Length
In this topic you will
- Estimate and measure lengths using centimetres and metres.
- Use a ruler and a metre ruler to measure length accurately.
- Find the difference between two lengths.
Key Words
- centimetre
- distance
- estimate
- height
- length
- metre
- ruler
- width
Show Definitions
- centimetre: A unit of length equal to $1$ hundredth of a metre, written as $\text{cm}$.
- distance: How far it is from one point to another, measured along a path.
- estimate: To make a sensible guess about a measurement without measuring exactly.
- height: The measurement from the bottom to the top of something (how tall it is).
- length: The measurement of how long something is from one end to the other.
- metre: A standard unit of length equal to $100$ centimetres, written as $\text{m}$.
- ruler: A measuring tool marked with units (such as centimetres) used to measure straight lengths.
- width: The measurement from one side to the other side across an object.
In this section you will learn more about length using centimetres and metres. You will use a ruler and a metre ruler. Centimetres are best for shorter lengths and metres for longer ones.
It is important to remember how to use a ruler.
Look at these two rulers.
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This ruler begins at the edge. We measure from the edge. The mark for $0$ is not at the edge. We measure from $0$. |
Quick Math Tip
Start at the Correct Place: Check the edge of your ruler before measuring—some rulers start at the edge, but others have the $0$ mark slightly in. Always line your object up with the true start (the edge or the $0$) so your measurement is accurate.
Each number on your ruler stands for a centimetre.
A metre is longer than a centimetre. A metre is made of $100$ centimetres.
The length of an object is the distance from one end of it to the other, along its longest side. Measuring the shortest side gives us the width of the object.
When we measure how tall or high something is, we are finding its height.
Key Words
- just over
- just under
Show Definitions
- just over: A measurement that is slightly more than a number (for example, a little more than $10$ cm).
- just under: A measurement that is slightly less than a number (for example, a little less than $10$ cm).
EXERCISES
$1$. Estimate and then measure the length of these pictures. Use a ruler.
Which is the tallest? ____________________________
Which is the narrowest? ____________________________
👀 Show answer
This question depends on the size of the printed (or displayed) page, so your measurements may be different.
For each picture:
• First write an estimate (for example “just under $10$ cm”).
• Then measure with a ruler and record the measurement in centimetres.
The tallest picture is the one with the greatest measured height.
The narrowest picture is the one with the smallest measured width.
$2$. Work with a partner.
Use a metre ruler to measure your height.
Are you one metre tall, just over one metre tall or just under one metre tall?
Use a metre ruler to measure these lengths.
Estimate first, then measure.
👀 Show answer
Your answers depend on your measurements.
Record your height and decide whether it is:
• just under $1$ m
• exactly $1$ m
• just over $1$ m
For the table, door, distance, and chair: write an estimate first, then measure in centimetres and write the measured value.
$3$. These ladders can be joined together to make different heights.
Which ladders are joined together to make exactly these heights?
a. $14$ metres ____________________________
b. $26$ metres ____________________________
c. $25$ metres ____________________________
d. $31$ metres ____________________________
e. $20$ metres ____________________________
👀 Show answer
a.$14$ metres: $14$ (or $8 + 6$).
b.$26$ metres: $20 + 6$.
c.$25$ metres: $14 + 11$.
d.$31$ metres: $20 + 11$ (also $14 + 11 + 6$ works).
e.$20$ metres: $20$ (or $14 + 6$).
$4$. This rope is $24$ metres long.
If $14$ metres of rope is cut off, how much is left?
The difference between $24$ and $14$ is ____________________________
👀 Show answer
$24 - 14 = 10$, so $10$ metres of rope are left.
$5$. These rulers are in centimetres. Find out the length of each coloured bar using the rulers underneath.
a. ________ centimetres
b. ________ centimetres
c. ________ centimetres
d. ________ centimetres
Quick Math Tip
Measure from the Starting Point: Some bars do not begin at $0$ on the ruler. Always start measuring from where the bar actually begins, then find the difference between the start and end marks.
👀 Show answer
a.$12$ centimetres.
b.$8$ centimetres.
c.$3$ centimetres.
d.$6$ centimetres.
Think like a Mathematician
Let’s investigate: How long is a piece of string?
You will need: a piece of string $1$ metre long; a pair of scissors; a metre ruler; paper for recording.
Work on your own. Take turns to cut off a piece of string.
Estimate the length that you cut off, then measure it.
Repeat the estimating and measuring.
Make $3$ cuts each.
Estimate and measure the length of string that is left.
Tip: When you measure length it is important to measure from the start of the measuring scale.
👀 show answer
Your measurements will be different depending on what you cut off, but the key idea is that estimating and measuring can give different results, and measuring is more accurate.
If your string starts at $1$ metre ($100$ cm) and you cut off pieces, the length left can be found by subtracting the total cut length from $100$.
For example, if you cut off $18$ cm and then $24$ cm, the total cut is $18 + 24 = 42$ cm, so the length left is $100 - 42 = 58$ cm.