8th Grade Task: Workers and Earnings

8th Grade Task: Workers and Earnings

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 1a - How could we answer this question using another method? What would have been different in this problem if the axes were switched? Is it better to use an equation, table, or graph to answer this question?
  • Part 1b – How fast are the two lines getting farther apart? If we made tables for both Workers, what would be similar if we compared the graphs and tables? Do both of these lines pass through the origin? What is the significance of this in terms of the problem?
  • Part 2a - What do you notice as we progress down the chart? What is different about this chart than we usually have? Are the workers’ earnings increasing or decreasing? What is the significance of 7.75? Is it more helpful to have a table, equation, or graph to determine the answer?
  • Part 2b - What is the most helpful thing you were given to answer this question? Is it more helpful to have a table, equation, or graph to determine the answer? Could you do this part without the table? What is the minimum amount of information needed to answer this question?
  • Part 2c– Who took the least amount of hours to earn $100? Would this be true if you had been asked to find who took the least amount of time to earn $200? What did you need to know to determine the answer to this question? To answer a question such as this is which representation is the easiest to work with? Why?

Activity/Task Variations

Blooms taxonomy level: 
Understanding
Differentiation suggestions: 

If students can’t get started….
Assessing

  • How much would each worker make for 1 hour of work? 2 hours?

Advancing

  • How much does each worker make per hour?
Extension suggestions: 

If students finish early….
Assessing Questions

  • Can you build your own scenario for worker E that other students could work on?

Advancing Questions

  • Could you redraw the worker A graph if he received $20 for reporting to work plus the same rate of pay in the original graph?
  • What do you notice about the new and old graph for worker A? How would your equation change?