Alignment: Overall Summary

The instructional materials reviewed for Math Expressions 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 the materials connect 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
16
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
38
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 Math Expressions Grade 2 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 Math Expressions Grade 2 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.

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 Math Expressions Grade 2 meet expectations that they assess grade-level content.

The materials provide an Assessment Guide for summative assessments. Within the Assessment guide there is a Prerequisite Skills Inventory Test and Beginning of Year Test. Each of the assessments contain a correlations document between standard and question number. Within each Unit, there is a Test Form A and Test Form B with a correlations document, and a Performance Assessment with a grading rubric and sample student responses. A Middle of Year Test is located at the end of Unit 4 and an End of Year Test at the end of Unit 8, contain correlation documents. Additionally, the Student Activity Book contains Unit Quick Quizzes and Unit Reviews.

Assessment items containing grade level content include, but are not limited to:

  • Unit 3, Form A, Question 7 states, “Estimate the length of the key in inches. Write your estimate. Measure the key to the nearest inch. Circle the actual measure.” (2.MD.1 and 2.MD.3)
  • Unit 4, Form A, Question 9 states, “Jasmine, Marcus, and Ian bring cans of food to school. Jasmine brings 22 cans. Marcus brings 13 more cans than Jasmine. Ian brings 15 fewer cans than Marcus. How many cans does Ian bring?” (2.OA.1)
  • Unit 7, Form A, Question 6 states, “Draw lines in each shape to make equal shares.” Students are given squares and circles and partition into halves, thirds, and fourths. (2.G.3)

Some above grade-level assessment item are included, but could be modified or omitted without a significant impact on the underlying structure of the instructional materials. Assessment items containing above grade-level content include:

  • Beginning of Year Test, Question 25 states, “Write the total amount of money. Jaden has 1 dollar, 1 quarter, 2 dimes, and 3 pennies.” The answer is in decimal format (4.MD.2).

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 Math Expressions Grade 2 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 at least 65 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 Math Expressions Grade 2 meet expectations for spending a majority of instructional time on major work of the grade.

  • The approximate number of units devoted to major work of the grade (including assessments and supporting work connected to the major work) is 7 out of 7, 100%.
  • The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 96 out of 99, approximately 97%.
  • The number of days devoted to major work (including assessments and supporting work connected to the major work) is 148 out of 153, approximately 97%.

A number of days level analysis is most representative of the instructional materials because some lessons require two days of instruction. As a result, approximately 97% 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 Math Expressions Grade 2 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 Math Expressions Grade 2 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Supporting standards/clusters are connected to the major work of the grade. In the Teacher Edition, the Day at a Glance for each lesson contains a bubble identifying the mathematical content standards and mathematical practices covered in the lesson, and can include connections between supporting and major work.

Examples include, but are not limited to:

  • In Unit 3, Lesson 6, students estimate the heights of students, measure actual heights of students, and use the data to create a line plot. This connects supporting standard represent and interpret data (2.MD.9) to the major work of measure and estimate length (2.MD.1 and 2.MD.3).
  • In Unit 4, Lesson 10, students view five items of different prices and choose the correctly priced item to complete the problem, “I have 162 cents in my pocket. I buy the _________. I have ________ cents left.” This connects supporting standard work with time and money (2.MD.8) to the major work of add and subtract within 1000 (2.NBT.7).
  • In Unit 5, Lesson 3, students work in a group and are given 8 pennies (Maya), 5 pennies (Anthony), and 2 pennies (Sona). As a group, students create a graph on their MathBoards. Students answer the following questions, “Who has the most pennies? Who has the fewest pennies? How many more pennies does Maya have than Anthony? How many fewer pennies does Anthony have than Maya?” This connects the supporting standard draw a picture and bar graph (2.MD.10) to the major work of use addition and subtraction within 100 to solve problems (2.OA.1).

Indicator 1d

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

Instructional materials for Math Expressions Grade 2 meet expectations that the amount of content designated for one grade-level is viable for one year.

As designed, the instructional materials can be completed in 142 days. The Pacing Guide can be found on page I18 in the Teacher Edition. 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.

  • There are 99 lessons, and most lessons require one day of instruction.
  • The Pacing Guide notes lessons that may take two days, but this is not noted in the Day at a Glance for each lesson.
  • All seven units designate two days for Unit Assessments.
  • Unit 1 designates one day for the Prerequisite Skills Inventory Test.
  • Units designate 2-4 days for Quick Quizzes/Fluency Checks in the Students Activity Book for each Big Idea.

Materials indicate a teacher will need to spend more than 60 minutes providing math instruction daily. Teaching the lesson is comprised of several activities with an estimated time equating to 60 minutes.

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 for Math Expressions Grade 2 meet expectations for the materials being consistent with the progressions in the Standards.

The instructional materials clearly identify content from prior and future grade-levels and use it to support the progressions of the grade-level standards. The Teacher Edition (page I19) states, “Standards are designed around coherent progressions from grade to grade. Standards are not stand alone events; they form cohesive links to major work within and across grade levels.” In the Teacher’s Edition (page I12) there is a chart, A Path to Fluency: Kindergarten through Grade 6 to “help students achieve fluency as described in the Common Core State Standards.” Each unit contains a Math Background section referencing the progressions in text boxes, and how they relate to work of the grade. Each Unit Overview section lays out how the progression of the grade moves towards standards in future grades. Examples of grade level progressions include, but are not limited to:

  • Teacher Edition, Unit 4, Unit Overview, the text box states, “In Grade 2, children will compute sums and differences within 1000 using place value. In Grade 3, children will build or maintain fluency for addition and subtraction within 1000.”
  • Path to Fluency, TE page I12, the chart notes in Grade 2 students, “Fluently add and subtract within 20 using mental strategies. By end of Grade 2 know from memory all sums of two one-digit numbers (2.OA.2).” In Grade 3 students, “Fluently multiply and divide within 100. By the end of Grade 3, know from memory all products of two one-digit numbers.” (3.OA.7)
  • Unit 2, Lesson 7, Addition-Show All Totals Method; and Lesson 8, Addition-New Groups Below Method, students progress from drawing models to add 2-digit numbers to connecting the models to two new methods including, “show all totals” and the “new groups below” methods. Both methods are consistent with the Grade 2 Progressions Document. These methods are continued and applied to 3-digit numbers in Unit 6.

The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. The structure of the Math Expressions program provides a variety of learning opportunities for students to master the grade-level curriculum and provide extensive work with grade-level problems. Knead Knowledge through Practice ensures students gain understanding and fluency with desired methods. Daily Routines, Quick Practice, Student Practice pages, Homework practice, Remembering pages, and Math Activity Centers support the classroom learning in every lesson. Some instances are evident where the full intent of the standard is not met, and there are some lessons that would need to be omitted as they attend to future grade standards.

Examples of materials meeting full intent of the standards include, but are not limited to:

  • Unit 1, Lesson 20 includes a Math Activity Center for on-level, challenge, and intervention work. On-Level Resources include Activity Card 1-20 which has students solve a word problem containing extra information. Challenge Resources include Activity Card 1-20 which has students solve a two-step word problem. Students needing intervention complete Activity Card 1-20 which has students solve a word problem (2.OA.1).
  • Unit 4, Daily Routines, the student leader points to a projected group of pennies and asks the students, “Each group of pennies shows the number of pennies in one dollar. How many pennies are in each dollar? How do you know? We are going to count these hundreds to find out how many pennies in all.” (2.NBT.2)
  • Unit 6, Lessons 3 through 8, Quick Practice, students use place value to add 100 to or subtract 100 from any 3-digit number. For example, “329 + 100 = and 957 - 100 =.” (2.NBT.8)

Instances where full intent of the standard is not met:

  • Two lessons in Unit 7 (Lessons 3 and 5) address standard 2.MD.6, relate addition and subtraction to length. No additional work to this standard is found in Daily Routines or Quick Practice.

