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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 2nd Grade
Alignment Summary
The instructional materials reviewed for Grade 2 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. 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.
2nd Grade
Alignment (Gateway 1 & 2)
Usability (Gateway 3)
Overview of Gateway 1
Focus & Coherence
The instructional materials reviewed for Grade 2 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. There is little explicit connection made to the progressions of learning in the standards.
Gateway 1
v1.0
Criterion 1.1: Focus
The instructional materials reviewed for Grade 2 meet the expectations for assessing material at the grade level. Although there are multiple units and sessions noted that align to and/or assess standards that are beyond Grade 2, 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 materials reviewed for Grade 2 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 4, session 2.8 assesses how to: order, represent, and describe a set of numerical data; describe what the data show about the group surveyed; interpret a data representation, including a line plot; compare two sets of data; sort a set of data by two attributes at one time; and use a Venn diagram to represent a sorted set of data. These expectations are appropriate for Grade 2 students, but there are seven sessions that should be omitted from the materials because of the way in which they assess the expectations. In the CCSSM, 2.MD.D.9 states “Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units,” and 2.MD.D.10 states, “Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.” Session 2.1 should be omitted because it uses number of pockets as the measure instead of lengths of objects, and there are problems with more than four categories. Session 2.2 continues to use measures other than lengths of objects. sessions 2.3 through 2.7 also use measures other than lengths of objects and expects displays of data other than the ones addressed in 2.MD.D.10. The omission of these sessions from the session does not significantly impact the underlying structure of the materials.
- The end-of-unit assessment for unit 5 assesses how to: find the value of one quantity in a constant ratio situation given the value of the other; connect the numbers in a table to the situation they represent; describe how the two numbers in the row of a table are connected to the situation the table represents; and determine the element of a repeating pattern associated with a particular counting number in an AB or AAB pattern. These expectations most closely align to 6.RP.A.3, “Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations” and 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.”. Since these expectations are two or more grade levels above the current one, the entire unit with 11 sessions should be omitted, but the omission of the entire unit does not significantly impact the structure of the materials.
- In unit 7, there are several sessions that use fraction notation and fractions as numbers. Investigation 2 is consistent with the partitioning required in 2.G.A.3, “Partition circles and rectangles into two three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc. and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.”, Sessions 1.1 to 1.4 and 2.1 to 2.6 use fraction notation. Unit fractions are included in these lessons but not introduced as unit fractions, 1/b, which aligns to 3.NF.A.1, “Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b,” and Session 1.4 introduces mixed numbers which aligns to 4.NF.B, “Build fractions from unit fractions.”. This unit occurs towards the end of the year, so it may be Mathematically reasonable to introduce fraction notation if the students are ready. Teachers should either omit the references to fraction notation in the lessons and assessments or make sure they are also introducing the concept of a unit fraction along with fraction notation.
*Evidence updated 10/27/15
Criterion 1.2: Coherence
The instructional materials reviewed for Grade 2 do not meet expectations for time spent of the major clusters of the grade. The materials are not aligned to the major work of Grade 2 and do not devote the large majority of class time to the major clusters.
Indicator 1B
The instructional materials reviewed for Grade 2 do not meet expectations for majority of class time spent on the major clusters of the grade. According to the unit instructional plans, there are 166 days of lessons and assessments. Between units aligned to supporting and additional work or content from future grade levels, 51 lessons are not aligned to major work. This leaves 115 sessions on the major work, or 69%. Examples of misaligned standards that would decrease the focus percentage include:
- Unit 1: 13 of the 27 sessions more appropriately align with standards from Grade 1, specifically 1.1, adding to ten; lesson 2.1 which involves counting, but in Grade 2 this should extend to counting within 1,000 and the examples are far less; session 2.6 involves adding 1 and 2 to a given number.
- Unit 1: Lessons 3.1-3.5 align with Grade 1 rather than Grade 2, as the work is all combinations of ten.
- Unit 2: Session 2.3 addresses area, a Grade 3 standard.
- Unit 3: Session 4.2 addresses telling time to the hour and half hour, which is addressed in Grade 1.
- Unit 7: Sessions 1.2-1.4 address fractions and include fractions of a set, which is beyond the scope of Grade 2 and is more appropriate for Grade 4.
- Unit 5: Lessons in all three investigations are aligned to patterns, a Grade 4 standard.
- Unit 8: The daily practice on session 3.5 worksheet "What is the Fraction?" has an example of fifths. Grade 2 denominators (partitions) are limited to halves, thirds and fourths.
- Unit 9: Lessons 2.3-2.8 are not truly aligned to 2.MD.D.9 as the data for the line plots is not measurement lengths.
- There is a noted absence of two-step word problems. One-step instead of two-step problems are evident and a missed opportunity in unit 1, sessions 4.3, 4.5 and 4.8 and in unit 8, sessions 3.1, 3.2, 4.1 and 4.4.
Criterion 1.3: Coherence
The instructional materials reviewed for Grade 2 do not meet expectations for coherence in the grade. The materials are not coherent with the progressions because work from future grades interferes with a coherent and consistent progression with the standards.
