3/18 Performance Task

3/18

Today, we are going to look at the Ratios and Proportion's performance task from the benchmark.

If you haven't already please write down this information.

Write down this information on your whiteboard - you will need it for the rest of the problems.

Let's determine the unit rates for each material

(divide the price by the pounds)

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It would be helpful to determine the unit cost for each material, so we have it moving forward. What is the unit cost for concrete, per pound?

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What is the unit cost for steel, per pound?

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What is the unit cost for wood, per pound?

Question 1

The company's chief financial officer plots material costs on a graph, where the x-axis represents the number of pounds of material bought, and the y-axis represents the total cost of the purchase, in dollars. Given that the cost per pound is proportional, complete the table to indicate which ordered pairs could represent material purchases of concrete steel, and/or wood.

What is it asking me?

• They're asking us to match coordinate points (x,y) to the unit cost of each item.

• We must figure out the unit rate of each coordinate point

(22, 1.32) means 22 pounds costs $1.32. What is the unit rate of this coordinate point?

$1.32 / 22 = $0.06

This matches with the concrete unit rate.

(68, 19.72) means 68 pounds costs $19.72. What is the unit rate of this coordinate point?

$19.72 / 68 pounds costs $0.29

This matches with the wood unit rate.

(110, 82.50) means 110 pounds costs $82.50. What is the unit rate of this coordinate point?

$82.50 / 110 pounds costs $0.75

This matches with the steel unit rate.

Let's write equations for each material

y=kx

k is the unit rate as a recimal

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Which equation represents the cost, y, of concrete in dollars, x? y=(unit rate)x

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Which equation represents the cost, y, of steel in dollars, x? y=(unit rate)x

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Which equation represents the cost, y, of wood in dollars, x? y=(unit rate)x

Question 2

How much would 156 pounds of wood cost?

• Remember that the cost for 1 pound of wood is $0.29

How many pounds could you purchase for $208.80?

• Remember that the cost for 1 pound of wood is $0.29

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The relationship between the cost, y, in dollars and the pounds of steel bought, x, can be modeled by what equation?

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Given the proportional steel cost, how much does 200 pounds of steel cost?

Let's switch gears and instead of looking at the cost per pound of steel, let's look at the cost per foot of steel.

What is the cost for 1 foot of steel?

Hint: find 1 foot of steel on your chart

Multiple Choice

What is the meaning of the point (1,12) on the graph?

• 1 pound of steel costs $12 dollars

• $1 of steel weighs 12 pounds

• 12 feet of steel costs $1

• $12 of steel is 1 foot long

Multiple Choice

What does the point (0,0) on the graph represent?

• Zero dollars represents zero pounds of steel.

• Zero dollars represents zero feet of steel.

• Zero dollars represents some amount of pounds of steel.

• Zero dollars represents some amount of feet of steel.

Multiple Choice

The relationship between the cost, y, in dollars, and the feet of the steel beam, x, bought can be modeled by the proportional equation

y = _ x

• y = 12x

• y = 0.75x

• x = 12x

• x = 0.75x