Number+facts

Representing addition and subtraction – number facts The final stage described by Fuson and also by Carpenter and Moser uses derived fact and known fact procedures. Here, children take the numbers given in the addition and subtraction problems, and redistribute them to make number facts that are already known (i.e. derive number facts). Alternatively, the problem may already involve a number fact that is known to the child. The extensive list of these strategies, as provided by Thompson (1999b, 2000a), is given below: • Use of doubles (addition and subtraction): Known facts, such as 18 − 9 is 9 because of doubles. • Use of near-doubles (addition and subtraction): Derived facts, such as 13 + 15 is 28 because of the 13 + 13 double. • Subtraction as the inverse of addition: Using known addition facts for subtraction, for example for 7 − 3, knowing that one adds 4 to 3 to get 7. • Using fives (addition): Derived number facts, separating out the fives and adding them first. For example, rearranging 6 + 7 as 5 + 5 and 1 + 2. • Bridging through tens (addition and subtraction): Derived facts, adding or subtracting to stages of ten as points at which to split up the quantities to be added or taken away. For example, 8 + 7 as 8 + 2 and 5, or 14 − 6 as 14 − 4 and taking away a further 2. • Compensation (addition and subtraction): Derived facts, altering the numbers to be added or subtracted to simplify the problem, and then ‘compensating’ for the alteration. For example, 14 + 8 could become 14 + 10 and then take away 2, or 13 − 8 could become 13 − 10 and then add 2. • Balancing (addition and subtraction): Derived facts, similar to compensation, but balancing out both parts of the sum to allow for any alterations. For example, again, 14 + 8 could become 12 + 10, or 13 − 8 could become 15 − 10. • Partitioning (addition and subtraction): Derived facts, splitting up both quantities into units, tens, etc. For example 18 + 17 as 10 + 10 and 8 + 7, or 24 − 11 as 20 − 10 and 4 − 1. • Sequencing (addition and subtraction): Derive facts, splitting up one of the quantities into tens and units, and then adding or subtracting these split quantities in sequence. For example, again, 18 + 17 as 18 + 10 + 7, or 24 − 11 as 24 − 10 − 1. • Mixed method (addition and subtraction): Derived facts with a combination of partitioning and sequencing, splitting both quantities into units, tens, etc., adding or subtracting the higher numbers but sequencing the smaller numbers. For example, 18 + 17 as 10 + 10 and 8 and 7, which becomes 20 + 8 and then add 7. For subtraction, 24 − 11 would become 20 − 10 and then add 4, then subtract a further 1.