S4-3: Investigate situations that involve elements of chance by comparing experimental distributions with expectations from models of the possible outcomes, acknowledging variation and independence.
This means students will understand that probability is about the chance of outcomes occurring. At Level Four students should recognise that it is not possible to know the exact probability of something occurring in most everyday situations, for example the probability of someone being left-handed. They should understand that trialling must be used to gain information about the situation and that the results of trial samples vary, for example different samples of 100 people will have different proportions. Contrived chance events are used to highlight the variation between expected outcomes from models, and experimental outcomes from trialling. Level Four students are expected to use systematic methods such as listing, tree or network diagrams with equally likely outcomes, and tables to find all the possible outcomes of simple one or two stage situations such as tossing two coins, drawing counters from a bag, or rolling two dice. Students should compare the distributions they get from trialling with the expectations obtained from models, accepting variation between samples and that the results of one sample do not impact on the next (independence), for example take samples of twenty counters, with replacement, from a bag that has one-half red, one-third blue and one-sixth yellow. Accept that an eight red, seven blue, and five yellow result is natural and that it will not be compensated by the next sample.
find all possible outcomes
explore outcomes in a probability game
find the probability of the outcome
design a fair dice for the game
- Investigate, state and justify the probability of events in common situations.
- Theoretically and experimentally examine the probabilities of games of chance.
- Construct nets.
- Measure mass, capacity, length, and temperature using scales and devices.
- Conduct investigations and present results.
- Carry out experiments and systematically record the results.
- Identify the possible outcomes of an event.
- Follow a logical argument.
- Write a rule for the pattern.
- Interpret information and results in context (logic, be systematic).
find all possible outcomes using a tree diagram
evaluate findings from probability activities
compare results of experimental probabilities with other people
write the probability as a fraction
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
list all possible outcomes using a table
- Apply counting strategies to problem solving tasks.
- Write an explanation of what they have done.
- Devise and use problem solving strategies to explore situations mathematically (constructing a tree diagram, be systematic, make a list).
find all possible outcomes
graph the outcomes from a simple probability experiment
compare theoretical and experimental results
find all possible outcomes using a tree diagram
evaluate findings from probability activities
- 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.
list all possible outcomes
play a probability game to find the chance of winning
find all possible outcomes to the probability game
decide from the data if the game is fair
explore number puzzles using addition (Problem 1)
find outcomes by using diagrams (Problem 2)
conduct a simple probability experiment
compare experimental estimates of probability outcomes with a claimed probability and draw a conclusion
- Create geometric shapes that satisfy the no three in a line condition on 4 by 4 grids.
- Devise a systematic approach to find possible outcomes.
find all possible outcomes
explore the outcomes in a probability game
list all possible outcomes
decide if a game is fair
calculate the theoretical probabilities
compare results of experimental probabilities with other people
make a conclusion from the results of probability experiments
- Explore random number tables.
- Use a simple test for randomness.
- Investigate sample sizes.
- Generate randowm numbers.