8th Grade Task: T-shirt Task

8th Grade Task: T-shirt Task

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.EE.C.7
Solve linear equations in one variable.
CCSS.Math.Content.8.EE.C.8
Analyze and solve pairs of simultaneous linear equations.
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 0806.3.2
Represent, analyze, and solve problems involving linear equations and inequalities in one and two variables.
GLE 0806.3.3
Solve systems of linear equations in two variables.
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 0806.3.1
Find solutions to systems of two linear equations in two variables.
SPI 0806.3.2
Solve the linear equation f(x) = g(x).
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 0806.3.6
Analyze the graph of a linear function to find solutions and intercepts.
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.EE.C.7
Solve linear equations in one variable.
TSS.Math.8.EE.C.8
Analyze and solve systems of two linear equations.
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: 

Questions:

  • Did you use the first name, the last name, or both the first and last names when you wrote your response to Ms. Shaw? Does it make a difference what you chose to use?
  • What ratios were given to you? How did you use the ratios to solve the problem? Did you have to use information besides the ratios to solve the problem?
  • Who was right—Andrea or Lexus? Why? (Note: Students should note that neither was completely right because the underlying assumptions each one makes do not support the overall argument.)

Activity/Task Variations

Blooms taxonomy level: 
Understanding
Differentiation suggestions: 

If students can’t get started. . .

  • If you bought your shirt from Company A, what name would you have on
  • the back? How much would your shirt cost?
  • What would be the cost of your shirt from Company B?
  • Is it always true that Company A will be cheaper (or more expensive, depending on the answers to the previous two questions) than Company B? Why or why not?
Extension suggestions: 

If students finish early. . .

  • How would you estimate the total cost of all of the shirts for this class?
  • What assumptions would you need to make about the shirts?
  • Do you think that if someone else estimated the total cost of all of the shirts, they would have a different answer than you? Why would their answer be different?