Common Core Mathematics and the Use of Manipulatives BTSA/AIP Spring Professional Development March 25, 2014 5:40-7:00 Nancy Hayashida, Math Coach nhayashida@lbschools.net X2962

Common Core Mathematics Instructional Shifts for Mathematics Focus Coherence Rigor fluency application deep understanding

Common Core State Standards for Mathematics Mathematical Standards Eight Mathematical Practices They both have equal weight

Common Core State Standards for Mathematics Mathematical Standards Grade level specific Informs what the goal is for each student at the grade level Common Core does not prescribe how the standards can be met

3 NF 3a Focus Areas Domains Clusters Standards Major work Grade Level Standards Focus Areas Domains Clusters Standards Major work Supports the major work Additional, not connected to the major work Grade level Domain Standard 3 NF 3a

Common Core Math Lead Teacher Training February and March 2013 This slide shows one level of focus: the shape of the content that is in. This table shows the domains and cluster headings for Kindergarten. But if a mathematician or a math education expert, with the knowledge of how things develop over time, looked at the content for this grade, she would see the main emphases for that grade rising to the surface. Here we see the items marked with green squares are the major clusters. These are the things that are the clear focus of the grade. The other content listed here, the supporting clusters (blue squares) and the additional clusters (yellow circles), are also things that are important for that grade. Everything in the Standards is important and all needs to be covered. What this slide shows is the relationship, the connections among the Standards, and how things support one another. These green squares are concepts that the student must leave Kindergarten knowing. Without a solid foundation of these ideas, they will be set up for failure as they continue through the years. They really have to leave Kindergarten with a secure knowledge of these things.   The other things are not to be left out. It is important to understand how the additional and supporting clusters interact with the major focuses when thinking about time and making decisions. Highlight the cluster headings green, yellow and blue in your standards document. Structure of the Standards and Deep Dive into the Shifts

Common Core Math Lead Teacher Training February and March 2013 Highlight the cluster headings green, yellow and blue in your standards document. Structure of the Standards and Deep Dive into the Shifts

Common Core Math Lead Teacher Training February and March 2013 Highlight the cluster headings green, yellow and blue in your standards document. Structure of the Standards and Deep Dive into the Shifts

Common Core Math Lead Teacher Training February and March 2013 Highlight the cluster headings green, yellow and blue in your standards document. Structure of the Standards and Deep Dive into the Shifts

Common Core Math Lead Teacher Training February and March 2013 Highlight the cluster headings green, yellow and blue in your standards document. Structure of the Standards and Deep Dive into the Shifts

Common Core Math Lead Teacher Training February and March 2013 Highlight the cluster headings green, yellow and blue in your standards document. Structure of the Standards and Deep Dive into the Shifts

Looking at your grade level Mathematical Standards: Standards Activity Looking at your grade level Mathematical Standards: Highlight the cluster headings: Green – major work, critical for the grade level Yellow – additional work, doesn’t connect directly to the major work Blue – supports the major work of the standard

Eight Mathematical Practices Consistent Kindergarten thru Grade 12 Mathematical Practices are to be done daily within the context of the lesson

Eight Mathematical Practices Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.

MP #5: Use appropriate tools strategically Read the MP5 “Tools” What have you used? Why did you choose to use that particular manipulative? What did you do with them? Students? What was the purpose?

Manipulatives Why should I use them in my lesson? Manipulatives provide students with a tactile and concrete experience to make sense of the concept. Manipulatives provide students with a “hook” to refer back to when working with the abstract.

Student made tools are also manipulatives Which one do I use? Purpose Unifix cubes, snap cubes, base ten blocks Ten-frames, two-sided counters Color tiles Pattern blocks, tangrams Judy clocks, rulers, protractors, fraction bars Student made tools are also manipulatives

These are Manipulatives Too!

Manipulatives Marilyn Burns-Base Ten Blocks: What are the concepts the students are practicing? How did one activity help support or lead into the next concept?

Concrete, Representational, Abstract In each lesson students should experience C-R-A

Concrete use of Manipulatives

Representation and Abstract

Summarize In terms of the Common Core Mathematical Practices and Mathematical Standards, what role do manipulatives play? Why is it important that manipulatives are used during instruction by students? What is C-R-A and why is it important?