1. Shifts 6, 7, and 9 Accessible Mathematics Day 2

2. Review of Day 1

3. Butterfly Fractions

4. Milking the data Instructional Shift 6:

5. What does this data stand for? 27,525 21,440 36,530 28,280 23,500 29,065 Ford Edge27,525 Ford Escape21,440 Ford Expedition 36,530 Ford Explorer28,280 Ford F-15023,500 Ford F-25029,065

6. What if I presented the data like this?

7. Describe what that looks like in a classroom. Why is the “So?” strategy so powerful?

8. How does using data to launch a lesson support quality instruction?

9. So What Should We See in an Effective Mathematics Classroom? An abundance of problems drawn from the data presented in tables, charts, and graphs. Opportunities for students to make conjectures and draw conclusions from data presented in tables, charts, and graphs. Frequent conversations, with and without technology, of data in tables and charts into various types of graphs, with discussions of their advantages, disadvantages, and appropriateness.

10. Tie the math to such questions as How big? How much? How far? To increase the natural use of measurement throughout the curriculum. Instructional Shift 7:

11. What do you think? This classroom is in pretty bad shape so one of the things I want to do is paint the walls. I have 1 ½ gallons of Carolina Blue paint. Do I have enough? Get with a partner to determine the answer.

12. Which would be more engaging? The previous problem or the following problem: Find the surface area of the rectangular prism with the given dimensions: L – 12 ft, W – 8 ft, and height – 9 ft.

13. So What Should We See in an Effective Mathematics Classroom? Lots of questions are included that ask: How big? How far? How much? How many? Measurement is ongoing part of daily instruction and the entry point for a much larger chunk of curriculum. Students are frequently asked, to find and estimate measures, to use measuring, and to describe the relative size of measure that arise during instruction. The teacher offers frequent reminders that much measurement is referential-that is, we use a referent (such as your height or a sheet of paper) to estimate measures.

14. Embed the mathematics in realistic problems and real-world contexts. Instructional Shift 9

15. How many of you have been asked the question by a student: When are we ever gonna use this?

16. Ashrita Furman of the United States holds the world record for sack racing.

17. What is Mr. Leinwand’s “secret” to raising mathematics achievement? Who are the most successful students in our mathematics classes?

18. “But once again, the critical question is ‘Why bother?’ Teaching this way is harder to do. This type of instruction takes longer to plan and it is often very messy as we share instructional power with our students…”

19. So What Should We See in an Effective Mathematics Classroom? Frequent embedding of the mathematical skills and concepts in real-world situations and contexts. Frequent use of “So, what questions arise from these data or this situation?” Problems that emerge from teachers asking, “When and where do normal human beings encounter the mathematics I need to teach?”

20. For next time, please read Chapters 4, 5, and 6.