Transcript Radical Reform for the Teaching & Learning of Algebra I

Direct Variation
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Learn the properties of a direct variation
equation
Graph a direct variation equation
Read a direct variation graph to find missing
values in the corresponding table
Use a direct variation equation to extrapolate
values from a given data set
Develop an intuitive understand of the
concepts of slope and linear equation
Direct Variation
Page 114
Materials Needed
Graph Paper
Graphing Calculators
Ship Canals
 In this investigation you will look at data
about canals to draw a graph and write an
equation that states the relationship
between miles and kilometers. You’ll see
several ways of finding the information that
is missing from the table.
 Complete steps 1 & 2 of the investigation
Ship Canals
Canal
Length (Miles)
Length (Kilometers)
Albert (Belgium)
80
129
Alphonse XIII (Spain)
53
85
Houston (Texas)
50
81
Kiel (Germany)
62
99
Main-Danube (Germany)
106
171
Moscow-Volga (Russia)
80
129
Panama (Panama)
51
82
St. Lawrence Seaway
(Canada/U.S.)
189
304
Suez (Egypt)
101
Trollhatte (Sweden)
87
 Complete step 3 by entering the data in your
graphing calculator.
 Turn to Calculator Note 1F if you need help
entering the data in the graphing calculator.
 Complete steps 4 to find the ratio L2:L1. See
Calculator Note 1K to create this list. Write
your answer to this step on your
Communicator®.
 Complete step 5 of the investigation. Show
how your determined your answer on the
Communicator®.
 How can you change x miles to y kilometers? Using
variables, write an equation to show how miles and
kilometers are related.
 Use the equation you wrote in the last step to find the
length in kilometers of the Suez Canal and the length in
miles of the Trollhatte Canal. How is using this equation
like using a rate?
 Graph the equation on your calculator. Compare this
graph to your hand-drawn graph. Why does the graph
go through the origin?
 Trace the graph of your equation. Approximate the
length in kilometers of the Suez Canal by finding when x
is approximately 101 miles. Trace the graph to
approximate the length in miles of the Trollhatte Canal.
How do these answers compare to the one you got from
your hand-drawn graph?
 Use the calculator’s table to find the missing
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lengths for the Suez Canal and the Trollhatte Canal.
In this investigation you used several ways to find
missing information: Approximating with a graph,
calculating with a rate, solving an equation, and
searching a table. Write several sentences
explaining which of these methods you prefer and
why.
Since the ratio was the same for every pair of
points, we say that kilometers and miles are
directly proportional.
The relationship between kilometers and miles is
called a direct variation.
It follows the form y = kx where k is a constant of
variation.
 Study the example on page 116
 Use the graphing calculator for parts c and
d
 Then complete problem 5 on page 118.