1. Leading with Algebra
April 28, 29, 30, 2015

2. Welcome!!
In your small groups, have a discussion using the following prompts:
My favorite math practice is _____ because….
My least favorite math practice is _____ because….
15 minutes, counting the welcome

3. Three Reads Strategy READ 1
Listen to the problem being read.
At your table, discuss the general context of the problem. What is the situation about?
Prepare:
One piece of chart paper with each math practice written and posted around the room
5 minutes

4. Three Reads Strategy READ 2
The Water Watch program is encouraging customers to reduce the amount of water they use each day. The program is selling low-flow showerheads, which use 2 gallons of water per minute, for $54.00 each.
A family currently has a showerhead that uses 5 gallons of water per minute and is considering replacing it with one of the low-flow showerheads. The family uses the shower an average of 20 minutes per day and pays $0.002 per gallons of water.
Identify all the quantities in the problem stem above.
What do they mean? How are they related?
Facilitator records the quantities shared from the problem
5 minutes

5. Three Reads Strategy READ 3
The Water Watch program is encouraging customers to reduce the amount of water they use each day. The program is selling low-flow showerheads, which use 2 gallons of water per minute, for $54.00 each.
A family currently has a showerhead that uses 5 gallons of water per minute and is considering replacing it with one of the low-flow showerheads. The family uses the shower an average of 20 minutes per day and pays $0.002 per gallons of water.
Generate a list of mathematical questions that could be answered using the information in the problem stem.
Write each question on a separate sticky note.
20 minutes (this includes categorizing)

6. Solving the Problem
Begin working individually to solve Part A of the Water Watch problem. After working individually, you may discuss strategies and work together.
Think about which practices closely align with Part A.
30 minutes for doing the problem and break. Give them the PARCC handout for doing the problem.
If they finish Part A, have them work on Part B. Share answers and thoughts about the problem.

7. Break
15 minutes

8. Mathematical Modeling
What do you think we mean by “modeling” as in SMP 4: “model with mathematics”?
What do you think are some components of modeling?
30 minutes
The idea is to elicit ideas from them.

9. Mathematical Modeling
Analyze Situation
Formulate Model
Validate
Report
Interpret Solution
Compute
This step usually involves making simplifying assumptions. It might also require gathering or collecting of information.

10. Water Conservation Task
Does showering use less water than bathing in a bathtub?

11. What information do we need?

12. What are some assumptions we need to make?

13. Key idea of model from article
Use the duration of a shower as an independent variable because it so strongly affects the amount of water used in a shower.
Using the assumption of a continuous shower, then
shower usage = (flow rate)∙(avg length of shower)
One assumption we make (which hopefully came out in the previous slide) is that the person takes a shower leaving the water on continuously. If one gets wet, turns off the water to soap up, then briefly turns on water to rinse off, then, with no doubt whatsoever, a shower is far more water-efficient than a bath!

14. Shower water usage model
y=3.4x
y=1.9x

15. Bath Usage model
Bathtubs range from 42 to 70 gallons. Assuming the bath is filled 75% full.
Lower limit: 0.75*42 = 31.5 gallons
Upper limit: 0.75*70 = 52.5 gallons

16. Bath usage model
y=52.5
y=31.5

18. ≅(15,52.5)
≅(28,52.5)
≅(9,31.5)
≅(16,31.5)
Potential questions to ask: For what length of shower is a shower always more water efficient?
For what length of shower is a bath always more water efficient?

19. Looking at More Items
Look at the Practice Exam Item. Decide on a solution.
Discuss which practice standards are addressed by this problem. How could we plan instruction to better reinforce the content as well as the practices?
Prepare questions

20. Reflections Fill out evaluation/reflections
Pick up a copy of the Practice Exit Exam on your way out.
10 minutes