Investigations and the Common Core: FAQs

Investigations in Number, Data and Space is a coherent and focused K-5 mathematics curriculum that can be used to implement the philosophy and content described by the Common Core State Standards (CCSS). Full alignment can be achieved by teaching the program fully, as written, and integrating the new content included in Investigations and the Common Core.

The Standards for Mathematical Practice are closely aligned with the goals and principles that guided the development of every Investigations Session. The Practices – which include making sense of and reasoning about mathematics, constructing arguments and explanations, and selecting appropriate tools to model mathematical concepts and solve problems – are and always have been deeply embedded in the fabric of the Investigations curriculum and facilitate the teaching and learning of mathematics. Virtually every lesson in Investigations includes one or more of these practices. (Read more about the Mathematical Practices in Investigations (PDF) .)

There is strong alignment between Investigations and the Math Content Standards. Each curriculum unit provides an in-depth study of a specific and related set of mathematical concepts and skills. The design of the materials offers students extended opportunities to make sense of, practice, and develop fluency with the key concepts and skills within a grade level and across grade levels. Most of the CCSS content standards are met by teaching the units, in order, as written. Investigations and the Common Core provides new content so that all Standards are covered. (Download PDFs of Pearson’s Correlations of Investigations and the CCSS at: K, 1, 2, 3, 4, 5 )

All of the new materials were submitted to Pearson before PARCC and Smarter Balanced came out with their assessment frameworks. Both consortia offer ways to sign up to receive news releases and other information, and occasionally ask subscribers for feedback on different aspects of their work.

Most of the CCSS content standards are met by teaching the grade level units, in order, as written. Investigations and the Common Core provides new content so that all Standards are covered. (Download PDFs that describe this content at: K, 1, 2, 3, 4, 5.)

 

 

 

 

The authors of Investigations worked with Pearson to develop materials to support teachers and schools that use Investigations to implement the Core Standards. These companion materials are designed for use in conjunction with the curriculum units at each grade level, K-5, and include everything needed to support teachers as they implement Investigations and the CCSS in their classrooms. (Learn more: Investigations and the Common Core.)

The Investigations and the Common Core companion materials include an instructional plan for each Investigation, which identifies the major Math Practice(s) and content standards for each session. To correlate the assessments/benchmarks with the CCSS, refer to the Instruction Plan for that Session.

No. The sequence at each grade remains the same. Instead, additional content has been added, and some content omitted. Additional content builds on existing content and uses familiar contexts and representations within the grade level.

Each grade level includes no more than 166 Sessions. Because Sessions have been added, Sessions to omit are suggested. (Download PDFs that contain information about pacing and content that’s been added and omitted at: K, 1, 2, 3, 4, 5.)

The Investigations authors closely examined each grade level to determine what Common Core Standards were not addressed, or were not fully addressed, in Investigations. Such content is addressed in a variety of ways, depending on the degree of alignment, in Investigations and the Common Core.

 

 

 

• Some standards involved language, vocabulary, notation, or levels of fluency specific to the CCSS. These are addressed by a new activity, a Teaching (or Math) Note, an edit to a Classroom Routine or Ten-Minute Math Activity, or through additional Homework or Daily Practice Pages.
• For bigger content changes, TERC identified the number of new Sessions needed. Most new Sessions were written by TERC authors; a few were written by Pearson.

Given the total number of new Sessions needed at each grade, decisions were made about what to omit. Sessions were selected if the math emphases were repeated for reinforcement (e.g. student data projects) or if the content was not included in the CCSS at that grade and was not seen by the Investigations authors as foundational for later/future work (e.g. the work on symmetry and timelines in grade 2, and probability in grade 4). It was easier, and resulted in a more coherent whole, to omit an entire chunk of work, rather than trying to omit a Session here and a Session there. (Download PDFs that contain information about pacing and content that’s been added and omitted at: K, 1, 2, 3, 4, 5.)

Not all “extraneous” content was omitted. Why? Work with data, geometry, and pattern and function supports the CCSS standards within and across grade levels. For example, counting is one of the key areas of focus in Kindergarten. The data unit in Kindergarten supports the development and consolidation of counting skills and concepts. In addition, work in these areas provides the foundation for the development of students’ understanding in later grade levels. Foundational work in volume remains in grades 3 and 4, to support the volume standard in grade 5. Deep understanding comes from making connections within and across content strands. For more information see FAQs about Content.

Investigations and the Common Core is available from Pearson, in hard copy and online, through Successnet. Information about distribution and cost is available from your Pearson sales rep or through the Pearson website.

