Student:
Class:
Date:
Modeling with inverse variation
Student Activity Sheet 2; use with Exploring “Traveling by train”
1. What is the total distance of the train trip (the constant)?
2. What values for the trip vary? Explain.
3. Complete the table for the train trip of 240 miles.
Time to complete
trip (hours)
1
100
1
10
1
3
1
2
Process
Speed (mph)
(rate)(time) = distance
1
2
3
10
100
n
4. What do you notice about the distance when you find the product of rate and time?
Copyright 2014 Agile Mind, Inc. ®
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
Page 1 of 4
With space for student work
Student:
Class:
Date:
Modeling with inverse variation
Student Activity Sheet 2; use with Exploring “Traveling by train”
5. Express, in terms of speed, the inverse relationship for the variables in the train trip.
speed (y)
=
6. Create a scatterplot of speed vs. number of hours traveled, using the data in the table.
Copyright 2014 Agile Mind, Inc. ®
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
Page 2 of 4
With space for student work
Student:
Class:
Date:
Modeling with inverse variation
Student Activity Sheet 2; use with Exploring “Traveling by train”
Look at the graph of the trip and the graph of the ice cream sandwiches.
7. What do you notice about the position of all the points on both graphs?
8. What do you notice about the behavior of both graphs?
9. REINFORCE Suppose that Van Smithers has 36 ice cream sandwiches to share with his
visiting friends. Graph the relationship between the number of people and the number of
ice cream sandwiches per person.
Copyright 2014 Agile Mind, Inc. ®
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
Page 3 of 4
With space for student work
Student:
Class:
Date:
Modeling with inverse variation
Student Activity Sheet 2; use with Exploring “Traveling by train”
10. REINFORCE Suppose that a train travels an uninterrupted route of 360 miles at a
constant speed.
a. Make a graph showing the relationship between the time needed to complete the trip
and the speed of the train.
b. Write a function rule that shows the relationship between time and speed.
11. REINFORCE The number of days it takes to build a house is inversely proportional to the
number of people helping to build it. If it takes 10 people 40 days to build the house,
how long will it take 8 people to build the house?
12. REINFORCE The number of people at a pizza party varies inversely as the number of
slices of pizza each person receives. If 20 people attend, each person receives 5 slices of
pizza. If 50 people attend, how many slices will each person get?
Copyright 2014 Agile Mind, Inc. ®
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
Page 4 of 4
With space for student work