# S4-4: Use simple fractions and percentages to describe probabilities.

Simple fractions and percentages in this objective are common benchmarks like one half (50%), thirds (33.3% and 66.6%), quarters (25% and 75%), fifths (20%, 40%, 60%, 80%), tenths (10%, 30%, etc). Students should know that outcomes that are certain are described by fractions equalling one, including 100%, and outcomes that are impossible are described by fractions equalling zero, including 0%. In contrived situations involving elements of chance, for example totalling two dice, students should know that the count of all possible outcomes gives the denominator of a probability fraction, for example 36 possible outcomes, and the number of desired outcomes gives the numerator, for example there are 9 ways to get a total of either 2,4 or 6 so the probability is 9/36 or 1/4 . In realistic situations where probabilities are estimated, for example the chance of a drawing pin landing safe, students are expected to accept variation from an exact fraction, for example 37 out of 100 were safe which is about or 33.3%.

- investigate probability in common situations
- make and justify the probability of events in common situations
- theoretically and experimentally examine the probabilities of games of chance

**Session One**

Use systematic approaches to find all the possible outcomes, e.g. tree diagrams, organised lists.

**Session Two**

Use tables, graphs, and word rules to represent growing patterns.

**Session Three**

Draw cube models using plan views.

**Session Four**

Draw cube models using isometric300

- Find whether a given whole number is prime or non-prime (composite) and whether the number is a multiple of three.
- Use exponents, square roots, factorials and place value to write expressions for whole numbers.
- Represent category data using bar charts and interpret those charts.
- Calculate300

- Find a theoretical probability.
- Use more than one way to find a theoretical probability.
- Check theoretical probabilities by trials.
- Identify what a fair game is and how to make an unfair game fair.

use tables to explore probabilities

- Investigate probability in the context of a dice game.

- use simulations to investigate probability in common situations
- predict the likelihood of outcomes on the basis of an experiment
- determine the theoretical probability of an event

use problem solving strategies to solve ordering problems

find all possible probability outcomes

describe an outcome as a fraction

- Learning to use numbers to represent probabilities.
- Understanding that trialling can be used to gain information but that results of trials can vary.
- Using appropriate language relating to probability.

- Using fractions to represent probabilities.
- Be systematic in recording possible outcomes, including using a tree diagram.
- Using appropriate language relating to probability.

- Exploring chance in everyday events.
- Understanding experimental and theoretical probability.
- Accepting that samples and results vary.

- Explore the mathematics of uncertainty.
- Compare the relative probability of outcomes.

explore the outcomes in a probability game

list all possible outcomes

decide if a game is fair

calculate the theoretical probabilities

calculate probabilities

- Find a theoretical probability.
- Use more than one way to find a theoretical probability.
- Check theoretical probabilities by trials.
- Identify what a fair game is and how to make an unfair game fair.

describe a probability using fractions

find all possible outcomes using a table

find the probability of an event occurring

evaluate a statement about a probability event

- Find simple exponential number patterns.
- Use exponential patterns to make predictions about further members of the pattern.
- Use tables and graphs to identify relationships between two variables.
- Create rules for relationships between two variables.
- Use fractions to measure probabilities.

- Explore the theoretical and experimental probabilities of situations involving chance.
- Recognise variability from theoretical expectations, especially with small numbers of trials.
- Estimate and find the relative frequencies of events.
- Distinguish between events and the outcomes that lead to300

place probability of events on a continuum