Grade 8 Math Assignment: Explore and Apply
Proportion, Ratio and Rate
Part A: Equivalent Ratios
Sam wants to paint a small picket fence that surrounds the vegetable garden in his back yard.
He has two different colours of paint: red and yellow. He wants to use a pattern of three red
pickets then two yellow pickets per panel. Let red and yellow counters (Red and yellow dots)
represent the pickets in each panel.
1. Complete the table.
Number of
Panels
1
2
3
4
Number of
Red
Pickets
3
Number of
Yellow Pickets
2
Total
Number of
Pickets
5
2. Add a new column to your table.
a. Write the ratio of red pickets to yellow pickets in one panel.
b. Write the ratio of red pickets to yellow pickets in two panels.
3. What would be the ratio of red pickets to yellow pickets in five panels? Six panels?
Add this information to your table.
4. Write the ratios from question 2a. and 2b. in fraction form. Are they equivalent? How
do you know?
5. Compare the other ratios from the table to the first ratio. What can you conclude?
6. Suppose you have 24 red pickets.
a. By what number are you multiplying the original number of red pickets?
b. How many yellow pickets will you have?
7. Equal ratios form a proportion. If you know three numbers in the proportion, how can
you find the fourth? Try the example below. Explain your answer.
3 27
=
2
?
8. Look at the set of counters (red and yellow dots) you used to represent one panel.
a. How many parts are in this ratio?
b. What fraction of the total number of pickets is red? Yellow?
9. How do you know when two ratios form a proportion? Give your own example.
a. How are ratios similar to fractions? How are they different? Explain with your
own examples.
Part B: The Meaning of Proportion
1. Copy the diagram onto grid paper
2. Predict how the diagram would change if each
side were half as long. Write your prediction on
the back of your grid paper. Check you answer by
drawing the new diagram.
3. Predict how the diagram would change if each
side were one block shorter. Write your prediction
on the back of your grid paper. Check your
prediction by drawing the new diagram. Was your
prediction correct?
4. Refer to your diagrams from question 2 and 3. Which diagram is in proportion to the
original diagram? Explain how you know.
Part C: Exploring Rates
Bus A, Bus B, and Bus C start from the bus station at the same time and travel in different
directions.
Bus A
10 min
Bus B
6 min
8 km
Bus
Station
5 km
Bus C
5 min
4 km
1. For each bus, write the distance travelled compared to the time taken. This is a rate (a
comparison of quantities measured in different units).
2. Which of the rates in question 1 are equivalent rates or are in proportion? Explain how
you know.
3. Which bus is travelling at the greatest speed? Explain how you know.
4. If Bus A travels at the same speed throughout its route, how far will it travel in 20 min?
in 30 min?