Perhaps, Perhaps Not
Probability themes, activities and investigations for all ages
Key Stage suitability • Explanation
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Perhaps, Perhaps Not
There are four elements which make up this P'raps, P'raps Not book.
There are certain key ideas that are addressed in work on probability in the National Curriculum. You might want to explore these references yourself. Each idea is briefly outlined with some examples of what children might say illustrating their intuition about the idea.
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Key words and key questions
Initiating discussion to try to ascertain what intuitions and experiences children bring to bear on a situation can help you to decide what do next. Language is vital in the development of children's mathematicaJ ideas. We have included some of the key words and questions which could stimulate discussion and the development of children's conceptual ideas about probability. The two lists are not exhaustive; they are intended as a starting point to which you can add your own key words and questions.
Starting from a topic
Work on probability can arise naturally from non-mathematical experiences. Activities for children are suggested arising from a range of topics in which probability can be explored using children's' prior experiences. Teachers interpretations can be made using the following framework:
What children say: the intuitions they bring to a situation.
What children bring to the situation: their past experiences of similar situations.
What children may do next: the experiments that may help to develop their understanding of similar situations.
We have outlined a range of activities which progress from level 1 to 6 of Ma 5. Entry and exit pOints are for teachers to decide. One teacher may build on from where another left off or use an end pOint as entry to another topic. Each topic begins with a partial brainstorm of possible elements. This is followed by some examples of what children have said about their intuitions about the topic. These quotes have helped us to form some starting questions to develop an aspect of the topic from which one of these questions has been explored in more detail within the framework outlined above.
Themes and activities
Several mathematical themes which lend themselves readily to the development of probability are explored under the headings of ordering, pattern, cards, dice, beads, 'upside down' and ladder games. They are intended as starting points and some questions are suggested which could develop the activities. It is hoped that both teachers and children will explore these activities further through their own curiosity.
Measurement is one of the ways in which we bring mathematics to bear upon the world as we find it. Probability is a perfect illustration of how mathematicians try to measure things - things that seemingly cannot be measured, things as strange as "the likelihood of events happening".
Probability is something we do naturally. It can be fun. It can be a delight. It can be surprising. It often deals with the unexpected and the expected, with certainty and uncertainty.
What's the chance of our train being on time?
It always raining when I have to take games or I'm on break duty.
If it's Wednesday the car won't start.
How quantifiable are these? Does it matter? What makes us say these things and believe them? It is all about the experiences we have had and the way we intuitively build up a sense of what is likely to happen and what is not?
Our lives are built around the need to be able to make the best decisions based on our experience of the world and what has gone before. In a similar way mathematicians like to make predictions about future events and have built a theory around uncertainty and randomness, the theory of probability.