8th Grade Task: Flower Pot

8th Grade Task: Flower Pot

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.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.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.
SPI 0806.1.2
Interpret a qualitative graph representing a contextual situation.
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.
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...
 
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: 
  • Explain how the dimensions of the flower pot can be used to find the y‐intercept of a linear model used to find the height of the stack of pots when the number of pots is known?
  • How can you use the linear model you created in part (b) to find out how many pots are in a stack that is 37 inches tall?
  • What other types of objects stack in ways similar to the flower pots?
  • If the model for a new stack of similar pots is y = 2 x + 9, what can you predict about the features of the flower pot?

Activity/Task Variations

Blooms taxonomy level: 
Understanding
Differentiation suggestions: 

If students can’t get started….
Assessing Questions

  • What is meant by the point (2, 4 ¾ )? … (5,7)?
  • Explain the meaning of the y‐intercept in terms of the context of the problem.

Advancing Questions

  • Why is the y‐intercept of the model not 4 inches?
  • Will the height of the stack of pots ever be 8 inches tall? Explain.
     
Extension suggestions: 

If students finish early….
Assessing Questions

  • Jim created a linear model based on data he found for stacking chairs. His equation was y = 4x + 60 where x is the number of chairs and y is the height of the stack in inches. Explain the meaning of the slope and y‐intercept in the context of the problem.
  • Max looked at Jim’s equation for stacking chairs and determined that the original chair must be 60 inches tall. Explain to Jim why he is mistaken.

Advancing Questions

  • Find a stackable object in the classroom and explain how to create a model that gives the height of the stack depending on the number of objects.
  • As the answer to part (d) Mark wrote y = 1.5(x‐1) + 10 where x is the number of pots and y is the height of the stack in inches. Explain whether Mark’s answer is correct and include your reasoning.
  • How many pots will fit in a shelf that is 30 inches tall?