Some lessons would need to be omitted as they attend to future grade standards. For example:

  • In Unit 2, Lesson 11, students are introduced to dollar notation with a decimal point and are expected to write money amounts using decimals. According to the progressions, decimals should not be introduced until Grade 4 (4.NF.6) and this is not explicitly stated as future content. Subtraction problems with decimal notation are also found in the Student Activity Book.
  • In Unit 6, Lesson 6, students solve 3-digit addition computations with a variety of strategies. The “New Groups Above Method” is the standard algorithm (4.NBT.4) and is not clearly identified as future grade level content.

The instructional materials relate grade-level concepts explicitly to prior knowledge from earlier grades. Learning paths are identified at the beginning of each unit that relate grade-level concepts to prior knowledge from earlier lessons. Examples where content is connected to prior grades includes, but is not limited to:

  • Teacher Edition, Unit 2, Learning Path in the Common Core Standards, the author states, “Relate Addition and Subtraction: Diagrams used in Grade 1 to show how quantities in the situation are related continue to be useful in Grade 2, and students continue to relate the diagrams to situation equations. Such relating helps students rewrite a situation equation like, __ - 38 = 49 as 49 + 38 = ___.”
  • Teacher Edition, Unit 3, Learning Path for Measurement, the author states, “Grade 2 length measurement with rulers begins the formal use of measurement tools that use a length scale in which numbers indicate the total number of unit lengths from the zero of the scale. Such length scales are number-line diagrams that are also used as bar graph scales and as scales on a line plot (dot plot).” The author cites two National Research Council reports which “recommend that work with such scales not begin before Grade 2 because of the conceptual difficulties described above in using such scales: Many students count the numerals on the scale rather than seeing and counting the length units. To overcome this difficulty, Math Expressions emphasizes marking and counting the length units. Initially, children draw marks to show the length units on things they are measuring, and then they count these length units. Through such activities, they mathematize length as consisting of small units of the same size that compose the total length....[D]rawing and then counting of the length units also helps children extend the work they did in earlier grades with seeing different kinds of measurement units for different kinds of measures. This is the basis for future work with other units: square units compose and are counted to make an area (initially of rectangles), and cubes compose and are counted to make volumes (initially of rectangular prisms).”
  • Teacher Edition, Unit 4, Relating Addends to Subtraction, Lessons 3 and 4, the author states, “children use their mathematical understanding of the relationship between finding an unknown addend and subtracting. They may use drawings or methods that they learned in Grade 1. These lessons prepare the children for the more formal introduction of methods of subtracting in Lesson 5.”

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 for Math Expressions Grade 2 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the Standards.

The instructional materials foster coherence through connections at a single grade, where appropriate and required by the Standards. Overall, the materials include learning objectives visibly shaped by CCSSM cluster headings, and provide problems and activities connecting two or more clusters in a domain or two or more domains when the connections are natural and important. ​

Examples where materials include learning objectives visibly shaped by CCSSM cluster headings include, but are not limited to:

  • Each unit is broken into several “Big Ideas” shaped by the CCSSM cluster headings. For example, Unit 6, 3-digit Addition and Subtraction, contains four Big Ideas:
    • Big Idea 1: Understanding Numbers to 1,000 is shaped by 2.NBT.A: Understand place value.
    • Big Idea 2: Adding to 1,000 is shaped by 2.NBT.B: Use place value understanding and properties of operations to add and subtract.
    • Big Idea 3: 3-Digit Subtraction is shaped by 2.NBT.B: Use place value understanding and properties of operations to add and subtract.
    • Big Idea 4: 3-Digit Addition and Subtraction is shaped by 2.NBT.B: Use place value understanding and properties of operations to add and subtract.
  • The Teacher Edition Planning Chart for each unit identifies the Big Ideas, CCSSM Domains, Clusters, and Standards for each lesson.
  • Unit 3, Big Idea 2, is designed around Grade 2 cluster 2.MD.A: Measure and estimate lengths in standard units. For example, in Lesson 7, students estimate and measure to the nearest inch. Students also estimate to the nearest foot (2.MD.1 and 2.MD.3).

Examples of connections between clusters and/or domains include, but are not limited to:

  • Unit 7, Lesson 7, connects Operations and Algebraic Thinking Clusters 2.OA.B: Add and Subtract within 20, and 2.OA.C: Work With Equal Groups of Objects to Gain foundations for multiplication. Students practice finding “unknown partners” as they solve, add to situations with with the change unknown, and put together/take apart problems with one addend unknown.
  • Unit 5, Lessons 4 through 10, connects 2.MD.B: Relate Addition and Subtraction to Length, to 2.OA.A: Represent and Solve Problems Involving Addition and Subtraction. Students have opportunities throughout the unit to use the data from graphs to solve word problems. For example, Homework and Remembering page 146, students use the picture graph of the number of crayons to answer the problem, “Five of Yoko’s crayons are new. The rest of her crayons are old. How many are old?”
  • Unit 7, Lesson 3, connects 2.NBT.B: Use Place Value Understanding and Properties of Operations to Add and Subtract, to 2.MD.B: Relate Addition and Subtraction to Length. Students solve word problems involving length by adding two- and three-digit numbers together.

Gateway Two

Rigor & Mathematical Practices

Meets Expectations

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Gateway Two Details

The instructional materials reviewed for Math Expressions Grade 2 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 partially 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 Math Expressions Grade 2 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 Math Expressions Grade 2 meet expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

Materials include problems and questions that develop conceptual understanding and provide opportunities for students to independently demonstrate conceptual understanding throughout the grade where called for in the standards. The Teacher Edition page vii states, “Through using objects, drawings, conceptual language, and real-world situations, students build mathematical ideas that make sense to them.”

Materials utilize MathBoards (laminated boards) for students to make their own drawings to communicate their conceptual understanding. Students have access to iTools to model conceptual understanding. Math Talk activities provide “frequent opportunities for students to explain their mathematical thinking and to ask questions of other explainers deepens their understanding of concepts.” Additionally, "What’s The Error?" activities with the Puzzled Penguin provide students the opportunity to identify errors, discuss why it is incorrect, and how to correct it. Finally, Learning Paths, found in each unit, explain how students will build understanding of concepts throughout the unit.

Examples include but are not limited to:

  • In Unit 2 Lessons 2, 3, and 4, students use math drawings (Quick Hundreds, Quick Tens, and circles), expanded form, Secret Code place value cards, and numerals to represent numbers to 200. In Unit 6, Lessons 1-4, this activity is extended to build numbers to 1,000 using the same representation models (2.NBT.1).
  • In Unit 2, Lesson 9, “What’s The Error?,” the Puzzled Penguin gives students double-digit addition problems with incorrect answers. Students make proof drawings to show the mistakes Puzzled Penguin made. Students also explain the method the Puzzled Penguin used to solve incorrectly in exercise 4 (2.NBT.6).
  • The Unit 2, Learning Path, explains how the materials will build understanding of place value. “In this unit, children work with place value, representing numbers in different ways, and comparing numbers. They add two, three, or four 2-digit numbers, sometimes resulting in new tens or new hundreds with sums to 200” (2.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 Math Expressions Grade 2 meet expectations that they attend to those standards that set an expectation of procedural skill and fluency.

