8th Grade Task: Downloading Songs

8th Grade Task: Downloading Songs

Standards & Objectives

Academic standards
CCSS.Math.Content.8.EE.B.5
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships...
CCSS.Math.Content.8.F.A.1
Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting...
CCSS.Math.Content.8.F.A.2
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal...
 
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Essential and guiding questions: 

PART A:

  • Who can tell me what this graph represents? Why is the graph going “down”? How many songs are in the album Marie and Scott are trying to download? How long did it take Marie to download the album? How can you determine this from looking at the graph?

PART B:

  • I see that some of you found unit rate to determine who could download the songs faster. But, I saw that some of you found unit rate one way and some of you found it a different way? Does it matter? How can finding unit rate both ways help you answer this question? Is there another way besides unit rate to determine who could download the songs faster?

PART C:

  • There were several different ways to determine how long it would take to download 30 songs. Someone who set up a proportion, tell us why you did and how you knew that would work. There were other equations used – why do those work? Who took the unit rate and scaled it up? What are the connections among all of these methods?

PART D:

  • Why is Scott’s graph steeper than Marie’s? What is the slope for each graph? How are the graphs related to the rate at which each person could download the songs? Why do we have two different graphs? Which representation is more useful in determining who can download the songs faster? Why?

Activity/Task Variations

Blooms taxonomy level: 
Understanding
Differentiation suggestions: 

If students can’t get started….
Assessing Questions

  • Tell me about what is going on in this problem. Explain what Marie’s graph tells you. What does Scott’s table tell you?

Advancing Questions

  • Think about the axes on Marie’s graph. What do the y-values represent?
  • The x-values?
  • How can you use Marie’s graph and Scott’s table to determine who can download songs faster?
Extension suggestions: 

If students finish early….
Assessing Questions

  • Explain how you decided who could download the songs faster.

Advancing Questions

  • Tell me how you described the relationship between the two graphs in terms of slope. What does the slope represent? What if Marie’s graph had intersected the time axis at (4, 0)? How would that change your graph in part D?