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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
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
1st Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
2nd Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
Math 3-5
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
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
4th Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
5th Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
Report for 4th Grade
Alignment Summary
The instructional materials reviewed for Grade 4 do not meet expectations for alignment. The materials do not devote the large majority of time to grade-level work and topics from future grades are assessed. There is little 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.
4th Grade
Alignment (Gateway 1 & 2)
Usability (Gateway 3)
Overview of Gateway 1
Focus & Coherence
The instructional materials reviewed for Grade 4 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, especially with the inclusion of Unit 7 which is aligned to above grade-level work. In addition, there is no explicit connection made to standards from prior or future grades, fostering coherence.
Gateway 1
v1.0
Criterion 1.1: Focus
The instructional materials reviewed for Grade 4 do not meet the expectations for assessing material at the grade level. The materials assess many topics that are above grade level. Statistical distributions, specifically, should not be assessed before Grade 6.
Indicator 1A
The instructional materials reviewed for Grade 4 do not meet expectations for assessment. The materials assess statistical distributions with questions that align to standards from 6.SP.A, “Develop understanding of statistical variability,” and 6.SP.B, “Summarize and describe distributions.”. There are also many other sessions in the materials that would need to be modified or omitted because of their alignment to above grade-level standards. 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 2, the end-of-unit assessment expects students to describe the shape of the data from a numerical data set, including where the data are concentrated and the highest, lowest, and median values. The scoring rubric indicates that in order to meet expectations, students are to recognize statistical distributions including range, median, mode, and outliers. These expectations align to standards within 6.SP. According to Table 2 on page 9 of the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics, assessment of statistical distributions should not occur before Grade 6.
- Problem 2 in the end-of-unit assessment for unit 4 assesses how to find the area of polygons, in this case a kite-shaped figure, using square units. The scoring rubric on page 161, indicates that the question is assessing student ability to find the area of polygons using a square unit of measure and counting them– square units and half units. Finding the area of shapes other than rectangles aligns to 6.G.A.1. , “Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.” This problem could be omitted from the assessment without impacting the structure of the assessment.
- The end-of-unit assessment for unit 7 expects students to clearly show an understanding of volume from the scoring rubric on page 106. This expectation aligns to 5.MD.C, “Geometric measurement: understand concepts of volume,” and all of the sessions in unit 7 could be omitted without significantly impacting the underlying structure of the materials.
- Problem 2 on the end-of-unit assessment for unit 8 expects students to solve division problems with 1-digit and 2-digit divisors by using at least one strategy efficiently. The scoring rubric on page 128 indicates that there are several strategies students could use to demonstrate proficiency (none of which is the standard division algorithm). The inclusion of 2-digit divisors goes beyond the language of 4.NBT.B.6, and the problem could either be omitted or modified to a 1-digit divisor without impacting the structure of the assessment.
- In Unit 9, all problems on the end-of-unit assessment are on the topics of line graphs, constant change, and representing constant change on tables. The scoring rubrics on page 145 indicate that students must be able to read and interpret line graphs involving constant rate of change and to complete tables based on a constant change and represent it with an arithmetic expression. Constant rate of change is a topic that aligns to 6.RP.A., “Understand ratio concepts and use ratio reasoning to solve problems.” Since this is the last unit of the grade-level materials, this unit could be omitted without affecting the structure of the materials.
*Evidence updated 10/27/15
Criterion 1.2: Coherence
The instructional materials reviewed for Grade 4 do not meet expectations for focus. The materials do not spend the majority of time on the major clusters in the grade. There were lessons in the CCSSM book that addressed one standard, but that is not adequate time to teach content in major focus areas. There was evidence found where actual student activities do not align with the standards labeled in the materials/table of contents and where students are engaging in work above the grade level, thus diminishing the focus.
Indicator 1B
Instructional materials reviewed for Grade 4 do not meet expectations for focus. The majority of class time is not spent on the major clusters of the grade. According to the alignment 62% of the time is spent on major work at the grade. Upon deeper examination of the content in the nine units at the grade level, in five of these units (2, 4, 5, 7 and 9) there is above grade-level content that is being taught and assessed, which accounts for a portion of each of these not being fully aligned. This would even further decrease the amount of material on major work of the grade. For example:
- Lesson 1.1 and 1.2 in unit 9 align with 8.F.
- Lesson 2.4 in unit 9 graphs a linear pattern-Grade 5 work-and in lesson 2.7 the work comparing the two quantities that are graphed with possible expressions and equations is Grade 6 work.
- Unit 7 has 13 lessons and three assessments. Of the 13 lessons, only two are truly aligned to the standards. Lesson 3.1 in investigation 3 is only aligned because five problems on the homework page ask for students to compare fractions to hundredths, the remaining three problems on the page that ask for decimal addition are not aligned and the lesson itself is on volume and nets, which is Grades 5 and 6 work.
Additionally, every 4.NF standard, which is major work at the grade, is covered in unit 6, with two additional lessons (3.1 and 3.2) in unit 7. The two lessons from unit 7 do not match to 4.NF.C.7 and were not included in the following calculation. Therefore in the fraction unit, there are 22 lessons out of 162 total lessons in the program, which allots for 13.5 % of the time, or 15% including the three assessments of fraction. With six major clusters in Grade 4, three of them being 4.NF.A, B and C, this is not enough time to spend on the work of extending equivalence, building fractions and understanding decimals.
