Component
Topic
Standards
Common Core
Learning
Target
Warm-Up
Exit Ticket
Key
Vocabulary
Homework
Monday – 5/12
Ratios and Proportional Relationships
Topic B Lesson 7
7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
Today I can find and interpret the unit rate and constant of proportionality within the context of a problem.
Lesson Plans – Taylor – 7 th Grade Math – Regular – Periods 1 & 5
Q4W9: Week of May 12-16
Tuesday – 5/13 Wednesday – 5/14
Ratios and Proportional Relationships
Topic B Lesson 8
7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
Today I can use the constant of proportionality to represent proportional relationships by equations in real world contexts.
Thursday – 5/15
Ratios and Proportional Relationships
Topic B Lesson 9
7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
Today I can define variables in a word problem and write an equation using the constant of proportionality.
TBD (10 min) Warm-Up: Graphing
Your uncle just bought a hybrid car and wants to take you and your siblings camping. The ratios in the table represent the number of gallons remaining to hours of driving. Create a graph and explain if the quantities are proportional to each other or not.
(10 min) Lesson 7 Exit Ticket
Susan and John are buying cold drinks for a neighborhood picnic. Each person is expected to drink one can of soda.
Susan says that if you multiply the unit price for a can of soda by the number of people attending the picnic, you will be able to determine the total cost of the soda. John says that if you divide the cost of a 12-pack of soda by the number of sodas, you will be able to determine the total cost of the sodas.
Who is right and why? constant proportional relationship constant of proportionality unit rate
Lesson 7 – Problem Set
DUE Tuesday
(10 min) Warm-Up: Mother’s Gas
Record
Find the constant of proportionality and explain what it represents in this situation, i.e. the unit rate.
(15 min) Lesson 8 Exit Ticket
John and Amber work at an ice cream shop. The hours worked and wages earned are given for each person. a.
Determine whether John’s wages b.
are proportional to time. If they are, determine the unit rate. If not, explain why not.
Determine whether Amber’s wages are proportional to time. If they are, determine the unit rate.
If not, explain why not. c.
Write an equation to model the relationship between each person’s wages. Identify constant of proportionality for each. Explain what it means in the context of the situation. d.
How much would each worker make after working 10 hours?
Who will earn more money? e.
How long will it take each worker to earn $50? constant variable equation proportional relationship constant of proportionality unit rate
Lesson 8 – Problem Set
DUE Wednesday
(15 min) Lesson 9 Exit Ticket
Oscar and Maria each wrote an equation that they felt represented the proportional relationship between distance in kilometers and distance in miles. One entry in the table paired150 km with 93 miles. k = number of kilometers and m = number of miles, who wrote the correct equation that would relate miles to kilometers?
Explain why. a.
Oscar wrote the equation k =
1.61m, and he said that the rate
1.61/1 represents miles per km. b.
Maria wrote the equation k =
0.62m as her equation and she said that 0.62 represents miles per km. constant variable equation proportional relationship constant of proportionality unit rate
Lesson 9 – Problem Set
DUE Friday constant variable equation proportional relationship constant of proportionality unit rate
Lesson 10 – Problem Set
DUE Monday
Friday – 5/16
Ratios and Proportional Relationships
Topic B Lesson 10
7.RP.2d Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0,0) and
(1, r), where r is the unit rate.
Today I can explain what a point on the graph of a proportional relationship means in the context of a problem including (0, 0) and (1, r), where r is the unit rate.
(10 min) Warm-Up: Cookie Recipe
Grandma’s Special Chocolate-Chip
Cookie recipe, which yields 4 dozen cookies, calls for 3 cups of flour to make 4 dozen cookies. Create a table comparing the amount of flour used to the amount of cookies.
(10 min) Lesson 10 Exit Ticket
Great Rapids White Watering Company rents rafts for $125 per hour. Explain why the point (0, 0) and (1, 125) are on the graph of the relationship, and what these points mean in the context of the problem.

Instruction
(5 min) Review Key Vocabulary
(20 min) Example 1: National Forest
Deer Population in Danger?
Model putting points from the word problem into the table.
Model finding the constant of proportionality.
1.
Why does it matter if the deer population is not constant in a certain area of the national forest?
2.
What is the population density of deer per square mile?
3.
