1. Sorting to Algebra Developing Mathematical Thinkers

2. Cross Number Puzzles P uzzles are not "dessert" for after the "real" work is done. Selected properly and introduced thoughtfully, they can be the real work. EDC

3. What am I supposed to do? What CAN I do?

4. Algebraic Ideas Breaking it up 44045 59 19 40 12111

5. What does the “thick line” do? 4

6. 421

7. What does the “thick line” do? 42125

8. What about this way? 100

9. What about this way? 100 27

10. What about this way? 100 73 27

11. Kindergarten Sorters

12. 4 + 5 = 9 3 + 1 = 4 7 Addition and Subtraction From sorting to algebra Challenge: can you find some that don’t work? 5x + 3y = 23 2x + 3y = 11 Is there anything interesting about addition and subtraction sentences? 13 += 6 5 1 4

13. Back to the very beginnings Picture a young child with a small pile of buttons. Natural to sort. We help children refine and extend what is already natural.

14. 6 4 7310 Back to the very beginnings Children can also summarize. “Data” from the buttons. bluegray large small

15. large small bluegray Abstraction If we substitute numbers for the original objects… 6 4 7310 6 4 73 42 31

16. A Cross Number Puzzle Don’t always start with the question! 5 21 8 13 9 12 76 3 1 st grade

17. Building the addition algorithm Only multiples of 10 in yellow. Only less than 10 in blue. 63 38 25 13 50 20 5 8 30 2nd grade

18. Relating addition and subtraction 6 4 7310 42 31 6 4 73 42 31 2nd grade

19. The subtraction algorithm 63 38 25 13 50 20 5 8 30 25 38 63 -5 30 60 3 8 30 25 + 38 = 6363 – 38 = 25

20. The subtraction algorithm 63 38 25 13 50 20 5 8 30 25 38 63 5 20 60 3 8 30 25 + 38 = 6363 – 38 = 25 50 13

21. Place Value Bonus 235 + 597

22. Place Value Bonus 235 + 597

23. Place Value Bonus 235 + 597

24. Place Value Bonus 235 + 597

25. Place Value Bonus 235 + 597

26. Place Value Bonus 235 + 597

27. Place Value Bonus 235 + 597

28. Place Value Bonus 235 + 597

29. Place Value Bonus 235 + 597 = 832

30. Cross Number Puzzles and Multiplication

31. Developing a familiar multiplication algorithm

42. The algebra connection: adding 42 31 10 4 6 3 7 4 + 2 = 6 3 + 1 = 4 10 += 7 3

43. The algebra connection: subtracting 73 31 6 4 10 2 4 7 + 3 = 10 3 + 1 = 4 6 += 4 2

44. The eighth-grade look 5x5x3y3y 2x2x3y3y 11 235x + 3y = 23 2x + 3y = 11 12 += 3x3x0 x = 4 3x3x0 12 All from sorting buttons!

45. Algebra At the Core Kindergarten – Grade 5 Focus on underlying principles allows “two for the price of one” subtraction is un-addition division is un-multiplication Mastery of traditional algorithms Easier and more exciting to learn and explore More competently used

46. For more information about Cross Number Puzzles and Think Math! visit thinkmath.edc.org