Estimation – JSS1 Mathematics Lesson Note (First Term)

Estimation is finding a rough but sensible value for a measurement or calculation, close enough to show what the correct answer should be.

Behavioural objectives

By the end of the lesson, students should be able to:

1. explain what estimation means;
2. name the common units of length, mass and capacity;
3. choose the most appropriate metric unit for measuring a given length;
4. round off a number to a given number of significant figures;
5. round off a number to a given number of decimal places;
6. use rounding to estimate the answer to a simple calculation.

What is estimation?

Estimation is a sensible guess of a value or the answer to a calculation.

• Not exact: an estimate is close to the true value but may not equal it.
• Useful: it gives an idea of what the correct answer should be.
• Checking work: it helps you notice a wrong answer, such as a misplaced decimal point.
• Everyday use: a trader guesses the number of oranges in a basket, or a driver guesses the time for a trip.
• Main tool: estimation in mathematics is done by rounding off numbers.

What are the common metric units of measurement?

The common metric units measure length, mass and capacity.

What are the units of length?

Length is the distance between two points.

• Kilometre (km): for long distances, such as the distance between two towns.
• Metre (m): for medium lengths, such as a room or a road.
• Centimetre (cm): for small lengths, such as a pencil or a person’s height.
• Millimetre (mm): for very small lengths, such as the thickness of a coin.

What are the units of mass?

Mass is the amount of matter in an object.

• Tonne: for very heavy objects, such as a truck load of sand.
• Kilogram (kg): for everyday objects, such as a bag of beans or a person.
• Gram (g): for light objects, such as a pinch of salt.

What are the units of capacity?

Capacity is the amount of liquid a container can hold.

• Litre (l): for larger containers, such as a bucket of water.
• Centilitre (cl): for small drinks containers.
• Millilitre (ml): for very small amounts, such as a spoon of medicine.

How do the units relate to each other?

How do you choose the most appropriate unit of length?

Choose a unit that gives a small, easy number for the object being measured.

• Short lengths: use millimetres (mm) or centimetres (cm).
• Large distances: use metres (m) or kilometres (km).

State the metric unit of length you would use to measure each of the following:

How do you round off a number?

Rounding off means replacing a number with a nearby number that is simpler to use.

1. Find the place you are rounding to.
2. Look at the digit just after that place.
3. If that digit is 0, 1, 2, 3 or 4, leave the digit in the rounding place unchanged (round down).
4. If that digit is 5, 6, 7, 8 or 9, add 1 to the digit in the rounding place (round up).
5. Drop the digits after the rounding place. For whole-number places, replace them with zeros.

How do you round to the nearest ten, hundred or whole number?

• Nearest ten: 3847 becomes 3850, because the digit 7 rounds the 4 up.
• Nearest hundred: 3847 becomes 3800, because the digit 4 rounds down.
• Nearest whole number: 12.5 becomes 13, because the digit 5 rounds up.

What are decimal places?

Decimal places (d.p.) are the digits counted after the decimal point.

• Counting: start counting immediately after the point.
• Example: 5.0678 has 4 d.p.
• Rounding: 5.0678 = 5.07 to 2 d.p., because the third decimal digit is 7.
• Short numbers: if the number has fewer d.p. than required, add zeros.

What are significant figures?

Significant figures (s.f.) are the meaningful digits of a number, counted from the first non-zero digit.

• Non-zero digits: they are always significant.
• Zeros between digits: they are significant, as in 4.07 (3 s.f.).
• Zeros at the start: they are not significant, as in 0.0407 (3 s.f.).
• Example: 0.00407 = 0.0041 to 2 s.f.

Example 1

Round off 492.763 to (a) 2 s.f., (b) 3 s.f., (c) 2 d.p., (d) 4 d.p.

Solution

• (a) 492.763 = 490 (2 s.f.). The third figure is 2, so it rounds down to zero.
• (b) 492.763 = 493 (3 s.f.). The next figure is 7, so the 2 becomes 3.
• (c) 492.763 = 492.76 (2 d.p.). The next digit is 3, so it is dropped.
• (d) 492.763 = 492.7630 (4 d.p.). The number has only 3 d.p., so we add a zero.

How do you estimate the answer to a calculation?

To estimate a calculation, round each number to an easy value, then calculate.

1. Round each number to one or two significant figures.
2. Do the calculation with the rounded numbers.
3. Compare the result with your exact answer to check it.

Example 2

Estimate 48 × 19.

• Round: 48 is about 50 and 19 is about 20.
• Calculate: 50 × 20 = 1000.
• Check: the exact answer is 912, which is close to 1000.

Evaluation

1. What is estimation?
2. List the standard units of mass and the standard units of capacity.
3. Which metric unit of length would you use to measure the length of a pencil?
4. Round off 492.763 to 1 d.p.
5. Round off 492.763 to 1 s.f.

Assignment

Answer both parts.

1. State the metric unit of length you would use to measure (a) the width of your exercise book, (b) the distance from your school to your house.
2. Round off 385.472 to (a) 2 s.f., (b) 3 s.f., (c) 2 d.p.