likelihoods

Three coins are tossed. A player wins if two heads and a tail come up. The unit looks at, analyses, and extends, this game of chance.

Two red and two blue multi-link cubes are placed in a bag. The player takes out two cubes. If the player gets two red cubes they win. The unit looks at, analyses, and extends, this game of chance.

The unit provides a focus on interpreting data displays, including analysing any distinctive features. It also focuses on moving students from intuitive and experimental ways of determining possible outcomes to the development of a more systematic approach. This movement from intuition to system and theory is a fundamental aspect of mathematics. It is also what distinguishes mathematics from other disciplines. Mathematics tries to quantify and organise the world on a sound and provable basis. Hence Pythagoras’ Theorem tells us without doubt that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides. This can be proved without doubt. Similarly we can prove that the probability of getting a 3 when two dice are rolled is 1/18. This certainty does not occur for instance in other sciences. Think about the development of our knowledge of the Universe. Once we believed that the Earth was supported on the back of a turtle. Later we believed that the Earth was at the centre of the Universe. Our ideas have grown from there and are still growing as we meet obstacles to the latest theory. Naturally this does not make mathematics better in any way. It is rather just different and it is trying to do a slightly different job.

In this unit students play the game "Top Drop" which has them predicting the outcome of dropping a plastic drink bottle top. The outcome of each drop is recorded and used to develop an understanding of relative frequency and probability and to increase the likelihood of winning. The unit culminates in a "Top Drop" tournament where students use the knowledge and understanding they have gained during the unit.

This unit uses one of the digital learning objects, Spinners, to support students as they explore probability. It includes problems and questions that can be used by the teacher when working with a group of students on the learning object, and ideas for independent student work.

In this unit we take samples of blocks from a bag and use them to make predictions about the blocks that the bag actually contains. We discuss the difference between theoretical and experimental probabilities.

In this unit we take samples of blocks from a bag and use them to make predictions about the blocks that the bag actually contains. The students learn that although we can't be 100% certain we can use the information that we gather from sampling to make reasonable predictions.

This week we investigate ways of systematically counting all the possible outcomes of an event. One approach that we focus on is the use of tree diagrams.

This week we use spinners to develop our understanding of the probability of simple events.

In this unit we experiment with cubes to make predictions about likelihood based on our observations. With these experiences the students find out that with probability there is no way of knowing for sure that will happen.