1. Doing Math vs. Understanding Math David “Coach G” Ginsburg david@ginsburgcoaching.com

2. How would you solve this problem? A pair of shoes that cost $124 was on sale for 35% off. What is the sale price? david@ginsburgcoaching.com

3. Would you use this approach? A pair of shoes that cost $124 was on sale for 35% off. What is the sale price? $124.00 x.35 = $43.40 $124.00 - $43.40 = $80.60 david@ginsburgcoaching.com

4. This approach? A pair of shoes that cost $124 was on sale for 35% off. What is the sale price? 100% - 35% = 65% $124.00 x.65 = $80.60 david@ginsburgcoaching.com

5. Or would you do something like this? A pair of shoes that cost $124 was on sale for 35% off. What is the sale price? 65% = 50% + 10% + 5% $124.00 x 50% = $62.00 $124.00 x 10% = $12.40 $124.00 x 5% = $ 6.20 Sale price = $80.60 david@ginsburgcoaching.com

6. Is one approach better than others? Why?  Procedural Fluency  Conceptual Understanding david@ginsburgcoaching.com

7. Procedural Fluency > Accuracy “Procedural fluency is the ability to apply procedures accurately, efficiently, and flexibly … ” NCTM Position Paper david@ginsburgcoaching.com

8. Approach #1: Efficient? Flexible? A pair of shoes that cost $124 was on sale for 35% off. What is the sale price? $124.00 x.35 = $43.40 $124.00 - $43.40 = $80.60 david@ginsburgcoaching.com

9. Approach #2: Efficient? Flexible? A pair of shoes that cost $124 was on sale for 35% off. What is the sale price? 100% - 35% = 65% $124.00 x.65 = $80.60 david@ginsburgcoaching.com

10. Approach #3: Efficient? Flexible? A pair of shoes that cost $124 was on sale for 35% off. What is the sale price? 65% = 50% + 10% + 5% $124.00 x 50% = $62.00 $124.00 x 10% = $12.40 $124.00 x 5% = $ 6.20 Sale price = $80.60 david@ginsburgcoaching.com

11. Approach #1: Conceptual understanding? A pair of shoes that cost $124 was on sale for 35% off. What is the sale price? $124.00 x.35 = $43.40 $124.00 - $43.40 = $80.60 david@ginsburgcoaching.com

12. Approach #2: Conceptual understanding? A pair of shoes that cost $124 was on sale for 35% off. What is the sale price? 100% - 35% = 65% $124.00 x.65 = $80.60 david@ginsburgcoaching.com

13. Approach #3: Conceptual understanding? A pair of shoes that cost $124 was on sale for 35% off. What is the sale price? 65% = 50% + 10% + 5% $124.00 x 50% = $62.00 $124.00 x 10% = $12.40 $124.00 x 5% = $ 6.20 Sale price = $80.60 david@ginsburgcoaching.com

14. Procedural Fluency and Conceptual Understanding 5 Supporting Practices for Your Classroom david@ginsburgcoaching.com

15. 1. A Purpose for Every Problem david@ginsburgcoaching.com

16. 2. Pencils Down, Minds On david@ginsburgcoaching.com

17. 3. Multiple Solution Strategies david@ginsburgcoaching.com

18. 4. Gradual Rapid Release of Responsibility david@ginsburgcoaching.com

19. 5. Assist Less, Assess More david@ginsburgcoaching.com

20. The Procedural Fluency and Conceptual Understanding Connection Join me tomorrow for “pencils down, minds on” math! 12:30 - Room 303 david@ginsburgcoaching.com