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New Zealand
Level 7 - NCEA Level 2

Filling a Swimming Pool (Investigation)



  • To practice differentiating between functions and relations.
  • To practice identifying linear relationships in real life.
  • To practice using the two point formula.


  • Clear measuring cup (holds at least 4 cups)
  • Marker
  • Sink
  • Stopwatch
  • Paper
  • Internet


  1. Place the measuring cup into the sink.
  2. Turn on the sink and begin the stopwatch at the same time.
  3. Every 5 seconds turn off the sink and record how much water is in the measuring cup.
  4. Use the following table to record your data: 
  5. Stop when the measuring cup is filled. 


  1. Pick two data points from what you collected and use the two point formula to create an equation describing how much water the sink will pump out over time. Put the formula in general form.
  2. Graph the equation you just found. Put time on the x-axis and amount of water on the y-axis. Label everything and include units.
  3. Should your graph be continuous or discrete? Explain in the context of the problem.
  4. Is the equation you graphed a function or relation? Does this make sense? Why or Why not?
  5. Is the equation you graphed linear? Why or why not?
  6. What is the y intercept of your graph? Explain why this makes sense in the context of the experiment.
  7. Would the graph look the same if you had begun the experiment with some water already in the measuring cup? If not, how would it have changed?
  8. Work with a partner to answer the rest of the questions.
  9. Compare your graphs. Did your measuring cup fill up faster than theirs? Why or why not?
  10. Determine how long it would take to fill up a swimming pool assuming the water was pumped into the pool at the same rate the sink was pumping out water. You may need to use the internet to find additional information.
  11. How long will it take for the pool to overflow?
  12. Is this a reasonable rate at which to fill up a pool? Why or why not?



Display the graphs of linear and non-linear functions and connect the structure of the functions with their graphs


Apply graphical methods in solving problems

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