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Progression in Subtraction

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Areas Addressed Partitioning Discussing subtraction strategies Developing Column Subtraction Column Subtraction 2

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Progression in Subtraction Subtraction Lower Key Stage 2 Partitioning

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Partitioning in different ways Numbers can be partitioned in different ways, but in this lesson the teacher highlights partitioning into hundreds, tens and ones. How might this be helpful for children moving towards a column method? 4

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Pattern Notice how Julie encourages the spotting of patterns and working systematically 5 143 100 + 40 + 3 100 + 30 + 13 100 + 20 + 23 100 + 10 + 33 143 100 + 40 + 3 90 + 50 + 3 80 + 60 + 3 60 + 80 + 3

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Progression in Subtraction Subtraction Lower Key Stage 2 Discussing subtraction strategies

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Arithmetic proficiency The teacher is encouraging children to think about different strategies for subtraction. How might this support the development of fluency in both mental and written calculation? 7

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Language Children are able to name the strategies they are using, for example: Adjusting Partitioning Consider the use and development of mathematical language and how this might support fluency in calculation. 8

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Progression in Subtraction Subtraction Lower Key Stage 2 Developing column subtraction Kibworth Video 1.3

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Re-partitioning and exchange One hundred and fifty and two is the same as one hundred and forty and twelve. How does the use of place value counters support children’s understanding of this important idea? 10

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Progression in Subtraction Subtraction Upper Key Stage 2 Column subtraction

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Fluency and Efficiency Consider when the traditional algorithm might be the most efficient method? Mental methods can sometimes be more efficient even when the numbers are large. Provide some examples 12

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Place value counters Notice how the place value counters support the concept of exchange. Notice how the use of the counters helps the children express a quantity value understanding of fifty being equivalent to five tens. 13

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What’s the same? What’s different? Consider how the use of these questions supported opportunities for children to transfer their conceptual understanding and explain their mathematical reasoning. Consider the vocabulary and language the children use. 14

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765 - 348 15 700 60 5 300 40 8 7 6 5 3 4 8

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The inverse operation Notice how the children are able to use an inverse operation to check the answer to their calculations. 16

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Important elements and next steps What elements does the teacher identify for successful movement to a compact written method? What does she identify as the next steps in children’s learning? 17

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