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Ratios and Proportions
Seventh Grade Teaching Lesson for April 29th
by
TweetTracie Forrester
on 16 December 2015Transcript of Ratios and Proportions
Ratios &
Proportions
What is a ratio?
What about rates?
What are Proportions?
Proportional Tables & Graphs
Unit Rate as a Scale Factor
This can be written in three ways!
A RATIO is a comparison or quotient of two quantities!
3:4
3 to 4
A parking lot is 150 yards long and 50 yards wide.
The ratio of the length to the width of the parking lot is...
A RATE is a ratio of different units.
A UNIT RATE is the rate or cost of a single unit (a one in the denominator)
A CONSTANT OF PROPORTIONALITY (k) is the number you multiply x by to get y in a proportional relationship.
EXAMPLE:
Tourists drive 300 miles on 15 gallons of gas.
What is the unit rate in miles per gallon?
A PROPORTION is a statement of equality between two ratios (or rates).
In a proportion, each side's ratio will simplify to the same rate or decimal.
Two quantities are proportional if ALL ratios or rates of the quantities are equivalent.
The table below shows the amount of candy and the price paid.
Is the cost of the candy proportional to the amount of candy?
Write an equation to illustrate the relationship between the amount of candy, x, and the cost, y.
Using the equation, predict how much it will cost for 12 pounds of candy.

5
2
=
7.5

3
=
12.5

5
=
kx=y
A proportional relationship can be represented by y=kx for the constant of proportionality/ unit rate, k= .
x
y
_
y=kx
k=
y
x
_
rate:
unit rate:
miles per gallon
WARMUP:
I go to Dollar General and want some orange juice. I can pay $1.50 for a 16ounce bottle or I can pay $3.50 for a half gallon (64ounces). How much does the 16ounce bottle cost per ounce? How much does the half gallon cost per ounce? Which is the better bargain?
Actual
Garden
Scale
Garden
8 feet
14 feet
1 foot
The scale factor corresponds to the unit rate and constant of proportionality.
The scale factor shows us how to go from an actual measurement to a scaled measurement.
The scale factor can be calculated from the ratio of any scale length to it's corresponding actual length.
(actual length)(scale factor)= scaled length
scale factor=
_____
scaled length
actual length
Actual Scale
Garden Garden
Ratio for
Scale Factor
Bottom
Side
How Do we fill in this table?
1. Fill in what you know.
2. Find what the scale factor is.
3. Apply the scale factor to get the scale bottom length.
Graphs of Proportional Relationships Have:
1. All Points on a straight line
2. The line going through the origin (o,0)
A cashier makes 72 dollars after 8 hours of work. Find the unit rate (hourly pay) and set up a proportion with these two ratios.
*(Try writing a ratio to compare the cost [numerator] to the ounces of orange juice [denominator] of each product)*
TASK CARD ACTIVITY DIRECTIONS:
1. Work on the first task card
2. write your work and answer clearly on the answer sheet
3. Put the task card back and pick up the next one!
*Make it as far as you can until I say to stop. I will collect the answer sheet and check how far you make it!
__
k=
Full transcriptProportions
What is a ratio?
What about rates?
What are Proportions?
Proportional Tables & Graphs
Unit Rate as a Scale Factor
This can be written in three ways!
A RATIO is a comparison or quotient of two quantities!
3:4
3 to 4
A parking lot is 150 yards long and 50 yards wide.
The ratio of the length to the width of the parking lot is...
A RATE is a ratio of different units.
A UNIT RATE is the rate or cost of a single unit (a one in the denominator)
A CONSTANT OF PROPORTIONALITY (k) is the number you multiply x by to get y in a proportional relationship.
EXAMPLE:
Tourists drive 300 miles on 15 gallons of gas.
What is the unit rate in miles per gallon?
A PROPORTION is a statement of equality between two ratios (or rates).
In a proportion, each side's ratio will simplify to the same rate or decimal.
Two quantities are proportional if ALL ratios or rates of the quantities are equivalent.
The table below shows the amount of candy and the price paid.
Is the cost of the candy proportional to the amount of candy?
Write an equation to illustrate the relationship between the amount of candy, x, and the cost, y.
Using the equation, predict how much it will cost for 12 pounds of candy.

5
2
=
7.5

3
=
12.5

5
=
kx=y
A proportional relationship can be represented by y=kx for the constant of proportionality/ unit rate, k= .
x
y
_
y=kx
k=
y
x
_
rate:
unit rate:
miles per gallon
WARMUP:
I go to Dollar General and want some orange juice. I can pay $1.50 for a 16ounce bottle or I can pay $3.50 for a half gallon (64ounces). How much does the 16ounce bottle cost per ounce? How much does the half gallon cost per ounce? Which is the better bargain?
Actual
Garden
Scale
Garden
8 feet
14 feet
1 foot
The scale factor corresponds to the unit rate and constant of proportionality.
The scale factor shows us how to go from an actual measurement to a scaled measurement.
The scale factor can be calculated from the ratio of any scale length to it's corresponding actual length.
(actual length)(scale factor)= scaled length
scale factor=
_____
scaled length
actual length
Actual Scale
Garden Garden
Ratio for
Scale Factor
Bottom
Side
How Do we fill in this table?
1. Fill in what you know.
2. Find what the scale factor is.
3. Apply the scale factor to get the scale bottom length.
Graphs of Proportional Relationships Have:
1. All Points on a straight line
2. The line going through the origin (o,0)
A cashier makes 72 dollars after 8 hours of work. Find the unit rate (hourly pay) and set up a proportion with these two ratios.
*(Try writing a ratio to compare the cost [numerator] to the ounces of orange juice [denominator] of each product)*
TASK CARD ACTIVITY DIRECTIONS:
1. Work on the first task card
2. write your work and answer clearly on the answer sheet
3. Put the task card back and pick up the next one!
*Make it as far as you can until I say to stop. I will collect the answer sheet and check how far you make it!
__
k=