Doing Math vs. Understanding Math David “Coach G” Ginsburg

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

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

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

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% $ x 50% = $62.00 $ x 10% = $12.40 $ x 5% = $ 6.20 Sale price = $80.60

Is one approach better than others? Why?  Procedural Fluency  Conceptual Understanding

Procedural Fluency > Accuracy “Procedural fluency is the ability to apply procedures accurately, efficiently, and flexibly … ” NCTM Position Paper

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

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% $ x.65 = $80.60

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% $ x 50% = $62.00 $ x 10% = $12.40 $ x 5% = $ 6.20 Sale price = $80.60

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

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% $ x.65 = $80.60

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% $ x 50% = $62.00 $ x 10% = $12.40 $ x 5% = $ 6.20 Sale price = $80.60

Procedural Fluency and Conceptual Understanding 5 Supporting Practices for Your Classroom

1. A Purpose for Every Problem

2. Pencils Down, Minds On

3. Multiple Solution Strategies

4. Gradual Rapid Release of Responsibility

5. Assist Less, Assess More

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