8th Grade Task: Flower Pot
8th Grade Task: Flower Pot
- Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships...
- 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...
- Solve linear equations in one variable.
- 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...
- Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal...
- 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...
- Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a...
- Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or...
- 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.
- Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
- 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.
- 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...
- Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear...
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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?
Blooms taxonomy level:
If students can’t get started….
- 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.
- 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.
If students finish early….
- 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.
- 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?