# Estimation

## What is Estimation?

Estimating is finding an approximate value or solution, which is not the exact answer but close enough for us to work with it. There are two different
ways of estimating:
•
Estimating Answers to Problems
This is the type of estimation that we will focus on the most. It involves rounding the numbers in a mathematical expression so that we can
easily calculate them without a calculator or long multiplication. For example 204 x 397 is rounded to become 200 x 400. We can then easily
calculate an approximate result. Another topic related to this type of estimation will be calculating the percentage error which shows by how
many percent the approximate answer was different to the actual answer.
•
Estimating Amounts
The second type of estimation is estimating amounts without counting them. For instance, if you are in a room with a lot of people, you can
estimate how many people are inside it. Other examples of this type of estimation would be guessing, the mass of things, the lengths of
things,etc. This can be quite useful in everyday life situations. However, since it is not very mathematical, it will not be the main focus in this
topic.
Estimating Amounts
Although, estimating amounts is not the main focus of this topic, here is a short introduction with examples and a few exercises which will give you the
basic idea of how it works. The only way to really work on your skills of estimating/guessing is to practise and then see how close you are. It is also
good to have a general idea of how large things are or how much they weigh. Underneath are three examples of estimation.
Example 1:
Look at this pile of coin. If someone asks you to estimate how much money is on the pile in 5 seconds, how would you proceed?
Well first, you would see what types of coins there are and how many of them there are. If you are familiar with €, then you can
identify that there are 2 and 1 Euro coins and 50 and 20 cent coins. However, the majority of coins is 2 and 1 Euro so you could
give each coin an average value of 1.50€. Then you just have to estimate how many coins are on the pile. It looks like there are
between 15 and 20 coins on the pile. Let’s say 18. If we then multiply 1.5 by 18, we get 27€. The exact answer would have been
24.10€, so we were not that far off. To get this estimated solution, we would probably need between 3 and 7 seconds.
Example 2:
Look at this bundle of grapes. How many grapes would you estimate are there?
There are two ways of estimating this. You could find an approximate value of about 1/5 of the grapes (this would
probably only be off by (1 or 2) and then multiply it by 5 or you could just guess. With both methods, you would
probably get between 30 and 50 grapes.
Example 3:
Look at the image on the right. How many spots do you think are on the back of the ray?
This is very difficult to guess as the spots are different sizes. However, you could use the time to look
at one side in detail and then just multiply the estimate by two. You will probably find that there are
about 5 spots on each side. This is just a rough estimate but it is within a reasonable area. Usually, the
larger the number of objects gets, the further off will be your estimate.
Check your Estimation Skills
Underneath, you will find three images. Try to estimate the answer without counting in less than 10 seconds. Then click on the image to see the
answer (which will be displayed above the image.)
Moving on to “Real” Estimation
Hopefully, you have done quite well in the estimation questions. Keep practising this skill as it is very useful. Let us now move on to mathematically
estimating answer to problems and finding percentage error. Please share this page if you like it or found it helpful!
Estimate the number of keys VISIBLE ON
THE IMAGE (in less than 5 seconds).

Estimate the number of flowers VISIBLE
ON THE IMAGE (in less than 5 seconds).

Estimate the number of toy soldiers
VISIBLE ON THE IMAGE (in less than 2
seconds).

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Chapter 5.0: Learning Outcomes
Students will know about the two main types of estimation: estimating
amounts and estimating answers to calculations!
Students will be able to estimate amounts accurately!

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