Investigations in Number, Data, and Space (2012)

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Report Overview

Summary of Alignment & Usability: Investigations in Number, Data, and Space | Math

Product Notes

Reviewed print materials include:

Investigations and the Common Core State Standards resource
Unit books for each grade, Kindergarten through Grade 5
Common Core Cards for each unit for each grade, Kindergarten through Grade 5
Implementing Investigations resource for each grade, Kindergarten through Grade 5
Student activity book, Common Core Edition for each grade, Kindergarten through Grade 5
Differentiation and Intervention Guide
Investigation Digital Resources, CD-ROM which housed all print materials for each grade level Kindergarten through Grade 5

Math K-2

Investigations Grades K-2 does not meet the expectations for Alignment to the Common Core State Standards and Usability. While numerous units of material are provided, they do not spend the majority of instructional time on major work of the grades. The sequence in which topics are covered is not consistent with the logical structure as outlined by the CCSSM and address topics before the grade level introduced in the standards. Therefore, materials are lacking important connections between standards, clusters and/or domains where appropriate and required. Overall, the instructional materials included in this series lack mathematical focus and coherence.

Kindergarten

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Gateway 1

Focus & Coherence

Gateway 2

Rigor & Mathematical Practices

Does Not Meet Expectations

Gateway 3

Usability

Not Rated

1st Grade

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Gateway 1

Focus & Coherence

Gateway 2

Rigor & Mathematical Practices

Does Not Meet Expectations

Gateway 3

Usability

Not Rated

2nd Grade

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Gateway 1

Focus & Coherence

Gateway 2

Rigor & Mathematical Practices

Does Not Meet Expectations

Gateway 3

Usability

Not Rated

Math 3-5

Investigations, Grades 3-5 does not meet the expectations for Alignment to the Common Core State Standards/Usability. While numerous units of material are provided, they do not spend the majority of instructional time on major work of the grades. The sequence in which topics are covered is not consistent with the logical structure as outlined by the CCSSM and address topics before the grade level introduced in the standards. Therefore, materials are lacking important connections between standards, clusters and/or domains where appropriate and required. Overall, the instructional materials included in this series lack mathematical focus and coherence.

3rd Grade

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Gateway 1

Focus & Coherence

Gateway 2

Rigor & Mathematical Practices

Does Not Meet Expectations

Gateway 3

Usability

Not Rated

4th Grade

View Full Report

Gateway 1

Focus & Coherence

Gateway 2

Rigor & Mathematical Practices

Does Not Meet Expectations

Gateway 3

Usability

Not Rated

5th Grade

View Full Report

Gateway 1

Focus & Coherence

Gateway 2

Rigor & Mathematical Practices

Does Not Meet Expectations

Gateway 3

Usability

Not Rated

Report for 1st Grade

Alignment Summary

The instructional materials reviewed for Grade 1 do not meet expectations for alignment. The materials do not devote the large majority of time to grade-level work, but the materials can be utilized to appropriately assess grade-level content. Materials do include lessons that use supporting work to continue learning in major work. There is no explicit connection made to the progressions of learning in the standards. Since the materials do not meet the expectations for focus and coherence in gateway 1, they were not reviewed for gateway 2.

1st Grade

Gateway 1

Focus & Coherence

Gateway 2

Rigor & Mathematical Practices

Alignment (Gateway 1 & 2)

Does Not Meet Expectations

Gateway 3

Usability

Usability (Gateway 3)

Not Rated

Overview of Gateway 1

Focus & Coherence

The instructional materials reviewed for Grade 1 do not meet expectations for focus on major work and coherence. The materials do not devote the large majority of time to grade-level work, but the materials can be utilized to appropriately assess grade-level content. Materials do include lessons that use supporting work to continue learning in major work. There is no explicit connection made to the progressions of learning in the standards.

Gateway 1

v1.0

Gateway 1

Focus & Coherence

Criterion 1.1: Focus

Criterion 1.2: Coherence

Criterion 1.3: Coherence

Does Not Meet Expectations

Criterion 1.1: Focus

Materials do not assess topics before the grade level in which the topic should be introduced.

