the materials give students extensive work with grade-level problems and relate grade-level concepts explicitly to prior knowledge from earlier grades, but the materials do not reach the full depth of the standards and do not always clearly identify work that is off grade level.
Material related to future grade-level content is not clearly identified or related to grade level work. The exception is the topic titled "Step up to 4th grade" where the materials are clearly identified as Grade 4 materials. The Grade 3 materials have some instances where future grade-level content is present and not identified as such. For example, lessons 13-5, 13-6 and 13-8 focus on comparing fractions with different numerators and denominators (4.NF.2).
The content does not always meet the full depth of the standards. This occurs due to a lack of lessons addressing the full depth of standards. For example:
- Students learn multiplication facts for 0, 1, 2, 5, 9 and 10 in 5 lessons in Topic 2. There are eight lessons to learn multiplication facts for 3, 4, 6, 7 and 8.
- 3.OA.8 has four lessons addressing two-step problems using the four operations, lessons 11-1 to 11-4.
- When looking at 3.NF.A, developing an understanding of fractions as numbers, there are thirteen lessons, and three of those lessons focus on fractions and the number line.
- Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects are major work of third grade, but in these materials, these topics are taught at the end of the year in 9 lessons in Topic 14.
The materials extensively work with grade-level problems, for example:
- All students complete grade-level materials, and suggestions for re-teaching and intervention are included with each lesson and at the end of each topic.
- Online resources include extra, on-level and advanced-practice materials.
- A mathematics and science project is available for each topic taught.
- Homework practice problems are identified in the teacher edition as intervention, on-level, and advanced.
- The numbers of topics focusing on Grade 3 domains are as follows: 3 out of 16 topics address number and operations in base ten; 2 out of 16 topics address number and operations - fractions; 6 out of 16 topics address operations and algebraic thinking; 4 out of 16 topics address measurement and data; and 1 out of 16 topics address geometry.
The materials relate grade-level concepts to prior knowledge within the introduction of each topic, for example:
- "Math Background: Coherence" includes "Look Back" and "Look Ahead" commentary, connecting to mathematics that came earlier in Grade 3, explaining connections to the content within the topic, and explaining what will come later in Grades 3 and 4. An example can be found on pages 605c-605d for Topics 12 and 13.
- Individual lessons also include coherence headings. An example is in lesson 12-1 on page 609A that includes the heading, "Coherence: In this lesson, students extend the work they did in Topic 6 with unit squares and area as they begin more extensive work with fractions as numbers. The lesson explores...".
- In lesson 3.1, for 3.OA.5, students extend their multiplication knowledge by splitting arrays into two smaller arrays to write equations and explore the distributive property.
- In lesson 7.1, for 3.MD.3, the connection to multiplication when using scaled bar graphs is made.
Indicator 1F
The instructional materials reviewed for Grade 3 partially meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards. Overall, the materials include learning objectives that are visibly shaped by CCSSM cluster headings, but the materials lack problems and activities that connect two or more clusters in a domain or two more domains in the grade.
The materials are designed at the cluster level, and this design feature is represented throughout the material in the form of a color-coded wheel identifying the cluster focus of each unit. The materials include learning objectives which are visibly shaped by CCSSM cluster headings, and the Topic Planner at the beginning of each topic has an example of this.
- The focus of Topic 14 is 3.MD.A: Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. Lesson objectives in Topic 14 include: L3 - Solve word problems involving addition and subtraction to measure quantities of time, L4 and L5 - Use standard units to estimate liquid volume, and L6 - Use standard units to estimate the masses of solid objects.
- A similar example for Topic 12 can be found on pages 605I - 605K.
The materials for Grade 3 enVision Math 2.0 do not foster coherence through grade-level connections. Most lessons in the Grade 3 program focus within a single domain and cluster. Of 110 lessons, 76 lessons focus within a single cluster and domain.
- In Topic 1, 1 of the 7 lessons addresses standards within two clusters (3.OA.A and 3.OA.B).
- In Topic 2, 5 of the 6 lessons address standards in two or more clusters (3.OA.A, 3.OA.B, and 3.OA.D).
