1. SD Counts-Mini Foundations Summer 2007 Relearning to Teach Arithmetic Addition, Subtraction, Multiplication and Division

2. SD Counts-Mini Foundations Summer 2007 Introduction In today’s session you will see a significant shift in the way students experience mathematics, this shift will be -“toward” mathematical reasoning; away from merely memorizing procedures -toward conjecturing, inventing, and problem-solving; away from an emphasis on mechanistic answer-finding

3. SD Counts-Mini Foundations Summer 2007 The way “they” learn math is different than the way “we” learned math. Most of us sitting here today learned math my memorizing particular algorithms for each operation. We don’t have images, experiences, or knowledge about how students can develop their understanding of whole-number computation because we never had to build it ourselves.

4. SD Counts-Mini Foundations Summer 2007 The question of fluency has come up several time in conversation with current SD Counts principals and teachers. Fluency will happen if…. students have knowledge of the base10 number system a repertoire of number relationships an understanding of the characteristics of each operation and how the operations are related

5. SD Counts-Mini Foundations Summer 2007 Do I need to know about every number operation if I will not teach it? By learning about computation across the grades, teachers will better understand how concepts build and connect and about the range of student understanding within their classroom. Teachers will also gain a better understanding of whole-number computation.

6. SD Counts-Mini Foundations Summer 2007 Let us begin the journey Addition Mental Math Solve and be ready to share your thinking of 48 + 25

7. SD Counts-Mini Foundations Summer 2007 Video-Segment Stacie, Harrison, Zoe, Elthea, James and Chris example of a “Math Talk” Watch closely as these students solve the same problem as we just did 48 + 25

8. SD Counts-Mini Foundations Summer 2007 The 2 nd stop on our Journey Subtraction Mental-math activity Solve and be ready to share your thinking 35-16

9. SD Counts-Mini Foundations Summer 2007 Video Segment Lisa, James and Naillil (NY-JILL) Watch closely as these three students solve the following subtraction problem 40 - 26 =

10. SD Counts-Mini Foundations Summer 2007 The Teacher’s Role Teaching and Learning About Addition and Subtraction

11. SD Counts-Mini Foundations Summer 2007 The 3 rd stop Multiplication Mental-math activity Solve and be ready to share your thinking of 27 x 4

12. SD Counts-Mini Foundations Summer 2007 Video Segment-Multiplication Darren, Tatia, Daniel, Rona, Jonathan, Rosa, Erica, and Terrance 27 x 4 and 128 x 38

13. SD Counts-Mini Foundations Summer 2007 The Last Stop Division Mental-math activity Solve and be ready to share your thinking of 140/8

14. SD Counts-Mini Foundations Summer 2007 Video Segment-Division Elaine, Yuriy, Amelinda, and Thomas 159/13

15. SD Counts-Mini Foundations Summer 2007 The Teacher’s Role Teaching and Learning About Multiplication/Division. Watch for the following: - behavior/comments of the teacher - how and when does the teacher intervene - what kinds of questions do they ask?