Solve addition and subtraction problems by compensating with tidy numbers (including equal additions).
Number Framework Stage 6
Previously this problem was reversed to solve 19 + ? = 73 by adding. Another useful and powerful method here is to subtract 20 from 73 to give 53 and add one to give 54.
A problem students often have with this second method is whether to add or subtract the one. The number line makes it obvious why one is added. Eventually, the students need to choose between these two methods for themselves.
Using Materials
Problem: “Frances the Frog lives at 73 on the number line. She is capable of leaps of any size. She wants to make a backwards jump of 19. Where does Frances end up?”
Discuss this and record 73 – 19 on the board or modelling book. On the class number line, show 73 and say that Frances decides to make a big jump of 20. Discuss whether Frances has jumped too far and how Frances will need to add a jump of one rather than subtract one.
Examples: Draw blank number lines and get the students to show the jumps needed to solve these problems: 72 – 59, 98 – 79, 45 – 18, 66 – 48 , 72 – 17, 103 – 88 ...
Using Imaging
Problem: “Frances jumps from 72 back 39.”
Record 72 – 39 on the board or modelling book. Encourage the students to image the number line. Drawing pictures in the air may be helpful. If this proves too hard, fold back to Using Materials by drawing the number line on the board or modelling book and discuss the solution.
Examples: Word stories and recording for: 82 – 29, 68 – 19, 65 – 28, 96 – 28, 82 – 47 ...
Using Number Properties
Examples: Word stories and recording for: 123 – 18, 228 – 19, 91 – 28, 596 – 89, 312 – 9, 991 – 87 ...