Task Set 1: Interpreting Points (modified from The Language of Functions and Graphs)
These four shapes each have an area of 36 square inches.
1. Label four points on the graph below, with the letters A, B, C, and D.
2. Can you draw a fifth shape, with an area of 36 square units, to correspond to the other point? Explain why your drawing corresponds to the point above.
3. Draw a scattergraph to show every rectangle with an area of 36 square units.
4. What happens if you include all shapes, with the same area on your graph?
On each graph, mark and label two points to represent aircraft A and B.
Task 2: Interpreting Points
School Report: |
What can you say about points A and B? |
What conclusion can be drawn from this graph? |
Each point on this graph represents a bag of sugar.
1. Which bag is the heaviest? _______________
2. Which bag is the cheapest? _______________
3. Which bags are the same weight? _______________
4. Which bags are the same price? _______________
5. Which point, F or C, would give a better value for money? _______________ How can you tell?
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6. Which point, B or C, would give better value for money? _______________ How can you tell?
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7. Which two bags would give the same value for money? _______________ How can you tell?
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Sharks and Fish
Below is a simplified description of what
can happen when two species interact. The
sharks are they predators and the fish are the
prey. The situation in statement A has been
represented on the graph by a point. How
does this point move as time goes by? Plot poins to represent B, C, D, E, and F.
(A) Due to the absence of many sharks, there is an abundant supply of fish in the area …
(B) Sensing a plentiful supply of fish for food, sharks enter the area.
(C) The sharks eat many of the fish until …
(D) … the fish population is insufficient to support all the sharks. Many sharks therefore decide to leave.
(E) With few sharks around, the fish population increases once again.
(F) The area now contains enough food to support more sharks, so they return …
Task 3: Sketching Graphs of Functions from Words
Write down an explanation of how you arrived at your answer. In particular, answer the following three questions.
1. Should the graph “slope upwards” or “slope downwards”? Why?
2. Should the graph be a straight line? Why?
3. Should the graph meet the axes? if so, where? If not, why not?
1. “Prices are now rising more slowly than at any time during the last five years”
Copy of Graph-Letter:____ | Explanation of your choice |
2. “The smaller the boxes are, then the more boxes we can load into the van.”
Copy of Graph-Letter:____ | Explanation of your choice |
3. “After the concert there was a stunned silence. Then one person in the audience began to clap. Gradually, those around her joined in and soon everyone was applauding and cheering.”
Copy of Graph-Letter:____ | Explanation of your choice |
4. “If movie theatre ticket charges are too low, then the owner will lose money. On the other hand, if they are too high then few people will attend and again they will lose. A cinema must therefore charge a moderate price in order to stay profitable.”
Copy of Graph-Letter:____ | Explanation of your choice |
5. How does the cost of a bag of potatoes depend on its weight?
Copy of Graph-Letter:____ | Explanation of your choice |
6. How does the time running a race depend upon the length of the race?
Copy of Graph-Letter:____ | Explanation of your choice |
7. How does the speed of a girl vary on a swing?
Copy of Graph-Letter:____ | Explanation of your choice |
Task 4: Sketching Graphs from Words
Graph | i. Explain in words what each graph means | ii. Which graph shows this situation most realistically? Explain. | iii. Which graph is the least realistic? Explain. |
(a) | |||
(b) | |||
(c) | |||
(d) | |||
(e) | |||
(f) |
Copy of Graph-Letter:____ | Explanation of your choice |
Copy of Graph-Letter:____ | Explanation of your choice |
Copy of Graph-Letter:____ | Explanation of your choice |
Copy of Graph-Letter:____ | Explanation of your choice |
Copy of Graph-Letter:____ | Explanation of your choice |
Copy of Graph-Letter:____ | Explanation of your choice |
1. How does your height vary with age?
2. How does the amount of dough needed to make a pizza vary with diameter?
3. How does the amount of daylight we get depend on the time of year?
4. How does the number of people in a supermarket vary during a typical Saturday?
5. How does the speed of pole-vaulter vary during a typical jump?
6. How does the water level in your bathtub vary, before, during, and after you take a bath?