1. Laurel County SSA Day 4 High School Breakout Session Jim Moore moore6346@bellsouth.net Jennifer McDaniel Jennifer.mcdaniel@clay.kyschools.us

2. House #1 House #2House #3House #4 This is the House That Jack Built Jack has been building houses - they look like this: 1. Draw and label each of these houses.

3. 2.For each house determine the number of squares. 3.For each house determine the number of triangles. 4. For each house determine the total number of pieces. 5. Organize your information in a table or in some other way.

4. 6.Describe what House #5 would look like. Draw a sketch of this house.

5. 7. Predict the number of triangles you would need to build House #10. Explain your reasoning. 8. Predict the number of squares you would need to build House #10. Explain your reasoning. 9.Predict the total number of pieces (squares and triangles) you would need to build House #14. Explain your reasoning.

6. 10. Graph these sets of data on graph paper.

7. Introducing Algebraic Notation Moving from the specific to the general case. Developing an understanding of variable and its uses. Tying abstract ideas to concrete situations. Fostering meaning to notation. Developing the concept of equivalent expressions. Encouraging efficiency and brevity in notation

8. 11. Write a rule that gives the total number of pieces needed to build any house in this sequence.

9. Jack’s friend, Jill also builds houses. Her houses look like this: House #1House #2House #3House #4 1. Draw and label each of these houses.

10. 2.For each house determine the number of squares. 3.For each house determine the number of triangles. 4. For each house determine the total number of pieces. 5. Organize your information in a table or in some other way.

11. 6.Describe what House #6 would look like. Draw a sketch of this house.

12. 7. Predict the number of triangles you would need to build House #10. Explain your reasoning. 8. Predict the number of squares you would need to build House #10. Explain your reasoning. 9.Predict the total number of pieces (squares and triangles) you would need to build House #14. Explain your reasoning.

13. 10. Graph these sets of data on graph paper.

14. 11. Write a rule that gives the total number of triangles needed to build any house in this sequence.

15. 12. Write a rule that gives the total number of squares needed to build any house in this sequence.

16. 13. Write a rule that gives the total number of pieces (triangles and squares) needed to build any house in this sequence.

17. 14. Compare all of the graphs – What do you notice?

18. Comparing The Two Mathematical Tasks zJack’s Houses zJill’s Houses

19. Comparing Two Mathematical Tasks How are the two Tasks the same and how are they different?

20. Similarities and Differences

21. A Critical Starting Point for Instruction Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking. Stein, Smith, Henningsen, & Silver, 2000

22. The level and kind of thinking in which students engage determines what they will learn. Hiebert, Carpenter, Fennema, Fuson, Wearne, Murray, Oliver, & Human, 1997

23. There is no decision that teachers make that has a greater impact on students’ opportunities to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages students in studying mathematics. Lappan & Briars, 1995