The instructional materials develop and provide independent opportunities for procedural skill and fluency throughout the grade-level. Math Expressions includes a Path to Fluency for each grade level.  “This plan provides targeted practice in the Student Activity Books, Teacher Editions, Teacher Resource Books, Math Activity Centers, as well as Fluency Checks in the Student Activity Books” (TE I12). In Grade 1 the fluency plan contains practice problems in the Student Activity Book identified by a Path to Fluency icon, Fluency Checks, Quick Practices, Daily Routines, Math Mountain Cards, Strategy Cards, Games, Homework and Remembering pages, and online resources. Examples include but are not limited to:

  • Practice for fluency within 20 is included in many Student Activity Book pages even in units where the emphasis is not number and operations, such as Unit 3, fluency appears in the Remembering spiral review pages (2.OA.2).
  • Unit 4, Lesson 14, Student Activity Book, 231, students solve addition and subtraction problems within 100 (2.OA.1).
  • Practice for fluency within 100 appears in many Homework and Remembering pages. For example, Unit 4, Lesson 14, Homework Practice provides problems for students to add and subtract within 100 (2.NBT.5).
  • Unit 7, in Lessons 7-15, Daily Quick Practice Routines, “Unscramble the Hundreds, Tens, and Ones.”
  • The Remembering Workbook pages spiral back to prior work and help build fluency. For example, in Unit 7, Lesson 10, Remembering 7-10, students add within ten (2.OA.2).
  • Periodic Fluency Checks assessing addition and subtraction fluency within 10, 20, and 100 are administered throughout the units. For example, Volume 1, Fluency Check 2, page 58, students add and subtract a one-digit and two-digit number (2.OA.2).
  • Online Resource, Poggles MX, interactive game providing addition and subtraction fluency practice.

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 Math Expressions Grade 2 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.

The instructional materials include multiple opportunities for students to engage in routine and non-routine application of mathematical skills and knowledge of the grade-level and to independently demonstrate the use of mathematics flexibly in a variety of contexts. Opportunities for contextual problem solving and non-routine problems are found in Math Talks. Students are provided real-world problem scenarios throughout each lesson. Performance Tasks at the end of each unit, provide students the opportunity to solve real world situations. Also, Math Readers embed math learning in a context appropriate story. Finally, online games provide problem solving practice.

Examples include, but are not limited to:

  • In Unit 2, Lesson 6, students solve word problems with a new ten. “Mr. Green puts 56 red peppers in the vegetable bin. Mrs. Green puts 28 yellow peppers in the bin. How many peppers do they put in the bin altogether?” Students are prompted to explain a method for finding the total number of peppers (2.OA.1).
  • In Unit 4, Lesson 23, students read a two-paragraph description of a Stegosaurus and find that the rear foot of a Stegosaurus was about 35 centimeters long. Students then make a paper strip that is 35 cm long and measure their own foot and compare the two measurements to determine the difference. They continue by measuring strides of the Stegosaurus and comparing to their own strides (2.MD.5).
  • Performance Tasks at the end of each unit provide students with the opportunity to solve a real world task. For example, Unit 4 Performance Task, students read, “Jacob has 2 quarters and 5 nickels. Cassie has 5 dimes and 3 nickels. Who has enough money to buy an apple. Explain.” (2.MD.8)
  • Math Talks provide opportunities for students to engage in routine problems. In Unit 4, Lesson 4, students are asked to write a word problem to match the given subtraction equation “63 - 35 = ___ and 92 - 54 = ____” and to use any method to solve the problem. Students share their solutions and discussion follows.
  • Students create their own story problems. In Unit 5, Lesson 8, students write 2-step word problems using data they previously collected on students’ favorite colors.
  • Math Readers provide opportunities for students to solve word problems in a different context. Unit 6’s Reader, “The If Game” includes word problems with unknown addends based on the pictures in the story.
  • Online activities provide additional opportunities for students to apply mathematical knowledge and skills to real-world contexts. For example, in the In-Depth Inquiry Based Task for Unit 6, Ticket Totals, students plan how six students will each use their 999 tickets at the carnival. Students use the information provided about the cost of food, games and activities to create six different plans.

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 Math Expressions Grade 2 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately.

The instructional materials attend to conceptual understanding, procedural skill and fluency, and application independently to develop students’ mathematical understanding of a single topic/unit of study throughout the grade level materials. The three aspects of rigor can be found in the Daily Routines, Quick Practice, Math Talks, Fluency Checks, Puzzled Penguin, Lessons, and Homework. For example,

  • Fluency can be found in any of the 20 Fluency Checks. For example, Fluency Check 11 has students adding and subtracting within 20 (2.OA.2).
  • Conceptual Understanding can be found in any of the Puzzled Penguins “What’s the Error?” questions. For example, in Unit 5, Lesson 2, students are shown a clock and the Puzzled Penguin’s time. Puzzled Penguin asks if he has the right time and students must help him tell the correct time.
  • Application can be found in Math Talk in Action activities. In Unit 6, Lesson 5, students work in groups of 3 to 5 to solve Problem 4, “A camping club buys some raisins. They buy 3 cartons that have 100 bags each. They also have 24 bags left from their last trip. How many bags of raisins does the club have?” Students work together using Secret Code Cards or proof drawings to find a solution.

Examples where the three aspects of rigor are treated together include, but are not limited to:

  • In Unit 2, Lesson 1, students engage with fluency and conceptual understanding as they write the numbers 1-110 on their math boards, discuss and create numbers greater than 100 using Secret Code cards to develop place value understanding, and write the numbers 101-200 in the Student Activity Book.
  • In Unit 4, Lesson 3, students engage with all three aspects of rigor. In the Quick Practice Teen Subtraction Flash, students practice subtraction fluency. Students develop conceptual understanding as they discuss various methods of finding unknown addends and relate to equations, for example, “73 = 34 +___” to break apart a sum. They relate addends with a sum of 100 to addends with a sum of 10, and build the concept 10 is made up of seven ones and three ones, but 100 is made up of seven tens and three tens. Students begin to explore other addends with a sum of 100. Students use their conceptual understanding to solve problems involving real-world contexts for subtracting a 2-digit number from 100, and solve a series of real-word problems involving 100. In the Student Activity Book, students engage in additional procedural skill practice subtracting from 100.
  • In Unit 4, Lesson 4, students solve two word problems using any method, “There were 100 puddles on the playground. 27 of them dried up. How many puddles are left on the playground.” Students apply their understanding of subtraction to write word problems to illustrate, “76 - 48 = _____.”

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
8/10
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Criterion Rating Details

The instructional materials reviewed for Math Expressions Grade 2 partially meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs). The MPs are identified, but the materials partially attend to the full meaning of each MP. The instructional materials also partially 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.
2/2
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Indicator Rating Details

The instructional materials reviewed for Math Expressions Grade 2 meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade-level.

Materials clearly identify Mathematical Practices being used in each lesson and are embedded in the content to enrich the mathematics. Instructions are provided for teachers on how to implement Mathematical Practices within the lesson. No Mathematical Practice is under or over used in the materials. While Mathematical Practices are not identified in the student materials, the Teacher Edition does provide highlighted narratives for Mathematical Practice activities found in the Student Activity Book.

Examples include, but are not limited to:

  • The Teacher Edition provides guidance on how to implement the Mathematical Practices in the Student Activity Book. For example, Unit 3, Lesson 6, Student Activity Book page 163, students estimate and measure objects. In the lesson narrative, MP5 is identified and the teacher narrative states, “make sure each small group has a centimeter ruler and a meter stick to use in exercises 4-7. In each exercise, children will select the tool to use, then measure the classroom object.”
  • All Mathematical Practices identified in the materials provide notes for the teacher. For example, in Unit 3, Lesson 7, Activity 2, the notes state, “MP7 Look for Structure. Hold up a yardstick and ask children to identify what it is. If a child calls it a meter stick, show the class that a yardstick is a bit shorter than a meter stick and that it has inch units instead of centimeter units.”
  • The Overview of every unit contains “Common Core State Standards for Mathematical Practices in this Unit”.  A table is provided that lists every Mathematical Practice along with corresponding lessons where that practice is embedded.
  • The “Using the Common Core Standards for Mathematical Practice” section contains a description of the Mathematical Practice along with examples of where to find it within the unit.  For example, in Unit 6, the MP1, “Encourage children to suggest as many ways to subtract as possible. See the next page for sample methods.”
  • Focus on the Mathematical Practices lessons are the last lesson in each unit. The lessons engage students in all eight practices, however, the practices are often over-identified. For example, in Unit 2 Lesson, 15, the activities involve recycling word problems, comparing methods and discussing solutions, money story problems, and patterns.

