2. Agenda: Introduction Quick activity Discussion on Manipulatives CRA…Concrete Representational, Abstract Some common, but powerful manilulatives Geoboard, base-10 blocks, Algebra tiles Algebra Tiles A couple of activities Visualizing mathematics …Three Act Math.

3. A small task (3 minutes) 1. Each of you has a tangram in your group. 2. Your job is to figure out what fraction the smallest triangle represents of the complete tangram.

4. Answer………

5. What concepts could be introduced using Tangrams?

6. Role Of The Teacher “The mere use of manipulatives does not guarantee that students understand concepts and procedures and be able to connect these concepts to abstract symbols without teachers making these connections explicit.” (Reimer & Moyer 2005)

7. A Question Could we become master teachers by just watching a master teacher?

8. What Are Manipulatives? Physical objects used to visualize abstract concepts and promote learning Concrete materials that can be used when exploring math ideas, performing math tasks or solving math problems

9. What the Research Says…. The most valuable learning occurs when students actively construct their own mathematical understanding Provide opportunities for children to explore, develop, test, discuss, and apply ideas The use of physical materials is conducive to the concrete kinds of learning that lay the foundation for the development of mathematical understanding NCTM, 2000

10. Let’s face the objections… Why should I use manipulatives…? “They can’t use them on the test” “My students don’t behave when they have toys in front of them.”

11. Why I should Use Manipulatives Motivate students Feel like they are playing Make math learning real and concrete Prompt discussions about math ideas Allow teachers to see students at work doing mathematics Increase engagement Accommodate various learning styles Visual learners Auditory learners Logical/Mathematical Musical/Rhythmic Bodily/Tactile/Kinesthetic learners Learn through moving, touching, and doing

12. C-R-A CONCRETE: The “doing” stage. Uses hands-on physical (concrete) models or manipulatives to represent numbers and unknowns. REPRESENTATIONAL : The “seeing” stage. Draws or uses pictorial representations of the models ABSTRACT: The “symbolic” stage. Involves numbers as abstract symbols of pictorial displays What grade should we start introducing manipulatives?

13. Role Of The Teacher PLANNING IS KEY!!!! Choose manipulatives to support the lesson’s objectives!! Provide opportunity to become acquainted with manipulatives before they are used in the lesson Encourage the students to talk and write about what they have learned. Help the students to move from concrete to paper-and- pencil abstraction.

14. Geoboards Aid in the teaching of basic geometric concepts and in developing conceptual understanding of area and perimeter Excellent Investigation for MYP Criteria B. Pick’s Theorem

15. Base 10 Blocks Aid to teach Base 10 place value Basic arithmetic operations Build an understanding of number sense … other bases?

16. Algebra Tiles Algebra tiles enable students to access algebraic concepts through geometric understanding. They are the real representations of a abstraction Arithmetic operations are facilitated easily with tiles representing both numbers and variables.

17. What are the most difficult idea in mathematics? Can algebra tiles help?

18. Virtual Manipulatives National Library of Manipulative Gizmos Math Playground … there are millions of apps available for free. Okay, maybe not millions, but certainly enough to get the job done.

19. Three Act Math…. Dan Meyers Problem Solving with a twist Accessible at all age groups Natural “story arc” that takes us from the concrete to the abstract. Students will participate as the resolution of the story demands it.