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 Examples Non-Examples Polygon

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

14. Definition (in own words) Facts/Characteristics Examples Non-Examples Polygon 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 Examples Non-Examples Polygon 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 Examples Non-Examples Polygon 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. Concept Circles and Variations Concept: Types of angles spherepyramid coneprism Concept: 3 dimensional figures Concept: Prime Numbers 5 11 29 7 2 13 17 ? obtuse right parallel acute 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. Multiplication What details were we able to come up with? Were we able to beat HCPSS 3rd graders?

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

33. Funny Numbers

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 2/35/8 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?

46. KNOWWANTSOLVE What do I KNOW about the problem? What do I WANT to find out?How will I SOLVE the problem?

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

49. Whole Part 3 strawberries6 grapes Pieces of Fruit

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

51. What are 6 numbers that describe you? Write down 6 numbers that describe you on your square. Choose one of those numbers to write largely on the back of the square.

52. Creating a number quilt Students identify numbers that describe them (2, 165, 5, 490, 78, 0.37)

53. Creating a number quilt Students identify numbers that describe them (2, 165, 5, 490, 78, 0.37) Students write the numbers with descriptions/illustrations on small rectangles of construction paper (different colors) 2165

54. Creating a number quilt Students write the numbers with descriptions/illustrations on small rectangles of construction paper (different colors) Students glue their quilt pieces on to a large piece of construction paper 2 165 490 78 5 0.37

55. Adapting a number quilt The number quilt can then be used to describe different ideas about a unit or topic. Numerator Equivalent fractions Of a whole Mixed numbers Of a set Denominator

57. An example of a number quilt…

58. 3 - topics/units I will be teaching 2 - organizers I would like to use 1 - way I will use an organizer with one of the topics

63. The Vocabulary Cube Important vocabulary words are written on 5 faces of a cube. The terms are described in writing with pictures and examples. The 6th face shows the topic or unit with the five words “webbed” around it. Fraction s numerator equivalent improper Mixed-number

64. Adapting the Vocabulary Cube Identify the main ideas of a topic or lesson Illustrate how topic applies to the real-world or other content area Describe different problem solving strategies In place of “number of the day” Fraction s numerator equivalent improper Mixed-number

65. An example…