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 Math Expressions Grade 2 partially meet expectations that the instructional materials carefully attend to the full meaning of each practice standard.

The instructional materials attend to all eight Mathematical Practices. However, the instructional materials do not address the full meaning of Standard MP5 as tools are chosen for students, and there are few opportunities for students to choose tools strategically. For example:

  • Student Activity Book, Unit 2 Lesson 13, students use Secret Code Cards to play the New Ten Challenge. MP5 is identified in the lesson narrative as Use Appropriate Tools. 
  • Unit 4 Lesson 23, guides teachers to have students use a meter tape to measure and cut a strip of paper that is 35 centimeters long. 
  • Unit 6 Lesson 5, students work together to solve the exercise: 200 + 20 = ____. The teacher is directed to ask two questions. “Who can show me how to add these two numbers using Secret Code Cards? Who can show the addition using boxes, sticks, and circles?” 

Examples where materials attend to the full meaning of Mathematical Practices:

  • In Unit 3, Lesson 6, students solve the problem, “There are 6 children swimming. Then 4 children go home. How many children are still swimming?” After determining the answer, the teacher asks if the answer makes sense and for students to explain why it makes sense. Students then explain why the answer “10 children would not make sense.” (MP1)
  • Unit 4, Lesson 19, students solve compare word problems by de-contextualizing four types of comparison problems: Difference Unknown (“more” version), Smaller Unknown (“fewer” version), Bigger Unknown (“fewer” version), and  Smaller Unknown (“more” version). Students draw comparison bars and write equations as they solve the problems. (MP2)
  • Unit 7, Lesson 3, Exercise 14, students model with mathematics as they create word problems to model addition and subtraction problems shown on the number line: “28-17.” 
  • In Unit 3, Lesson 3, students are given one side length of a square. Students must determine and label all remaining side lengths. (MP6)
  • In Unit 4, Lesson 13, MP7 Look for Structure | Identify Relationships is identified as students look at columns of two equations, for example, 14 - 6 = 8 and 8 = 14 - 6. “The equations in the second column are the same as those in the first column, but with the sides of the equation reversed. Emphasize that 8 and 6 are addends and 14 is the total.

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.
2/2
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Indicator Rating Details

The instructional materials reviewed for Math Expressions Grade 2 partially meets expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. 

There are lessons throughout the series that prompt students to make comparisons, or determine whether statements are true or false. Some of these lessons require students to construct arguments, and some of these lessons require students to provide an explanation. Examples include:

  • In Unit 2, Lesson 15, Activity 3, Justify Conclusions about Money, students are presented with the following statement, “A bag holds 4 nickels, 4 pennies, and 4 dimes. If 3 coins are taken out of the bag, the value of the 3 coins can never be more than 16 cents.” Students must decide if the statement is true or false, and then volunteers share their positions and explanations with the class. 
  • Unit 6, Lesson 6, Math Talk, students solve and explain word problems. Students explain why they solved word problems in a particular way, and engage in Math Talk about good types of questions to ask for justification. For example, “How did you know you were supposed to add? Why did you put the 7 under the 8? 7 +8 is 15. What happened to the 10 in 15? I see only 5.” (2.OA.1). Students need to construct arguments to justify why.
  • Stretch Your Thinking problems found in the Student Activity Book and Homework and Remembering pages often require students to take a position and explain their thinking. For example, in Unit 4, Lesson 14, Stretch Your Thinking, the problem states, “Allison solved this problem. ‘46 + 17 = 53’ Is she correct? If not, explain and solve.” 

Puzzled Penguin problems are found throughout the materials and provide students an opportunity to correct errors in the penguin’s work. These tasks focus on error analysis, and many of the errors presented are procedural. Examples of Puzzled Penguin problems include:

  • Unit 2, Lesson 5, Puzzled Penguin, What’s the Error, “I know that 9 is greater than 6. Did I make a mistake?” The Puzzled Penguin wrote: “149 > 176” Problem 17: Make a proof drawing to help Puzzled Penguin. Write <, >, or =.” 
  • Unit 6, Lesson 3, Puzzled Penguin, What’s the Error, Compare Numbers, “I know that 3 is greater than 2. Did I make a mistake? 35 > 245.” Problem 11: “Draw boxes, sticks and circles to help Puzzled Penguin.” Students do not need to explain the error, simply show the correct comparison.

Indicator 2g.ii

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

The instructional materials reviewed for Math Expressions Grade 2 partially meet expectations that the instructional materials assist teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

There are some missed opportunities where the materials could assist teachers in engaging students in both constructing viable arguments and analyzing the arguments of others.

Missed opportunities include, but are not limited to:

  • In Unit 1, Lesson 1, teachers assist students with solving and discussing Math Mountain Structures in the Student Activity Book on page 5. Teachers direct students attention to the first two Math Mountains in the bottom row. The teacher notes state, “Volunteers give word problems for these Math Mountains, and ask everyone  to check that the equations on the board are their own equations on the board and their own equations can show or be used to solve that solution.” Teachers are not provided questions or sentence stems that would help students construct viable arguments.
  • In Unit 2, Lesson 4, MP3 is identified at the beginning of the activity. The teacher notes state, “How is 32 + 1 different from 39 + 1?” There is no guidance for the teacher on how to engage students in MP3 with this question.
  • In Unit 6, Lesson 9, the MP3 teacher notes state, “ask children to compare the situation equations and Math Mountains for Problems 1 and 2. Be sure children understand that these problems can both be solved by subtracting. Do the situation equations look the same for the first two problems? What is different in each one? Do the Math Mountains looks the same? How can you solve Problem 2?” These questions asked by the teacher will not guide the students to construct viable arguments.

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 Math Expressions Grade 2 meet expectations that materials use accurate mathematical terminology.

There are instances where materials use “A classroom research-based term developed for Math Expressions.” These terms are used in the Student Activity Book. Examples include but are not limited to: 

  • Math Mountain: a visual representation of the partners and total of a number. The total appears at the top, and the two partners that are added to produce the total are below to the right and left.
  • Secret Code Cards: student cards that display the numerals 1-9, decade numbers 10-90, and 100.
  • New Group Above method: a strategy for multi-digit addition. The new groups are placed above the existing groups.
  • New Group Below method: a strategy for multi-digit addition. The new groups are placed below the existing groups.
  • Show All Totals method: a strategy for multi-digit addition. Add the tens column together and place the total under the problem. Next, add the ones column together and place the total under the tens total. Add up the tens and ones totals to find the answer.
  • Adding Up Method for Subtraction: a method of finding an unknown addend in which children add up from the known addend until they reach the total.
  • Ungroup First Method: a method of subtraction in which children check each place to see if they need to ungroup in order to subtract. Children then complete all necessary ungrouping before they subtract.

In addition to a Glossary in the Student Activity Book, there are Teaching Notes on vocabulary and language. These are found in Unit 1 as students are introduced to mathematical language. For example:

  • Unit 1, Lesson 2, Teaching Notes, Vocabulary: “In the Student Activity Book, at the beginning of each unit, there are Vocabulary Cards that can be cut out. The cards can be used in the classroom or sent home for children to review the math vocabulary in Math Expressions. These cards can also be used with the Vocabulary Activities found in the back of this Teacher Edition.”

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 Math Expressions Grade 2 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 for Math Expressions Grade 2 meet expectations that materials distinguish between problems and exercises.

Materials provide the opportunity for students to learn new mathematics through problem solving activities. In a typical lesson, Activity 1 and Activity 2 develop the new math content of the lesson. Lessons are outlined according to an Inquiry Lesson Path based on four phases: Phase 1 Guided Introduction, Phase 2 Learning Unfolds, Phase 3 Knead Knowledge (practice stage), and Phase 4 Maintaining and Integrating Fluency. Students build mastery through practice problems/exercises. In a typical lesson, during Activity 2 and Activity 3, students complete problems in the Student Activity Book which provide practice with the math content. The purpose of each Activity within a unit is explained in the “Teaching the Lesson Section” found on the first page of each lesson.

