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Achievement objective S6-3

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

  • Investigate situations that involve elements of chance:
    • A. comparing discrete theoretical distributions and experimental distributions, appreciating the role of sample size
    • B. calculating probabilities in discrete situations.


A. Comparing discrete theoretical distributions and experimental distributions, appreciating the role of sample size:

B. Calculating probabilities in discrete situations:

  • Uses systematic lists, tables of outcomes, and tree diagrams with counts to solve probability problems in discrete situations.

What is new/changed?

  • Appreciating the role of sample size, the connection between sample size and variation.
  • Laying down foundations for the binomial distribution (discrete situations).

Possible context elaborations

  • CensusAtSchool is a valuable website for classroom activities and information for teachers on all things statistics.
  • Investigate a situation in which the probability of success is unknown (for example, bottle top drop or probability of a long drawing pin landing point up).
  • Investigate a game (for example, bingo with the sum (or differences) of two dice, students filling in own 3 by 3 grid). Make a prediction of the probability distribution, create a theoretical model, collect experimental data, compare and draw conclusions.
  • Investigate a situation that involves a random variable, for example, predict the length of the longest run of heads or tails in 50 coin tosses and guess the likely value for this. Then toss a coin 50 times, repeat (or compare with results of others), and compare variation between samples.
  • Investigate a simple probability situation with increasingly large sample sizes, for example, flipping a coin 10 times each, then combining student data to create successively larger samples, and finally using a computer simulation for very large samples.
  • After investigating the probability of the sum of two dice, calculate the probability of a sum of 7, a sum of more than 5, a sum of less than 4, using their experimental probability and the theoretical probability model and discusses reasons why they may be different.
  • After playing Marble Snap, use a tree or table to determine outcomes and estimate the probability of winning.
  • Is this die fair?
  • Odd dice: Instead of using an ordinary symmetrical dice, use a match box with the sides numbered 1-6. Do trials to calculate the long run relative frequency to estimate probabilities.

Assessment for qualifications

NCEA achievement standards at level 1, 2 and 3 have been aligned to the New Zealand Curriculum. Please ensure that you are using the correct version of the standards by going to the NZQA website.

The following achievement standard(s) could assess learning outcomes from this AO:

  • AS91037 Mathematics and statistics 1.12 Demonstrate understanding of chance and data
  • AS91038 Mathematics and statistics 1.13 Investigate a situation involving elements of chance

Refer to the mathematics and statistics matrix.

Last updated September 26, 2013