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, state 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 isometric projections.
Session Five300
- Calculate the theoretical probability of an event by finding all the possible outcomes.
- Use more than one way to find a theoretical probability.
- Check theoretical probabilities using trials.
- Identify what a fair game is and how to make an unfair game fair.
use tables to explore probabilities
- 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
explore the outcomes in a probability game
list all possible outcomes
decide if a game is fair
calculate the theoretical probabilities
- Make a list of possible outcomes as a method of finding probability.
- Express the outcome as a fraction.
- Devise and use problem–solving strategies to explore situations mathematically (make an organised list).
calculate probabilities
- Find the theoretical probability of an event occuring.
- 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 to those events
- Di300
place probability of events on a continuum