Examples include but are not limited to:

  • In Unit 6 Lesson 2, Teaching the Lesson Section, Activity 1, Quick Practice Routines: Strategies to Add 3-Digit Numbers, is stated as important because “These strategies to add 3-digit numbers provide practice in building addition and subtraction fluency. Activity 2, Draw to Represent 3-Digit Numbers, is stated as important because “By representing 3-digit numbers with boxes, sticks, and circles, children reinforce their understanding of the structure of numbers and the base-ten place value system.” Activity 3, Expanded Form, is stated as important because “Understanding expanded form helps children see the value of each digit in a 3-digit number.”
  • In the Student Activity Book, Unit 7 Lesson 2, Activity 1, with guidance from the teacher, students fold paper to make equal shares and discuss the terms halves, thirds, and fourths. In Activity 2, students build on this knowledge as they draw different ways to make halves, thirds, and fourths of rectangles.

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 for Math Expressions Grade 2 meet expectations that materials provide tasks in an intentional sequence.

The design of the assignments follows a natural progression, leading to full understanding and mastery of new mathematics. Lessons follow a consistent pattern of two or three activities per lesson. Activity 1 usually focuses on the new learning. This learning is reinforced in Activity 2, and then students practice the new learning by completing Student Activity Book pages during Activity 3. Activity 3 either reinforces the new skill,or it reviews previously learned content.

Examples include but are not limited to:

  • In Unit 2, Lesson 12, students learn about counting money through skip counting; they write the count by 5 numbers under pictures of nickels, and draw circles with 5s written in the circle to represent nickels.
  • In Unit 4, Lesson 3, students find unknown addends in two-digit plus two-digit equations through the sequence of counting on using ten-sticks and circles, breaking apart the total into two addends using sticks and circles, and finally using numbers as they add up from the first addend to find the total.
  • In the Student Activity Book, Unit 5, Lesson 1, students create their own analog clock to practice telling time to the hour. Students look at pictures of analog clocks and write the time shown on the clocks. In the final activity, students draw the minute and hour hands on the pictures of blank analog clocks to show the time identified in the exercises.

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 for Math Expressions Grade 2 meet expectations that materials provide varied opportunities for students to present their mathematical knowledge.

Examples of how students produce answers and solutions include but are not limited to:

  • Modeling numbers to 1,000 with dollars
  • Modeling 3-digit numbers with hundred-squares, ten-sticks, and circles. 
  • Representing 3-digit numbers with Secret Code Cards
  • Providing thinking explanations as they answer Check for Understanding questions in the Student Activity Book
  • Completing fluency checks and practice in the Student Activity Book 
  • Critiquing the Reasoning of others by asking “good thinker questions” and using “good justifications” 
  • Practicing “good explanations” 
  • Identifying the error and correcting it (Puzzled Penguin)
  • Solving problems and exercises in the Student Activity Book

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 for Math Expressions Grade 2 meet expectations that materials provide virtual and physical manipulatives that are faithful representations of the mathematical objects they represent and are connected to the written material.

Students use a variety of manipulatives including counters, Secret Code Cards, base-ten blocks, Make-a-Ten cards, connecting cubes, Math Mountains, and Math Mountain Cards. Most of the manipulatives are available virtually in the itools found in ThinkCentral. Manipulatives are often connected to written methods when appropriate. 

Examples include but are not limited to:

  • Unit 2, Lesson 1, students use their Math Boards to draw circles on the ten-by-ten dot grid. This is connected to drawings of the hundred-square, ten-stick, and circles for ones. 
  • Unit 1, Lesson 5, students use Math Mountain Cards to practice solving addition and subtraction equations with the unknown in all positions. In the Homework and Remembering pages 9-10 for the lesson, students “complete the Math Mountains and equations.”

Indicator 3e

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

The instructional materials for Math Expressions Grade 2 meet expectations that materials provide a visual design that is not distracting or chaotic but supports students in engaging thoughtfully with the mathematics.

Student Activity Book pages include many exercises per page, but they follow a consistent layout and do not feel cluttered because there are no extra and unnecessary pictures on the pages. Additionally, students are provided ample space to show their work. When needed, models, which are consistent with the materials used in the lesson, are included on the pages. For example, on Student Activity Book page 7, Math Mountains are shown, and students write two equations for each Math Mountain using a square to represent the unknown number. Illustrations, when included, are simple and do not distract from the math.

In the Teacher Guide, lessons follow a consistent layout, moving from one activity to another. Each Activity includes a large blue box that highlights the mathematical content and practice standards, the focus of the lesson, and materials needed. Parts of the lesson, such as MathTalk, are clearly labeled. For example, in Unit 2, Lesson 14, a MathTalk in Action box shows examples of how students might share their methods for adding four numbers.

The digital interactive game, Poggles, includes simple, appealing characters that do not distract students as they practice addition and subtraction. Poggles are small squarish characters with animated faces whose appearance can be changed by adding hair and hats to the Poggle squares.

Criterion 3f - 3l

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

The instructional materials reviewed for Math Expressions Grade 2 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 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 for Math Expressions Grade 2 meet expectations that materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students’ mathematical development.

Examples of teacher support include but are not limited to:

  • Questions for teachers to pose are consistently included in the lesson narrative. They are italicized, making them easily visible. 
  • MathTalk in Action boxes include questions for the teacher to ask and potential student responses. For example, in Unit 2, Lesson 5, the teacher is guided to ask the questions: “Why did you compare the hundreds first? What do you do if the numbers you are comparing have the same number of hundreds? What do you do if the numbers you are comparing have the same number of tens? What does it mean if the 3-digit numbers you are comparing have the same number of hundreds, the same number of tens, and the same number of ones?”
  • Teacher Notes are also provided at the bottom of the lesson pages and include questions to deepen students understanding of the mathematics. For example, in Unit 4, Lesson 7, the Inquiry notes provide several probes to promote student thinking and discussion: “What are you doing when you write the numbers with hundreds, tens, and ones? Why do you check to see if you can subtract? Why can you subtract from left to right or from right to left? Why can you add to check your work?”
  • Teacher Notes at the bottom of lesson pages also include information about best practices to strengthen teachers questioning techniques. For example, in Unit 1, Lesson 4, the MathTalk note provides the following questions for teacher reflection: “What types of questions are you asking your students? Are you asking questions that elicit a short answer, or do you probe to learn more about children’s thinking as they tell about their work?"

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 for Math Expressions Grade 2 meet expectations that 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. Materials also, when necessary provide teacher guidance for the use of embedded technology to support and enhance student learning.

Ample guidance is provided in the Teacher Guide for planning. The Pacing Guide provides guidance for each unit. Charts show the Learning Progression for the Content Standards Across Grades for the standards addressed in the Unit. A Planning Chart for each Unit that includes Math Activity Center Resources, Big Idea Resources, and Lesson Resources is provided. The Planning Chart also includes the standards addressed in each lesson, the digital and print resources for each lesson, and the assessments for the Unit. A table of the Standards for Mathematical Practice and the lessons where each is embedded is included. Also, a Table of the Math Content Standards and the lessons where they are taught is provided. Finally, a list of Assessment, Review, and Intervention Resources for the Unit is provided.

