Four Representations

Warmup

Activity #1

Find Pairs that Satisfy a Proportional Relationship.

The equation  shows how much it costs to buy gas at a gas station on a certain day. In the equation, c  represents the cost in dollars, and g represents how many gallons of gas were purchased. g represents how many gallons of gas were purchased.

(1). Write down at least four (gallons of gas, cost) pairs that fit this relationship.

• Create a graph of the relationship below.

(2.) What does 2.95 represent in this situation?

(3.) Jada’s mom remarks, “You can get about a third of a gallon of gas for a dollar.” Is she correct?

(4.) How did she come up with that?

Activity #2

Write an Equation for a Proportional Relationship.

There is a proportional relationship between a volume measured in cups and the same volume measured in tablespoons. 3 cups is equivalent to 48 tablespoons, as shown in the graph.

• Plot and label at least two more points that represent the relationship above.

• Use a the line tool , to draw a line that represents this proportional relationship.

(1.) For which value y, is on the line you just drew?

(2.) What is the constant of proportionality for this relationship?

(3.) Write an equation representing this relationship. Use c   for cups and  t for tablespoons.

Activity #3

Add More Points on a Graph of Proportional Relationship.

The equation c = 2.95g shows how much it costs to buy gas at a gas station on a certain day. In the equation, c  represents

(1). Write down at least four (gallons of gas, cost) pairs that fit this relationship.

• Use the applet below to create a graph of the relationship.

(1.) What does 2.95 represent in this situation?

(2.) Jada’s mom remarks, “You can get about a third of a gallon of gas for a dollar.” Is she correct?

(3.) How did she come up with that?

Challenge #1

A gas station charges four different prices for gas: a day price, a night price, a weekend price, and a weekend night price. Each price is represented in a different way:

What are the similarities and the differences among the different representations?

Challenge #2

Which group of blocks is the bluest? Explain your reason.

Challenge #3

Order the groups of blocks from least blue to bluest.