# Stage 2 - number – chance

Distinguish between certain and uncertain events; use chance terms to describe the likelihood of events happening

## Strategy

Students can:

• distinguish between certain and uncertain events
• use chance terms to describe the likelihood of events happening

## Activities to support the strategy

In the Number strand of the mathematics syllabus students are required to investigate situations involving chance.

In teaching about chance it is important that students:

• describe and use the language associated with chance appropriately
• use both fractions and percentages to assign numerical values to the likelihood of simple events occurring in real-life contexts
• use samples to make predictions about a larger 'population'.

### Activity 1 – certain and uncertain events

The teacher prepares sets of cards describing a variety of events. Students, working in pairs, classify the events under the following headings: The event is certain; the event is impossible and the event could happen.

### Activity 2 – chance terms

1. The teacher introduces the concept of a cline using an example in a familiar context e.g. temperature.

Discuss the cline using language associated with chance events; least likely, more likely and most likely.

#### 2. Lucky Dip

The teacher makes sets of the same object in different colours, such as counters, coloured paddle pop sticks or blocks, with each set containing three different colours, for example, 1 green counter, 2 blue counters, 3 red counters.

Each set is placed in a bag or box. The teacher demonstrates by pulling out one item from a set without looking. This is repeated a number of times, returning the object that has been pulled out each time.

The teacher tallies the results on the board and students interpret the results by asking questions such as, Which counter was I most likely to pull out?

The teacher adds data to cline by recording the probability of each colour being chosen (1 chance, 2 chances etc.).

The teacher models true statements referring to the probability recorded on the cline, e.g. Red was the most likely colour to be chosen because there were three chances to pull out red/because there were more chances to pull out red.

The teacher makes tokens for free ice-creams, free yoyos and free movie passes in three vastly differing amounts. Students in groups take turns at pulling tokens out of a container. After each turn students record the results by putting a tally mark on a grid. (see example below)

At the end of the Lucky Dip, the students tally the results and record totals. Students then circle the statement that determines the probability of each token being chosen.

Students write true statements using the model provided.

The teacher prepares a small bag of jellybeans containing three different coloured jellybeans. One colour has to be a large number, one a medium-sized number and the other a small number. Then students complete a cloze describing the contents of the bag and predict which colour jellybean is more likely/least likely to be drawn out.

3. Students are presented with cards containing terms often used when describing situations involving chance. In pairs or small groups, discuss the meaning of the chance terms and place these cards in order from least likely to most likely.

4. The class plays a variety of games to demonstrate the principles of chance and help students to make predictions. It is important that the teacher listens to the student's use of language to assess their level of understanding.

a) The teacher rolls a die. Students are asked to predict answers to questions such as:

• How many throws will it take for you to get your favourite number?
• If everyone in the class rolls a die, how many of each number would you expect?

b) The teacher has 5 blue, 4 red and 3 green counters in a box. Students are asked to choose a colour from red, blue, green or white.

The teacher says, I have a box with 12 counters. You score 5 points each time I take a counter in your colour out of the box. (The counter is returned to the box after the colour is noted.) Repeat the activity 6 times. Students are asked to predict what colour counters are in the box and decide if the game is fair.

The teacher labels a large die with three faces displaying an apple, two faces displaying a banana and one face displaying an orange, and shows the die to the class. Students are asked to order the fruits from least likely to most likely to be rolled.

After a number of rolls, the students compare the results with their predictions. Students discuss whether their predictions were supported by their experiment and explain the differences between expected results and actual results in this simple chance experiment.

#### Possible questions include:

How can we change the labels on the die so that the orange is most likely to be rolled? The labels are then changed accordingly, and the die rolled a number of times to compare the results with the students' predictions. Students are encouraged to make other suggestions about altering the labels to change the outcomes and these suggestions are tested.

## References

### Australian curriculum

ACMSP047: Identify practical activities and everyday events that involve chance. Describe outcomes as 'likely' or 'unlikely' and identify some events as 'certain' or 'impossible'.

CMSP067: Conduct chance experiments, identify and describe possible outcomes and recognise variation in results.

ACMSP094: Identify events where the chance of one will not be affected by the occurrence of the other.

### NSW syllabus

MA2-19SP: Describes and compares chance events in social and experimental contexts.