Math Expressions
Downloadable Resources
Publisher Response
2013

Math Expressions

Publisher
Houghton Mifflin Harcourt
Subject
Math
Grades
K-5
Report Release
02/13/2015
Review Tool Version
v1.0
Format
Core: Comprehensive

EdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Partially Meets Expectations

Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
NE = Not Eligible. Product did not meet the threshold for review.
Not Eligible
Downloadable Resources
Publisher Response
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Additional Publication Details

Title ISBN
International Standard Book Number
Edition Publisher Year
9780547824734
9780547824963
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2nd Grade

About This Report

Report for 2nd Grade

Alignment Summary

The materials reviewed for Grade 2 are partially aligned to the CCSSM. The materials are focused within assessments and spend the majority of time on the major work of the grade. The materials are also coherent, following the progression of the standards and connecting the mathematics within the grade level. The Grade 2 materials include all three aspects of rigor but procedure is emphasized over conceptual understanding. The MPs are identified and generally used to enhance the mathematical content, but the materials do not attend to the full meaning of each MP nor do they fully support the teacher and students in mathematical reasoning. Overall, the materials are only partially aligned to the CCSSM.

2nd Grade
Gateway 1

Focus & Coherence
14/14
0
7
12
14
Gateway 2

Rigor & Mathematical Practices
12/18
0
10
16
18
Alignment (Gateway 1 & 2)
Partially Meets Expectations
Gateway 3

Usability
Usability (Gateway 3)
Not Rated
Gateway 1
Gateway 2
Gateway 3
Viewing:
Gateway 1
Overview of Gateway 1

Focus & Coherence

The instructional materials reviewed for Grade 2 meet the expectation for Gateway 1: Focus and Coherence. Materials do not assess any topics before the grade level in which the topic is introduced in the standards and spend the majority of time on major work. No above grade level content was assessed on summative unit assessments. All assessments relate to Grade 2 standards. For instance, students are assessed on their understanding of place value, their fluency with addition and subtraction to 20 and their ability to compare two three-digit numbers. The instructional materials reviewed for Grade 2 meet the expectations for focus by spending the majority of the time on the major clusters of the grade. This includes the first two clusters of 2.OA, all of 2.NBT and the first two clusters of 2.MD. The instructional materials reviewed for Grade 2 also meet the expectation for coherence. The materials use supporting content as a way to continue work with the major work of the grade. For example, money is often used to support work in addition, subtraction and place value. The materials include a full program of study that is viable content for a school year including 150 lesson and assessment days. This set of materials is consistent with the mathematical progression of learning set forth in the standards. All students, including struggling students, are given extensive work on grade level problems and this work progresses mathematically. These instructional materials are visibly shaped by the cluster headings in the standards. Connections are made between domains and clusters within the grade level. For instance, materials make connections between place value and money and telling time and foundations for multiplication. Overall, the Grade 2 materials support focus and coherence and meet the requirements for Gateway 1.

 

 

Gateway 1
v1.0
Gateway 1

Focus & Coherence
14/14
0
7
12
14
Criterion 1.1: Focus
02/02
Criterion 1.2: Coherence
04/04
Criterion 1.3: Coherence
08/08
Meets Expectations

Criterion 1.1: Focus
02/02
Materials do not assess topics before the grade level in which the topic should be introduced.

The instructional materials reviewed for Grade 2 meet the expectation for this criterion by not assessing any topics before the grade level in which the topic is introduced in the standards. No above grade level content was assessed on summative unit assessments. All assessments relate to Grade 2 standards. For instance, students are assessed on their understanding of place value, their fluency with addition and subtraction to 20 and their ability to compare two three-digit numbers. Overall, the instructional materials meet the expectations for focus within assessment.

Indicator 1A
02/02
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.

The instructional materials reviewed for Grade 2 meet the expectations for focus within assessment. Overall, the instructional material does not assess any content from future grades within the summative assessment sections of each unit.