The instructional materials reviewed for Grade 1 meet the expectations for assessing material at the grade level. Although there are multiple units and sessions noted that align to and assess standards that are beyond Grade 1, the inclusion of these sessions and units is either Mathematically appropriate or, where not appropriate, their omission would not significantly alter the structure of the materials.

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.

The instructional materials reviewed for Grade 1 meet expectations for assessment because above grade-level assessment items and their accompanying lessons, sessions, or units, could be modified or omitted without significantly impacting the underlying structure of the instructional materials. For this indicator, all of the identified assessments and end-of-unit assessments for the nine units were reviewed. Units and sessions accompanying above grade-level assessment items are noted in the following list.

In unit 7, session 1.8 assesses how to: construct, describe, and extend a repeating pattern with the structure AB, ABC, AAB, or ABB; identify the unit of a repeating pattern for patterns with the structure AB or ABC; and determine what comes several steps beyond the visible part of an AB, ABC, AAB, or ABB, and repeating pattern. In unit 7, session 2.7 assesses how to: identify what comes several steps beyond the visible part of a repeating pattern; identify the unit of a repeating pattern; and determine the element of a repeating pattern associated with a particular counting number. The scoring rubrics on page 120 clearly demonstrate an expectation of the understanding of patterns. These expectations for students align to 4.OA.C.5. “Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.” The materials explain the inclusion of these expectations by saying they “raise student awareness of pattern and regularities that occur in the relationships among mathematical objects – numbers and shapes. They also raise awareness of pattern and regularity and introduce students to some common number sequences” (page 13). These topics are not clearly identified as beyond Grade 1, and due to these topics aligning to a standard three grade levels above the current one, the inclusion of these topics is not Mathematically reasonable within the materials. However, the omission of these lessons and sessions would not significantly alter the underlying structure of the materials.
In unit 8, session 2.8 assesses how to count by groups in meaningful ways, counts of ones, twos, fives or in combinations is required. The scoring rubrics on page 142 demonstrate that a student who records and counts by ones instead of organizing into groups is not meeting expectations. This expectation for students aligns to 2.NBT.A.2, “Count within 1000; skip-count by 5s, 10s, and 100s”, and 2.OA.C.3, “Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.”. In unit 8, session 3.6 assesses how to count by equal groups in meaningful ways. The scoring rubrics on page 150 demonstrate that a student is still meeting expectations if he draws a representation and counts by ones, instead of by groups, and arrives at the correct answer. This expectation for students could align to 2.OA.C.4, “Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends”, but since the scoring rubrics allow meeting expectations when counting by ones, this expectation does not directly align to 2.OA.C.4. These topics are not clearly identified as beyond Grade 1, but their inclusion is Mathematically reasonable since the topics are only one grade level beyond Grade 1 and do not constitute a large number of lessons. Also, the omission of these lessons and sessions would not significantly alter the underlying structure of the materials, especially since this would more than likely be the near the end of the school year.

*Evidence updated 10/27/15

Criterion 1.1: Focus

Indicator 1A

Criterion 1.2: Coherence

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 1 do not meet expectations for time spent of the major clusters of the grade. The materials are 68% aligned to the major work of Grade 1, which is not devoting the large majority of class time to the major clusters.

Indicator 1B

Instructional material spends the majority of class time on the major cluster of each grade.

The instructional materials reviewed for Grade 1 do not meet expectations for class time spent on the major clusters of the grade. According to the unit instructional plans, there are 161 days of lessons and assessments. Within that, there are areas where the work is aligned to supporting and additional clusters or is work outside of the grade level. Examples to support this are:

Unit 7: All 15 sessions are more appropriately aligned to Grade 4 pattern work.
Unit 2: All 13 sessions are aligned to additional work at Grade 1 in geometry.
Unit 4: All 11 sessions are aligned to supporting and additional work at Grade 1 in measurement and data.
Unit 9: All nine sessions are aligned to additional work in geometry.
Within unit 5, there are four sessions that focus on the additional work of geometry.

These examples consist of 52 total lessons. Of the 161 sessions provided, there are 109 sessions aligned to the major work of Grade 1, with 68% of time spent on major clusters. This is not enough time spent on major work. There are instances where supporting work enhances focus standards, however that is not enough to warrant the materials meeting expectations for this indicator.

