1. 7th Grade Math Lesson 4.2.3

2. ENTERING THE CLASSROOM
Class Leader calls class to ATTENTION
Class at ATTENTION in back of chairs, hand at sides
Take SEATS – Say: “Per Ardua Ad Astra”
Secure your gear—place backpack on back of chair!
Take out your notebook, and a pencil

3. THE CURRENT CLASSROOM “MODE”
Quiet Mode
Let others think too
Stand & Deliver
Open Discussion
Team Work

4. STANDARDS FOR QUIET WORK: Let others think too
I am listening to the teacher or speaker.
I am not talking.
I am taking notes or doing other silent work as directed.
I am paying complete attention to the teacher or speaker.

5. Starter: Notebook
Entry #22 --Starter:

6. ENTRY # 23 – Today’s Objectives
I can find unit rates in proportions.

7. THE CURRENT CLASSROOM “MODE”
Quiet Work
Stand & Deliver
Open Discussion
Table Team Work

8. Direct Instructions—Discussion Mode Entry #24-copy
A relationship is proportional if one quantity is a multiple of the other.
This relationship can be identified in tables, graphs, and equations.
Graph: A straight line through the origin.
Equation: An equation of the form y = kx where k is the constant of proportionality.

9. Direct Instructions—Discussion Mode
Example: Three pounds of chicken costs $ What is the cost for x pounds?
Equation: y = x

10. The relationship between pounds and cost is proportional.
The table has equivalent ratios ( = = ), the graph is a straight line through the origin, and the equation is of the form y = kx.

11. THE CURRENT CLASSROOM “MODE”
Quiet Work
Stand & Deliver
Open Discussion
Table Team Work

12. Team work—Entry #25
4-46. Robert’s new hybrid car has a gas tank that holds 12 gallons of gas. When the tank is full, he can drive 420 miles. Assume that his car uses gas at a steady rate.

13. Team Work
Is the relationship between the number of gallons of gas used and the number of miles that can be driven proportional? For example, does it change like Sonja’s birdseed prediction, or is it more like Gustavo’s college savings? Explain how you know.

14. Team Work-25
Show how much gas Robert’s car will use at various distances by copying and completing the table below in your notebook.

15. Team Work-25
Robert decided to graph the situation, as shown. The distance Robert can travel using one gallon of gas is called the unit rate. Use Robert’s graph to predict how far he can drive using one gallon of gas. That is, find his unit rate.

16. Work with your team to write an equation to find the exact number of miles Robert can drive with any number of gallons of gas. Be prepared to share your strategy.
Use your equation to find out how many gallons of gas Robert will need to drive 287 miles.

17. Entry 25 , cont.
4-47. THE YOGURT SHOP Jell E. Bean owns the local frozen yogurt shop. At her store, customers serve themselves a bowl of frozen yogurt and top it with chocolate chips, frozen raspberries, and any of the different treats available. Customers must then weigh their creations and are charged by the weight of their bowls.

18. Jell E. Bean charges $32 for five pounds of dessert, but not many people buy that much frozen yogurt. She needs you to help her figure out how much to charge her customers. She has customers that are young children who buy only a small amount of yogurt as well as large groups that come in and pay for everyone’s yogurt together.

19. ($32 for 5 pounds)
Is it reasonable to assume that the weight of the yogurt is proportional to its cost? How can you tell?
Assuming it is proportional, make a table that lists the price for at least ten different weights of yogurt. Be sure to include at least three weights that are not whole numbers.

20. What is the unit rate of the yogurt
What is the unit rate of the yogurt? (Stores often call this the unit price.) Use the unit rate to write an equation that Jell E. Bean can use to calculate the amount any customer will pay.
If Jell E. Bean decided to start charging $0.50 for each cup before her customers started filling it with yogurt and toppings, could you use the same equation to find the new prices? Why or why not?

21. 4-49. Additional Challenge: Use your reasoning skills to compute each unit rate (the price per pound).
$4.20 for pound of cheese
$1.50 for pound of bananas
$6.00 for pound of deli roast beef
$7.50 for pound of sliced turkey

22. THE CURRENT CLASSROOM “MODE”
Quiet Work
Stand & Deliver
Open Discussion
Table Team Work

23. Stand and Deliver, Entry #

24. Stand and Deliver

26. THE CURRENT CLASSROOM “MODE”
Quiet Mode
Let others think too
Stand & Deliver
Open Discussion
Team Work

27. Planner: Homework Quiet Mode
Entry # Homework: Problems

28. END OF CLASS Quiet Mode: Let Others Think Too
Planner check by class leader (homework must be recorded for each class period today)
SECURE YOUR GEAR
Class, ATTENTION
Dismissal by group