NAME _______________________________________________________ PERIOD ____ DATE______________________
Advanced 6 Math: Grade 7 Topic 2 Extending Scale Factor & Proportional Reasoning
Objectives:
 Calculate a scale factor and use it to determine an unknown dimension of a similar figure.
 Use a given scale factor and proportional reasoning to determine a distance or linear
measurement.
 Use proportional reasoning to solve problems related to recipes, where ingredients must
change in proportion to portions or serving sizes.
Vocabulary:
Map scale:
Example:
1 inch = 5 miles
Linear measurement:
the length of a line
Similar figures:
figures that have the same shape, but are different sizes.
EXPLORE: Explore different applications of scale factors.
Page 5:
Similar Figures
Write and solve a proportion to determine the height of
the flag pole.
=
Page 6:
Eli is trying to determine the height of a statue. The statue is too tall for him to measure
directly. Play the animation to see how he uses ratios in the side lengths of triangles to determine the height
of an object.
Write and solve the proportion that Eli uses to determine the height of the statue.
How did Eli determine the scale factor that he would use?
Page 7:
Complete the puzzle on page 7 to check your understanding.
First calculate the scale factor:
Ratio of new to old:
Use your scale factor:
22.5 • __________ = ___________ inches
Page 2:
Apply proportional reasoning to mixing paint: Follow the instructions in the
animation to mix purple paint.
Panel 2: What is the ratio of blue paint to red paint that you need to use: _____________
Panel 3: If you have 4 pints of red, how many pints of blue do you need? _____________
Panel 4: What scale factor is used to make the correct shade of purple
when you used 2 parts of blue and 4 parts of red paint?
_____________
Panel 5: Now make brown paint. You will need 1 part purple to 1 part yellow.
You do not have purple, but remember blue and red in the ratio of 1:2 make purple.
Parts of:
Page 3:
blue ______
red _______
yellow ______
You can use a scale map to determine the distances between places.
The scale on the map in the animation is 1 inch = 5 miles
What two math strategies are used in the animation to determine the actual number of miles
between the two cities?
1) ________________________________________________________________
2) ________________________________________________________________
Page 4:
Did you know that you also apply proportional reasoning when you cook? Recipes
are written to make a certain amount of food, or number of portions. To make more or fewer
portions, you change the amount of each ingredient. You must change each ingredient by the
same proportion or the food will not taste the same.
What scale factor is used to increase the ingredients for the strawberry ice cream? ________
Original Recipe
yields 1 quart
1 gallon (4 quarts)
2 egg yolks
cup condensed milk
cup strawberries
cup sugar
1 ¼ cup whipping cream
Page 5:
Rewrite the strawberry ice cream recipe to make 6 quarts. Check your answers by
completing the table online. Do your work below.
How many eggs will you need?
_______
How much milk?
_______
How many cups of strawberries?
_______
How many cups of sugar?
_______
How many cups of whipping cream?
_______
EVALUATE: Check your understanding.
Complete the SKILL CHECK Gr7 Applying Proportional Reasoning. (separate assignment)
1)
1 ¼ cups of shrimp for 5 people needs to be changed proportionally in order to feed 12 people.
Write and solve a proportion. What scale factor will you use?
2)
How much shrimp is needed?
It is 375 miles from San Francisco to Los Angeles. On a map of California, the scale shows that 2
centimeters equals 10 actual miles. How far apart on the map are the two cities?
MORE PRACTICE: Complete the practice problems for this lesson. (Separate assignment)
Do the work neatly on the back of this worksheet or in your math notebook.