1. Addition and Subtraction Algorithms

2. 38 + 49 Making Exchanges

3. Chip Abacus HundredsTensOnes Making Exchanges

4. Place-Value Representation ThousandsHundredsTensOnes 347 675 Making Exchanges

5. Standard Addition Algorithm Right to left (But left to right is better). WE use a word, “carrying,” that does not explain what students are doing. Countries where the vocabulary for numbers and operations is more descriptive have students who do ________ at math.

6. Lattice Addition “lines up” Powers of Ten

7. Scratch Addition 38 92 75 67 31 78 65 + 44 138 792 875 467 231 978 165 + 744

8. 44 – 27 with base 10 pieces Making Exchanges

9. 85 – 68 with Chip Abacus

10. 447 – 375 Making Exchanges ThousandsHundredsTensOnes 447 -375

11. 447 – 375 Subtracting from the Base 4 4 7 – 3 6 5 2 (10 – 6) + 4 versus (10 + 4) - 6 3 10

12. 447 – 375 Subtracting from the Base 4 4 7 – 3 6 5 8 2 3 10

13. Adding the Compliment What my mother learned! 743 – 567 = 743 + (433 – 1000) = (743 + 433) – 1000 = 1176 – 1000 = 1 1 7 6 …. = 176 Just a bit different from your book, but really the same thing.

14. A Few Favorite Algorithms Cashiers subtraction B11 Equal additions B12

15. Base 5 Anyone? 34 5 + 42 5 4331 5 + 3442 5

16. And in every base! Base n pieces Chip abacus Place-Value Boards