Examples include but are not limited to:

  • Each lesson includes guidance on the focus of each Activity and why it is important. For example, in Unit 1, Lesson 5, Activity 2, Create and Solve Compare Word Problems, is stated as important because “Writing word problems using more and fewer helps children enhance their understanding of the Compare structure.”
  • Each Activity includes an explanation of what the teacher should do or say and includes possible correct responses to questions posed by the teacher. 
  • Formative Assessment and Check for Understanding questions are highlighted in the Teacher Guide.
  • Math Practices are highlighted in the lesson narratives.
  • A list of questions that can be used to build a Math Talk community is included at the beginning of each Unit. 
  • Notes at the bottom of each page of the lesson narrative give useful suggestions for implementing the lesson, asking questions, acquiring vocabulary, and building concepts. For example, in Unit 3, Lesson 2, the Teaching Notes for What to Expect from Students states, “Some of the children may benefit from making a set of index cards to identify different shapes. Each index card should show the shape. Then children write the name of the shape and the number of sides and angles that the shape has.”
  • Digital Resources for each lesson are highlighted on the first page of the lesson, and itools, which include virtual manipulatives, are shown in the lesson narrative when it may be beneficial to use them. For example, in Unit 2, Lesson 2, a picture of itools MathBoard is shown because they may be used in the lesson.

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.
2/2
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Indicator Rating Details

The instructional materials for Math Expressions Grade 2 meet expectations that materials contain a teacher’s edition that contains full, adult-level explanations and examples of the more advanced mathematics concepts and the mathematical practices so that teachers can improve their own knowledge of the subject, as necessary.

Notes are provided at the bottom of each lesson narrative in the Teacher Edition to deepen teacher understanding of the mathematics and to improve instruction. Math Background Notes provide information about the math topic to deepen teacher’s understanding. Watch For! Notes provide information about potential misconceptions and things to watch for as students complete the lesson. What to Expect from Students notes provide information about how students might engage with the math and why the math is important. Building Concepts notes provide explanations of the math and how students learn.

Examples include but are not limited to:

  • Path to Fluency Charts are provided.
  • Chart of the Addition/Subtraction and Multiplication/Division problem types is provided.
  • Table of the Major Work and Major Clusters of the Grade is provided.
  • Table of the Common Core State Standards for Mathematical Content is provided.
  • Table of the Common Core State Standards for Mathematical Practice with an explanation for each Mathematical Practice is provided.
  • The Putting Research into Practice section at the beginning of each unit provides research about best practices in teaching children mathematics.
  • The Math Background section, prior to each unit, includes sections that deepen teacher knowledge of the math in the unit. Examples include Learning Path in the Common Core Standards, Help Students Avoid Common Errors, Effective Practice Routines, Relate Mathematics to the Real World, and Focus on Mathematical Practices. 
  • The Math Background section, prior to each unit, provides excerpts from the Progressions for the Common Core State Standards.
  • The Mathematical Practices section, prior to each unit, provides information on how students will engage with the Practice Standards throughout the unit.
  • A Teacher Glossary is provided.

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 Math Expressions Grade 2 meet expectations that materials contain a teacher’s edition that explains the role of the specific mathematics standards in the context of the overall series.

A Path to Fluency: Kindergarten through Grade 6 Chart is provided and highlights the fluency requirements of each grade level, activities that target fluency, and interventions for Grades 3, 4, 5, and 6. Also, a Major Work and Major Clusters of the Grade Chart for grades K-6 is provided. Finally, for each unit, a Learning Progressions for the Common Core State Standards Chart for the domains addressed in the unit, which includes the current, prior, and next grade level standards is provided.

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 Math Expressions Grade 2 provide a list of lessons in the teacher's edition, cross-referencing the standards addressed and providing an estimated instructional time for each lesson, chapter, and unit.

Math Expressions does not include chapters, but rather units which are divided by Big Ideas, which are further divided into lessons. The Pacing Guide provides estimated instructional time for lessons and units. This Pacing Guide provides an estimated number of days for each unit, including lessons that may take two days and the number of days for assessments and quizzes. It should be noted that Lessons identified as taking two days in the Pacing Guide are not identified in the lesson narratives, nor is a breaking point indicated.

Examples include but are not limited to:

  • The Table of Contents provided in the introduction to the materials includes standards for all units’ Big Ideas.
  • The Chart of the Common Core State Standards for Mathematical Content provided identifies the lessons in which each standard will be addressed. 
  • The Chart of the Common Core State Standards for Mathematical Practice provided identifies the lessons in which each Mathematical Practice will be addressed. 
  • A Planning Chart is provided in the Overview for each unit that includes the standards that are addressed in each lesson. 
  • Charts of the Math Content Standards and Math Practice Standards is provided in the Overview for each unit. These charts include a list of each standard and the lessons where they are addressed. 
  • The Content and Practice Standards are identified on the first page of each lesson. The standards are also listed for each Activity within a lesson.

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 Math Expressions Grade 2 contain strategies for informing students, parents, or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

Family Letters for each unit are found in the Student Activity Book. These letters explain content, manipulatives students may use, and an explanation of terminology that may be unfamiliar to parents. Most units include between 1-3 Family Letters. Spanish versions of the letters are also included in the Student Activity Book.

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 for Math Expressions Grade 2 contain explanations of the instructional approaches of the program and identification of the research-based strategies.

The Teacher Edition contains explanations of the program’s instructional approaches and research-based strategies. An Inquiry Learning Path describes the four phases of the Math Expressions classroom: Guided Introduction, Learning Unfolds, Knead Knowledge, and Maintaining and Integrating Fluency. The Putting Research into Practice pages at the beginning of each Unit explain best practices related to the content of the Unit. Excerpts from the Progressions for the Common Core State Standards are included in the Math Background section of each Unit. Research Notes are sometimes included in the Teaching Notes at the bottom of the lesson narrative in the Teacher Edition. For example, the Research Teaching Notes for Unit 1, Lesson 10, Solve and Discuss state, “In Math Expressions, a problem-solving approach that focuses on problem types is used. Students will interpret the problem, represent the situation, solve the problem, and check that the answer makes sense.”

Criterion 3m - 3q

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

The instructional materials reviewed for Math Expressions Grade 2 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, 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 Math Expressions Grade 2 meet expectations that materials provide strategies for gathering information about students’ prior knowledge within and across grade levels.

Examples include but are not limited to:

  • The Assessment Guide contains a 25 question Prerequisite Skills Inventory Test, organized by Domains, and a corresponding Prerequisite Skills Inventory Test Correlation document. The correlation aligns each question with a description of the prerequisite skill addressed, as well as the DoK level of the question. This correlation document is formatted as a table so each student’s performance by question/skill can be recorded. The Prerequisite Skills Inventory Test is designed to be administered at the beginning of the school year.
  • When a student completes practice opportunities and tests in the Personal Math Trainer, all of the performance data and adaptive learning information follows each student to the next grade.
  • Teaching Notes within lessons alert teachers to prior knowledge opportunities. For example, In Unit 1, Lesson 2, the Teaching Note states, “In this lesson, children just practice with the yellow Math Mountain Cards which contain sums less than or equal to 10” (Teacher Edition page 14). Teachers are directed to use this as a diagnostic opportunity because, at this point, children should know these from memory or be counting on which is prior learning. Those students not demonstrating this skill will need intervention.
  • Quick Practice activities at the beginning of each lesson are designed to “provide opportunities for students to call to mind their prior understanding of a topic that has already been discussed in class or to begin to build a prerequisite skill for a topic that is to come later” (Teacher Edition page I4). 
  • Quick Quizzes and Fluency Checks are embedded within the units to check understanding of Big Ideas prior to moving on to the next Big Idea instruction, and to monitor progress toward computational fluency. For example, in Unit 2, Lesson 13, the Teaching Note states, “Fluency with sums to 100 will pave the way for success in Unit 6 where students will find sums within 1,000” (Teacher Edition page 256). This progress toward fluency is assessed in the Quick Quiz and Fluency Check 6 after Lesson 15 to be sure students are developing this crucial prerequisite skill. This skill continues to appear in Quick Quizzes and Fluency Checks throughout the year.
  • Students take three progress monitoring assessments to assess grade level skills and concepts students have learned. The Beginning of Year test assesses concepts they will learn throughout the year, the Middle of Year Test shows progress made in the first half of the year, and the End of Year Test measures growth throughout the school year.

