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Analyzing Graphs

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Analyzing Graphs

4 different equations of functions each representing from a different function family. All functions represented in the same graph. Students play with calculators inputting values to see which correspond to the appropriate function in the graph.

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As the wheel turns

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As the wheel turns

This Illustrative Mathematics task assesses if students can construct a trigonometric model that represents a context.

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Bicycle Wheel

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Bicycle Wheel

From the Illustrative Mathematics website, "the purpose of this task is to introduce radian measure for angles in a situation where it arises naturally."
 

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Bisecting an Angle

Geometry
Unit 1: Tools of Geometry
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Bisecting an Angle

This task provides the most famous construction to bisect a given angle. It applies when the angle is not 180 degrees. Since the rays forming a 180 degree angle are collinear, this case can be handled separately by constructing the perpendicular to a line through a given point: note that the construction in the collinear case is actually the same as the one employed here except that the two circles in step (b) need to have radii larger than r so that they meet in two points.
 

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Building a quadratic function from f(x)=x²

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Building a quadratic function from f(x)=x²

Students sketch the parent function and then sketch different transformations of that function to compare them.

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Carbon 14 dating in practice

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Carbon 14 dating in practice

This task focuses on using Carbon 14 isotope exponential decay to date when plant died. If plant died at a certain time, how much Carbon 14 should still be present?

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Choosing an Appropriate Growth Model

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Choosing an Appropriate Growth Model

A table comparing the populations of three different cities every 10 years. Students figure out which family of functions best models each city.

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Comparing Graphs of Functions

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Comparing Graphs of Functions

Students use equations, graphs, and tables to compare linear, exponential, and quadratic functions. As students compare the functions they should use rate of change and end behavior to help differentiate the function families and their unique properties. Meant to be supported with some kind of graphing technology whether graphing calculators, Desmos, Geogebra, or some other similar tools.

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Comparing Graphs of Functions #2

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Comparing Graphs of Functions #2

Students compare three functions: f(x)=2x, g(x)=x2 and h(x)=2x and analyze rates of change. It would be good to modify the activity by having students also graph and create tables for the three functions then describe how they compare in each of those representations.

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Dilating Lines: An Exploration

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Dilating Lines: An Exploration

These student worksheets have the students use slope and distance to dilate a line.

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Distance

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Distance

Student worksheet to find the distance of a line.

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Finding rate of change from graphs

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Finding rate of change from graphs

These four questions can help you surface how students understand finding rate of change from a set of graphs.

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