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Variables & Patterns Investigation 3
Problem 3.1
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I CAN WRITE A ONE-STEP EQUATION TO SHOW THE RELATIONSHIP BETWEEN TWO VARIABLES
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RULE EQUATION
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RULE
A summary of a predictable relationship that tells how to find the value of a relationship.
A rule that contains variables that represent a mathematical relationship.
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Malcolm finds out that it costs $21 per person to visit Wild World.
Liz suggest they make a table or graph relating the admission price to the number of people.
Malcolm says there is a simple rule for calculating the cost.
What is the rule?
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Rule Equation
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Rule
Multiply the price of admissions (21) by the number of people (n)
Cost = 21 X number of people
Equation
C = 21 x N?????
C = 21n
C = 21 N
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Part C – Do the following for each of the three average speeds Write a rule in words for the distance travelled at any
given time
Write an equation for your rule using letters to represent the variables
Describe the pattern of change that shows up in the table, graph and equation
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Part C1
Rule in words
Distance equals 50 mph times the time.
Distance equals 55 mph times the time
Distance equals 60 mph times the time
Part C2
Equation D = 50 t D = 55 t D = 60 t
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Part C3 For each speed, the distance increases by a constant
(same) amount each hour.
This pattern is shown in the table because of the constant change in distance for each hour
This pattern is shown in the graph by the straight line pattern of points
This pattern is shown in the equation by the fact d is equal to the speed time the time.
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Part D For each each of the given speeds (50, 55, and 60 mph)
tell how far you would travel in the given time:
3 hours
4 ½ hours
5 ¼ hours
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Part D1
3 hours @ 50 mph = 150 miles
3 hours @ 55 mph = 165 miles
3 hours @ 60 mph = 180 miles
Table
Read it directly from the table
Graph
Estimate the points on the graph
Equation
Substitute (replace) 3 for the time and multiply it by the speed to find the distance
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Part D1
3 hours @ 50 mph = 150 miles
3 hours @ 55 mph = 165 miles
3 hours @ 60 mph = 180 miles
Table
Read it directly from the table
Graph
Estimate the points on the graph
Equation
Substitute (replace) 3 for the time and multiply it by the speed to find the distance
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Part D2
3 hours @ 50 mph = 150 miles
3 hours @ 55 mph = 165 miles
3 hours @ 60 mph = 180 miles
Table
Read it directly from the table
Graph
Estimate the points on the graph
Equation
Substitute (replace) 3 for the time and multiply it by the speed to find the distance
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COMPLETE PART E AND THE ACE QUESTION ON YOUR HANDOUT