*Probability progression, 1st–2nd steps *

## The purpose of the activity

In this activity, the learners develop an understanding of the words used to describe the probability or likelihood of events. The learners also learn to identify all the possible outcomes for a simple probability event.

## The teaching points

- The learners understand that the probability that a future event will occur can be described along a continuum from impossible to certain.
- The terms that can be used for probability include “chance”, “likelihood”, “odds”, “percentage” and “proportion”.
- A sample space is the set of all possible outcomes for an event. For example, the sample space for drawing balls from a bag that only holds black and white balls is {black, white}.
- Discuss with the learners the fact that the outcomes of events are not usually equally likely. For example, the possible outcomes for a basketball free throw are either to make the goal or miss it, with the likelihood of making it dependent on the skill of the player. On the other hand, tossing a fair coin does have two equally likely outcomes.

## Resources

- Two colours of counters, beads or paper (For the remainder of this sequence, we assume that black and white are the two chosen colours.)
- Non-transparent bags or containers.

## The guided teaching and learning sequence

1. Begin the session by drawing a line on the board and writing the words “Impossible” and “Certain” at either end of the line.

2. Have the learners work in pairs or small groups. Give each group 10 black counters, 10 white counters and a container. Explain that you want them to put counters into a container so that the chance or probability of getting a black counter is certain.

3. Ask one of the groups to hold up their container for you to select a counter from. Before revealing the counter, ask the group to confirm that they are certain that you have a black counter in your hand.

“Are you certain that I have selected a black counter?” “Why?”

4. Hopefully you have a black counter in your hand and only black counters were in the container. Discuss with the learners whether they think that the number of black counters placed in the container makes a difference to the outcome.

“Does it make a difference how many black counters you have in the container?”

(No, because the only possible outcome is black and it doesn’t matter whether there is 1 or 100 counters in the container.)

5. Ask the class to explain what it means to be certain about an outcome. Listen to ensure they understand that being certain means there is no chance of any other outcome.

6. Under “Certain” on the probability line, draw a picture of a container with a number of black counters and record beside it the statement

“It is certain that you will draw a black counter from this container”.

7. Ask the learners to put counters into the container so that the chance or probability of drawing a black counter is impossible. Record “It is impossible to draw a black counter from this container”. Ask for volunteers to draw their container under “Impossible” on the probability line.

8. If necessary, explain that the container can only have white counters or no counters in it for this to happen and that the number of white counters does not influence the outcome

9. Draw a circle around the centre of the line and ask the learners for words that describe that area on the line. Record suggested words on the board, looking for words such as: “likely”, “equally likely”, “even chance”, “possible”, “maybe”, “probably”.

10. Ask the learners to put counters in their container so that it is “possible” that you will get a black counter. Ask the learners to draw their container on the board.

11. Ask the learners to tell you what the possible outcomes are for each container. (There are two possible outcomes: black counter, white counter.

12. Tell the learners that you have a container that holds 1 black and 100 white counters. Once more, ask the learners to describe the chance of taking out a black counter from this container and where that chance sits on the probability line. Possible descriptors include: “very unlikely”, “highly unlikely”, “not likely”, “almost impossible”, “poor chance”, “not a very good chance”, “a weak chance”. Check that the learners understand that while it is highly unlikely it is not impossible, and therefore the container should be place closed to but to the right of “Impossible”.

## Follow-up activity

Ask the learners to work in pairs to draw a line and label each end “Impossible” and “Certain”. Then have them record (in words or drawings) examples of events that are either impossible or certain.

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