1. Introduction to Addition and Subtraction Presented by Frank H. Osborne, Ph. D. © 2015 EMSE 3123 Math and Science in Education 1

2. Introduction to Addition and Subtraction We use manipulatives to illustrate addition and subtraction in early grades. Addition is the union of two sets. We start with numbers less than ten. This is followed by grouping by tens when working with numbers over ten. 2

3. Introduction to Addition and Subtraction We use manipulatives to illustrate addition and subtraction in early grades. Addition is the union of two sets. 3

4. Introduction to Addition and Subtraction We use manipulatives to illustrate addition and subtraction in early grades. Subtraction begins with a set and we "take away" a sub-set. 4

5. Introduction to Addition and Subtraction Sums of 10. Done by coloring circles. 5

6. Introduction to Addition and Subtraction Decomposing: Sums of 10. 6

7. Introduction to Addition and Subtraction How many more do you need to make 10? 7

8. Introduction to Addition and Subtraction How many more do you need to make 10? 8

9. Introduction to Addition and Subtraction Fluently add and subtract within five. Children need to practice math skills all the time. Your job as their teacher is to make it interesting and enjoyable to them so that they show positive affective behavior. 9

10. Introduction to Addition and Subtraction Decomposing numbers: 10

11. Introduction to Addition and Subtraction Decomposing numbers: 11

12. Introduction to Addition and Subtraction Addition using word problems. “Mary has 3 apples and John has 2 apples. How many apples do they have in all?” 12

13. Introduction to Addition and Subtraction Subtraction using word problems. “They give one apple to the teacher. How many do they have left over?” Word problems are very, very important. This is how math gets related to the real world. It also helps to reinforce ties to language arts skills. 13

14. Introduction to Addition and Subtraction We transition into first grade Addition and subtraction within 20 Word problems involving 3 numbers Properties of operations Working with equations –Understand the meaning of the equals sign. It means that both sides are the same. That is why it is made up of two lines that are the same. (=) 14

15. Introduction to Addition and Subtraction Combine the two sets of objects and express the result by grouping accordingly. This introduces the concept of grouping by tens. 15

16. Introduction to Addition and Subtraction Repeat the above example to demonstrate the following additions. In each case draw a diagram showing the manipulatives. a. 5 + 6 b. 8 + 9 16

17. Introduction to Addition and Subtraction 5 + 6 17

18. Introduction to Addition and Subtraction 8 + 9 18

19. How Many Tens, How Many Ones We see how many tens and ones result from each addition. Note that a. and d. already contain a ten. In b. and c. one number has to be decomposed to make ten by addition to the other. 19

20. How Many Tens, How Many Ones We see how many tens and ones result from each addition. In b. the green 6 was decomposed into 1 + 5 The 1 was added to the blue 9 to make a 10. In c. the brown 8 was decomposed into 4 + 4 One 4 was added to the 6 to make a 10. 20

21. Introduction to Addition and Subtraction Decomposing numbers: 21

22. Introduction to Addition and Subtraction Decomposing numbers: 22

23. Introduction to Addition and Subtraction Counting ladybugs. Continue up to 10 + 9 = 19. Remember groups of 10 and ones. 23

24. Introduction to Addition and Subtraction Word problems involving three numbers. “Claudia has 8 pencils, Juan has 2 pencils and Ana has 6 pencils. How many pencils are there in all? 24

25. Introduction to Addition and Subtraction “Claudia has 8 pencils, Juan has 2 pencils and Ana has 6 pencils. How many pencils are there in all? Strategy: We observe that 8 + 2 = 10 so the equation 8 + 2 + 6 becomes 10 + 6 = 16. 25

26. Introduction to Addition and Subtraction Commutative Property of Addition If we know that 4 + 7 = 11, then we also know that 7 + 4 = 11. 26

27. Introduction to Addition and Subtraction Associative Property of Addition Add: 3+ 8 + 7 Method: We see that 3 + 7 = 10 so the problem now becomes 3 + 8 + 7 = 10 + 8 = 18 27

28. Introduction to Addition and Subtraction Subtraction as an unknown-addend problem. Subtract: 10 – 7 = ? Method: We ask what number when added to 7 makes 10? Since we know that you need to have add 3 to 7 in order to make 10, we conclude that 10 – 7 = 3 28

29. Introduction to Addition and Subtraction Counting is related to addition and subtraction. Add: 3 + 8 We count 3 hops followed by 8 hops for a total of 11, so 3 + 8 = 11. Note that with addition we count to the right. 29

30. Introduction to Addition and Subtraction Counting is related to addition and subtraction. We think of subtraction the same way. Subtract 7 from 16. We start at 16, and hop back 7, so 16 – 7 = 9. Note that in subtraction we count back to the left while in addition we count on to the right. 30

31. Introduction to Addition and Subtraction Children must practice and become fluent in addition and subtraction within 20. Strategies: Counting on see Van De Walle, page 133ff) 31

32. Introduction to Addition and Subtraction Children must practice and become fluent in addition and subtraction within 20. Strategies: Skip counting (at least with 2, 3, 4 and 5) Making ten –(e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) 32

33. Introduction to Addition and Subtraction Children must practice and become fluent in addition and subtraction within 20. Strategies: Decomposing a number leading to a ten –(e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9) Using the relationship between addition and subtraction –(e.g., knowing that 8 + 4 = 12, one knows that 12 - 8 = 4); Creating equivalent but easier or known sums –(e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). 33

34. Introduction to Addition and Subtraction Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? –A) 6 = 6 –B) 7 = 8 – 1 –C) 5 + 2 = 2 + 5 –D) 4 + 1 = 5 + 2. 34

35. Introduction to Addition and Subtraction Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? –A) 6 = 6 True –B) 7 = 8 – 1 True –C) 5 + 2 = 2 + 5 True –D) 4 + 1 = 5 + 2. False 35

36. Introduction to Addition and Subtraction Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations. –A) 8 + ? = 11 8 + 3 = 11 –B) 5 = [] – 3 5 = 8 - 3 –C) 6 + 6 = 6 + 6 = 12 36

37. The End 37