  • No above grade level content was assessed on summative unit assessments.
  • All assessments, rubrics and topics relate to Grade 2 standards or below.
  • Students are assessed on adding and subtracting within 20, 100 and 1000.
  • Students are assessed on their understanding of place value.
  • Students are assessed on measurement, telling time and money as indicated by the standards.

Criterion 1.1: Focus
02/02
Indicator 1A
02/02

Criterion 1.2: Coherence

04/04
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.

The instructional materials reviewed for Grade 2 meet the expectations for focus by spending the majority of the time on the major clusters of the grade. This includes the first two clusters of 2.OA, all of 2.NBT and the first two clusters of 2.MD.

Indicator 1B
04/04
Instructional material spends the majority of class time on the major cluster of each grade.

The instructional materials reviewed for Grade 2 meet the expectations for focus by spending the majority of the time on the major clusters of the grade. This includes the first two clusters of 2.OA, all of 2.NBT and the first two clusters of 2.MD.

  • While some lessons include multiple standards, approximately 94 out of 113 lessons are devoted to major work.
  • Units 1, 2 and 6 focus exclusively on major work.
  • Units 3, 4 and 5 focus the majority of the lessons on major work.
  • Unit 7 spends less than 50% of the time on major work.
  • More than 80% of the lessons focus on the major work of the grade level.

Criterion 1.2: Coherence
04/04
Indicator 1B
04/04

Criterion 1.3: Coherence
08/08
Coherence: Each grade's instructional materials are coherent and consistent with the Standards.

The instructional materials reviewed for Grade 2 meet the expectations for coherence. The materials use supporting content as a way to continue work with the major work of the grade. For example, money is often used to support work in addition, subtraction and place value. The materials include a full program of study that is viable content for a school year including 150 lesson and assessment days. This set of materials is consistent with the mathematical progression of learning set forth in the standards. All students, including struggling students, are given extensive work on grade level problems and this work progresses mathematically. These instructional materials are visibly shaped by the cluster headings in the standards. Connections are made between domains and clusters within the grade level. For instance, materials make connections between place value and money, telling time and foundations for multiplication. Overall, the Grade 2 materials support coherence and are consistent with the progressions in the standards.

Indicator 1C
02/02
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The instructional materials reviewed for Grade 2 meet the expectations for their use of supporting content as a way to enhance coherence. For Grade 2, reviewers focused on the use of data and money as methods for supporting addition and subtraction and place value.

  • Units 2 and 4 use money (2.MD.C.8) to continue work on addition, subtraction and place value.
  • Units 3 and 5 use data to continue work on addition and subtraction and to compare quantities.
  • Connections are also made with counting by 5s, telling time and using length as a connection to addition and subtraction.

Indicator 1D
02/02
The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.

The instructional materials reviewed for Grade 2 meet the expectation for this indicator by providing a viable level of content for one school year.

  • Materials provide for 150 days of instruction, quizzes, fluency checks and formal assessment.
  • Most lessons are appropriate in length for Grade 2.
  • Some lessons may take longer than indicated.

Indicator 1E
02/02
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.

The instructional materials reviewed for Grade 2 are consistent with the mathematical progressions in the standards and meet the expectation for this indicator.

  • Materials develop according to the progressions laid out in the standards.
  • Students work on strategies for addition and subtraction and fluency.
  • There is a progression of difficulty of the problem types throughout the materials.
  • Differentiation materials offer support to struggling students while maintaining a focus on grade level content.
  • There are no connections to content from prior grades explicitly made for students.
  • Minimal connections are made for the teacher within the lessons to prior knowledge from previous grades. One example is the learning progression chart included in each unit that shows connections to previous and future grades.

Indicator 1F
02/02
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.

The instructional materials reviewed for Grade 2 foster coherence through grade level connections.

