Your favorite number…

1. Your favorite number…

2. Today’s Objectives • Identify how the processes of connections and representation improve student understanding, retention, and achievement • Identify ways to incorporate connections and representations into math class

3. Developing Understanding through Connections John SanGiovanni Elementary Mathematics Office

4. What is 12? • Think of as many different ways to show 12 that you can. • We will come together as a group in a few minutes to share our ideas.

5. How many different ways can we show 12?

8. Students naturally connect ideas they already have to construct a new idea. Van de Walle, J. (2007). Elementary and Middle School Mathematics: Teaching Developmentally (6th ed). Boston, MA: Pearson

9. Students naturally connect ideas they already have to construct a new idea. The more ideas used and the more connections made, the better we understand. Van de Walle, J. (2007). Elementary and Middle School Mathematics: Teaching Developmentally (6th ed). Boston, MA: Pearson

10. Think-Pair-Share • What things do we do in reading to build understanding and/or comprehension?

11. The Frayer Model

12. Definition (in own words) • Facts/Characteristics Polygon • Non-Examples • Examples

13. Definition (in own words) • Facts/Characteristics Polygon • Non-Examples • Examples A simple closed, plane figure made up of three or more line segments.

14. Definition (in own words) • Facts/Characteristics Polygon • Non-Examples • Examples A simple closed, plane figure made up of three or more line segments. • Closed • Simple • 2-dimensional • 3 or more line   segments

15. Definition (in own words) • Facts/Characteristics Polygon • Non-Examples • Examples A simple closed, plane figure made up of three or more line segments. • Closed • Simple • 2-dimensional • 3 or more line   segments

16. Definition (in own words) • Facts/Characteristics Polygon • Non-Examples • Examples A simple closed, plane figure made up of three or more line segments. • Closed • Simple • 2-dimensional • 3 or more line   segments

20. Concept Circles

21. 5 13 acute right sphere pyramid 11 2 7 ? parallel obtuse cone prism 29 17 Concept Circles and Variations Concept: 3 dimensional figures Concept: Prime Numbers Concept: Types of angles Variation: What could the “ ?” be? Variation: Which does not belong?

22. Webbing Take a moment with a partner to come up with as many supporting details about the topic as you can.

23. Were we able to beat HCPSS 3rd graders? Multiplication What details were we able to come up with?

27. Using numbers, how many ways can you express 50?

33. Funny Numbers Regular Number Regular Number 64 50 14

34. Funny Numbers Regular Number Regular Number 64 50 14 88 70 18

35. Funny Numbers Regular Number Regular Number 64 50 14 88 70 18 39 ?

36. Combining Predictions and Data

37. Do you agree or disagree?

38. 7/13 is close to 1/2. 6/37 is close to 0. 17/24 is close to 1.

40. Organized Tables can be used for highlighted characteristics of numbers or concepts. Ideas can be added as units progress.

41. Consider these fractions. 1/4 2/3 5/8 2/5 Draw a picture. Are they close to 0, 1/2, or 1. What do they mean? What are they equivalent to? On a number line

43. Representing Numbers, 1st Grade

44. Organizer’s to help develop problem solving…

45. There are 3 tennis balls in a can. The tennis team has 13 cans. How many tennis balls does the team have?

48. A primary example… Annie put 3 strawberries on her plate. She put 6 grapes on her plate. How many pieces of fruit did she have?

49. Whole Pieces of Fruit Part Part 3 strawberries 6 grapes

50. 2 165 5 490 78 0.37 • Choose 2 numbers. • Think about how those numbers might describe John.