1. Wisconsin Mathematics Council Annual Conference Green Lake, WI 2011 Melissa Hedges, MathematicsTeaching Specialist, MTSD Beth Schefelker, Mathematics Teaching Specialist, MPS Mary Mooney, Mathematics Teaching Specialist, MPS As the World Terns: Reason Abstractly and Quantitatively The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding by the National Science Foundation.

2. Learning Intention To deepen our understanding of quantitative reasoning To understand CCSS Math Practice #3 The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding by the National Science Foundation.

3. Success Criteria We will be successful when we can reason quantitatively to make sense of quantities and their relationships in problem situations. The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding by the National Science Foundation.

4. Reviewing Quantitative Reasoning “…the process of coming to an understand the quantities and relationships between those quantities in a word problem.” Quantity vs. Value A quantity is anything that can be measured or counted The value of the quantity is its measure or the number counted and involves a number and a unit. The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding by the National Science Foundation.

5. Quantity vs. Value Examples Turkey costs $1.29 per pound Quantity: Cost of turkey per pound Value: $1.29 per pound Ice Melt weighs 50 lbs per bag Quantity: weight of Ice Melt Value: 50 lbs per bag Mary saved 365 quarters for parking Quantity: # of quarters Mary saved Value: 365 quarters The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding by the National Science Foundation.

6. As the World Terns… Dr. McLeod tells his students about an interesting bird, the Arctic Tern. He found an informative piece about the bird. Read the article on arctic terns. Identify the different quantities. Share what you found with a neighbor. What questions do you have when thinking about these quantities? The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding by the National Science Foundation.

7. What do you wonder about? What was the average flying speed of the tern? How does the tern sleep? What does the tern eat? The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding by the National Science Foundation.

8. Route of the Arctic Tern

9. Think Aloud Read the story Flip your paper over Retell the story to another person at your table. Use the guiding questions on the worksheet to quantitatively analyze the problem. Work with your partner (or individually) to solve the problem The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding by the National Science Foundation.

10. Applying Quantitative Analysis to contextual situations Guiding questions: What quantities are involved in this situation? For which quantities do we know the values? For which quantities do we not know the value? What quantities are we trying to find? Which quantities are critical to the problem?

11. Quantity Value Known – record. Unknown Useful in solving problem ? Applying Quantitative Analysis Worksheet

12. As the World Terns… Dr. McLeod tellSs his students about an arctic tern that flew from the Farne Islands off the British coast to Melbourne, Australia. The bird made the journey in 3 months and traveled 14,000 miles. Assuming the arctic tern flew for 6 hours a day, what was the average flying speed for the trip? The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding by the National Science Foundation.

13. Your tern… What was the average flying speed of the tern?

14. Teacher Moves How is this process different from traditional mathematics instruction? How will you take the message back to the classroom teachers in your building? The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding by the National Science Foundation.

15. Reason Abstractly and Quantitatively Read practice standard #3 silently to yourself Highlight 3 phrases in the standard that connect to the Tern task. Read one of your phrases aloud to the group and share why you selected that phrase. As a phrase is shared, use the “Whip Around” strategy to share your thoughts within your group. The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding by the National Science Foundation.

16. Walking Away We’ve explored the Standard for Mathematical Practice #2: Reason abstractly and quantitatively How might you start to infuse this practice into the lessons? What conversations would you have with teachers who are not here?