The purpose of this unit is for students to use games to gather and present data in a systematic way. In turn, this allows them to determine the likely outcomes of some everyday events.
The unit provides an introduction to probability, the measurement of chance. Just like 2.3 metres is a measure of length, 50% (or 1/2) is a measure of the chance of getting heads with a single coin toss.
Probabilities range from zero to one (0-100%). An event that always occurs is certain and has a probability of 1 or 100%. An event that never occurs is impossible and has a probability of 0 or 0%.
There are two ways to estimate or calculate the probability of an event occurring. An experiment consists of trials where the event may occur. For example, a dice might be rolled 100 times and the results used to estimate the probability of heads occurring. The experimental probability is unlikely to be exactly 50% but the results will provide an approximate measure for the likelihood.
The likelihood of some events can be worked out theoretically. A model must find all the possible outcomes and identify which of the outcomes leads to the event occurring. The probability is expressed as a part-whole fraction: Number of outcomes that lead to the event/Total number of possible outcomes. In the simple case of a coin toss there are two possible outcomes, and one of those outcomes leads to the event of heads. Therefore, the probability of heads equals 1/2.
In more complex situations involving chance, models of theoretical probability become more complex. Events are independent if they do not influence each other. Tossing two separate coins involves independent events as the result from the first coin has no impact on the result from the second coin. Selecting two coloured pegs from a bag without replacement involves two dependent events. The result of the first peg draw affects the possible outcomes for the second peg draw.
The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to support students include:
The context for this unit can be adapted to suit the interests and cultural backgrounds of your students. Most students are captivated by games of chance and are intrigued when their expectations about fairness do not match what occurs. This unit uses dice and card games as the primary context. Story shells can be added to make the context more engaging for students, such as framing the games in a television gameshow, or in a legend where the main character makes a difficult decision.
Te reo Māori kupu such as tūponotanga (chance, probability), putanga (outcome), whakamātau tūponotanga
(probability experiment), whakamātau (test, trial, experiment), putanga tātai (theoretical outcome), and hoahoa rākau (tree diagram) could be introduced in this unit and used throughout other mathematical learning.
Beat-it
B | E | A | T | I | T |
B | E | A | T | I | T | |
8 6
| 4 5 5 7 | 6 8 9 10 5 | 3 6 5 7 | 2 11 8 9 12 2 5
| 5 3 9 5 12 7 | |
Totals | 14 | 0 | 38 | 0 | 49 | 0 |
Grand total = 101
5 | 4 |
6 | 0 9 |
7 | 1 1 3 5 7 |
8 | 5 5 8 9 2 |
9 | 4 7 8 |
10 | 1 5 7 9 9 |
11 | 7 9 2 |
12 | 6 |
13 | 2 |
Application Game
Dear parents and whānau,
This week in maths we have been playing games!
We have been studying the chance or probability linked to each game to see if we could find winning strategies. We have also looked at the games to see if they were fair. Play a game of Winning Differences with your child and help them think about whether the game is fair or not.
Winning Differences
You will need:
- 1 Dice
- Ten cards from a suit from the ace = 1, to the 10
Rules:
Place the cards face down in the centre. Each turn consists of throwing a dice, choosing a card, and taking the difference of the two numbers.
Player 1 wins if they get a difference of 0, 1, 2, 3, 4.
Player 2 wins if they get a difference of 5, 6, 7, 8, 9.
Is the game fair? If not how can it be made fair?
Printed from https://nzmaths.co.nz/resource/beat-it at 12:18pm on the 26th April 2024