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

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

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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

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

14. 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.

15. 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?

16. 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.

17. 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

18. These are Manipulatives Too!

19. 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?

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

21. Concrete use of Manipulatives

22. Representation and Abstract

23. 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?