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 Math Expressions Grade 2 meet expectations that materials provide support for teachers to identify and address common student errors and misconceptions.

Examples include but are not limited to:

  • Common student errors are identified for each Unit Review/Test question along with a direction on how to help students. For example, on the Unit 6 Review/Test, if a student misses Question 5 or 6, the common error identified states, “Students may have difficulty counting by 10s or 100s.” Teachers are directed to “Have children practice counting by 10s with a hundreds chart. Have them list the hundreds numbers. Practice changing the tens and/or ones digits and counting by 100s”.
  • The Math Background section of each Unit provides a narrative called “Help Students Avoid Common Errors”. 
  • Puzzled Penguin activities highlight typical student mistakes and misconceptions by challenging students to find the Puzzled Penguin’s mistake and correct it. Teachers are provided questions in order to lead classroom conversations through a MathTalk format that revolve around the mistake and its correction, helping students understand the mathematics.
  • Watch For! are teaching notes periodically found in each unit. These notes alert teachers to common misconceptions they should be on the lookout for. For example, in Unit 4, Lesson 6, the Watch For! note states, “The errors shown here are the most common mistakes children make when learning 2-digit subtraction. Address these and any other mistakes you may have noticed.” The teacher note also includes three common errors with illustrations such as subtracting smaller from larger, failing to ungroup the tens, and ungrouping unnecessarily.

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 Math Expressions Grade 2 meet expectations that materials provide support for ongoing review and practice, with feedback, for students in learning both concepts and skills.

Examples include but are not limited to:

  • Homework and Remembering pages provide a review of recently taught topics as well as a spiral review throughout the year. The Personal Math Trainer online platform allows students to complete homework tasks for each lesson, receive instant feedback, and  step-by-step guidance if needed.
  • Unit Review/Test and Performance Tasks for each unit are found in the Student Activity Book. The author states, You can use this Unit Review/Test as an end-of-unit review to determine if children have mastered the content of the unit. You can assess children’s knowledge with one of the forms of the Unit 1 Test in the Assessment Guide.” Teachers are provided with a Data-Driven Decision Making Table which suggests specific reteaching activities for students who incorrectly answer the correlated questions, as well as suggestions for which Standards Quiz to assign in the Personal Math Trainer which provides a personalized intervention for the student. The Performance Task includes a detailed scoring rubric which can be used to provide feedback to students.
  • The Personal Math Trainer can be used for homework practice, fluency practice, standards practice, unit pre-tests with instant feedback, and step-by-step guidance when needed. Everything a student completes in the platform helps to improve the adaptive workflow (powered by Knewton Adaptivity) for the student throughout the year.  
  • The Knewton Adaptivity, Homework with Daily Intervention and Enrichment can be used in multiple ways in the classroom. A 5-minute Warm-Up provides students with personalized review prior to the assignment. On-level and advanced students may receive less or no warm-up, as determined by Knewton. After the warm-up, the HMH pre-built assignment is given to students. A 10-minute personalized enrichment is provided for students who demonstrate mastery (95% or higher) on the assignment.  Enrichment shows students proximate, forward-looking concepts based on the assignment content.
  • Other Formative Assessment opportunities include: daily Check Understanding tasks on select Student Activity Book pages, daily observation with anecdotal notes, observations during Math Talk conversations, and analyzing student work samples and student responses in the Student Activity Book. Portfolio suggestions are also provided at the end of each unit.

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 materials reviewed for Math Expressions Grade 2 meet the expectation for offering ongoing assessments that clearly denote which standards are being emphasized.

Examples include but are not limited to:

  • Every unit includes two versions of a Unit Assessment, Form A and Form B, found in the Assessment Guide. Both assessments provide PARCC and Smarter Balance question formats and a Standards Correlation Document which can be used to collect student performance data. This document also aligns each question to a DoK Level and Standard(s). 
  • Each unit contains a Performance Assessment which can be found in the Assessment Guide. The standards are clearly noted for the assessment as a whole, and not by specific question. 
  • Quick Quizzes are found throughout each unit and standards are clearly noted in the Teacher Edition.
  • There are three Benchmark Assessments (Beginning of the Year Inventory, Middle of the Year Inventory and End of Year Assessment) found in the Assessment Guide. Standards for these assessments are clearly noted on the Correlation Document and DoK Levels are noted.

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.
2/2
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Indicator Rating Details

The instructional materials for Math Expressions Grade 2 meet expectations that assessments provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

Examples include but are not limited to:

  • Scoring Guides are provided for each Unit Performance Assessment found in the Assessment Guide. Each question is assigned a point value and a rubric is provided to determine Performance Levels 0-3 based on the number of points earned. Additionally, each Performance Level is further defined on a task-specific basis and indicates specifics about student understanding to assist teachers in interpreting student work. Sample student work for each Performance Level is also provided in the Assessment Guide. 
  • Answer keys for the Unit Assessments, Form A and Form B, are located in the back of the Assessment Guide. However, no guidance or suggestions for follow-up instruction are included in the Assessment Guide. 
  • The online Personal Math Trainer can be utilized to administer Beginning, Middle and End of Year Tests, Unit Assessments, and Fluency Checks. The data from these assessments is collected and analyzed, and a Personal Study Plan is prescribed through Adaptive Workflow settings (through Knewton Adaptivity) based on the data and the mastery threshold percentage established for the assessment. The primary use is for end of unit assessments, or to provide targeted students with occasional review, intervention, and re-assessment opportunities. Students must complete an initial assignment (test). Students who do not demonstrate mastery receive a Personal Study Plan, consisting of a personalized review and intervention assignment lasting 15 minutes. After completing the Personal Study Plan, the initial assignment is given again, but the numbers in the assessment are changed.

Indicator 3q

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

The instructional materials for Math Expressions Grade 2 do not encourage students to monitor their own progress and do not provide direction for teachers to encourage students to monitor their 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 Math Expressions Grade 2 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 for Math Expressions Grade 2 meet expectations that materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

Teachers guide students through an inquiry path to become mathematically proficient. The four stages of the path to learning are guided introduction, learning unfolds, knead knowledge through practice, and maintain fluency. As stated by the publisher, “Within the curriculum, a series of learning progressions reflect research on students’ natural learning stages when mastering concepts such as computation and problem-solving strategies. These learning stages informed the order of concepts, the sequence of units, and the positioning of topics in Math Expressions.” 

Examples include but are not limited to:

  • Unit 1, Lesson 5, students add and subtract with teen totals. Prompts are given for EL students at three different levels: emerging, expanding, bridging. A teaching note is included to help teachers diagnose if students are at an Emerging, Expanding, or Bridging level. Teachers are instructed, “By the end of Grade 2, all children need to be fluent with addition and subtraction with teen totals. . . Check that children are at least counting on (Level 2) for addition. Children should not be counting all (Level 1) at this time.” 
  • In Unit 2, Lesson 12, the Universal Access/Extra Help teaching note instructs teachers to “Relate the fingers of one hand to pennies and a nickel. Have children count the number of fingers (including the thumb) on one hand. Point out that there are 5 fingers on 1 hand just like there are 5 pennies in 1 nickel.”
  • In Unit 5, Lesson 8, students collect data by creating a survey. The Universal Access/Special Needs teacher note states, “Some children may have difficulty completing an assignment correctly. Give verbal feedback that involves first giving praise for what is correct and then giving suggestions for what could be improved.”

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 Math Expressions Grade 2 meet expectations that materials provide teachers with strategies for meeting the needs of a range of learners.

Examples include but are not limited to:

  • An explanation of differentiated instruction is provided in the Teacher Edition.
  • A list of intervention resources is provided for each unit in the Unit Overview Assessment.
  • Math Activity Centers resources for on-level, challenge, and intervention are provided for each unit’s lessons. 
  • Teaching notes for English Learners are provided for emerging, expanding, and bridging students and are provided for each unit’s lessons.
  • Some lessons have Differentiated Instruction notes provided for universal access/extra help.

