Decomposition - A Written Form of Subtraction

Problems:

1. “To work out 856 – 138, Jane rearranges 856 as 800 + 40 + 16. Why does she do this?” Explain, using play money, if necessary. (In the decomposition method of subtraction, there are sufficient hundreds and tens to solve the problem, but there are insufficient ones.) “So find 856 – 138.”

2. “To work out 856 – 162, Jane rearranges 856 as 700 + 150 + 6. Why does she do this?”Explain, using play money, if necessary. (In the decomposition method of subtraction, there are sufficient hundreds and ones to solve the problem, but there are insufficient tens.) “So find 856 – 162.”

3. “To work out 856 – 168, Jane rearranges 856 as 700 + 140 + 16. Why does she do this?” Explain, using play money, if necessary. “So find 856 – 168.”

4. “To work out 856 – 123, Jane does not have to rearrange 856 at all. Why not?” Explain, using play money, if necessary. “So find 856 – 123.” Examples: In each of these subtractions, explain how to split up 953 to solve the problem, then find the answers: 953 – 234   953 – 184     953 – 594      953 – 284   953 – 388 ...

Now establish a standard written form for subtraction using a similar method to A Standard Written Form for Addition.  
 

A good way to do this is to explain why 546 – 278 requires 546 to be renamed 4 hundreds + 13 tens and 16 ones and link this to the setting out on the right.

Examples: 456 – 259 1 034 – 429 781 – 678 ...

Ask the students to explain why 953 – 631 and 953 – 630 do not need the written form.