1. Making Subtraction Concepts Meaningful Rosemary Reuille Irons Senior Lecturer Queensland University of Technology r.irons@qut.edu.aur.irons@qut.edu.au or mathmates@ozemail.com.au

2. What is a concept? A concept is the picture in your mind of an idea. Images built through language experiences help develop concepts?

3. What steps do we follow to develop operation concepts? Child’s Language Materials Language Mathematical Language Symbols

4. CONCRETE/ VISUAL VERBAL SYMBOLIC Student Language oral  written Representations

5. Eight mice are playing by the cheese. Two mice run away. How many mice are playing now?

6. CONCRETE/ VISUAL VERBAL SYMBOLIC Student Language oral  written Materials Language oral and written Representations

7. Concrete/pictorial materials – take away 8 take out 2 8 cover up 2

8. CONCRETE/ VISUAL VERBAL SYMBOLIC Student Language oral  written Materials Language oral and written Mathematical Language oral and written Representations

9. The new mathematical words that are used with the concept 8 5spend 3 leaves 8 5take 3is 8 5subtract 3equals

10. CONCRETE/ VISUAL VERBAL SYMBOLIC Student Language oral  written Materials Language oral and written Mathematical Language oral and written Symbolic Language written Representations

11. The mathematical abbreviations and formulae. 8 5 3=

12. Teaching the Subtraction Concept

13. Subtraction Concept Finding the missing part. The missing part could be what is left after a take away. The missing part could be how many to add on. The missing part could be the difference in number.

14. Rosie needs 12 apples. She has picked 7 apples. How many more apples does she need? Rosie had 12 apples in a bag. She took out 7 apples. How many apples are in the bag now? Rosie has 12 red apples and 7 green apples. How many fewer green apples does she have?

15. Take Away Child’s language Materials language Mathematical language Symbolic language Missing addend Child’s language Materials language Mathematical language Symbolic language Difference Child’s language Materials language Mathematical language Symbolic language

16. Child's language Everyday language – take away Eight mice are playing? Two mice run away? How many mice are playing now?

18. Child's language Everyday language – missing addend There are 8 mice altogether. How many mice are hiding in the cheese?

19. Four cars in the carpark. How many more will drive in to make ten cars in the carpark?

20. Child's language Everyday language – difference Eight mice are playing in front of the cheese. Two mice are playing in the back. How many more mice are playing in front?

22. Materials language Concrete/pictorial materials – take away spend 2

23. Materials language Concrete/pictorial materials – take away 8 take out 2 8 cover up 2

24. Materials language Concrete/pictorial materials – missing addend There are 8 altogether. How many are covered?

25. Materials language Concrete/pictorial materials – difference 8 cover up 2 How much more is 8 than 2?

26. Make the number of objects to represent the two groups.

27. Cover the parts of the groups that are the same to show the difference.

28. Mathematical language The new mathematical words that are used with the concept subtract [Try to avoid using the word minus. In mathematics this is best associated with negative numbers.]

30. Symbol language The mathematical abbreviations and formulae. 8 5 3=

31. Rosie needs 12 apples. She has picked 7 apples. How many more apples does she need? Rosie had 12 apples in a bag. She took out 7 apples. How many apples are in the bag now? Rosie has 12 red apples and 7 green apples. How many fewer green apples does she have? What are the features of the stories that make them all subtraction?

32. For each subtraction situation, the total and number in one part of the total are known. The unknown value is the other part of the total. For addition, 2 or more parts are known. The unknown value is the total.

33. Stories provide the opportunity to relate the operations. Make sure that both are introduced when the addition concept is developed.

34. Relate subtraction to addition How can you work out the number of covered dots? 6 13 altogether

35. Build links to addition during the work with missing addend subtraction. 5 + 8= 8 5 =

36. Teaching the number fact strategies

37. The approach to number facts Number facts are best learned in clusters. Each cluster is organised around one strategy – a strategy that can be used to learn facts and then with numbers beyond the facts.

38. The stages for each cluster introduce the strategy reinforce the strategy practice the facts extend to examples beyond the fact range.

39. Cluster 1: Count on Count on 1 Count on 2 and for some students, Count on 3

40. 6

42. Cluster 2: Use Doubles Double Double-add-1 Double-add-2

43. Cluster 3: Make Ten Number facts in this cluster have one addend close to 10. 9 + 4 = ____ is the same as 10 + 3 = ____

44. Teaching the subtraction number facts

45. Use the sequence for addition facts to plan the sequence for subtraction facts Count on facts Use doubles facts Make to 10 or bridge to 10 facts

46. For each subtraction cluster, encourage students to use the strategy ‘think addition.’ The connection between addition and subtraction is essential. Begin the links to subtraction when the addition concept is taught.

47. The stages for each cluster introduce the strategy reinforce the strategy practice the facts extend to examples beyond the fact range.

48. 8 Introduce the strategy There were 8 cubes in the cup. I have taken out 2 cubes. How many cubes are still in the cup? What are all of the ways you know?

49. How can you work out the number of covered dots? 6 8 altogether Count on/Count back subtraction facts

50. The addition facts 6 + 2 = ___2 + 6 = ___ are in the count-on cluster. The related subtraction facts are 8 – 2 = ___8 – 6 = ___. Initially, students might work out 8 – 2 =__ using a count back strategy.

51. Ask questions such as: How would you work out the answer? 11 - 9 = ___ How could you work out the number that is covered? 2 + = 10 Reinforce the strategy

52. Use addition to plan the sequence Count on facts 6 + 2 = __8 – 2 = __ 8 – 6 = __ Doubles facts 6 + 7 = __13 – 6 = __ 13 – 7 = __

53. Use doubles subtraction facts How can you work out the number of covered dots? 6 13 altogether

54. Use addition to plan the sequence Count on facts 9 + 2 = __11 – 2 = __ 11 – 9 = __ Doubles facts 6 + 8 = __14 – 6 = __ 14 – 8 = __ Make to ten facts 6 + 9 = __15 – 9 = __ 15 – 6 = __

55. Make to 10 subtraction facts How can you work out the number of covered dots? 6 15 altogether

56. Consideration of interests does not mean indulging children or abdicating responsibility. It means that children are more likely to find curriculum meaningful and engaging when it relates to and respects their interests. NAEYC- Developmentally Appropriate Practice 1997

57. Learning never ends and as teachers we should approach each day – the same way as a child does everything is a new discovery. Discover something new each day about each child in your learning environment.