F-IF.2.4

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

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Formative Assessments
Formative Assessments
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Students are asked to evaluate three verbal descriptions and to state why each does or does not match a given graph.
Bike Race
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Students are given a table of functional values and asked to describe and interpret key features of the graph in the context of the problem.
Surf’s Up
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Students are asked to interpret key features of a graph (intercepts and intervals over which the graph is increasing) in the context of a problem situation.
Uphill and Downhill
Virtual/Hands-on Manipulatives
Virtual/Hands-on Manipulatives
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Identify important features of lines. Precisely describe these features to peers. Increase vocabulary relevant to lines.
Desmos: Polygraph Lines
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This activity follows up on Polygraph: Lines, using the discussions (and students' informal language) in that activity to develop academic vocabulary related to the graphs of linear functions.
Desmos: Polygraph Lines 2
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This activity asks students to notice and use properties of linear functions to make groups of three. Different properties will lead to different groupings by different students. Later we ask students to make conjectures about different groupings – why might another student have grouped the cards in a particular way?
Card Sort: Linear Functions
Assessment Questions
Assessment Questions
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FSA Sample Question
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Videos of Expert Instruction
Videos of Expert Instruction
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SCCA race car drivers discuss how using a chassis dyno to graph horsepower and torque curves helps them maximize potential in their race cars.
Graphing Torque and Horsepower for Dyno-mite Racing
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Jump to it and learn more about how quadratic equations are used in robot navigation problem solving!
Jumping Robots and Quadratics
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Richard Bertram discusses his mathematical modeling contribution to the Birdsong project that helps the progress of neuron and ion channel research.
Birdsong Series: Mathematically Modeling Birdsong
Hook/Performance Tasks
Hook/Performance Tasks
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In this task students are given graphs of quantities related to weather. The purpose of the task is to show that graphs are more than a collection of coordinate points; they can tell a story about the variables that are involved, and together they can paint a very complete picture of a situation, in this case the weather. Features in one graph, like maximum and minimum points, correspond to features in another graph. For example, on a rainy day, the solar radiation is very low, and the cumulative rainfall graph is increasing with a large slope.
Telling a Story with Graphs
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This context makes for an interesting application of calculating interest.
How Much Did Peterson Lose By Not Cashing His Check?
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Students will have to decompose 450 and account for the nine rolls.
How Can You Win Every Prize At Chuck E. Cheese’s?
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The purpose of this task is to give students practice constructing functions that represent a quantity of interest in a context, and then interpreting features of the function in the light of the context. It can be used as either an assessment or a teaching task.
The Canoe Trip, Variation 1
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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 will be able to verify their answers by using the Finland’s police website that has an English language “Ticket Calculator” where students will be able to plug in values to verify that their answer is correct.
How Did He Get A $103,000 Speeding Ticket In Finland?
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This task could be used for assessment or for practice. It allows students to compare characteristics of two quadratic functions that are each represented differently, one as the graph of a quadratic function and one written out algebraically. Specifically, students are asked to determine which function has the greatest maximum and the greatest non-negative root.
Throwing Baseballs
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Students add the monthly payments together with the initial down payment and compare it to the single annual payment.
Is It Cheaper To Pay Monthly or Annually?
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The purpose of this task is to model the population data for London with a variety of different functions.
Modeling London’s Population