Criterion 1.3: Coherence
The instructional materials reviewed for Grade 4 do not meet expectations for coherence in the grade. The materials are not coherent with the progressions because work from Grade 5 volume is included and fraction work is underrepresented.
Indicator 1C
The instructional materials reviewed for Grade 4 partially meet expectations for supporting content to enhance focus and coherence simultaneously by engaging students in major work of the grade. In some cases, the supporting work enhances and supports the major work of the grade level and in others, it does not. For example:
- Work in line plots in unit 2 does not support the major work of 4.NF.A and B because they do not involve fractions and the only focus is on the shape of the data.
- In unit 6, session 2.7A, a line plot with fractional measures is used to solve problems with operations (addition and subtraction) on fractions, thereby connecting 4.MD.B.4 to 4.NF.B.3.
- In unit 3, work with multiples in investigation 3 and understanding the effect of multiplying by a multiple of 10 supports students in the partial products and other multiplication strategies they will be using when performing multi-digit multiplication and even when using the standard algorithm. This illustrates that work in 4.OA.B supports the major work in 4.NBT.B.4 and 4.NBT.B.5.
- Unit 4 lessons 1.1-1.5 do not fully support 4.NBT.B.4 as truly developing fluency for adding and subtracting within one million.
- In unit lessons 4 and 3.1-3.3 students write equations and add and subtract angle measures aligning to 4.MD.C, connecting the work in this standard to computation in 4.NBT.B. These are not, however, in real-world problems.
- In unit 9, fast and slow growth in lesson 3.1 does not fully support 4.NF standards, nor is the data truly a set of measurements in fractions of a unit where students are solving problems with the fractional measurements displayed.
- In unit 9 lesson 3.2 also labeled as aligned to 4.MD.B.4 supports work above the grade level (shape of the data, comparisons) and does not foster coherence within Grade 4.
- Two-step story problems are not evident in the materials. This does not foster coherence nor does it support focus of the grade level.
Indicator 1D
The instructional materials reviewed for Grade 4 do not meet expectations for viability of content for the scope of one year. The curriculum consists of 162 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, the review team found that the major work accounts for about 62% of the lessons. The major work of 4.NF is greatly underrepresented in this series. In addition, unit 6 teaches addition of decimals which is above the grade level in three of the 24 lessons that deal with 4.NF.A, 4.NF.B and 4.NF.C.
Indicator 1E
The instructional materials reviewed for Grade 4 do not meet expectations for consistency with the progressions. The materials do not develop according to the progressions, nor do they give students extensive work with grade-level problems. In the front matter of each unit, there are detailed explanations of the content addressed that appears in a section called mathematics in this unit. Within this section, the "Looking Back" and "Looking Forward" pieces explains content from entering school to future grades within the program. There are not explicit connections to CCSSM, however. For example:
- "Understanding Volume" in unit 7, investigation 3, does not follow the grade-to-grade progression due to the concept being misaligned. Volume is introduced as a standard in Grade 5.
- Investigation 4 in unit 4 is completely not in the grade-to-grade progression because it has lessons on finding the area of special quadrilaterals which is a Grade 6 standard.
- The major work of 4.NF is greatly underrepresented in this series. There are only 22 of 162 sessions that appropriately support number fraction work.
- Unit 6 includes language around extending equivalence understanding in number fraction from Grade 3. There is a small note on page 10 about connections to Grades 2 and 3, but not an explicit connection to the standards. These connections could be enhanced in the next edition.
- In the area of 4.OA.A, only one lesson is focused on multiplicative comparison and this isn't enough to engage the students in this major work. There is an all-around lack of multi-step problem opportunities throughout. For the most part, students are guided through a three-part progression to guide them to solve.
Indicator 1F
The instructional materials reviewed for Grade 4 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. For example:
- In unit 1, sessions 1.1-1.4 have math focus points mentioning arrays, yet the lessons are aligned to the 4.OA.A domain, whereas a 4.NBT alignment might be more appropriate.
- Unit 1, sessions 2.2-2.3 have math focus points that use the specific terminology of "fluency," however fluency standards in Grade 4 are specific to addition and subtraction, but the work is on multiplication.
- In unit 6, the objectives are not clearly shaped by the cluster heading. Most mention adding or subtracting fractions, but do not reference anything that can be tied to extending previous understandings of whole number computation.
- There is evidence to show that students' work with units of measurement conversion (4.MD.A.1) is connected with the multiplicative comparison work (4.OA.1). In unit 7 session 3.5A, the lesson description includes cues to teachers to discuss how measurement equivalents charts tell how different units are related. For example, "The first equation in the chart (1 pound = 16 ounces) tells you that there are 16 ounces in a pound. That means a pound is 16 times as heavy as an ounce," thereby relating to a multiplicative comparison.
- No evident connections between multiplicative comparison and the multiplication of a fraction by a whole number (4.NF.B.4) is found in the pertinent lessons (unit 6, sessions 3.A.1-3.A 2).
- There is also evidence to show that a connection is made between addition of fractions (4.NF.B.3) and angle measurement (4.MD.C.5) in unit 4 session 3.4.A, where an angle measure of 1 degree is related to being 1/360th of a circle when discussing measuring with a protractor.