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**Explore how unit price and constant of proportionality are related**.

For purposes of this activity, keep the price under $10. Use the purple slider to set your unit price. Use the slider scale to set the unit price. Round to the nearest whole dollar.

(1). Describe the table- do you notice a pattern? How does buying 1 more unit (x) impact the cost?

How can you find the unit price * k*(constant of proportionality) from the graph?

(1). In you own words how you would use the number of items you buy and the unit price to find the cost.

(2). Write an equation using your unit price to show the relationship between the quantity and cost.

(3). What would your total cost be if you were buying 20 items?

(4). Write your own word problem using the item you selected and it’s unit price.

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**Explore graphs of proportional relationships**.

Sort the graphs into groups based on what proportional relationship they represent.

Write an equation for each *different* proportional relationship you find.

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**Explore Distance Time Graphs.**

A giant tortoise travels at 0.17 miles per hour and an arctic hare travels at 37 miles per hour. Draw separate graphs that show the relationship between time elapsed, in hours, and distance traveled, in miles, for both the tortoise and the hare.

(1). Would it be helpful to try to put both graphs on the same pair of axes?

(2). Why or why not?

(3). The tortoise and the hare start out together and after half an hour the hare stops to take a rest. How long does it take the tortoise to catch up?

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Here is a graph that could represent a variety of different situations.

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The tortoise and the hare are having a race. After the hare runs 16 miles the tortoise has only run 4 miles. The relationship between the distance, x, the tortoise “runs” in miles for every y miles the hare runs, is . Graph this relationship.

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The table shows a proportional relationship between the weight on a spring scale and the distance the spring has stretched. Complete the table.

Describe the scales you could use on the and axes of a coordinate grid that would show all the distances and weights in the table.

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