Yes. Users of the copyright 2008 edition of the curriculum need to buy Investigations and the Common Core State Standards at Grade X for each teacher. In addition to a set of “snap in” instructional plans for each unit, and new activities and sessions, this book also includes blackline masters of all new Teacher Resources and Student Activity Book pages. These masters are used in addition to the existing Student Activity Book for the grade level. For those who have not yet purchased the Student Activity Book, a CCSS-specific version is available at each grade that includes all of the Student Activity Book pages needed, in chronological order. Any new materials are available individually, from Pearson. For more information, contact your Pearson Sales Rep.

Schools or districts buying the curriculum for the first time should buy the CCSS curriculum package and the CCSS-specific Student Activity Book, both with a copyright of 2012. (Depending on budgets, and what classrooms already have, additional purchases might include: materials kits, Student Math Handbooks, access to digital components, the Spanish component, and Investigations for the Interactive Whiteboard. For more information, contact your Pearson Sales Rep.)

Yes. You can continue to use the 2008 edition, or can purchase the 2012 edition, without any of the CCSS-related components.

The TERC authors and Pearson are currently working on a 3rd edition of Investigations ©2017. Classroom implementation is planned to begin fall, 2016. Investigations 3rd edition will maintain its standard of excellence as a focused, coherent program that embodies the Common Core State Standards for Mathematical Practice and fully aligns to the Content Standards.

A timeline for a CCSS version has not yet been determined. However, many of the activities and tools that currently exist as part of Investigations for the Interactive Whiteboard can be used to support many of the new CCSS activities and sessions.

A timeline for a CCSS version has not yet been determined. However, new CCSS activities and sessions include suggestions for Intervention, Extension and English Language Learners, as part of the Differentiation: Supporting the Range of Learner section found in nearly every Investigations lesson.

Users of Investigations ExamView should “Check for Content Updates” from within the product to access a new Test Bank with the Common Core State Standards assessment items. A Common Core Standards version of Investigations SuccessTracker will require customers to enter a new Access Code into their PSN account. Contact your Pearson sales rep to order the new SuccessTracker Online Access Pack.

Because student learning takes place over time and at different paces, all mathematics curricula include opportunities to review and practice concepts and skills. Work that has been introduced in a previous grade will be review for most students. As always, the teacher must use her judgment about how to move through that content, based on her observations of and knowledge about the students in her class.

Whenever possible, new activities and Sessions build on existing content and on familiar contexts and representations within a grade level. Counting to 100 is introduced at the beginning of Unit 6, How Many Do You Have?, because it builds on the understandings developed in Units 1-5, and best fits with the work of this unit. Once introduced, practice is incorporated throughout Units 6 and 7, as a new Classroom Routine. Similarly, counting to 100 by 10s – a difficult concept for Kindergarteners – is introduced in Unit 7 so that students are as solid as possible with counting by ones, and so that it can be tied to an actual context (the number of fingers in a group of 10 children) that builds on work students have already been doing (thinking about the number of noses and eyes there are in their class). Again, practice with counting by 10s is then built into a familiar Classroom Routine, Attendance.

Given that Investigations is a complete K-5 curriculum that provides a coherent year of mathematics at each grade, we strove to maintain that whole as much as possible. If removing a piece of content from a Session/Investigation/Unit would damage the integrity of that Session/Investigation/Unit, we kept it. We also kept content that:

 

 

• Connects to the CCSS in ways that people don’t necessarily “see” or expect to see (e.g. counting is a major focus of the Kindergarten data unit; multiplication ideas are embedded in the work on area in grade 3)
• A particularly good opportunity to focus on one or more of the math practices (e.g. the pattern units in K-1)
• Is foundational to the work of that or later grades (e.g. patterns in K-1, percents in 5th grade)

The pattern units at K-1 and percents in grade 5 are examples of such content.

The work with repeating patterns and number sequences in K-1 builds a critical foundation for students’ work with linear and non-linear contexts involving relationships between two variables in grades 2-5. These units also embody several of the Mathematical Practices, particularly modeling with mathematics and looking for and making use of structure. This work is one of the ways that Investigations addresses the four areas identified as foundational to the study of algebra: 1) generalizing and forming patterns, 2) representing and analyzing the structure of numbers and operations 3) using symbolic notation to express functions and relations and 4) representing and analyzing change.

Percents are an integral part of Grade 5 Unit 4, What’s That Portion?. Removing them would have damaged the integrity of the mathematics of that unit, and the decimal unit (Unit 6). In addition, we knew from field testing that many students enter 5th grade knowing a lot about percents and that this knowledge helped many of them make connections among and build conceptual understandings of fractions and decimals. The work with percents—based on a 10 x 10 grid representation or reasoning (e.g. 5/8 is 62 ½% because it’s the same as ½ plus 1/8)—prepares students to use numerical procedures for finding percents in grade 6.

Most of the standards that address fluency with the facts are covered by teaching Investigations in sequence, as written. The Investigations and the Common Core companion materials include the following new content.

