Choose the unit first
To estimate a measurement is to give a number close to it without measuring. Start by choosing the unit. A pencil is much shorter than a meter and much longer than a millimeter, so centimeters suit it. Then choose the number: a pencil is about 15 cm long, about the length of a hand with the fingers spread.
The unit matters as much as the number. A pencil 15 m long would be longer than a bus, so 15 m cannot be right, even though the number 15 is.
A pencil is about 15 cm long.
Mass and capacity too
Masses are estimated the same way. An apple sits easily in one hand, so grams suit it: an apple has a mass of about 150 g. An apple of 150 kg would be heavier than two adults.
So are capacities. A teaspoon holds about 5 mL, a glass holds about 250 mL, and a bathtub holds about 150 L.
An apple has a mass of about 150 g.
Sizes to compare with
Estimates are easier with a few objects whose sizes you already know. A door is about 2 m tall. A bag of flour has a mass of 1 kg. A glass holds about 250 mL.
To estimate something new, compare it with one of these. A classroom ceiling is about one and a half doors high, so it is about 1.5 × 2 = 3 m high. A bag of potatoes that feels about as heavy as three bags of flour has a mass of about 3 kg.
A door is about 2 m tall.
A bag of flour has a mass of 1 kg.
A glass holds about 250 mL.
Estimate one, then multiply
For something too large to picture all at once, estimate one piece and multiply. An apple is about 150 g, so a bag of 20 apples is about 20 × 150 = 3000 g, which is 3 kg. That is as heavy as three bags of flour, which is a sensible mass for a big bag of apples.
An estimate checks an answer
An estimate also catches an answer that has gone wrong. If a calculation says a door is 20 cm tall, compare it with a door: 20 cm is about the length of a hand, and nobody could walk through that. If it says an adult has a mass of 700 kg, that is the mass of a small car. The unit or the number must be wrong.
Worked example: A Sensible Estimate Chosen by Its Unit, Then Used
Question The length of one of Mei's walking steps is one of these: 6 cm, 60 cm or 6 m. (a) Which is the reasonable length for one step? (b) Mei takes 1250 steps to walk from her home to her school. Using the length from part (a), about how far is her school from her home, in meters?
1.Compare each length with something familiar. 6 cm is about the length of a finger, and 6 m is about the length of a car. One walking step is a little more than half a meter.
The three bars are drawn to the same scale. A walking step is a little more than half a meter. 2.(a) The reasonable length for one step is 60 cm.
(a) 60 cm is the reasonable length for one step. 3.Multiply by the number of steps: 1250 × 60 = 75 000 cm.
The 1250 steps cover 1250 × 60 = 75 000 cm. 4.(b) There are 100 cm in 1 m, so the distance is 75 000 ÷ 100 = 750 m.
(b) There are 100 cm in 1 m, so the distance is 75 000 ÷ 100 = 750 m.
Answer: (a) 60 cm; (b) about 750 m
Common mistakes
- Choosing 6 m because a walk to school is a long distance. The 6 m would be the length of a single step, and nobody can step the length of a car.
- Dividing 75 000 cm by 1000 to get 75 m. There are 100 centimeters in a meter. It is a kilometer that has 1000 meters.