Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Monthly Update sign up
Mailing List signup
Learning Math Home
Patterns, Functions, and Algebra
Session 1 Part A Part B Part C Homework
Algebra Site Map
Session 1 Materials:

B C 


Solutions for Session 1, Part C

See solutions for Problems: C1 | C2 | C3 | C4 | C5 | C6| C7 | C9

Problem C1

1 = Dennis

2 = Alice

3 = Freda

4 = Brenda

5 = Errol

6 = Cathy

7 = Gavin

<< back to Problem C1


Problem C2

<< back to Problem C2


Problem C3


Top left: Peter; top right: Jane; center: Paul; bottom left: Graham; bottom right: Susan


A good guess would be that Paul and Graham each biked to school.


It cannot be a ride, because Peter, who goes in his dad's car, arrives so quickly. It cannot be a walk, because Susan takes so long to arrive. Also, notice that Graham, Paul, and Jane's points lie on one diagonal line through the intersection of the axes. (What would the value of distance divided by rate represent?)


This suggests that all three used the same mode of transportation. Because Jane biked to school, it is likely that Paul and Graham did as well.

<< back to Problem C3


Problem C4

The graph begins at zero, climbs to (or near) 30 mph, slows down at the first turn, then stays at 30 mph for a long time, then slows at the sharp turn by Graham's, then returns to 30 mph, then slowly drops back to zero at the school.

<< back to Problem C4


Problem C5



Number 8 is the best graph, if the vertical axis measures happiness. The horizontal axis measures the temperature of the milk, and the vertical axis measures the enjoyment of the speaker. Other answers are possible with alternate labelings of the axes; for example, number 11 could be the solution if you measured dislike on the vertical axis.


Number 7. Time is on the horizontal axis, and price is on the vertical axis.


Numbers 9, 12, and 3 are all pretty good choices. The number of boxes is on the horizontal axis, and the size is on the vertical axis.


Number 5 (note the concert audience's initial stunned silence). Time is on the horizontal axis, and volume is on the vertical axis.


Number 11. Price is on the horizontal axis, and profit is on the vertical axis.


Number 1: If I work more hours, I'll make more money. Number 3: I've got $100 to spend on Slurpees or gasoline. The more I spend on Slurpees, the less I have remaining for gas. Number 15: The population of frogs at the pond really exploded last year, but now it's leveling out.

<< back to Problem C5


Problem C6



Number 2 is the best graph. A small bag still costs more than zero dollars.


Number 6


Number 4


Number 13 because they are slowest at the top and bottom of the swing.


Number 14 because speed is zero when the ball changes direction, fastest at the bouncing point

<< back to Problem C6


Problem C7

<< back to Problem C7


Problem C9


Since the bottle is narrower at the top, it will fill faster near the top. This means that the top half of the bottle fills in less time than the bottom half, because it holds less liquid.


Animated version of the solution to Problem C9(b). Requires the Flash plug-in.
Ink bottle: F
Conical flask: D
Evaporating flask: I
Bucket: A
Vase: E
Plugged funnel: B


Graphs C and G would require quick changes to a constant width. Graph C would go from a small width to a large width; G is the opposite. As for graph H, notice the similarity to graph E.

<< back to Problem C9


Learning Math Home | Algebra Home | Glossary | Map | ©

Session 1 | Notes | Solutions | Video


© Annenberg Foundation 2017. All rights reserved. Legal Policy