  • Lesson and test objectives are visibly shaped by the cluster headings in the CCSSM.
  • Connections are made between place value and money.
  • Lengths are used to continue work on addition and subtraction.
  • Telling time and money are connected to work that builds the foundation for multiplication.

Criterion 1.3: Coherence
08/08
Indicator 1C
02/02
Indicator 1D
02/02
Indicator 1E
02/02
Indicator 1F
02/02
Overview of Gateway 2

Rigor & Mathematical Practices

The materials reviewed for Grade 2 partially meet the requirements for Gateway 2. All three aspects of rigor are present in the materials, but they are not balanced. There is a prevalence of procedural lessons, problems and assessment items. There are few conceptual understanding lessons, problems or assessment items. The MPs are listed in the specifics of the lessons and the way they are listed enhances the learning. Attention is not paid to the full meaning of each MP and one lesson in each unit focuses on MPs separately from content standards. The materials are not strong in their expectation for mathematical reasoning. The students and teachers are not given enough support nor is the vocabulary development sufficient. The materials reviewed for Gateway 2 do not align with the expectations for rigor and mathematical practices.

Gateway 2
v1.0
Gateway 2

Rigor & Mathematical Practices
12/18
0
10
16
18
Criterion 2.1: Rigor
06/08
Criterion 2.2: Math Practices
06/10
Partially Meets Expectations

Criterion 2.1: Rigor
06/08
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.

The materials reviewed for Grade 2 partially meet the requirements for this criterion. All three aspects of rigor are present in the materials, but they are not balanced. There is a prevalence of procedural lessons, problems and assessment items. There are few conceptual understanding lessons, problems and assessment items. The balance of rigor in the standards is not present in the materials for Grade 2.

Indicator 2A
01/02
Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

The materials reviewed in Grade 2 for this indicator partially meet the requirements of attending to conceptual understanding within the lessons.

  • In unit 2 students use place value "secret code" cards and layered place value cards and are expected to write expanded form. Throughout the rest of the lessons there is a lack of emphasis on place value strategies.
  • Place value work is often procedural and building conceptual understanding of place value is not prevalent.
  • The "Formative Assessment: Check Understanding" boxes attend to conceptual understanding. These could be used for classroom discussions instead of individual assessment checks.

Indicator 2B
02/02
Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

The materials reviewed in Grade 2 for this indicator meet the requirements by attending to fluency and procedural work within the lessons. In Grade 2 this includes adding and subtracting single digit sums from memory (2.OA.B.2) and fluently adding and subtracting within 100 using strategies (2.NBT.B.5).

Lessons include quick practice for fluency.

Lessons include targeted practice in fluency.

●      Student workbook includes opportunities to practice fluency.

Indicator 2C
02/02
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

The materials reviewed in Grade 2 for this indicator meet the requirements by attending to application within the lessons.

  • Each unit ends with a real-world problem to solve.
  • Word problems are interspersed throughout the lessons in all units.
  • Students are given opportunities to generate their own word problems.
  • In unit 6, students are working with mixed operation problems.
  • By unit 7, students are working with 2-step problems.
  • Multiple problem types are attended to and described for the teacher.

Indicator 2D
01/02
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.

The materials reviewed in Grade 2 for this indicator partially meet the requirements of providing a balance of rigor. The three aspects are not always treated together nor are they always treated separately.

  • While all three aspects of rigor are included, there is a heavy emphasis on procedures and a lack of emphasis on conceptual understanding.
  • Within the assessments there are more procedural questions and very few conceptual or application problems.

Criterion 2.1: Rigor
06/08
Indicator 2A
01/02
Indicator 2B
02/02
Indicator 2C
02/02
Indicator 2D
01/02

Criterion 2.2: Math Practices
06/10
Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice

The materials reviewed for Grade 2 partially meet the requirements of this criterion. The MPs are listed in the specifics of the lessons, and the way they are listed enhances the learning. Attention is not paid to the full meaning of each MP and one lesson in each unit focuses only on the practices and not the content standards. The materials are not strong in their expectation for mathematical reasoning. The students and teachers are not given enough support nor is the vocabulary development sufficient.

