Variables & Patterns Investigation 3

Problem 3.1

I CAN WRITE A ONE-STEP EQUATION TO SHOW THE RELATIONSHIP BETWEEN TWO VARIABLES

  RULE   EQUATION

  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.

  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?

  Rule   Equation

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

  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

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

  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.

  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

  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

  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

  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

COMPLETE PART E AND THE ACE QUESTION ON YOUR HANDOUT