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Framework for teaching mathematics

The Framework's five strands

The Framework has five strands. The first three have direct links to the National Curriculum programme of study for number. The fourth strand is linked to measures, shape and space, while the fifth incorporates handling data. Using and applying mathematics is integrated throughout. The strands, and the topics they cover, are:

Numbers and the number system

• counting
• properties of numbers and number sequences, including negative numbers
• place value and ordering, including reading and writing numbers
• estimating and rounding
• fractions, decimals and percentages, and their equivalence; ratio and proportion

Calculations

• understanding number operations and relationships
• rapid mental recall of number facts
• mental calculation, including strategies for deriving new facts from known facts
• pencil and paper methods
• using a calculator
• checking that results of calculations are reasonable

Solving problems

• making decisions: deciding which operation and method of calculation to use (mental, mental with jottings, pencil and paper, calculator...)
• reasoning about numbers or shapes and making general statements about them
• solving problems involving numbers in context: 'real life', money, measures

Measures, shape and space

• measures, including choosing units and reading scales
• properties of 2-D and 3-D shapes, position, direction and movement

Handling data

• collecting, presenting and interpreting numerical data

Although the strands are described separately, mathematics has many connections within and across topics. For example, when pupils are being taught to multiply by multiples of 10, they will make connections within a topic by drawing on their knowledge of multiplication table facts and understanding of place value. Using counters to form rectangles to introduce factors and division of numbers helps to link different topics such as properties of shapes, numbers and calculation. The statement 3 + 2 = 5 represents and summarises a range of situations which appear different but which are equivalent, such as making three whole turns followed by two whole turns, or starting with £3 and being given £2 more. Showing pupils how to multiply using partitioning, so that 12 × 3 becomes (10 + 2) × 3, prepares the way for later connections such as long multiplication or work in algebra.

You need to be clear about what can be connected within and across topics, to make these connections visible for pupils and to help them to make some of their own. Providing different examples and activities and expecting pupils to make the links is not enough; pupils need to be shown them and reminded about their work in earlier lessons. Explanations, demonstrations and illustrations of connections should all be part of the direct teaching pupils receive during the main teaching activity.

The diagrams below illustrate the five strands. Using and applying mathematics is integrated throughout: for example, in making and justifying decisions about which method, equipment or unit of measurement to use; in describing properties of numbers or shapes and in reasoning about them; in explaining methods of calculation; in devising and refining methods of recording calculations; in checking results...