- In Topic 3, 6 of the 8 lessons address standards in two or more clusters (3.OA.A, 3.OA.B, and 3.OA.D).
- In Topic 4, 8 of the 9 lessons address standards in two or more clusters (3.OA.A, 3.OA.B, and 3.OA.D).
- In Topic 5, 5 of the 8 lessons address standards in two or more clusters (3.OA.A, 3.OA.C, and 3.OA.D).
- In Topic 6, 0 of the 7 lessons address standards in two or more clusters.
- In Topic 7, 5 of the 5 lessons address standards in two or more domains (3.OA and 3.MD).
- In Topic 8, 0 of the 9 lessons address standards in two or more clusters.
- In Topic 9, 0 of the 8 lessons address standards in two or more clusters.
- All of the 4 lessons within Topic 10 are within a single cluster and domain.
- All of the 4 lessons within Topic 11 are within a single cluster and domain.
- In Topic 12, 2 of the 8 lessons address standards in two domains (3.NF and 3.G).
- All of the 8 lessons within Topic 13 are within a single cluster and domain.
- All of the 9 lessons within Topic 14 are within a single cluster and domain.
- All of the 4 lessons within Topic 15 are within a single cluster and domain.
- In Topic 16, 2 of the 6 lessons address standards in two clusters (3.MD.C and 3.MD.D).
Overview of Gateway 2
Rigor & Mathematical Practices
The instructional materials reviewed for Grade 3 do not meet the expectations for rigor and practice-content connections. The instructional materials partially meet the expectations for rigor and balance with spending sufficient time on engaging applications being especially strong. The instructional materials do identify the MPs and give students opportunities to construct viable arguments, but they do not always use the MPs to enrich the mathematics content and rarely have students critique the reasoning of other students. The materials do not attend to the full meaning of each MP and partially assist teachers in engaging students in constructing viable arguments and analyzing the arguments of other students. The materials meet the expectations for attending to the specialized language of mathematics.
Gateway 2
v1.0
Criterion 2.1: Rigor
The instructional materials reviewed for Grade 3 do not meet the expectations for rigor and practice-content connections. The instructional materials partially meet the expectations for rigor and balance with spending sufficient time on engaging applications being especially strong. The instructional materials do identify the MPs and give students opportunities to construct viable arguments, but they do not always use the MPs to enrich the mathematics content and rarely have students critique the reasoning of other students. The materials do not attend to the full meaning of each MP and partially assist teachers in engaging students in constructing viable arguments and analyzing the arguments of other students. The materials meet the expectations for attending to the specialized language of mathematics.
Indicator 2A
The instructional materials reviewed for Grade 3 enVision Math 2.0 partially meet the expectations for giving attention to conceptual understanding. The materials sometimes develop conceptual understanding of key mathematical concepts where called for in specific content standards or cluster headings.
Most of the lessons in the materials have students filling out student pages in a very procedural manner. Rarely do the materials feature high quality conceptual problems or conceptual discussion questions. Some of the lessons start with a problem which could develop conceptual understanding; however, the lessons quickly transition to simply filling out the pages in the student book. For example, lesson 1-1 begins with the question "Ms. Witt bought 3 boxes of paint with 5 jars of paint in each box. What is the total number of jars Ms. Witt bought?" Students are given time to solve this; however, instead of spending time exploring this concept, the lesson quickly moves to filling out pages in the student book in a prescribed manner. In lesson 3-3, the standard is to understand properties of multiplication and the relationship between multiplication and division. The opening question is a good question if students were given time to explore; however, students are quickly immersed into the pages in the student book and a procedure. In lesson 4-2, the standard is to understand properties of multiplication and the relationship between multiplication and division; however, instead of students exploring the conceptual understanding, students are simply doing a procedure using fact families.
Standards 3.OA.1 and 3.OA.2 focus on representing and solving problems involving multiplication and division and understanding properties of multiplication and the relationship between multiplication and division.
