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Estimate the answer before you work it out

What this lesson is about

Guess the size of an answer first. Then a wrong answer looks wrong straight away.

You ask an assistant how many litres a tank of 180 by 90 by 60 centimetres holds. What comes before its reply?

Why this matters

A rough guess made first is a fence. An answer outside the fence is wrong, and you see that in a second, without doing the sum again.

You can guess the size of an answer before working it out, so a wrong one looks wrong at once.

A rough guess made first is a fence. An answer outside the fence is wrong, and you see that in a second, without doing the sum again.

Round every number to one digit and do the sum in your head first.
Check the order of size first: thousand, lakh or crore, not the last digits.
A wrong answer is usually wrong by a whole multiple, not by a little.

Task

You ask an assistant how many litres a tank of 180 by 90 by 60 centimetres holds.

Weak approach Reading the reply first, then working the whole multiplication out on paper. The last two digits agree, so the tank is recorded as holding that many litres.

Stronger approach Guessing first: about 2 by 1 by 0.6 metres, so a little under one cubic metre, near 1,000 litres.

Why the stronger approach works Because the guess came first, the reply of 9,720 litres was visibly ten times too big.

Try a changed situation A contractor's quotation for painting your school says the walls come to eight thousand square metres. How do you check it in ten seconds?

Make something yourself Ask an assistant three questions whose answers are numbers. Write your rough guess first for each, then its reply, then say which one you would go and check.

Lesson 3 of 9 on Reasoning and maths for AI worknextSplit a claim from its supportPart 1 ends in a work sample you can send The rules this work sample is read against

Read the primary or official source: NCERT · Class 8 Maths, Exponents and Powers