Basic Strategies

Don't waste time (and points!) working out the exact answers

Although the additions and subtractions may be simple, you almost certainly won't have time to calculate them exactly!

Try rounding the numbers in the question to one significant figure

Doing the calculation with the rounded values will be a lot quicker and easier and it will give you some idea of where the "real" answer is. For example, if the question is 6.1 × 4.2, think about 6 × 4 instead. This tells you that that the "real" answer will be near to 24.

Next, think about whether the answer will be bigger than or smaller than the number you got

For example, it's clear that 6.1 × 4.2 will be a bit bigger than 6 × 4 and that 5.8 × 3.9 will be a bit smaller than 6 × 4. You should take this into account when you position the iceberg. What about 6.1 × 3.9?

If you are taking percentages or fractions of numbers then try to visualize how much of the number you need on a number line

For example, if the question is ⅓ of 74.4 imagine where 74.4 is on the number line and think about where ⅓ of the way to that number is.

Emperor Penguin Path - Addition & Subtraction

Round whole numbers to the nearest 10

When dealing with whole numbers you may find that rounding the numbers to the nearest 10 is a useful way to estimate the result.

It is often easier to add instead of subtract

When dealing with subtraction it is often easier to add on rather than subtract. For example, 121 − 78 can be estimated as 120 − 80. Starting with 80 you can add on 40 more to make 120. So the estimate is 40.

Round large numbers to the nearest 100

When dealing with large numbers that include decimals you can often make a quick estimate by rounding to the nearest hundred. For example, 128.4 + 187.3 can be quickly estimated to 300.

Adelie Penguin Path - Multiplication & Division

Times Tables to help with Division

You can use your knowledge of times tables to help with division questions. For example, 35.4 ÷ 6 can be estimated by knowing that 6 × 6 makes 36.

Take short cuts

When estimating more difficult divisions you can try to use some short cuts. For example, take 132.5 ÷ 6.23. You can think of this as 12 ÷ 6 to make 2, but the estimate is actually ten times larger, giving an estimate of 20.

Macaroni Penguin Path - Fractions

Compare the fraction to a half

When estimating a fraction of an amount, you can often compare the fraction to a half. For example, ⅓ of 41.4 will be less than half of 40. So place the iceberg just below 20.

Fractions close to 1

If the fraction is close to 1, for example, ⁸⁄₉ of 43, then the answer will be just below 43 – in this case, an estimate around 40 would be good.

Fairy Penguin Path - Percentages

Divide by 10 to get 10%

You can find 10% of an amount by dividing the amount by 10. For example, to find 10% of 450, divide 450 by 10 to get 45.

Use 10% to find other percentages

Finding 10% first can really help when trying to find other percentages. For example, to find 28.1% of 502, first estimate 10% of 500, which is 50. Then, as 28.1% is nearly 30%, find 30% by working out 50 × 3. An estimate of 150 will be a close approximation.