1. Making Sense of Place Value and Multidigit Addition and Subtraction Juli K. Dixon, Ph.D. University of Central Florida

2. Solve this – aloud… Empowering Young Learners

3. Solve this – aloud… Was the language you used in talking through the solution “precise”? Empowering Young Learners

4. Solve this – aloud… Does our math talk sound more like this? http://video.google.com/videoplay?docid=7106559846794044495 Empowering Young Learners

5. The 8 Standards for Mathematical Practice: Making Sense of the Mathematical Practices 1Make sense of problems and persevere in solving them 2Reason abstractly and quantitatively 3Construct viable arguments and critique the reasoning of others 4Model with mathematics 5Use appropriate tools strategically 6Attend to precision 7Look for and make use of structure 8Look for and express regularity in repeated reasoning

6. Counting on the Open Number Line 48 58687073 +10 +2 +3 A solution for 48 + 25

7. Counting on the Open Number Line 48 586870 48 5070 +20 +2 73 +10 +2 +3 73 +3

8. Consider Subtraction on the Open Number Line Solve 53 – 37 with an open number line.

9. Consider Subtraction on the Open Number Line Solve 53 – 37 with an open number line. Compare your solution with someone near you.

10. Consider Subtraction on the Open Number Line Solve 53 – 37 with an open number line. Compare your solution with someone near you. What did you do? Did you: - Count Up? - Count Back? Or - Take Away?

11. 37 475053 + 10 + 3 164353 - 10- 7- 10 33 - 10 23 A C 37 404353 - 10 - 3 B

12. Solve this – aloud… Empowering Young Learners It is unlikely you used counting strategies to solve this – you probably used place value concepts.

13. Add this – aloud… 1 4 9 + 2 8 5 It is unlikely you used counting strategies to solve this – you probably used place value concepts.

14. Making Sense of Place Value to 1,000 The 10-to-1 relationship – –Issues with base ten blocks – –Pennies and string – –Candy Shop Exploring algorithms – –Candy Shop – –Invented Algorithms – –Standard Algorithms

15. Grouping Strategies Making sense of Place Value with the Candy Shop.

16. Grouping Strategies Making sense of Place Value with the Candy Shop. How will you package your candy?

17. Grouping Strategies BoxesRollsPieces

18. Grouping Strategies How else can you package this candy?

19. Grouping Strategies Base-ten Blocks 1 4 9 + 2 8 5

20. Grouping Strategies Base-ten Blocks Partial Sums 1 4 9 + 2 8 5

21. Grouping Strategies Base-ten Blocks Partial Sums Column Addition 1 4 9 + 2 8 5

22. Grouping Strategies Base-ten Blocks Partial Sums Column Addition Traditional Algorithm 1 4 9 + 2 8 5

23. Grouping Strategies 4 3 6 - 8 2

24. Grouping Strategies 4 3 6 - 8 2 Base-ten Blocks

25. Grouping Strategies 4 3 6 - 8 2 Base-ten Blocks Flexible Grouping

26. Solve this… 2 0 3 - 6 8

27. Grouping Strategies 4 3 6 - 8 2 Base-ten Blocks Flexible Grouping Trade First Subtraction

28. Grouping Strategies 4 3 6 - 8 2 Base-ten Blocks Flexible Grouping Trade First Subtraction Traditional Algorithm

29. Making Sense of Computation with Whole Numbers Conceptual understanding MUST precede memorization and procedural algorithms. Quick recall is still important, it is when this is the focus that must change. Students should be expected to explain their mathematical moves.