- Eleven lessons are focused specifically on 3.OA.1 and 3.OA.2. Lessons 1.1, 1.2, 1.3, 1.5, 1.6, 1.7, 2.1, 2.2, 2.3, 2.4 and 2.5 specifically address standards which are explicitly outlined as conceptual standards.
- In Lesson 1.1 students use counters to create arrays to show the relationship between repeated addition and multiplication. However, students get very little time to really explore the connection between repeated addition and multiplication before the lesson transitions into more procedural type problems in the student book.
- In Lesson 1.2, students use number lines as a way to represent multiplication.
- In lesson 1.4, students draw arrays using the same number of counters and write the corresponding equations to demonstrate understanding of the commutative property of multiplication.
- In lesson 1.5 students use counters and drawings to show equal groups and represent division as sharing.
- In lesson 1.6 students use counters and pictures to show division as repeated subtraction.
- Topic 2 begins each lesson with a problem or two to develop conceptual understanding, but the topic is really focused on patterns, not conceptual understanding. The title of the topic is “Multiplication Facts: Use Patterns.” For example, in lesson 2-2 students use patterns to multiply by 9.
Cluster 3.NF.A focuses on developing understanding of fractions as numbers.
- Cluster 3.NF.A is the focus of Lessons 12-1 thru 12-5, Lesson 12-8, and Topic 13.
- Lesson 12-1 is the first lesson addressing 3.NF.1. Page 609A of the teacher edition explains that “The lesson explores the basic idea of a fraction and a unit fraction. Knowing what makes up a fraction -- the numerator and the denominator -- helps students understand the concept of number of equal parts and total number of equal parts.” Lesson 12-5 focuses on number lines and fractions greater than 1. On page 633A in the teacher’s edition, the rigor portion states “Some students may find it challenging to consider a number greater than 1 as a fraction. However, if students keep in mind that a fraction is made up of a numerator and a denominator, either of which can be the greater number, they should have few problems remembering that fractions can represent numbers greater than 1 as well as numbers less than 1.” Careful attention should be paid to ensure that students are not given only these descriptions of fractions. Standard 3.NF.1 clearly states that students should understand a fraction 1/b as the quantity formed by 1 part when a whole is portioned into b equal parts and understand a fraction a/b as the quantity formed by a parts of size 1/b.
- Lesson 12.1 jumps quickly into representing fractions in numerical form and using numerator/denominator vocabulary; students may need more time to develop concept of equal parts, partitioning, and using fractional unit vocabulary.
- In Lesson 12-5, students are representing fractions greater than 1 on a number line. The pages in the student book all provide number lines with some fractions already filled in making it difficult to determine if students have truly understood the concept.
There are some interventions that encourage the development of conceptual understanding; however, these interventions are not meant for all students, only those not meeting the standard.
- For example, in lesson 1-1 students in the intervention activity are actually using counters to make equal groups instead of just being shown a picture in the lesson.
- In the lesson 1-3 intervention students are using graph paper to make arrays.
- In the lesson 1-4 intervention students explore the Commutative Property using color-counters.
- On page 203A in the teacher edition students explore division using color-counters.
- On page 323A, the intervention for teaching area gets more to the concept than the one problem on page 320 in the student edition that shows that it is the square units in the square or rectangle.
Indicator 2B
The materials partially meet the expectations for procedural skill and fluency by giving limited attention throughout the year to individual standards, which set an expectation of procedural skill and fluency. The majority of the lessons are done in a very procedural manner.
Fluency practice activities do not always focus on Grade 3 fluencies. For example, the fluency practice activity on page 49 in Topic 1 addresses addition and subtraction within 20; this is a Grade 2 fluency. The fluency practice activity on page 97 in Topic 2 addresses addition within 100; this is a Grade 2 fluency. The fluency practice activity on page 157 in Topic 3 addresses subtraction within 100; this is a Grade 2 fluency.
3.OA.7 is fluently multiplying and dividing within 100, using strategies such as the relationship between multiplication and division or properties of operations. By the end of Grade 3, students should know from memory all products of two one-digit numbers.
- Only 1 lesson deals with division, 5-7, and one lesson, 5-4, has both division and multiplication.
