1. Math Leadership Support Network ’08-’09 MLSN 2008 - 2009 Leadership NCTM Principles and Standards Number Sense Elementary and Middle School Math

2. Math Leadership Support Network ’08-’09 Agenda Registration/Breakfast Problem Registration/Breakfast Problem Advance Organizer Advance Organizer How Students Learn How Students Learn Literature Connection – Math Talk Literature Connection – Math Talk Elementary and Middle School Mathematics: Teaching Developmentally, Van de Walle Elementary and Middle School Mathematics: Teaching Developmentally, Van de Walle Literature Connection – Counting on Frank Literature Connection – Counting on Frank Grade-Level Breakouts – Measurement Estimation Grade-Level Breakouts – Measurement Estimation Reflections Reflections

3. Math Leadership Support Network ’08-’09 Advance Organizer Focus for today: How Students Learn – We constantly talk about national, state, district, school, and classroom testing and assessment. In How Students Learn, the assessment lens is one of four lenses in a teaching and learning environment. With this reading about student learning in mind, write your thoughts about how and why you assess students in your classroom.

4. Math Leadership Support Network ’08-’09 Advance Organizer Number – How does estimation (understanding and application) play a role in helping our students develop number sense?

5. Math Leadership Support Network ’08-’09 Advance Organizer Focus for today: Elementary and Middle School Mathematics – What does it mean to measure something? How can the three-step general instructional plan for measurement improve student understanding of measurement?

6. Math Leadership Support Network ’08-’09 Advance Organizer (cont’d) Focus for today: Number – Why is measurement estimation important? How does estimation improve a student’s understanding of measurement and his/her measuring skills?

7. Math Leadership Support Network ’08-’09 Fish is Fish

8. Math Leadership Support Network ’08-’09 Chapter One Introduction How Students Learn Mathematics in the Classroom

9. Math Leadership Support Network ’08-’09 What is That Measurement?

10. Math Leadership Support Network ’08-’09 Elementary and Middle School Mathematics: Teaching Developmentally Chapter 20 Developing Measurement Concepts

11. Math Leadership Support Network ’08-’09 Literature Connection:

12. Math Leadership Support Network ’08-’09 Literature Connection: Connection:

13. Math Leadership Support Network ’08-’09 The Role of Estimation in Learning Measurement Focuses on attributes and the measurement process Focuses on attributes and the measurement process Provides intrinsic motivation Provides intrinsic motivation Develops familiarity with measurement units Develops familiarity with measurement units Promotes multiplicative reasoning Promotes multiplicative reasoning

14. Math Leadership Support Network ’08-’09 Techniques of Measurement Estimation Develop and use benchmarks for important units Develop and use benchmarks for important units Use “chunking” when appropriate Use “chunking” when appropriate Use subdivision Use subdivision Iterate a unit mentally or physically Iterate a unit mentally or physically

15. Math Leadership Support Network ’08-’09 Reflections Sounding Boards

16. Math Leadership Support Network ’08-’09 Grade-Level Breakouts

17. Math Leadership Support Network ’08-’09 Middle School Breakout COMMIT TO AN OUTCOME: Which one has the greater volume? Container A, B, C, D, or E ?

18. Math Leadership Support Network ’08-’09 EXPOSE BELIEFS: EXPOSE BELIEFS: Share your answer with other members of your group. Share your answer with other members of your group. Discuss each other’s predictions. Discuss each other’s predictions. Is there more than one answer that makes sense? Is there more than one answer that makes sense? Select a member of your group to write down everybody’s ideas - share the answers with the rest of the class. Select a member of your group to write down everybody’s ideas - share the answers with the rest of the class.

19. Math Leadership Support Network ’08-’09 CONFRONT BELIEFS: CONFRONT BELIEFS: In your group, come up with an agreement about how to test the strategies for comparing and estimating the volume of the cylinders using the materials provided. Avoid counting every seed. In your group, come up with an agreement about how to test the strategies for comparing and estimating the volume of the cylinders using the materials provided. Avoid counting every seed. How does what you found out compare to your original answer? Prepare to share your group’s ideas with the rest of the class. How does what you found out compare to your original answer? Prepare to share your group’s ideas with the rest of the class.

20. Math Leadership Support Network ’08-’09 ACCOMMODATE THE CONCEPT ACCOMMODATE THE CONCEPT Share your group’s findings with the class. Share your group’s findings with the class. Justify your findings. Justify your findings. Based on what you have observed and heard, what generalizations can you make about the volume of cylinders? Based on what you have observed and heard, what generalizations can you make about the volume of cylinders? In your own words, explain a strategy for comparing the volume of a cylinder. In your own words, explain a strategy for comparing the volume of a cylinder.

21. Math Leadership Support Network ’08-’09 EXTEND THE CONCEPT EXTEND THE CONCEPT Which one has the greater volume – a paper rolled horizontally or a paper rolled horizontally or vertically (lengthwise or vertically (lengthwise or widthwise) to create a cylinder? widthwise) to create a cylinder? How do you know?

22. Math Leadership Support Network ’08-’09 GO BEYOND Look at the different bases on activity sheet A. Find the perimeter or circumference of each base. Given the half sheets of paper to use for the sides (consistent height), which base do you think would support the container that will have the largest volume? Look at the different bases on activity sheet A. Find the perimeter or circumference of each base. Given the half sheets of paper to use for the sides (consistent height), which base do you think would support the container that will have the largest volume?

23. Math Leadership Support Network ’08-’09 Measurement and the Number Line 1212 2828 3434 3 16

24. Math Leadership Support Network ’08-’09 Fractional Parts of a Ruler

25. Math Leadership Support Network ’08-’09 Estimating Angle Measures Estimating Angle Measures A

26. Math Leadership Support Network ’08-’09 Estimation Scavenger Scavenger Hunt Hunt