1. Components of Number Sense Overview Unit 4

2. What’s the “Big Idea”? Multiple authors recommend that teachers utilize the “Big Ideas” in their instruction. Generally authors present the “Big Ideas” as lesson specific. Often lessons are disconnected from each other and / or focus on one “Big Idea” for that lesson. Big Ideas Revisited We use the “Components of Number Sense” to connect every part of the curriculum in almost every lesson, thus, making our lessons more powerful and more efficient. Outcome equals stronger teachers and stronger math students.

3. How does this fit with the NCTM? The NCTM utilizes a strands curriculum The Components of Number Sense are not in conflict with the NCTM strands. The Components enable teachers to build true understanding of the mathematical strands. This helps maintain and build connections for the way students think about mathematics.

4. NCTM Strands Without Number Sense Number & Operations Measurement Geometry Data Analysis and Probability Algebra

5. NCTM Strands With Number Sense Number & Operations Measurement Geometry Data Analysis and Probability Algebra

6. What are the Components of Number Sense? Language Connections Classroom Implementation of the Components of Number Sense Components of Number Sense

7. Quantity and Magnitude

8. Numeration

9. Equality

10. Base Ten

11. HundredsTensUnitsOne tenth One hundredth Weights10 2 10 1 10 0 10 -1 10 -2 Digits65452 Weighted Value 6005040.50.02Total 654.52 * Table taken from Binary Number Systems, 2007

12. Form of a Number

13. Proportional Reasoning

14. Geometric and Algebraic Thinking

15. “Arithmetic in American Mathematics Education” 1.What are the steps for solving a mathematical problem in China? 2.What is the American equivalent to Lie Shi? 3.Using 10 sticks model a figure and then talk about the mathematical expressions that exist within the visual. 4.What are the key points that Ma makes in this article?

16. Reflection Write down individually: –Reinforced –Learned –Want to Know Share with a partner or a small group Complete this task in five minutes.

17. Numeration Quantity/Magnitude Base Ten Equality Form of a Number ProportionalReasoning Algebraic and Geometric Thinking The Components of Number Sense © 2007 Cain/Doggett/Faulkner/Hale/NCDPI Language

18. Analyze the Lesson! How is that each component of the Components of Number Sense gets expressed in the teaching of the lesson as we connect the language and build true mathematical understanding?

19. Story One You have a dime (1/10 of a dollar) and seven nickels (7/20 of a dollar). In fractional form show how much money you have all together.

20. Story Two A team has two team members –3-point shots 1/10 and 7/20. How did the two of them perform as a team ?

21. Just Do It!

22. Language and Math Language Is math-language language? How can we use some of what we do in reading instruction to improve our mathematics instruction?

23. Numeration Quantity/Magnitude Base Ten Equality Form of a Number ProportionalReasoning Algebraic and Geometric Thinking Components of Number Sense © 2007 Cain/Doggett/Faulkner/Hale/NCDPI Language

24. We have to teach math like we teach reading! How is math exactly like a mystery novel? Do we really try to see the BIG picture? How does our chapter in the novel fit the whole story?

31. Two stories You have a dime (1/10 of a dollar) and seven nickels (7/20 of a dollar). –In fractional form show how much money you have all together. Two team members record their 3-point shots as 1/10 and 7/20. –How did they do as a team?

32. Set 2 WCPSS Middle School Remedial Warm-ups Developed with Wake County Public School System/Valerie Faulkner © 2006 Valerie N. Faulkner/Wake County Public School System

33. Trashketball The Power to Understanding Percents, Fractions and Decimals

34. Let’s Try It! Agreements –How far will the foul line be from the basket? –Are backboards allowable? –What else? Demo with two players –How hot is their shot as a team? –Representing their stats

35. Trashketball Procedures Team members rotate shots. After you shoot, you record your result. Return to end of line for your next shot Team Members stay positive with team members: “Nice shot!” “Nice try.” “You’re getting better.” “We’re doing great.” Stay humble with other teams: “Great percentage!”, “Thanks”. In teams of four, play Trashketball.

36. Trashketball Stats Group Name _____________ Group Members: 1._________,(2)________,(3) _________(4) __________ Shots taken: Make or Miss: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Total made/Total taken _______/20 Decimal _____ Percentage_____

37. What was our percent? How do we determine this ratio? ___ / ___

38. How Do We Represent the Money Problem Story One? How do we determine this ratio? _45_ /_100__ 1 Dime 7 Nickels

39. Trashketball Stats for Story Two Group Name _____________ Group Members: 1._________,(2)________,(3) _________(4) __________ 1.Shots taken: Make or Miss: 1 2 3 4 5 6 7 8 9 10 Total made/Total taken 1/10 Decimal ___.10__ Percentage__10%_ 2.Shots taken: Make or Miss: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Total made/Total taken 7/20 Decimal __.35___ Percentage_35%___

40. 100s Grids for Story Two How can our ratios be represented? ___ / 10 ___ / 20

41. How Did the Team Do Altogether? Story Two How do we determine this ratio? __8_ /_30_

42. “Move it over two” or Percentage and Decimal relationship using the Components of Number Sense 45% and.45 out of 100 out of 1

43. How can the Quantity and its connections to the Math Structure provide understanding for the Symbolic?

44. What Do We Ask? Quantity/Magnitude Numeration Equality Base Ten Form of a Number Proportional Reasoning Algebraic and Geometric Thinking

45. Trashketball Stats Group Name _____________ Team Members: 1._______,(2)_______,(3)________,(4)________ 1.Shots taken: Make or Miss: 1 2 3 4 5 6 7 8 Total made/Total taken _______5/8 Decimal _____ Percentage_____ 2.Shots taken: Make or Miss: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Total made/Total taken _______7/14 Decimal _____ Percentage_____ 3.Shots taken: Make or Miss: 1 2 3 4 5 6 7 8 9 10 11 Total made/Total taken _______7/11 Decimal _____ Percentage_____ 4.Shots taken: Make or Miss: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Total made/Total taken ______7/16 Decimal _____ Percentage_____

46. ___5/ 8___7/ 14 ___7/ 11 ____7/ 16 PICTURE IT!

47. Bobcats Stats! A coach can choose any one player to shoot “technical fouls.” If you were the assistant coach of the Bobcats and your team had to shoot technical fouls, who would you suggest to the head coach to shoot the foul shots and why?

48. Bobcats Stats

49. Numeration Quantity/Magnitude Base Ten Equality Form of a Number ProportionalReasoning Algebraic and Geometric Thinking Components of Number Sense © 2007 Cain/Doggett/Faulkner/Hale/NCDPI Language

50. It is all about the language--- “I have heard many People say, ‘Give me the Ideas. It is no matter what Words you put them into.’” To this he replies, “Ideas cannot be Given but in their minutely Appropriate Words.” William Blake (quoted by J. Newman, The World of Mathematics, 1956)

51. Assignments from Units 3 and 4 Due Day 3 Required Reading: –“Subitizing” Doug Clements –Continue to read Knowing and Teaching Elementary Mathematics Liping Ma