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# Errors and misconceptions: Year 2 multiplication and division

Understand the operation of multiplication as repeated addition or as describing an array, and begin to understand division as grouping or sharing; know by heart facts for the 2 and 10 multiplication tables; and know and use halving as the inverse of doubling. (National Numeracy Strategy (NNS) Framework for teaching mathematics, supplement of examples, section 5, pages 47, 49, 53, 57)

Associated knowledge and skills Errors and misconceptions Tracking charts Teaching sequences and spotlights
• Carry out repeated addition, recognise the relationship between multiplication and repeated addition, and use the associated vocabulary of multiplication.

Still counts in ones to find how many there are in a collection of equal groups; does not understand vocabulary, for example, ‘groups of’, ‘multiplied by’.

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• Multiply 2 or 10 by a single-digit number, by counting up in twos and tens from zero.

Does not link counting up in equal steps to the operation of multiplication; does not use the vocabulary associated with multiplication.

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• Interpret an array as a repeated addition and as a multiplication, and recognise how the array can be described as, for example,
3 + 3 + 3 + 3, 3 × 4
or as
4 + 4 + 4, 4 × 3.

Does not focus on ‘rows of’ or ‘columns of’, but only sees an array as a collection of ones.

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• Recognise that doubling and multiplying by 2 are the same, and use known multiplication facts and partitioning to double numbers to 15.

Has difficulty relating multiplying by 2 to known facts about doubles; records double 4 as 4 + 4.

Does not use partitioning to find double 12 or double 35.

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• Recognises that when finding the double of a number, half the answer is the original number. Uses the inverse of double to find halves of small even numbers to 10, using known facts.

Does not use knowledge of doubles to find half of a number; for example, continues to find half by sharing using a ‘one for you’ approach and cannot apply knowledge of doubles.

• Share a given number of objects out equally, recognise the relationship between sharing equally and division and use the vocabulary of division to describe the process, for example ‘divide by’, ‘share equally’.

Is not systematic when sharing into equal groups, using a ‘one for you’ approach; does not use the language of division to describe the process.

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• Begin to understand division as repeated subtraction or grouping.

Does not understand that ‘sets of’ or ‘groups of’ need to be subtracted to solve the problem.

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