8th Grade Task: Flower Pot

8th Grade Task: Flower Pot

Standards & Objectives

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?