Section 1.8 Proportional & Direct Variation Functions Task Instructions The following tasks will formalize the mathematics, vocabulary, and the characteristics of direct variation functions. Group the students in pairs to answers the questions. Each letter card (A thru M) has a point value on it. The students can earn up to 100 points by answering enough cards that will add up to be 100 points. Each pair of students must answer a minimum number of 10 cards. Student must show all work on the “Student Work Sheet” to get the points.
A
12 pt
Direct Variation Function
Draw Frayer’s vocabulary model on work/answer sheet
Name the type of relationship (correlation), as one variable increase the other variable increase. _______________
Write a direct variation function rule to model the situations.
B
On a map scale, 1 cm represents a distance of 25 miles. Two cities on the map are 3.2 cm apart. What actual distance separates the two cities?
C
8 pts 3 pts
n
2
R
30
20
1000 450
A local theme park charges $21 for admission. The amount of revenue generated by admission sales can be found using the function “R = 21n�, Where R is the total revenue and n is the number of admissions sold.
D 30,000
For each of the five ordered pairs on the table,
R calculate the ratio . Complete the table. n
What is the least amount of tickets that can be sold in order for the revenue to exceed $100k?
State what you notice:
10 pt 8 pts
E
Â
F Is each equation a direct variation? If it is, find the constant of variation.
G
a. Write an equation of the direct variation that includes the point (4, -3).
a. 5x + 2y = 0
b. 5x + 2y = 9 b. Write an equation of the direct variation that includes the point (-3, -6). c. 7y = 2x
12 pt
Your distance from lightning varies directly with the time it takes you to hear thunder. If you hear thunder 10 seconds after you see the lightning, you are about 2 miles from the lightning. Write an equation for the relationship between time and distance.
5 pts
A_______________(correlation) is one which as one variable increase, the other decreases.
I
3 pts
H
10 pt
A recipe for a dozen cupcakes calls for one cup of flour. The number of cupcakes varies directly with the amount of flour you use. Write a direct variation for the relationship between the number of cups of flour and the number of cupcakes.
5 pts
K # of Marbles (m)
Mass in Ounces (w)
1
1.5
2
3.0
4
6.0
8
12.0
10
15.0
3 pts a.) What is the independent variable? b.) What is the dependent variable? c.) What is the proportional relationship?
J L
If no trend is apparent between two variables, then we say there is ___ __________ between the variables.
Remember that direct variations pass through the origin, or through the point (0, 0). Is the equation of the line joining each pair of points a direct variation? If so write the equation. A. (2, 4), (-1, -2)
M
B. (4, 3), (-2, 1)
3 pts Â
18 pt
Student Work/Answer Sheet Name(s)__________________________ Question Number A
B
C
D
Period_________
Show Work Here
Date_______________Â Answers
Points
E
F
G
H
I
Â
J
K
L
M
# of questions answered: _______
Total points earned: _______