Criterion 1.2: Coherence

Indicator 1B

Criterion 1.3: Coherence

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

The instructional materials reviewed for Grade 1 partially meet expectations for coherence. The materials are not fully coherent with the progressions, as pattern work goes beyond the scope of the grade and the consistency within the standards is evident in some occasions, not all, particularly with need for more connections and materials for 1.NBT.C.

Indicator 1C

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The instructional materials reviewed for Grade 1 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. Units 2, 4, 5 and 9 are aligned to supporting and additional work of the grade. Within those units, evidence was gathered where the supporting work enhances focus. This is evident in the following examples.

Unit 2, lesson 1.2 "Same Shape, Different Pieces" asks the students to create a composite shape and to count the number of different shapes used then record the number of each shape. This lesson engages students in the major work of 1.NBT.A.1.
Unit 2, geometry (1.G.A.1 and 1.G.A.2) lessons and activities support the major work of 1.NBT.A and 1.OA clusters. For example, pattern-block activities in sessions 1.1-1.7 involve composing shape design using the simple shapes and counting/representing the number of each type used and then finding the total number used.
Unit 4, lessons 2.1-2.5 engage students in the major work of 1.NBT.
Unit 5, the measurement activities include opportunities to solve story problems (1.OA.1) with the measurements. Some examples of this can be found within the lessons in Sessions 1.4, 1.5A and 2.4 as well as in student activity sheets.
Time activities found in units 4-9 provide opportunities to write numbers when writing digital times and practice reading numbers, connecting the work in 1.NBT.A.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.

The instructional materials reviewed for Grade 1 partially meet expectations for viability of content for the scope of one year. The curriculum consists of 161 total sessions according to the provided pacing in the Investigations and Common Core State Standards Resource. Although this is a manageable number of days for a school year, with the inclusion of unit 7 on patterns, the review team determined that the amount of content was not fully viable for one school year to foster coherence between grades. In addition, one shortcoming is that 1.NBT.C ("Use place value understanding and properties of operations to add and subtract")-one of the major work focus standards-is only evident in five lessons in unit 8. This raises a concern that this will need more attention in order to prepare students for the work in Grade 2.

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.

The instructional materials reviewed for Grade 1 partially meet expectations for consistency with the progressions. The materials partially develop according to the progressions and partially give students extensive work with grade level problems. In addition, while there are teacher notes in the "looking back" section of each unit, there is not explicit connection to specific standards addressed in prior grades. For example:

Unit 3 story problems go beyond 20 in session 3.3 student work but are identified as "Challenging Story Problems" and an extension.
Unit 3 sessions 4.1-4.3 involve counting using an "area" type of activity, but the author includes a teacher note (page 139) which addresses this and states that the purpose of the activity is counting and recording larger numbers.
In unit 5, students use partial units when measuring although there is a teacher note on page 89.
In unit 4, students carry out their own survey in order to collect and organize data.
In unit 5, during lessons 3.A.2-3.A.4 the teacher represents fractions using notation. However it is not expected that students do so; it is merely done in passing without any explanation of how to write using correct notation. Fraction notation is appropriate for Grade 3.
In unit 7, all sessions address patterns, which is not a Grade 1 expectation and is a Grade 4 standard.
In unit 8, counting and working with twos and fives is a focus, which is a Grade 2 standard.
Only 5 lessons in unit 4 address 1.NBT.C.4, 5 and 6 for the entire year, so the work provided in this area cannot be considered extensive.

While the following notes exist, they are not explicitly tied to the standards:

The looking back note in unit 1 (page 10) specifically references how the number, counting and story problem work in this unit builds upon the work in the Kindergarten units.
The looking back note in Unit 5 (page 10) describes this unit's connection to the prior work in Kindergarten measurement.

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.

The instructional materials reviewed for Grade 1 partially meet expectations for fostering coherence through connections at a single grade. The materials include some instances where learning objectives are shaped by cluster headings and include some problems that connect clusters and domains. Examples for both arguments are below.

