Estimating

Introduction to Estimation

Estimation is a mathematical skill used to roughly calculate or judge a value or quantity without having to find an exact or precise answer.
It is used to quickly find an answer that is reasonably close to the correct value or to check the plausibility of other results.

Identify the problem: Understand the nature of the problem for which you are estimating an answer.
Make an initial guess: Based on the information provided, make a rough guess or approximation.
Refining your guess: Use reasoning, context, and mathematical rules to refine your estimate. This may involve deciding to round numbers to a particular place value, or choosing to simplify complex calculations by using related, simpler calculations.

Rounding is a tool used to simplify numbers to make estimation easier.
Rounding involves changing a number to the nearest multiple of ten, hundred, thousand, etc., or the nearest whole number, tenth, hundredth, etc.
For example, 37 rounded to the nearest ten is 40, and 1.73 rounded to the nearest whole number is 2.
When estimating the result of a calculation, it is common to round all numbers to the highest place value of the numbers involved before performing the operation.

When estimating, it’s important to understand the concepts of overestimation and underestimation.
Overestimation occurs when you estimate a result to be larger than it actually is. This might happen, for instance, if you round up all numbers in a multiplication or addition calculation.
Underestimation occurs when you estimate a result to be smaller than it actually is. This might happen, for instance, if you round down all numbers in a multiplication or addition calculation.
The terms overestimate and underestimate are often used in the context of problem solving and decision making, where accuracy of estimation is considered important.

One common mistake is not rounding accurately. Make sure you understand the rules of rounding and practice regularly.
Another common mistake is not realising when an estimate is an overestimate or an underestimate.
Incorrectly choosing which operation (addition, subtraction, multiplication, or division) to use based upon the estimation can also lead to misinterpretation of the result.
Not using estimation to check answers: Even once you’ve used your maths skills to find a precise answer, you should still use estimation to check that your official answer seems sensible.