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New Zealand
Level 6 - NCEA Level 1

Birthday party at the cinemas (Investigation)



  • To practice creating inequalities to model real-life situations.
  • To practice solving two step inequalities.


  • Internet
  • Paper

For this investigation pretend that it is your birthday. You have been given \$500 to pay for your birthday party at the movie theater. You must use the \$500 to pay for everyone’s tickets, and a snack for yourself, however you must remember to leave \$10 so you can pay for an ice cream cake after the movie.


  1. Create an inequality to illustrate this scenario.
  2. What value(s) do you need to look up to solve this inequality? Use the internet to find this information.
  3. How many people can you invite to your birthday party?
  4. Make an estimate that is definitely too high.
  5. Do all the numbers that solve this inequality make sense? Why or why not?
  6. Create a number line and shade in the amount of people you can bring to your birthday party. Note that if you decided in 3(b) that some values don’t make sense you should exclude those values from your number line.


Work with a friend!

  1. Did they create their inequality the same way you did? How were they the same? How were they different?
  2. Think of other situations in life that can be modeled by an inequality. Together with your partner(s) think of at least 3 other situations that can be modeled by a two-step inequality. Pick one of the 3 and create an inequality for it. Then solve it.



Form and solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns


Apply algebraic procedures in solving problems

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