A review of the lesson objectives (Math Focus Points) for all of the lessons which reference an alignment to 1.OA.B reveals that even though the lessons themselves are sometimes actually aligned to the standards in this cluster, the outcomes never explicitly mention properties of operations or the relationship between addition and subtraction. This is evident in units 1, 3, 6 and 8.
In unit 8 in the five new lessons which were added to the curriculum (Sessions 4A.1-4A.5), the outcomes do show evidence of the attention given to the CCSSM cluster heading. For example, "adding a 1-digit number or 10 to a 2-digit number" appears in sessions 4A.2 and 4A.3 and "adding or subtracting a multiple of 10 to a 2-digit number appears in 4A.3-4A.5.

There are multiple pieces of evidence to show that the materials include problems and activities that connect two or more domains or two or more clusters in a domain. Some examples of this include:

Unit 5 session 3A.1 connects 1.G.A.3 (partitioning shapes, particularly circles, into halves) to telling time to the half-hour (1.MD.B.3) by partitioning the analog clock into halves.
Unit 5 sessions 1.4, 1.5A and 2.4 connect 1.MD.A (measurement) to 1.OA.A by using measurements as a context for addition and subtraction story problems and solving.
Unit 2 Sessions 1.1-1.7 activities involve composing/decomposing shapes (1.G.A.2) connect to 1.NBT.A.1 by asking students to count and record the number of each shape used and then find the total number of shapes used by adding them all (1.OA.C).
Unit 4 sessions in investigation 1 and 2 connect 1.MD.C.4 as an interesting context with which to work on addition and subtraction when comparing two data sets to find how much larger one is than the other, and other addition and subtraction situations (1.OA.A, 1.OA.C).
In unit 6 sessions 1.8A and 1.8B, solving story problems with missing parts (1.OA.A) connects to applying properties and the relationship between addition and subtraction (1.OA.B) by using addition/counting up strategies to solve the subtraction situations.
However, with the inclusion of unit 7 on patterns there is evidence to refute cluster to cluster and domain to cluster connection.

Criterion 1.3: Coherence

Overview of Gateway 2

Rigor & Mathematical Practices

Materials were not reviewed for Gateway Two because materials did not meet or partially meet expectations for Gateway One

Gateway 2

v1.0

Gateway 2

Rigor & Mathematical Practices

Criterion 2.1: Rigor

Criterion 2.2: Math Practices

Not Rated

Criterion 2.1: Rigor

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.

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.

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.

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

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.

Criterion 2.2: Math Practices

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

Indicator 2E

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

Indicator 2F

Materials carefully attend to the full meaning of each practice standard

Indicator 2G

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:

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.

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.

Indicator 2G.iii

Materials explicitly attend to the specialized language of mathematics.

Criterion 2.2: Math Practices

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

Criterion 3.1: Use & Design

Criterion 3.2: Teacher Planning

Criterion 3.3: Assessment

Criterion 3.4: Differentiation

Criterion 3.5: Technology

Not Rated

Criterion 3.1: Use & Design

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.

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.

Indicator 3B

Design of assignments is not haphazard: exercises are given in intentional sequences.

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.

Indicator 3D

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.

Indicator 3E

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

Criterion 3.2: Teacher Planning

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.

Indicator 3F

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

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.

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.

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.

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).

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.

Indicator 3L

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.

Criterion 3.2: Teacher Planning

Criterion 3.3: Assessment

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.

Indicator 3M

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.

Indicator 3N

Materials provide strategies for teachers to identify and address common student errors and misconceptions.

Indicator 3O

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

Indicator 3P

Materials offer ongoing formative and summative assessments:

Indicator 3P.i

Assessments clearly denote which standards are being emphasized.

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.

Indicator 3Q

Materials encourage students to monitor their own progress.

Criterion 3.3: Assessment

Criterion 3.4: Differentiation

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.

Indicator 3R

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

Indicator 3S

Materials provide teachers with strategies for meeting the needs of a range of learners.

Indicator 3T

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

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).

Indicator 3V

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.

Indicator 3W

Materials provide a balanced portrayal of various demographic and personal characteristics.

Indicator 3X

Materials provide opportunities for teachers to use a variety of grouping strategies.

Indicator 3Y

Materials encourage teachers to draw upon home language and culture to facilitate learning.

Criterion 3.4: Differentiation

Criterion 3.5: Technology

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

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.

Indicator 3AB

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.

Indicator 3AC

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

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.).

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.

Criterion 3.5: Technology

Downloadable Resources

2012