F-IF.3.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

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Formative Assessments
Formative Assessments
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Students are given a linear function represented by an equation and an exponential function represented by a graph in a real-world context and are asked to compare the rates of change of the two functions.
Comparing Linear and Exponential Functions
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Students are given two linear functions, one represented by a graph and the other by an equation, and asked to compare their intercepts in the context of a problem.
Comparing Linear Functions
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Students are asked to compare two quadratic functions, one given by a table and the other by a function.
Comparing Quadratics
Virtual/Hands-on Manipulatives
Virtual/Hands-on Manipulatives
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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 interactive simulation investigates graphing linear and quadratic equations. Users are given the ability to define and change the coefficients and constants in order to observe resulting changes in the graph(s).
Equation Grapher
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Assessment Questions
Assessment Questions
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Videos of Expert Instruction
Videos of Expert Instruction
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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
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Hook/Performance Tasks
Hook/Performance Tasks
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In the middle grades, students have lots of experience analyzing and comparing linear functions using graphs, table, symbolic expressions, and verbal descriptions. In this task, students may choose a representation that suits them and then reason from within that representation.
Kimi and Jordan
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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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