Topic
Standards
Common Core
Learning
Target
Warm-Up
Exit Ticket
Key
Vocabulary
Homework
Monday – 5/12
Ratios and Proportional Relationships
Topic B Lesson 8
7.EE.4 Use variables to represent
quantities in a real-world or
mathematical problem and construct
simple equations and inequalities to
solve problems by reasoning about the
quantities.
Today I can use the constant of
proportionality to represent proportional
relationships by equations in real world
contexts.
(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
are proportional to time. If they
are, determine the unit rate. If not,
explain why not.
b. 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 Tuesday
Guest Teacher
Component
Lesson Plans – Taylor – 7th Grade Math – Accelerated – Periods 3
Q4W9: Week of May 12-16
Tuesday – 5/13
Wednesday – 5/14
Thursday – 5/15
Ratios and Proportional Relationships
Ratios and Proportional Relationships
Topic B Lesson 9
Topic B Lesson 10
7.EE.4 Use variables to represent
7.RP.2d Explain what a point (x, y) on
quantities in a real-world or
the graph of a proportional relationship
mathematical problem and construct
means in terms of the situation, with
simple equations and inequalities to
special attention to the points (0,0) and
solve problems by reasoning about the
(1, r), where r is the unit rate.
quantities.
Today I can define variables in a word
Today I can explain what a point on the
problem and write an equation using
graph of a proportional relationship
the constant of proportionality.
means in the context of a problem
including (0, 0) and (1, r), where r is the
unit rate.
(10 min) Warm-Up
(10 min) Warm-Up: Cookie Recipe
Find the constant of proportionality,
Grandma’s Special Chocolate-Chip
determine appropriate variables, and
Cookie recipe, which yields 4 dozen
write an equation to represent this
cookies, calls for 3 cups of flour to
situation.
make 4 dozen cookies. Create a table
comparing the amount of flour used to
the amount of cookies.
(15 min) Lesson 9 Exit Ticket
(10 min) Lesson 10 Exit Ticket
Oscar and Maria each wrote an
Great Rapids White Watering Company
equation that they felt represented the
rents rafts for $125 per hour. Explain
proportional relationship between
why the point (0, 0) and (1, 125) are on
distance in kilometers and distance in
the graph of the relationship, and what
miles. One entry in the table paired150
these points mean in the context of the
km with 93 miles. k = number of
problem.
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 Thursday
constant
variable
equation
proportional relationship
constant of proportionality
unit rate
Lesson 10 – Problem Set
DUE Monday
Friday – 5/16
Ratios and Proportional Relationships
Mid-Module Assessment
7.RP.1
7.RP.2
7.EE.4
TBD
TBD
Instruction
(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?
5. How do you determine the
meaning of any point on a graph
that represents two quantities that
are proportional to each other?
4.