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# Stage 4 - number – probability

Solve simple probability problems; use practical activities to investigate possible outcomes and chance; conduct an experiment; determine if a game is “fair”; collect data and record in a table; interpret data including the range, mode, mean; display data in a line graph; state and apply the rule (definition) for probability

## Strategy

Students can:

• solve simple probability problems
• use practical activities to investigate possible outcomes and chance
• conduct an experiment
• determine if a game is "fair"
• collect data and record in a table
• interpret data including the range, mode, mean
• display data in a line graph
• state and apply the rule (definition) for probability

## Activity 1

1. Students brainstorm the different ways we can describe the chance of something happening. Encourage students to think of both words and numbers to describe probability.

Make a chart to list their suggestions. Place these cards in order from 0 (impossible) to 1 (certain).

Students think of events to match each of these labels: impossible, unlikely, even chance, likely, certain, e.g. View/print (PDF 40.21KB)

2. The teacher models how to express probability as a fraction. The students in pairs solve this problem and use a fraction to express probability.

A bag has 10 coloured balls. The balls are blue, red, green or yellow. Complete the number line to show the probability, expressed as a fraction, of taking out different combinations of balls. View/print (PDF 39.48KB)

3. Students list all the possible outcomes when a standard six-sided dice is rolled. Using this dice, they determine the probability that the result will be an odd number, a number greater than 4, a multiple of 2, a prime number, etc.

4. Play the Sums and differences game and discuss the fairness of the game. Two standard dice are rolled; Player A wins a point if the difference is 0, 1 or 2; Player B wins if the difference is 3, 4 or 5.

5. Use the Spinner series learning object to explore basic concepts, language and reasoning related to chance. Students build their own spinners and investigate what colour the pointer lands on. ### Activity 2

1. The teacher challenges the students to a dice game. Two dice are rolled.

If the total is 7 the teacher wins. If the total is not 7 the students win.

The game is played 20 times with the total recorded each time.

#### Positions include:

• Was the game fair? Why? What are your reasons for thinking that?
• What total occurred most often? Why?
• Can you design a die so that a particular outcome is more likely to occur than another? How will you start?

### 2. Design a chance game

#### The teacher tells the story:

Two students decide to invent an addition dice game, where they are sure to win. Before they invent the game they decide to determine the odds. Students roll two dice 20 times. They add the numbers shown on the two dice, tally the results and record the chance of each answer occurring e.g. 6 occurred 3 out of 20 times.

### Possible questions include:

• Do all totals have an equal chance of being rolled?
• How could you change the likelihood of certain totals occurring?

Students construct a game where they have a greater chance of winning using two dice which they have designed. They explain and discuss the approach taken in constructing their game.

### Extension activity

Students invent a multiplication or division dice game where they have a greater chance of winning.

### Activity 3

1.  Introduce activity with a demonstration of the game: rock, scissors, paper.

• Divide the class into pairs (player A and player B) and have them play the game 18 times.
• Use a grid to graph the wins of player A in red (how many A players won one game, two games, etc.)
• Do the same for all B players in a different colour.

Help students to determine the range, mode and mean for each set of data. Compare the results.

#### Discuss:

• Is the game fair?
• Do both players have an equal chance of winning in any round? (Yes)
• How many different outcomes are there? Record the possible outcomes in a diagram. 2.  Compare the mathematical model with what happened when students played the game.

3.  Use this as an introduction to a unit on probability.

#### Follow up with a discussion about how probability is used in daily life.

4.  Play rock, scissors, paper game again using 3 students.

#### Using the following rules:

• A wins if all 3 hands are same.
• B wins if all 3 hands are different.
• C wins if 2 hands are same.

There will be 27 outcomes this time. 3 to the power of three = 33 = 3 x 3 x 3 = 27

As a class, discuss:

• Who won most often?
• Who won the least often?
• Did they have 'bad' luck or is there a better way to write the rule so they will win more?

## References

### Australian curriculum

ACMSP167: Construct sample spaces for single – step experiments with equally likely outcomes.

### NSW syllabus

MA4-21SP: Represents probabilities of simple and compound events.

### NSW numeracy continuum

Aspect 6: Fraction Units – Fractions as Numbers.

### NSW literacy continuum

VOCC13M3: Vocabulary knowledge, Cluster 13, Marker 3: Selects appropriate vocabulary in response to context, purpose and audience.

### Other literacy continuum markers

SPEC13M7: Aspects of speaking, Cluster 13, Marker 7: Collaborates effectively in pair and group work when exploring subject content, concepts and ideas.  SPEC13M8: Aspects of speaking, Cluster 13, Marker 8: Asks relevant clarifying questions.  SPEC13M9: Aspects of speaking, Cluster 13, Marker 9: Listens critically to spoken texts to discuss and support opinions based on evidence in the text.