Indicator 1C
The instructional materials reviewed for Grade 2 partially meet expectations that supporting content enhances focus and coherence by engaging student in the 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. Examples that support a partial rating include:
- Unit 2, lesson 1.4 "Addition Combinations and Ways to Fill" asks the students to fill in a shape using pattern blocks, count the number of shapes used and record the number of each shape. This lesson engages students in the major work of 1.NBT.1 not the major work of Grade 2.
- Lessons in unit 4, 1.4A bar graphs connect to 2.OA.A.1 and 2.OA.B.1 through counting questions asked and provides contexts for solving problems (although numbers are small). Pictographs are absent.
- "How many teeth?" in unit 4 has the potential to go beyond 2.MD standards. In Grade 2, students should work with data in up to four categories, but a question posed to students in Kindergarten to Grade 5 in the sessions could go well beyond four categories and therefore, Grade 2 work.
- Unit 9, session 1.5, doesn't really align with 2.MD, as the activities do not fully align with standard measurement. Therefore it is not connected to 2.MD.A.1 (measuring length) as students do not use a ruler to generate measurement.
- Time to the five minutes is developed through a progression of daily routines throughout all units that span the curriculum. In unit 6, session 2.5, students begin practicing counting by fives to tell time, which supports their work in 2.NBT.A.2.
Indicator 1D
The instructional materials reviewed for Grade 2 do not meet expectations for viability of content for the scope of one year. The curriculum consists of 166 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, there is a concern that major clusters, 2.MD.A (measure and estimate lengths) and part of 2.MD.B.5 (word problems involving measurement) are addressed in unit 9 and if a teacher runs out of time in the school year, these important clusters which are needed to prepare for Grade 3 may be shortchanged. Additionally, in that same unit, a great deal of time is devoted to non-standard measure, and only four lessons in investigation 3 actually hit the mark with the measurement of length using U.S. customary and metric measurement. Also, 2.NBT.A (place value and comparing numbers to 1000) is minimally touched upon. Three-digit place value is only addressed in four lessons in unit 6 (5A.2-5A.5), and this will definitely not prepare students for the computation and number work in Grade 3.
Indicator 1E
The instructional materials reviewed for Grade 2 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. Detailed explanations of the content addressed appears in in the front matter of each unit in a section called Mathematics in this Unit. Within this section, the Looking Back and Looking Forward pieces explain content from entering school to future grades within the program. There are not explicit connections to CCSSM, however. Some examples of misalignment with the indicator as a whole include:
- Unit 6, session 5.A2 and 5.A3 have math focus points shaped by the cluster heading for 2.NBT
- Unit 6, investigation 1 is about story problems. This is an extension of 2.OA.A.1 with furthering knowledge of addition and subtraction properties and extension of place value.
- Future standards are included that weaken an appropriate grade by grade progression, as in unit 5 "Growing Patterns: Ratio and Equal Groups."
- Lessons and quality problems are noticeably missing in the series relating to 2.MD.D.9 and would need to be included in order to qualify as extensive work with grade level problems.
- Work in 2.NBT.B.7 is limited in frequency (five lessons in unit 8; lessons 5A.1-5A.5). More work is needed in this area.
- Throughout, the review team noted the absence of two-step word problems in all instructional materials.
Indicator 1F
The instructional materials reviewed for Grade 2 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:
- All of the lessons in investigation 1 contain objectives that indicate developing strategies for accurate measurement and iterating units to measure length. However, instead of identifying work with standard units, all of the objectives in the investigation refer to non-standard measure. In investigations 2 and 3, the objectives become more visibly shaped by the cluster heading. Objectives can be found which include statements such as "using a ruler as a standard measurement tool," and "identifying strategies for accurate measurement." However, noticeably missing from the objectives in investigations 2 and 3 is the word "estimate."
- Unit 5 addresses topics aligned to Grade 6 standards, such as describing the relationship between two quantities in a constant ratio situation and using tables to represent ratio relationship between two quantities as well as finding the value of one quantity in a constant ratio situation.
- Unit 7 includes work from Grades 3-5 in the NF domain, such as finding equal parts of a group and naming them with fractions, finding one half of a set, solving problems about finding halves of quantities in different contexts and solving problems that result in mixed numbers.
- Problems involving dollars, dimes and pennies (2.MD.C.8) are connected with the place value learning of 100s, 10s and 1s (2.NBT.A.1) and in fluently adding and subtracting within 100 using strategies based on place value (2.NBT.B.5).
- In Unit 1, sessions 2.3 and 2.4 illustrate that a dime is a bundle of ten pennies.
- Unit 3 sessions 3.6 and 3.7 lessons involve counting money and trading into groups of dimes and also grouping objects into tens to count them by tens.
- Unit 3 investigation 4 lessons on place value (4.1-4.5) focus on grouping tens and ones and in the student activity pages 67-70 for those lessons, there are money problems involving dimes and pennies included, thereby making a natural connection. Also, student activity page 74 connects place value and money.
- Unit 6 Investigation 3 involves applying place value understanding to computation of 2-digit numbers. In investigation 3, "Get to 100" is introduced in session 3.1 and is then connected with "Collect $1.00" in the next session. Unroll a square (subtraction from 100) is introduced in session 3.4 and then immediately following that, connecting money to place value is the "Spend $1.00" activity. In the discussion in Session 3.6, "How many 10's in 100?" a connection between 10 tens in 100 and 10 dimes in a dollar is specifically demonstrated.