Building an Understanding for Linear Functions. Jim Rahn LL Teach, Inc. www.jamesrahn.com [email protected] Mathematical Ideas . These ideas will be integrated throughout the development of linear functions: Proportions
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These ideas will be integrated throughout the development of linear functions:
This chart shows the lengths of several lakes in both miles and kilometers.
Predict the two other lengths. and kilometers.
Create a hand graph of miles (x) vs. km. (y)
What pattern or shape do you see in your graph?
Connect points to illustrate your pattern.
L1 and kilometers.
Create a L3=L2/L1
What is the meaning of this value?
Use this value to predict the length of the other two lakes.
L1 and kilometers.
Create a table that fits your equation. Predict the two lengths in the using the table.
If x represents miles and y represents Km, what equation connects the two variables?
Graph the equation in your calculator.
Trace on the graph to predict the two lengths in the chart.
We just found out that graphs and the graphing calculator can be used to
The Empire State Building has 102 floors and is 1250 feet high. How high are you when you are reach the 80th floor?
Explain your reasoning.
A van leaves High Point and heads south for Cape May. At the same time a pickup truck leaves Atlantic City and a sports car leaves Cape May and head toward High Point.
The van is traveling at 72 mph, the pickup truck is traveling 66 mph, and the sports care is traveling at 48 mph.
When and where will they pass each other?
Explore time-distance relationship
Write walking instructions or act out walks for a given graph
Sketch graphs based on given walking instructions or table data
Use an electronic device, motion sensor, and graphing calculator to collect and graph data
Study one of the pictures above. Each describes a 6 second walk. The vertical axis shows 0 to 4 meters.
Write a set of walking instructions for each graph. Tell where the walk begins, how fast the person walks, and whether the person walks toward or away from the motion sensor.
Make a paper graph of a 6 second walk based on your instructions.
Obtain a CBR (motion detector) to use with your graphing calculator to complete set of instructions. Be ready to discuss the results of your investigation.
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