Achievement objective S63
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.
Indicators
A. Comparing discrete theoretical distributions and experimental distributions, appreciating the role of sample size:
 Describes
frequency distributions and notes key features.
 Calculates, graphs, and describes simple
theoretical distributions.
 Compares
theoretical distributions to
experimental distributions, noting similarities and differences, using graphs and measures.
 Carries out experimental investigations of
probability situations, understanding that even when the
theoretical distribution is a good model for the experimental situation, the
experimental distribution will differ due to experimental or
sampling variation, and that real life situations may differ from the
experimental distribution.
 Makes predictions in complex situations and compares their predictions to experimental data, adjusting their predictions to fit their observations.
 Investigates
probability situations, understanding that there is likely to be relatively less variation in the frequencies of the outcomes when the sample size is larger and begins to develop an understanding of how this relates to complex situations.
 Demonstrates understanding of the use of an
experimental distribution (with a very large sample size) to estimate the theoretical probabilities when the
theoretical distribution cannot be modelled.
 Learns that situations involving real data from
statistical investigation can be investigated from a probabilistic perspective.
 Appreciating the role of sample size, the connection between sample size and variation.
 Laying down foundations for the binomial distribution (discrete situations).
B. Calculating probabilities in discrete situations:
 Uses systematic lists, tables (including twoway tables), and tree diagrams with counts to solve probability problems in discrete situations.
 Calculates expected number and informal simple conditional probabilities from a twoway table.
Progression
S63 links to
S74.
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?

Exploring paper, scissors, or rock
 Odd dice: Instead of using an ordinary symmetrical dice, use a match box with the sides numbered 16. 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:
Last updated September 17, 2018
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