# Specific Strategies for Developing Estimation Skills

According to the Standards published by the National Council of Teachers of Mathematics, designed to guide math education, “Continual emphasis on computational estimation helps children develop creative and flexible thought processes and fosters in them a sense of mathematical power.” It isn’t just for getting a decent approximation; it’s a crucial tool for helping children strengthen their fundamental understanding of, and facility with, numbers.

In a previous post I made the case for the importance of developing estimation skills in students. Here is a collection of specific strategies you can use to do this. It is by no means meant to be exhaustive; hopefully, in addition to some specific tools that you can teach your children now, this post also sparks some ideas for similar strategies that you can help your children develop. I strongly suggest that you frame these as mental math games or puzzles and not as important skills to master for a successful future in mathematics, or some such lofty goal! Truth be told, however, estimation activities can be a lot of fun AND are quite important to one’s developing facility with numbers.

Estimate the sum of the following three numbers:

283 + 512 + 637

Traditionally, students in the US are taught to line these up by place value and add from the right side, carrying (regrouping) when needed. Instead, for a quick estimate, start on the left and add the digits in the hundreds place: 200 + 500 + 600 = 1300. Now ‘eyeball’ what’s left, and you can see something in the eighties, something in the teens, and something in the thirties. The numbers in the eighties and the teens add up to close to 100, and add to that the remaining number and you end up with about 150 from the tens and one places. 1300 + 150 = 1450, which isn’t far from the exact sum of 1432. If you just need an estimate, this is a very effective way of doing it, and in many situations an estimate is all we really need.

Grouping Friendly Numbers

Estimate the sum of the following five numbers:

32 + 54 + 82 + 71 + 15

Glancing quickly at the tens place, look for digits that add to 10 (or even 20). For example, I see that 3 + 7 = 10, so I could mentally replace 32 and 71 with 100. I could also replace 82 and 15 with another 100. Overall, a reasonable estimate of the sum would be 100 + 100 + 50, or 250. The precise sum is 254.

Front-End Estimation: Multiplication

The technique of focusing on the left-most digit works well for multiplication as well as for addition.

Estimate the product of 312 x 7.

Mentally calculate 300 x 7. This is done by removing the two zeros, multiplying 3 x 7, and putting the two zeros back.

300 x 7 = 2100

To obtain a closer estimate, if one so desires, keep 2100 in your head, round 12 down to 10, and multiply 7 by 10. Then add that to the 2100 you already have.

300 x 7 = 2100 and 10 x 7 = 70 à 2100 + 70 = 2170

The precise product is 2184.