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- 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.

- A sample space diagram is used to show all the outcomes from a combination of two events. This follows on from Permutations of Two Events.
- Mutually exclusive outcomes are those that cannot occur together. For example, when you toss a coin you can not get a head and a tails.
- A set is a collection of items or numbers. Sets are shown by curly brackets { }. The items or numbers in a set are called elements.
- Venn diagrams are used to display sets and show where they overlap. Circles are used to represent each set. The rectangle that contains the sets is called the universal set. Elements that belong to more than one set are shown through the overlap between the set's circles.

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

Probability

- Understand that the probabilities of all possible outcomes sum to 1
- Enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams
- Generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities.

January 21, 2018

To add and subtract with numbers in standard form students apply a range of skills and knowledge of different topics. They need to be equally confident converting large numbers to standard form as they are with writing small numbers from standard to ordinary form. Column subtraction and addition may seem basic skills, but they become […]

January 14, 2018

Schemes of Work for Maths Teachers As a Head of Maths I understand the importance of a detailed, flexible and simple scheme of work. I designed the Key Stage 3 and GCSE schemes of work for maths teachers available at mr-mathematics.com to be just that. They are fully aligned with the current specifications and are […]

December 19, 2017

Solving Problems with Non-Right-Angled Triangles Solving problems with non-right-angled triangles involves multiple areas of mathematics ranging from complex formulae to angles in a triangle and on a straight line. As the GCSE mathematics curriculum increasingly challenges students to solve multiple step problems it is important for students to understand how to prove, apply and link […]