# Chance and Probability

Students learn how to write a probability as a simplified fraction.  As learning progresses they use equivalent fractions to compare probabilities and predict outcomes by finding a fraction of an amount.

This unit takes place in Term 5 of Year 7 and is followed by probability, outcomes and Venn Diagrams in Year 8.

##### Prerequisite Knowledge
• Compare and order fractions, including fractions > 1
• Use common factors to simplify fractions; use common multiples to express fractions in the same denomination
• Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions
##### Key Concepts
• The terms outcome, event and probability are key to describing the likelihood of an event occurring
• Outcome is the result of an experiment
• An event is a set of outcomes of a probability experiment
• Probability describes the likelihood of an event occurring.  A probability can be given as fraction, decimal or percentage.
• An event which is impossible has a  probability of zero.  An event which is certain to occur has a probability of one.
• When listing all the permutations of two or more events students need a logical and exhaustive systematic method.
• When working with experimental data a probability can only be estimated as contextual factors are likely to have been a factor in the outcome.
##### Working mathematically

Develop fluency

• Use language and properties precisely to analyse numbers, algebraic expressions, 2-D and 3-D shapes, probability and statistics.

Reason mathematically

• Explore what can and cannot be inferred in statistical and probabilistic settings, and begin to express their arguments formally.

Solve problems

• Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.
• Begin to model situations mathematically and express the results using a range of formal mathematical representations
##### Subject Content

Probability

• Record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0-1 probability scale.
• Understand that the probabilities of all possible outcomes sum to 1
• Generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities.

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