Indicator 2E
02/02
The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.

The materials reviewed for Grade 2 meet the requirement of this indicator by identifying the Standards for Mathematical Practice (MPs) and using this identification to enhance the learning.

  • MPs are identified in the "Getting Ready to Teach" sections in every unit.
  • MPs are identified within the lessons in a way that supports the learning.
  • For example, in unit 6 MP6 is identified as students are asked to explain 3-digit subtraction using place value words. This is a way to use vocabulary to enhance the learning.

Indicator 2F
01/02
Materials carefully attend to the full meaning of each practice standard

The materials reviewed for Grade 2 partially meet the requirement of this indicator.

  • MP1 is consistently expected as students solve problems throughout the year.
  • The full meaning of MP5 is not attended to. Students rarely choose their own mathematical tools.
  • The final lesson in each unit focuses on all 8 MPs instead of focusing on content standards. These lessons do not attend to the full meaning of all 8 MPs.

Indicator 2G
Read
Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
Indicator 2G.i
01/02
Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.

The materials reviewed for Grade 2 partially meet the requirement of this indicator of attending to the standards' emphasis on mathematical reasoning.

  • Students are rarely prompted to construct viable arguments. One example is found on the assessment for unit 6 where students are prompted to "Explain how and why you can use addition to check your answer."
  • In the differentiation cards students are occasionally prompted to discuss their strategies with the group.
  • Most of the student pages include numbers, symbols and spaces for answers, but they do not include spaces for students to explain their thinking or opportunities to share these explanations.
  • Students are asked to analyze a response from the "Puzzled Penguin," but this is simply an opportunity for catching errors and not an opportunity for reasoning.

Indicator 2G.ii
01/02
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.

The materials reviewed for Grade 2 partially meet the requirement of this indicator of attending to the Standards' emphasis on mathematical reasoning.

  • In unit 6 teachers are given an activity called "Discuss Good Explanations." This provides students with the opportunity to construct their own arguments and help other students to make a full explanation.
  • The teacher's manual provides questions to promote MP3.
  • In several lessons, an element called "Math Talk in Action" is a way to promote to high quality classroom discussions.
  • Teacher questions often simply ask for the answer and not the reasoning nor the opportunity to analyze arguments of other students.

Indicator 2G.iii
01/02
Materials explicitly attend to the specialized language of mathematics.

The materials reviewed for Grade 2 partially meet the requirement of this indicator of attending to the standards' emphasis on mathematical reasoning.

  • There are vocabulary terms listed for most lessons, however this often includes strategies specific to the curriculum instead of mathematical language. For example, the phrase "hidden information" is listed as a vocabulary word in unit 1. In unit 6, the phrases "New Groups Above" and "New Groups Below" are listed as vocabulary.

Criterion 2.2: Math Practices
06/10
Indicator 2E
02/02
Indicator 2F
01/02
Indicator 2G
Read
Indicator 2G.i
01/02
Indicator 2G.ii
01/02
Indicator 2G.iii
01/02
Overview of Gateway 3

Usability

This material was not reviewed for Gateway Three because it did not meet expectations for Gateways One and Two
Gateway 3
v1.0
Gateway 3

Usability
NE = Not Eligible. Product did not meet the threshold for review.
NE
0
22
31
38
Criterion 3.1: Use & Design
NE = Not Eligible. Product did not meet the threshold for review.
NE
Criterion 3.2: Teacher Planning
NE = Not Eligible. Product did not meet the threshold for review.
NE
Criterion 3.3: Assessment
NE = Not Eligible. Product did not meet the threshold for review.
NE
Criterion 3.4: Differentiation
NE = Not Eligible. Product did not meet the threshold for review.
NE
Criterion 3.5: Technology
NE = Not Eligible. Product did not meet the threshold for review.
NE
Not Rated

