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.EE.B.6
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive...
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...
CCSS.Math.Content.8.F.A.3
Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For...
CCSS.Math.Content.8.F.B.4
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a...
CCSS.Math.Content.8.F.B.5
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or...
CCSS.Math.Content.8.SP.A.1
Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe...
CCSS.Math.Content.8.SP.A.3
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For...
GLE 0806.3.4
Translate among verbal, tabular, graphical and algebraic representations of linear functions.
GLE 0806.3.5
Use slope to analyze situations and solve problems.
GLE 0806.5.2
Select, create, and use appropriate graphical representations of data (including scatterplots with lines of best fit) to make and test conjectures.
SPI 0806.1.2
Interpret a qualitative graph representing a contextual situation.
SPI 0806.1.3
Calculates rates involving cost per unit to determine the best buy.
SPI 0806.3.4
Translate between various representations of a linear function.
SPI 0806.3.5
Determine the slope of a line from an equation, two given points, a table or a graph.
SPI 0806.3.7
Identify, compare and contrast functions as linear or nonlinear.
SPI 0806.5.3
Generalize the relationship between two sets of data using scatterplots and lines of best fit.
TSS.Math.8.EE.B.5
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in...
TSS.Math.8.EE.B.6
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; know and derive...
TSS.Math.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 of an...
TSS.Math.8.F.A.2
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
TSS.Math.8.F.A.3
Know and interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.
TSS.Math.8.F.B.4
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description...
TSS.Math.8.F.B.5
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear...
TSS.Math.8.SP.A.3
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a...
 
Alignment of this item to academic standards is based on recommendations from content creators, resource curators, and visitors to this website. It is the responsibility of each educator to verify that the materials are appropriate for your content area, aligned to current academic standards, and will be beneficial to your specific students.
 
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?