Box 6–8 A Model for Multidigit Addition: 568+876=? Stage 1: Sustained linking of quantities to written algorithm to quantity meanings. Stage 2: Only do algorithm but occasionally explain using quantity words.

Students can construct multidigit subtraction procedures, though often these procedures are less similar to standard algorithms than is the case for addition. Still, as with addition, research has shown that students can learn a subtraction algorithm meaningfully if provided with appropriate experiences. In most cases, subtraction algorithms require more time and support than addition algorithms, but students can learn to execute them accurately and to explain why they work.⁷²

Two subtraction procedures are shown in Box 6–9. Method A is an algorithm commonly taught in the United States. It moves from right to left and alternates between the two major subtraction steps. Step 1 involves regrouping (or borrowing or trading) to get 10 or more in the top position. Step 2 is subtracting after the top number has been fixed. Alternating between these two steps presents three kinds of potential difficulties for students. The first is learning this alternation and the reasons for it. The second is remembering to alternate the steps. The third is that the alternation renders students susceptible to a very common subtracting error: subtracting a smaller top digit from a larger bottom digit. In the example, after subtracting bottom digit in