F-LE.1.2

Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input- output pairs (include reading these from a table).

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Formative Assessments
Formative Assessments
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Students are asked to write a function given its graph.
Functions From Graphs
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Students are asked to write a function to model the relationship between two variables described in a real-world context.
The Cost of Water
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Students are given a table of values and are asked to write a linear function.
Writing a Function From Ordered Pairs
Virtual/Hands-on Manipulatives
Virtual/Hands-on Manipulatives
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A series of graphing challenges designed to build student understanding of linear functions in various forms.
Desmos: Match My Line
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Restrict, reposition, and rotate lines at will using slope-intercept form. Use precision in describing these transformations using words and/or symbols.
Marbleslides: Lines
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In this activity, students plug values into the independent variable to see what the output is for that function. Then based on that information, they have to determine the coefficient (slope) and constant(y-intercept) for the linear function. This activity allows students to explore linear functions and what input values are useful in determining the linear function rule. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the Java applet.
Linear Function Machine
Assessment Questions
Assessment Questions
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FSA Sample Question
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Videos of Expert Instruction
Videos of Expert Instruction
Decorative Light Bulb. Image includes gray lightbulb on purple background.
When will the pixel pattern break through the box? After how many seconds? Will it break through the top, the sides, or the corner?
Pixel Pattern
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If you wanted to topple over a domino the size of a skyscraper, how many dominoes would you need?
Domino Skyscraper
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If Dan shrinks the dollar nine times like this, how big will it be? Will you still be able to see it?
Incredible Shrinking Dollar
Hook/Performance Tasks
Hook/Performance Tasks
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This problem complements the problem ``Do two points always determine a linear function?'' There are two constraints on a pair of points R1 and R2 if there is an exponential function f(x) = ae^bx whose graph contains R1 and R2. First, the y-coordinates of R1 and R2 cannot have different signs, that is it cannot be that one is positive while the other is negative. This is because the function g(x) = ex takes only positive values. Consequently, f(x) = ae^bx cannot take both positive and negative values. Furthermore, the only way aebx can be zero is if a = 0 and then the function is linear rather than exponential. As long as the y-coordinates of R1 and R2 are non-zero and have the same sign, there is a unique exponential function f(x) = ae^bx whose graph contains R1 and R2.
Do two points always determine a linear function?
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This awesomely gross lesson provides students with a real world context for building linear functions.
How Much Does A 100×100 In-N-Out Cheeseburger Cost?
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Students are asked to select the best model for a given context and use the model to make predictions.
Basketball Bounces, Assessment Variation 1
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The task provides a reasonably straight-forward introduction to interpreting the parameters of an exponential function in terms of a modeling context.
Exponential Parameters
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This task asks students to analyze a set of data from a physical context, choose a model that reasonably fits the data, and use the model to answer questions about the physical context. This variant of the task is not scaffolded; for a more scaffolded version, see F-LE Basketball Bounces, Assessment Variation 1.
Basketball Bounces, Assessment Variation 2