Rule 1 in how to estimate calculations –
Don’t underestimate the power to estimate.
Probably the most used arithmetic skill by adults is the power to estimate. We’re actually pretty good and can work out a handful of change or the weight of a bag of shopping fairly accurately. There is always an emphasis on getting the correct answer in maths but… it does help if you have a rough idea before attempting the question.
My maths teacher would always say “yes, but is it reasonable?” Unfortunately this seems to have fallen out of favour, although I really think he had something. The constant questioning caused us to look at the problem in a slightly different way, and evaluate each solution against what we thought it should have been. The more estimation, the more accurate the answer, as we began to trust our own judgment.
I’ve had quite a few occasions where the student has a good grasp of method, but flounders when asked what they think the answer will be. A good example is division. Try asking how many 2’s are there in 257. It’s good to be able to work this out using a mathematical method but it’s quite refreshing when they can say “about 130 ish.” The student who can estimate is exceptional. They seem to have a more relaxed attitude to numbers; although can use methods to get an exact answer.
Rule 2 – Don’t try to be too accurate
31 x 79 = ?
31 is nearly 30 and 79 is nearly 80.
So really a good estimation would be 30 x 80 = 2400
The actual answer is 2449. That’s only 49 or 2% out – not a bad guess!
The whole idea is to use quick calculations that should generally be done as mental arithmetic. You’ll need to use a couple of skills
- times tables
- and these might be in two or three steps.
There’s no real accuracy involved when learning how to estimate calculations, it’s just a ‘feel’ for the correct direction and a check that you’re not going the wrong way. For instance, in the following calculation, your estimation might be (slightly) different to mine. It’s usually based on how confident you are with manipulating numbers.
(268 + 370 -97 + 250) all divided by 2
I would estimate:
(300 + 300* + 300) divided by 2 = 450
* notice that I calculated the 370-97 as around 400 – 100 = 300
The actual answer is 395.50 – so my estimation wasn’t great, although good enough to know that I hadn’t added too many tens or divided by 20.
Learning how to estimate calculations seems to be the right sort of balance to calculation methods. I’m sure that estimating has its place. Perhaps the next time your child asks about homework you could try asking them what they think the answer will be.
With a few prompts the child can sometimes “reverse engineer” back to the method.
Is that reasonable?
What do you think?
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