F-IF.2.6

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

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Formative Assessments
Formative Assessments
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Students are given a graph of an exponential function and are asked to calculate and compare the average rate of change over two different intervals of time.
Air Cannon
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Students are given a table of functional values in context and are asked to find the average rate of change over a specific interval.
Pizza Palace
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Students are asked to estimate the average rate of change of a nonlinear function over two different intervals given its graph.
Estimating the Average Rate of Change
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 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
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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's focus is slope. The goal is to sharpen students’ focus on slope. In particular, the activity asks students to estimate first, then to calculate, then to notice proportionality as they place points on an imaginary line.
Desmos: Put the Point on a Line
Assessment Questions
Assessment Questions
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Videos of Expert Instruction
Videos of Expert Instruction
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Meteorologist, Michael Kozar, discusses the limitations to existing hurricane scales and how he is helping to develop an improved scale.
Improving Hurricane Scales
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``Slope`` is a fundamental concept in mathematics. Slope is often defined as `` the rise over the run``....but why?
Slope
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Hook/Performance Tasks
Hook/Performance Tasks
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This task asks students to consider functions in regard to temperatures in a high school gym.
The High School Gym
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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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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 the first question is to give students a question that they can sink their teeth into. There are many ways for them to determine that together the pair ate 36 hot dogs in the first four rounds (1 + 2 + … + 8).
How Many Hot Dogs Did They Eat?!
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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?