- Six lessons are multiplication and align to 3.OA.7.
- Fluency Practice Activities aligned to 3.OA.7 are found at the end of Topics 5-8, 11, 13 and 15. These activities are all either "Point & Tally," “Follow the Path,” or "Find a Match" activities. These seven pages are found at the end of each topic, not within a lesson, so teachers would have to intentionally incorporate these activities into the lessons. Also, the activities often focus on multiplication and division separately. In Topic 5 on page 285, the activity focuses only on multiplication within 100. In Topic 6 on page 343, the activity focuses only on division. In Topic 7 on page 389, the activity focuses only on multiplication. In Topic 8 on page 459, the activity focuses only on division.
- Six Fluency Practice/Assessment pages in the student book aligned to 3.OA.7 are included in the instructional materials. These pages in the student book can be seen on page 71 of the teacher's edition. These pages in the student book each have 25 problems.
3.NBT.2 is fluently adding and subtracting within 1,000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
- 3.NBT.2 is addressed in Topics 8 and 9.
- In Topic 8 students learn concepts and procedures to add and subtract.
- Topic 9 focuses on fluency with addition and subtraction within 1,000. Although two lessons focus on using partial sums to add and subtract, in most of the lessons in this topic students learn and use the standard algorithm for addition and subtraction.
- Fluency practice activities aligned to 3.NBT.2 are found at the end of Topics 9, 10, 12, 14 and 16. These activities are all either "Point & Tally," “Follow the Path,” or "Find a Match" activities. These five pages are found at the end of each topic, not within a lesson, so teachers would have to intentionally incorporate these activities into the lessons. Also, the activities sometimes focus on addition and subtraction separately. In Topic 9 on page 523, the activity focuses only on addition within 1,000. In Topic 14 on page 793, the activity focuses only on subtraction within 1,000.
Page 235M in the teacher's guide outlines the framework for assessing, providing practice and intervention, and providing summative assessment information at the end of the year to check mastery of fluencies. There are also resources for students to self-monitor and track their own growth for multiplication mastery.
The Game Center at PearsonRealize.com provides online mathematics games to help build fluency. There is one game for multiplication and division fluency and one for addition and subtraction fluency.
Indicator 2C
Materials are designed so that teachers and students spend time working with engaging applications of the mathematics, without losing focus on the major work of each grade.
In the materials application is limited to word problems. Daily Spiral Review, lesson openers, guided/independent practice questions, and homework include word problems. In addition, a full range of question types is found, especially in the guided practice/problem solving workpages and homework. However, many of the problems do not require the context; the numbers can be pulled out of the problem and solved by using key words, a strategy included in the instructional materials.
Most topics have at least one lesson designated application. For example, lesson 8-9 page 453A has word problems that require students to add and subtract within 1,000.
3.OA.3 is using multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities. Topics 1, 2, 3, 4, 5 and 7 include lessons aligned to 3.OA.3, and word problems are found throughout these topics. For example, in Topic 1 students begin to build their understanding of multiplication and division of whole numbers. Each lesson includes word problems, and the final lesson of the topic, Lesson 1-7, provides more complex word problems.
Topic 11 is aligned to 3.OA.8 which requires students to solve 2-step problems using the four operations. There are four lessons in Topic 11; one lesson is devoted to addition and subtraction, one lesson to multiplication and division, and two lessons have a mixture of the four operations.
Indicator 2D
The Grade 3 enVision Math 2.0 instructional materials partially meet the expectations for balance. Overall, the three aspects of rigor are neither always treated together nor always treated separately within the materials, but a balance of the three aspects of rigor within the grade is lacking.The majority of the lessons are very procedural. However, the fluency of facts is not thoroughly addressed, and division fluency is only given two lessons in the materials, one of which is shared with multiplication. Application is found throughout the materials. Most lessons only focus on one aspect of rigor at a time, and there are many missed opportunities to connect the different aspects of rigor.