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 for Math Expressions Grade 2 meets expectations that materials embed tasks with multiple entry points that can be solved using a variety of solution strategies or representations.

MathTalks provide “an inquiry environment that encourages constructive discussion of problem-solving methods through well-defined classroom activity structures. . . comprises four components: questioning, explaining math thinking, contributing math ideas, and taking responsibility for learning” (Teacher Edition page I3). Initially teachers model MathTalks and then students run the MathTalk. For example, in Unit 2, Lesson 1, the MathTalk instructs teachers to “Direct the children's attention to the dots below the grids on their Math Boards. Have them count and circle each dot in one column. Children should begin at the top of the column and count out loud as they circle the dots. Then, have children label each column as a group of ten. Explain that the ten-groups underneath each column show how many groups of ten have already been counted.” Then teachers are provided several prompts to facilitate student discussion.

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 for Math Expressions Grade 2 meets expectations that 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.

Examples include but are not limited to:

  • Scaffolding of vocabulary is provided. For example, in Unit 5, Lesson 10, the words bar graph and picture graph are explained for EL students. Teachers are instructed to say, “‘A bar graph uses bars to show data. A picture graph uses pictures to show data.’ Have children repeat.” 
  • Extra support is provided for EL students. For example, in Unit 1, Lesson 3, students use pennies to make tens. Teachers are instructed to “Trace both your hands on the board. Instead of fingernails, draw pennies. Next to your hands, draw a dime. A penny is one cent. A dime is ten cents.” 
  • Each unit lesson contains a Math Activity Center with activities and resources for students who are on-level and those needing challenge and intervention.
  • Teaching notes included in some lessons provide specific guidance for teachers to support students who are emerging, expanding, and bridging language acquisition.

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 Math Expressions Grade 2 meets expectations that materials provide opportunities for advanced students to investigate mathematics content at greater depth.

Examples include but are not limited to:

  • Math Lessons contain Differentiated Instruction Math Activity Centers. Challenge Resources specify which Activity Card will challenge advanced students.
  • The online Personal Math Trainer provides personalized enrichment with learning supports.
  • Challenge worksheets for each lesson are available in print and digitally and are noted on the Differentiated Instruction page for each lesson.
  • Math Readers, books in the Math Activity Center, place math content in the context of stories and support higher levels of critical thinking.

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 Math Expressions Grade 2 meets expectations that materials provide a balanced portrayal of various demographic and personal characteristics. 

Examples include but are not limited to:

  • Puzzled Penguin appears throughout the unit to provide opportunities to help students avoid common errors. These errors are presented as letters to students. Students teach Puzzled Penguin the correct way and explain why the penguin is wrong. 
  • Math Readers contain a variety of animals, children, and adults.

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 for Math Expressions Grade 2 provide opportunities for teachers to use a variety of grouping strategies.

Examples include but are not limited to:

  • Math Activity Centers are provided at the conclusion of each lesson and students can be grouped individually, in pairs, or in groups to complete the Activity Cards. For example, in Unit 3, Lesson 9, Intervention Activity card 3-9, students combine shapes to make new shapes. 
  • Math Writing Prompts are part of the Math Activity Centers and provide opportunities for students to work individually, in pairs, or in groups. For example, in Unit 6, Lesson 7, the Challenge Math Writing Prompt states, “Each shape stands for a different number. Find the value of each shape.” 
  • MathTalks provide various grouping structures. During Solve and Discuss, 4-5 students go to the board and solve the problem while the rest of the class is solving independently or as part of a small group consisting of 2-3 students. During Scenarios, a group of students act out a particular mathematical situation for other students to see.

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 Math Expressions Grade 2 sometimes encourage teachers to draw upon home language and culture to facilitate learning.

Family Letters for each unit are found in the Student Activity Book. Spanish versions of these letters are also included in the Student Activity Book. However, instructional materials do not encourage teachers to draw upon home language and culture to facilitate learning. English Learner notes in the Teacher Edition do not reference Spanish vocabulary to facilitate learning.

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 Math Expressions Grade 2: 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; are intended to be easily customized for individual learners; and do not include 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 for Math Expressions Grade 2 integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.

Examples include but are not limited to:

  • The Student Activity eBook provides audio, ability to submit answers online, a drawing tool for math drawings, guided practice to help students solve problems, and virtual manipulatives.
  • The Personal Math Trainer is an online adaptive assessment and personalized learning system for students. It analyzes student activity to determine strengths, weaknesses, learning style preferences, and pace. It provides a personalized learning path for students and generates reports for teachers to inform instruction.
  • The online Math Activity Center provides online differentiated instruction opportunities for practice, reteach, and challenge. Teachers can assign RTI assignments to students who struggle on Big Idea Quick Quizzes. Fluency Builders develop students’ basic facts and automaticity.
  • OSMO is an interactive gaming system for iPads to build students’ fluency and problem-solving skills. It offers physical manipulatives and provides immediate feedback.

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 Math Expressions Grade 2 are web-based and compatible with multiple internet browsers. In addition, materials are platform neutral and allow the use of tablets and mobile devices.

Web-based instructional materials for both teachers and students can be accessed using multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, both students and teachers can use multiple devices to access instructional materials (desktop computer, tablet, iPad, Smartboard, laptop, or cellphone). Students with disabilities can use mobile devices, assistive technology, or PCs to access materials. For example, non-readers have the option to have the entire text in an audio format. Additionally, the materials are platform-neutral for a variety of operating systems.

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 Math Expressions Grade 2 provide opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.

Online assessments are available. Teachers have the ability to create their own assessments or customize those provided by the program. A variety of assessment types are provided: multi-step, fill in the blank, multiple-choice, or teacher-created questions. For example, teachers giving the computer adaptive test may edit the format and/or values of the text causing the corresponding complexity of the lesson to change accordingly.

The Personal Math Trainer is an online adaptive assessment and learning system of mathematical understanding and procedural skill/fluency. Teachers can identify question types, assignment type, or standard tested. Once students have completed the task or assessment, various charts and graphs can be generated based on standards to inform instruction. Reports are available for individual students and the entire class.

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 Math Expressions Grade 2 include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations.

Teachers can manipulate the Personal Math Trainer to create learning experiences for students targeting their needs. Additionally, teachers can create lesson materials that are specific to the learning targets for specific unit lessons. For example, in Unit 1, Lesson 3, students need to “Make a ten to solve. Draw to show work.” Students can use digital manipulatives to solve and write a corresponding equation online.

The instructional materials for Math Expressions Grade 2 can be easily customized for local use. 

Digital materials include adaptive technological innovations for teachers to personalize learning for students. Digital materials can be differentiated based on individual student’s needs. For example, when using the Personal Math Trainer, teachers can add or modify existing tasks to a student’s personalized learning path. Additionally, adaptive technology allows teachers to provide two flexible differentiated styles (Daily Intervention and Enrichment or Personal Study Plan) for 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 Math Expressions Grade 2 do not include reference technology that provides opportunities for teachers and/or students to collaborate with each other.

Materials do not provide opportunities for students and teachers to participate in discussion groups using technology.

Additional Publication Details

Report Published Date: 09/04/2019

Report Edition: 2018

Title ISBN Edition Publisher Year
CCSS Homework and Remembering BLM Grade 2 9781328703576 Houghton Mifflin Harcourt 2018
CCSS Assessment Guide BLM Grade 2 9781328703644 Houghton Mifflin Harcourt 2018
Teacher Resource Book Grade 2 9781328703712 Houghton Mifflin Harcourt 2018
CCSS Teacher Edition Collection Grade 2 9781328741424 Houghton Mifflin Harcourt 2018
CCSS Softcover Consumable Student Activity Book Collection w/Mathboards Grade 2 9781328764256 Houghton Mifflin Harcourt 2018

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.

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