1. Everything you do in mathematics should make sense to you (Sense making and the effective teaching practices) Linda Gojak Immediate Past President, NCTM

2. Effective Mathematics Teaching Practices 1.Establish mathematics goals to focus learning. 2.Implement tasks that promote reasoning and problem solving. 3.Use and connect mathematical representations. 4.Facilitate meaningful mathematical discourse. 5.Pose purposeful questions. 6.Build procedural fluency from conceptual understanding. 7.Support productive struggle in learning mathematics. 8.Elicit and use evidence of student thinking.

3. Effective Mathematics Teaching Practices 1.Establish mathematics goals to focus learning. 2.Implement tasks that promote reasoning and problem solving. 3.Use and connect mathematical representations. 4.Facilitate meaningful mathematical discourse. 5.Pose purposeful questions. 6.Build procedural fluency from conceptual understanding. 7.Support productive struggle in learning mathematics. 8.Elicit and use evidence of student thinking.

4. Whole Numbers 3 9 9 9 ? 8. Elicit and use evidence of student thinking

5. 1. Establish mathematics goals to focus learning

6. The “No Purpose” Zero 207 x 106 1242 0000 20700 21942 393 x 30 000 11790 6. Build procedural fluency from conceptual understanding

7. Watch your language... 3. Use and connect mathematical representations

8. “Reducing” Fractions 15 25 3535 8. Elicit and use evidence of student thinking =

9. 1. Establish mathematics goals to focus learning

10. Adding Fractions 3535 5. Pose purposeful questions

11. Adding Fractions 3535 3. Use and connect mathematical representations

12. Mixed Numbers 5 - 2 3 2. Implement tasks that promote reasoning and problem solving

13. Division of Fractions 7. Support productive struggle in learning mathematics

14. Division of Fractions 6. Build procedural fluency from conceptual understanding

15. Decimals 6. Build procedural fluency from conceptual understanding

16. 4. Facilitate meaningful mathematical discourse

17. Communication 8. Elicit and use evidence of student thinking

18. Using Formulas…… 2l +2w l x w πr 2 2πr ½ab r x t = d p r t = i L x W x H

19. l x w πr 2 2πr ½ab Using Formulas…… r x t = d 3. Use and connect mathematical representations

20. Everything you do in mathematics should make sense to you…. …except trapezoids!