Criterion 2.2: Math Practices
The instructional materials reviewed for Grade 3 do not meet the expectations for practice-content connections. The materials meet the expectations for attending to the specialized language of mathematics. The materials partially meet the expectations for attending to indicators 2e, 2gi, and 2gii, but they do not meet expectations for 2f. Overall, in order to meet the expectations for meaningfully connecting the Standards for Mathematical Content and the MPs, the instructional materials should carefully pay attention to the full meaning of each MP, especially MP3 in regards to students critiquing the reasoning of other students and giving teachers more guidance for implementing MP3.
Indicator 2E
The materials partially meet the expectations for identifying the MPs and using them to enrich the mathematics content within the grade. Overall, the MPs are identified and used in connection to the content standards, but the materials do not always use the MPs to enrich the mathematics content. In the materials, the MPs are over-identified, and the connections between the MPs and the content standards are not clear.
According to the teacher overview, the MPs are identified as follows:
- MP 1: approximately 75 lessons.
- MP 2: approximately 75 lessons.
- MP 3: approximately 90 lessons.
- MP 4: approximately 70 lessons.
- MP 5: approximately 35 lessons.
- MP 6: approximately 50 lessons.
- MP 7: approximately 50 lessons.
- MP 8: approximately 40 lessons.
The total number of lessons identified for the 8 MPs is approximately 485, with 110 lessons total in the materials, so this would lead to approximately 4 to 5 MPs per lesson. With this many practices identified in each lesson, there are many times when the entire meaning of the MP is not evident in the lesson, which leads to students not being able to develop a complete understanding of the MP and its connection to the grade-level content.
- In Topic 12, Lesson 8 cites that MP1, "Make sense and persevere," is the focus MP and 3.NF.1 is the content objective. The lesson focuses on students working to figure out which information from a word problem is necessary to solve. It doesn't enhance the understanding of 3.NF.1.
- In Topic 8, Lesson 1 cites MP8, "Generalize Listen and look for students who correctly ... regardless of the order of the numbers." The meaning of MP8 is not evident in the "Solve & Share" item because students ultimately are using the associative and commutative properties of addition to answer a question, and by using the properties, the students are engaging in MP7, "Look for and make use of structure."
- The directions to help teachers make connections are often vague. For example, lesson 12-6 cites MP1 but does not give teachers any guidance on how to help students make sense of the problem or persevere.
The Math Practices and Problem Solving Handbook in the front of the teacher's edition is a resource for understanding the MPs and knowing what to look for in student behaviors. For example, page F23A lists six indicators to assess MP3, "Listen and look for the following behaviors to monitor students' ongoing development of proficiency with MP3." A proficiency rubric is also included.
Indicator 2F
The instructional materials reviewed for Grade 3 do not meet the expectations for carefully attending to the full meaning of each practice standard. Overall, the materials do not treat each MP in a complete, accurate, and meaningful way.
The lessons give teachers very little guidance on how to implement the MPs, and many of the MPs are misidentified in the materials. Also, the materials often do not attend to the full meaning of some of the MPs.
- MP1: Lesson 8-3 cites MP1; helping students understand the only possible answer does not get the student to make sense and persevere in problem solving. Lesson 8-5 cites MP1; telling the students two ways to subtract numbers mentally is not having them make sense or persevere in problem solving. Lesson 9-2 cites MP1; however, a rich problem is not included for the students to make sense of and persevere in problem solving.
- MP4: Lesson 8-4 cites MP4; however, telling students how to model their problems does not meet the intent of the MP. Lesson 8-9 cites MP4, but the lesson tells students how to model their problems. Lesson 9-4 cites MP4; the problem instructs the students to write an equation as a model. Equations are appropriate mathematical models; however, telling the students which model to use does not meet the intent of the MP.
- MP5: Lesson 9-1 cites MP5; however, giving the students the tool to use does not meet the intent of the MP. Lesson 9-6 cites MP5, and the lesson tells the students which tools to use. Lesson 10-3 cites MP5; however, asking students which of two tools they would use to solve a problem and to explain why is not meeting the intent of students choosing their own tools and solving problems with the tools.