Criterion 3.1: Use & Design

NE = Not Eligible. Product did not meet the threshold for review.
NE
Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
Indicator 3A
00/02
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.
Indicator 3B
00/02
Design of assignments is not haphazard: exercises are given in intentional sequences.
Indicator 3C
00/02
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.
Indicator 3D
00/02
Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
Indicator 3E
Read
The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
Criterion 3.1: Use & Design
NE = Not Eligible. Product did not meet the threshold for review.
NE
Indicator 3A
00/02
Indicator 3B
00/02
Indicator 3C
00/02
Indicator 3D
00/02
Indicator 3E
Read

Criterion 3.2: Teacher Planning

NE = Not Eligible. Product did not meet the threshold for review.
NE
Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
Indicator 3F
00/02
Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
Indicator 3G
00/02
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.
Indicator 3H
00/02
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.
Indicator 3I
00/02
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.
Indicator 3J
Read
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).
Indicator 3K
Read
Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
Indicator 3L
Read
Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
Criterion 3.2: Teacher Planning
NE = Not Eligible. Product did not meet the threshold for review.
NE
Indicator 3F
00/02
Indicator 3G
00/02
Indicator 3H
00/02
Indicator 3I
00/02
Indicator 3J
Read
Indicator 3K
Read
Indicator 3L
Read

Criterion 3.3: Assessment

NE = Not Eligible. Product did not meet the threshold for review.
NE
Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
Indicator 3M
00/02
Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
Indicator 3N
00/02
Materials provide strategies for teachers to identify and address common student errors and misconceptions.
Indicator 3O
00/02
Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
Indicator 3P
Read
Materials offer ongoing formative and summative assessments:
Indicator 3P.i
00/02
Assessments clearly denote which standards are being emphasized.
Indicator 3P.ii
00/02
Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
Indicator 3Q
Read
Materials encourage students to monitor their own progress.
Criterion 3.3: Assessment
NE = Not Eligible. Product did not meet the threshold for review.
NE
Indicator 3M
00/02
Indicator 3N
00/02
Indicator 3O
00/02
Indicator 3P
Read
Indicator 3P.i
00/02
Indicator 3P.ii
00/02
Indicator 3Q
Read

Criterion 3.4: Differentiation

NE = Not Eligible. Product did not meet the threshold for review.
NE
Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
Indicator 3R
00/02
Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
Indicator 3S
00/02
Materials provide teachers with strategies for meeting the needs of a range of learners.
Indicator 3T
00/02
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
Indicator 3U
00/02
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).
Indicator 3V
00/02
Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
Indicator 3W
00/02
Materials provide a balanced portrayal of various demographic and personal characteristics.
Indicator 3X
Read
Materials provide opportunities for teachers to use a variety of grouping strategies.
Indicator 3Y
Read
Materials encourage teachers to draw upon home language and culture to facilitate learning.
Criterion 3.4: Differentiation
NE = Not Eligible. Product did not meet the threshold for review.
NE
Indicator 3R
00/02
Indicator 3S
00/02
Indicator 3T
00/02
Indicator 3U
00/02
Indicator 3V
00/02
Indicator 3W
00/02
Indicator 3X
Read
Indicator 3Y
Read

Criterion 3.5: Technology

NE = Not Eligible. Product did not meet the threshold for review.
NE
Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
Indicator 3AA
Read
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.
Indicator 3AB
Read
Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
Indicator 3AC
Read
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.
Indicator 3AD
Read
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.).
Indicator 3Z
Read
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
Criterion 3.5: Technology
NE = Not Eligible. Product did not meet the threshold for review.
NE
Indicator 3AA
Read
Indicator 3AB
Read
Indicator 3AC
Read
Indicator 3AD
Read
Indicator 3Z
Read
Gateway 1
Gateway 2
Gateway 3
Viewing:
Gateway 1