Mental Math Grade 6 Teacher's Guide

Adding or subtracting the same amount from both numbers
maintains the distance between them and makes the mental
subtraction easier. Examining pairs of numbers on a number line
such as a metre stick can help students understand the logic of this
strategy.
• Balancing For a Constant Difference (Review)
This strategy for subtraction involves adding or subtracting the same
amount from both the subtrahend and the minuend to get a ten, hundred or
thousand in order to make the subtraction easier. This strategy needs to be
carefully introduced to convince students that it works because the two
numbers are the same distance apart as the original numbers.
Examining pairs of numbers on a number line such as a metre stick can
help students understand the logic of the strategy. For example, the
difference or distance between the numbers 66 and 34 (66 - 34) on a
number line is the same as the difference between 70 and 38, and it’s
easier to mentally subtract the second pair of numbers.
Because both numbers change, many students may need to record at least
the first changed number to keep track.
Examples
1) For 87 -19, think, “Add 1 to both numbers to get 88 – 20, so 68 is the
answer.”
For 76 – 32, think, “Subtract 2 from both numbers to get 74 -30, so
the answer is 44.”
2) For 345 – 198, think, “Add 2 to both numbers to get 347 – 200; the
answer is 147.”
For 567 – 203, think, “Subtract 3 from both numbers to get 564 -200;
so the answer is 364.”
3) For 8.5 – 1.8, think, “Add 2 tenths to both numbers to get 8.5 – 2.0;
That’s 6.7.”
For 5.4 - 2.1, think, “Subtract 1 tenth from both numbers to get 5.3 –
2.0 or 3.3.”
Mental Math – Grade 6 35