Solve addition and subtraction problems by compensating with tidy numbers (including equal additions).
Number Framework Stage 6
There are at least two useful methods for solving such a problem. For example, in the case of 78 + 99: either 78 + 100 = 178, but this is one too many, so the answer is 177, or transfer one from the 78 to the 99.So 78 + 99 is the same as 77 + 100 = 177.
Using Materials
Problem: “Work out $99 + $78.”
Record 99 + 78 on the board or modelling book. Draw an empty number line on the board. Show on the number line why 100 + 78 is one too many. Record the answer on the board or modelling book.
Examples: Draw empty number lines and work out: 56 + 99, 67 + 98, 97 + 63, 38 + 298, 123 – 99, 456 – 98 ...
Problem: “Work out $98 + $38.”
Record 98 + 38 on the board or modelling book. The students model $98 and $38 with play money. Discuss what transferring $2 from the $38 to the $98 does and how this shows that the answer is $136. Record the answer on the board or modelling book.
Examples: Using play money, work out: 151 – 99, 62 + 98, 97 + 73, 338 – 98, 103 + 197, 295 + 456 ...
Using Imaging
Problem: “Work out $175 – $99.”
Encourage the students to image this in two ways, namely, by number line and using play money, and to choose the method they like better.
Shielding: Examples: Word stories and recording for: 141 – 98, 55 + 98, 97 + 86, 18 + 298, 603 – 198, 299 + 456 ...
Using Number Properties
Examples: Word stories and recording for: 834 – 99, 456 – 98, 297 + 198, 818 + 698, 1 000 – 797, 1 200 – 998 ...