Strategies for Mentally Adding Number Lists
mental math series, part 13
Every once in a while you come across a list of numbers to add that leaves you reaching for your calculator. Today we’ll look at some alternatives for summing those numbers mentally.
These techniques take a little practice but can be quite helpful when you get the hang of them. And they serve as great examples of how we can approach numbers strategically instead of linearly.
Summing Single-Digit Numbers
If the numbers are single-digit values try a compliment strategy.
Recall from lesson seven, number compliments are pairs that add to ten.
Begin by scanning the list and searching out as many number compliments as possible. I’ll use some color coding to highlight the pairs.
There are three pairs: 7 and 3, 4 and 6, 8 and 2. That’s three pairs of ten which equals 30, plus the following:
They total 21, so combine with 30 for the grand total.
Summing Numbers Around a Common Value
Perhaps you have numbers all near a common value such as 100.
A clever way to add these numbers is to count how far away from 100 each value is and then subtract it from the total if each were 100. I’ll write the distance value in blue. Feel free to do this mentally by keeping a running total.
Sum the blue values. Ignore any pairs that add to zero.
That leaves us with:
The grand total will be 30 less than if all 10 values were 100.
These are just a couple quick ideas to get you started. Remember that due to commutativity, we have a lot of flexibility with addition.
Next Lesson: What do Fractional Exponents Mean?
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