 

• In Kindergarten, an activity has been added to several Sessions in Unit 6, to give students the opportunity to practice, and teachers the opportunity to assess and record her observations about students’ ability to “fluently add and subtract within 5.” (K.OA.5)
• In grade 1, sidebars have been added reminding teachers to assess “fluency for addition and subtraction within 10.” (1.OA.6) A tool for recording his/her observations over time is included.
• In grade 2, a set of subtraction cards related to the addition combinations up to 10 + 10 has been added to provide opportunities for students to practice and for teachers to assess whether students can “fluently …subtract within 20 using mental strategies.” (2.OA.2)
• In grade 3, the six additional problems students must “know from memory”—6 x 9, 7 x 8, 7 x 9, 8 x 8, 8 x 9, and 9 x 9— have been incorporated into students’ sets of array and multiplication cards. (3.OA.7)

In grades 2 and 3, the standards make a distinction between “fluency” and “know from memory.” The latter includes a more limited set of facts (i.e. sums or products of two one-digit numbers) while the former includes problems involving 2-digit numbers (e.g. 16+2 and 19-3, or 14 x 5 and 80 ÷ 10).

 

The CCSS’s description of fluency in grade 1: “Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).” (1.OA.6)

For one of the CCSSM authors’ opinions on the difference between “fluently” and “from memory, ” see Tools for the Common Core Standards.

Teachers need to understand the standards, which includes knowing what they mean and what they do not mean. For example, second graders needs to be fluent adding and subtracting within 100. They are expected to use drawings, models, and representations with numbers to 1000. In Grade 4, students are expected to multiply a fraction and a whole number, not a fraction by a fraction.

 

Teachers at all grade levels need to know how the materials are organized—how to integrate the use of the Instructional Plans with the existing curriculum—and any new materials they may need to gather or prep.

The Standards for Mathematical Practice should be studied, discussed, and implemented at every grade level.

In terms of specific content:

• K-2 teachers should consider how the new materials address the standards for Number and Operations Base Ten (NBT) in their grade and across K-2. Similarly, understanding what “properties of operations” means in the primary grades, and how those ideas play out in Investigations, will be important.
• In grades 3-5, new ideas in the rational number strand will need attention. Third graders now work with fractions on a number line (Unit 7). Fourth graders multiply fractions and whole numbers (Unit 6). In Grade 5, professional development can focus on working through the 10 new Sessions on multiplying and dividing fractions (Unit 4), doing and discussing the mathematics and thinking about what students might do. It should also include thinking through the new work with multiplying and dividing decimals (Unit 6), and why this isn’t a simple transition from work with whole numbers.

A: Common Core State Standards were published in June 2010 as part of the work of The Common Core State Standards Initiative. They include standards for English Language Arts and Mathematics (which include Standards for Mathematical Practice). Also see the CCSS website’s answers to Frequently Asked Questions.

A: The Standards for Mathematical Practice “describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise.” These Standards include making sense of and reasoning about mathematics, constructing arguments and explanations, and selecting appropriate tools to model mathematical concepts and solve problems. This diagram, from one of the lead authors, is “an attempt to provide some higher order structure to the practice standards, just as the clusters and domains provide higher order structure to the content standards.” (http://commoncoretools.wordpress.com/2011/03/10/structuring-the-mathematical-practices/)

A: The standards can be read on or downloaded from the Core Standards website. A blog written by William McCallum, one of the lead authors, provides a hyperlinked version of the same document, as well as documents that compile the K-8 Standards by domain. The Illustrative Math Project has developed an online expandable/collapsible version of the K-8 Standards. The National Council of Supervisors of Mathematics (NCSM) has published an Expanded version that includes the overall introduction to the standards, as well as “Standards-setting Criteria, Standards-Setting Considerations, and Applications of the Standards for English Language Learners (ELLs) and Students with Disabilities”. Another project uses learning trajectories to display the information visually. Also in progress: Progressions Documents that describe “the progression of a topic across a number of grade levels, informed both by research on children’s cognitive development and by the logical structure of mathematics” and “examples of student tasks that develop and assess [the] skills, understandings and practices [described in the CCSS].”

A: The CCSS website maintains a regularly updated map of states that have adopted the Common Core State Standards. Adoption means committing to 100% of the Standards within 3 years. Schools must spend a minimum of 85% of the school year on this content; they can focus on other topics in the remaining 15%.

A: Two state-led consortia are developing assessments that align with The Common Core State Standards. They are The Partnership for the Assessment of Readiness for College and Careers (PARCC) and The Smarter Balanced Assessment Consortium (SBAC). States that have adopted the Common Core State Standards have signed on to one (or occasionally both) consortium, and will use the test developed by it. The new assessments are expected to be available/in use for school year 2014/2015. Visit the PARCC and SBAC websites for more information, and to find out which states are working with which consortium.