- MP7: Lesson 9-5 cites MP7; telling students to break the problem into two smaller problems is not the students using structure to solve problems. Lesson 9-8 cites MP7; telling the students that since both of the boys set different goals means they need a different amount of minutes to reach their goals is not having the students use structure to solve problems. Lesson 13-1 cites MP7; however, the students are told what to look at and are not seeing and using the structure on their own.
Indicator 2G
Indicator 2G.i
The materials partially meet the expectation for prompting students to construct viable arguments and analyze the arguments of others. Although the materials at times prompt students to construct viable arguments, the materials miss opportunities for students to analyze the arguments of others, and the materials rarely have students do both together. In most lessons, when students explain their thinking, the explanations are directed by the teacher and are not independent student thinking.
MP3 is identified 90 times in the student edition. In many of the places where MP3 is identified, the students are not attending to the full meaning of the MP. For example, "What You Write" in lesson 13-4 on page 692 cites MP3, however students read an already-written argument and are not asked to either create an argument or analyze the argument already given. Additional examples of not attending to the full meaning of the MP can be found in the following lessons: 2-1, 3-3, 4-2, 5-5, 8-4, 9-7, 10-1, 12-5, 13-6, 14-2, 15-3 and 16-4.
Examples of opportunities to construct viable arguments but not analyze the arguments of others:
- In lesson 9-8, students are asked to create an argument explaining whether addends in a different order would have a sum greater than, less than, or equal to the original sum.
- In lesson 12-4, students construct an argument for approximately locating 2/3 if they know where the point for 1/3 is located.
- In lesson 13-8, students must explain if the two fractions they wrote are equivalent.
- In Topic 9, performance assessment question 5B asks students to explain how they determined the number of green tokens used.
- In Topic 12, performance assessment question 4 asks students to explain what fraction represents a whole cake.
- In Topic 13, performance assessment question 6 asks students to construct an argument to justify a given conjecture.
Examples of opportunities to analyze the arguments of others.
- Topic 8, item 17 on page 420. Zoe says 247 rounded to the nearest hundred is 300 because 247 rounds to 250 and 250 rounds to 300. Is Zoe correct? Explain.
- Topic 10, "Solve & Share" on page 545. Three students found 5 X 30 in different ways. Which student is correct? Explain.
- Topic 13, "Convince Me!" on page 692. Julia says 1/8 is greater than 1/4 because 8 is greater than 4. Is she correct? Explain.
Indicator 2G.ii
The instructional materials reviewed for Grade 3 partially meet the expectations for assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards. Usually questions have one correct answer, and there is not much guidance for teachers on how to lead discussions beyond the provided questions. There are many missed opportunities to guide students in analyzing the arguments of others.
Teacher materials sometimes prompt students to have discussions.
- In Lesson 13-2 on page 680 of the TE, the teacher is instructed to ask questions about comparing fractions.
- In Lesson 14-1 on page 740 of the TE, the teacher is instructed to ask students about the hour hand.
- In Lesson 15-2 on page 818 of the TE, students must draw a quadrilateral and explain their reasoning about why it doesn’t fit in a group. Teachers are encouraged to have students come to the board, share their drawings, and explain their reasoning.
Indicator 2G.iii
The Grade 3 instructional materials explicitly attend to the specialized language of mathematics. The vocabulary words are taught and worked with at the beginning of each topic and, again, at the very end of the topic. The assumption is that Grade 3 students will remember all words from the beginning of the topic and will not need them reintroduced before they are used in a lesson.
- Each lesson includes a list of important vocabulary in the topic organizer which can be found at the beginning of each topic.
- Each topic opener has a vocabulary review activity, and each topic ends with a vocabulary review activity. However, there isn't any direction on how or when to use the activities.
- There is an online game for vocabulary, Save the Word.
- Student edition contains a mathematical vocabulary glossary.
- Online animated glossary in Spanish and English.
- “My Word Cards” is a set of mathematical language flash cards available for each Topic in the student edition.
- Students must use precise language in lesson 8.1 when talking about the addition properties.
- Reteach pages in the student book contain a vocabulary section of questions (i.e, 8-3, 12-3 and 14-3)
- Vocabulary questions are in the independent practice (SE page 588).