I am constantly estimating…

photocopying: Roughly 30 students in each class, 3 lessons a week, 5 classes, so about 500 sheets, 2p a copy…

Petrol: Its 1.29 a litre so roughly 1.30 and i got 40 litres so its under 52

Shopping: This costs £4.99 and I have 7 items at 99p, so roughly £12

Time: It takes about 30 mins to get there and same back, add 10 mins for traffic (total), about 1hr there so ill be gone more than 2 hours

I don’t think it is something students find natural.

This question was a common exam question until the exam changed:

By rounding to 1sf calculate 3.6 x 110

Most students can get 400 for the above question but when left to chose how to round and estimate, the answers are more varied. Some choose not to round the 110 others will keep the 3.6. You could argue they have a more accurate answer this was as 360 is closer to 396 and similarly with 440.

Admittedly the calculation isn’t too challenging if its 4 x 110 but if a students is faced with a calculation such as;

13.8 x 19.1 and they approximate it to 13 x 19 they would make their answer slightly easier to work out. I suppose it can depend on why and for what use you are estimating.

The other issue I find with estimation is students are not always clear whether the answer is an over or under estimate and when they have an answer that’s a decimal students don’t know when to round up or down. For example

After students calculated 37/3.5 = 10.57… approx 11 but 11 wouldn’t work in this situation.

So i like students thinking about estimating

How were these estimation calculated?

Without working out the exact answers, which were over/under estimates?

How would you work out an estimate for each?