A recipe says that 2 cups of dry rice will serve 6 people. Complete the table as you answer the questions. Be prepared to explain your reasoning.
How many people will 1 cup of rice serve?
How many people will 3 cups of rice serve? 12 cups? 43 cups?
How many people will cups of rice serve?
cups of dry rice
number of people
1
2
6
3
12
43
A recipe says that 6 spring rolls will serve 3 people. Complete the table as you answer the questions. Be prepared to explain your reasoning.
How many people will 1 spring roll serve?
How many people will 10 spring rolls serve? 16 spring rolls? 25 spring rolls?
How many people will spring rolls serve?
number of
spring rolls
number of
people
1
6
3
10
16
25
How was completing the table about spring rolls different from completing the table about rice? How was it the same?
4.3
Activity
A plane flew at a constant speed between Denver and Chicago. It took the plane 1.5 hours to fly 915 miles.
Complete the table.
time (hours)
distance (miles)
1
1.5
915
2
2.5
How far does the plane fly in 1 hour?
How far would the plane fly in hours at this speed?
If represents the distance that the plane flies at this speed for hours, write an equation that relates and .
How far would the plane fly in 3 hours at this speed? in 3.5 hours? Explain or show your reasoning.
4.4
Activity
To bake coco bread, a bakery uses 200 milliliters of coconut milk for every 360 grams of flour. Some days they bake bigger batches and some days they bake smaller batches, but they always use the same ratio of coconut milk to flour.
Complete the table.
Use to represent the grams of flour needed for milliliters of coconut milk. Write an equation that relates and .
How much flour is needed for 680 milliliters of coconut milk? 945 milliliters? Explain or show your reasoning.
coconut milk
(milliliters)
flour
(grams)
100
200
360
450
Student Lesson Summary
In this lesson, we wrote equations to represent proportional relationships described in words and shown in tables.
This table shows the amount of red paint and blue paint needed to make a certain shade of purple paint, called Venusian Sunset.
Note that “parts” can be any unit for volume. If we mix 3 cups of red with 12 cups of blue, you will get the same shade as if we mix 3 teaspoons of red with 12 teaspoons of blue.
red paint
(parts)
blue paint
(parts)
3
12
1
4
7
28
1
The last row in the table shows that if we know the amount of red paint, , we can always multiply it by 4 to find the amount of blue paint needed to make Venusian Sunset. If is the amount of blue paint, we can say this more succinctly with the equation . So, the amount of blue paint is proportional to the amount of red paint, and the constant of proportionality is 4.
We can also look at this relationship the other way around.
If we know the amount of blue paint, , we can always multiply it by to find the amount of red paint, , needed to make Venusian Sunset. So, the equation also represents the relationship. The amount of red paint is proportional to the amount of blue paint, and the constant of proportionality .
blue paint
(parts)
red paint
(parts)
12
3
4
1
28
7
1
In general, when is proportional to , we can always multiply by the same number —the constant of proportionality—to get . We can write this much more succinctly with the equation .