Use the unit rate of deer per square mile to determine how many deer there are for every 207 square miles.
4.
Use the unit rate to determine the number of square miles in which you would find 486 deer.
(5 min) Discussion
How is the constant of proportionality related to the unit rate?
(15 min) Example 2: You Need
WHAT???
1.
Is the number of cookies proportional to the number of sheets used in baking? Create a table that shows data for the number of sheets needed for the total number of cookies needed.
2.
It took 2 hours to bake 8 sheets of cookies. If Brandon and his mother begin baking at 4:00 p.m., when will they finish baking the cookies?
(15 min) Example 3: French Class
Cooking
1.
Considering the amount of eggs necessary to make the crepes, what is the constant of proportionality?
2.
What does the constant of proportionality mean in the context of the problem?
3.
How many eggs will be needed for 50 crepes?
(5 min) Closing
How is the constant of proportionality related to the unit rate?
(5 min) Review Key Vocabulary
Add “variable” and “equation”
(20 min) Example 1: Do We Have
Enough Gas to Make it to the Gas
Station?
1.
Knowing that there is a half-gallon left in the gas tank when the light comes on, will you make it to the nearest gas station 26 miles away? Explain why or why not.
2.
Write and equation that will relate the miles driven to the number of gallons of gas.
3.
Using the equation, determine how far your mother can travel on
18 gallons of gas.
4.
Using the equation, determine how many gallons of gas would be needed to travel 750 miles.
(20 min) Example 2: Andrea’s
Portraits
1.
Write three ordered pairs from the graph and explain what one coordinate pair means in the context of this graph.
2.
Determine the constant of proportionality and explain what it means in this situation.
3.
Write an equation that would relate the number of portraits drawn to the time spent drawing the portraits.
(5 min) Closing
How can unit rate be used to write an equation relating two variables that are proportional?
(5 min) Review Key Vocabulary
(20 min) Example 1: Jackson’s
Birdhouse
1.
Write an equation that you could use to find how long it will take him to build any number of birdhouses.
2.
How many birdhouses can
Jackson build in 40 hours?
3.
How long will it take Jackson to build 35 birdhouses? Use the equation from part a to solve the problem.
4.
How long will it take to build 71 birdhouses? Use the equation from part a to solve the problem.
(20 min) Example 2: Al’s Produce
Stand
1.
Which makes more sense: to use a unit rate of “ears of corn per dollar” or of “dollars/cents per ear of corn”?
2.
Based on the previous question, which would be the independent variable?
3.
Which would be the dependent variable and why?
4.
How do you write an equation for a proportional relationship?
5.
Write the equation for Al’s
Produce Stand.
6.
Write the equation for Barbara’s
Produce Stand.
7.
If you used E = number of ears of corn and C = cost for the variables instead of x and y how would you write the equations?
(5 min) Closing
1.
What type of relationship can be modeled using an equation in the form y = kx, and what do you need to know to write an equation in this form?
2.
Give an example of a real-world relationship that can be modeled using this type of equation and explain why.
3.
How do you determine which value is���(independent) and which value is ��(dependent)?
4.
Give an example of a real-world relationship that cannot be modeled using this type of equation and explain why.
(5 min) Review Key Vocabulary
(15 min) Example 1: Cookie Recipe
1.
Is the number of cookies proportional to the amount of flour used? Explain.
2.
What is the unit rate, and what is the meaning in the context of the problem?
3.
Create a graph with a title and axes labeled with units.
4.
Does the graph show the two quantities being proportional to each other? Explain.
5.
Write an equation that can be used to represent the relationship.
(15 min) Example 2: Sugar for
Cookies
1.
Record the coordinates of flour of the points from the graph in a table. What do these ordered pairs (values) represent?
2.
Grandma has 1 remaining cup of sugar, how many dozen cookies will she be able to make? Plot the point on the graph above.
3.
How many dozen cookies can grandma make if she has no sugar? Can you graph this on the grid provided above? What do we call this point?
(15 min) Exercises
(10 min) Closing
1.
What points are always on the graph of two quantities that are proportional to each other?
2.
How can you use the unit rate to create a table, equation, or graph of a relationship of two quantities that are proportional to each other?
3.
How can you identify the unit rate from a table, equation, or graph?
4.
How do you determine the meaning of any point on a graph that represents two quantities that are proportional to each other?