Learning Targets
Here are the prices for some smoothies at two different smoothie shops:
For Smoothie Shop A, smoothies cost $0.75 per ounce no matter which size we buy. There could be a proportional relationship between smoothie size and the price of the smoothie. An equation representing this relationship is
p=0.75s
where s represents size in ounces and p represents price in dollars. (The relationship could still not be proportional, if there were a different size on the menu that did not have the same price per ounce.)
For Smoothie Shop B, the cost per ounce is different for each size. Here the relationship between smoothie size and price is definitely not proportional.
In general, two quantities in a proportional relationship will always have the same quotient. When we see some values for two related quantities in a table and we get the same quotient when we divide them, that means they might be in a proportional relationship—but if we can't see all of the possible pairs, we can't be completely sure. However, if we know the relationship can be represented by an equation is of the form y=kx, then we are sure it is proportional.
A lemonade recipe calls for the juice of 5 lemons, 2 cups of water, and 2 tablespoons of honey.
Invent four new versions of this lemonade recipe:
Entrance to a state park costs $6 per vehicle, plus $2 per person in the vehicle.
Notice that the relationship is NOT proportional.
Han and Clare were running laps around the track. The coach recorded their times at the end of laps 2, 4, 6, and 8.
Han's run:
Clare's Run:
In this lesson, we learned some ways to tell whether a table could represent a proportional relationship. Revisit one or more of the activities in the lesson, highlighting the following points: