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Year 3 Maths Length & Perimeter

Compare & order lengths

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Theory

Comparing and ordering lengths is a Year 3 measurement skill: deciding which length is longer or shorter and putting lengths in order. The trick is to convert to the same unit first — centimetres or metres — then compare the numbers, use greater than and less than, and work out how much longer one length is. Curriculum: VC2M3M02 / AC9M3M02.

Length is measured in centimetres (cm) and metres (m). To compare two lengths means to decide which is longer, which is shorter, or if they are equal.

You can only compare lengths that are in the same unit. If two lengths use different units, you must convert one of them first. For example, \(1\) m is the same as \(100\) cm, so to compare \(1\) m with \(85\) cm you change \(1\) m into \(100\) cm and see that \(100 > 85\).

To order lengths means to line them up from shortest to longest, or from longest to shortest. The difference between two lengths is how much longer one is than the other, which you find by subtracting.

Three lengths lined up at the same end Three bars starting at the same left line: bar A is 40 cm, bar B is 25 cm, bar C is 55 cm. Bar C reaches the furthest, so 55 cm is the longest and 25 cm is the shortest. ABC 40 cm25 cm55 cm
Line the lengths up at the same end — the longest bar reaches furthest.
Comparing 128 cm with 1 m 15 cm Two bars starting at the same end. The top bar is 128 cm and the bottom bar is 1 m 15 cm, which is 115 cm. The top bar reaches 13 cm further, shown in red. 128 cm1 m 15 cm 13 cm
Change to the same unit: \(1\) m \(15\) cm \(=115\) cm, so \(128\) cm is \(13\) cm longer.

Comparing lengths has no formula, but these conversions let you put every length in the same unit before you compare.

\[ 100 \text{ cm} = 1 \text{ m} \]
100 cm =1 m
\[ 1 \text{ m } 45 \text{ cm} = 145 \text{ cm} \]
1 m 45 cm =145 cm
Same unit first. A bigger number is not always a longer length. \(95\) cm is shorter than \(1\) m because \(1\) m \(=100\) cm. Always match the units before you compare the numbers.

How to compare or order lengths

  1. Match the units. Change every length to the same unit, usually centimetres.
  2. Compare the numbers. With the same unit, the larger number is the longer length. Use \(>\), \(<\) or \(=\).
  3. Order or subtract. To order, write them smallest to largest (or largest to smallest if the question asks for longest first). To find the difference, take the smaller length from the longer one.
  4. Answer in the units asked. Change back if needed: \(170\) cm \(=1\) m \(70\) cm. If something is higher or longer by an amount, add that amount on.
Example 1 — Longest length
Which is the longest: \(63\) cm, \(39\) cm or \(58\) cm?
Three bars measuring 63 cm, 39 cm and 58 cm Three bars lined up at the same left end: bar A is 63 cm, bar B is 39 cm, bar C is 58 cm. Bar A reaches the furthest, so 63 cm is the longest. ABC 63 cm39 cm58 cm
Solution
\(\text{same unit (cm)}\)
\(63\)\(>\)\(58 > 39\)
63>58>39

The longest length is \(63\) cm.

Example 2 — Same unit first
Which is longer, \(1\) m \(45\) cm or \(160\) cm?
Solution
\(1\text{ m }45\text{ cm}\)\(=\)\(145\text{ cm}\)
\(160\)\(>\)\(145\)
160 cm >145 cm

So \(160\) cm is longer than \(1\) m \(45\) cm.

Example 3 — Order shortest to longest
Put these in order from shortest to longest: \(1\) m \(8\) cm, \(97\) cm, \(1\) m \(12\) cm.
Solution
\(1\text{ m }8\text{ cm}\)\(=\)\(108\text{ cm}\)
\(1\text{ m }12\text{ cm}\)\(=\)\(112\text{ cm}\)
\(97\)\(<\)\(108 < 112\)
97<108<112

In order: \(97\) cm, \(1\) m \(8\) cm, \(1\) m \(12\) cm.

Example 4 — How much longer
Rope A is \(2\) m long and rope B is \(165\) cm. How much longer is rope A?
Comparing rope A of 2 m with rope B of 165 cm Two bars lined up at the same end. Rope A is 2 metres, which is 200 centimetres. Rope B is 165 centimetres. Rope A reaches 35 centimetres further, shown in red. AB 2 m165 cm 35 cm
Solution
\(2\text{ m}\)\(=\)\(200\text{ cm}\)
\(200 - 165\)\(=\)\(35\)
200-165=35

Rope A is \(35\) cm longer than rope B.

Example 5 — Watch the zero
Ben has three sticks: \(1\) m \(6\) cm, \(160\) cm and \(1\) m \(60\) cm. Which two are the same length? Which is the shortest?
Solution
\(1\text{ m }6\text{ cm}\)\(=\)\(106\text{ cm}\)
\(1\text{ m }60\text{ cm}\)\(=\)\(160\text{ cm}\)
\(106\)\(<\)\(160\)
1 m 6 cm = 106 cm, 1 m 60 cm = 160 cm

\(160\) cm and \(1\) m \(60\) cm are the same length. The shortest is \(1\) m \(6\) cm, which is only \(106\) cm.

Example 6 — Longest to shortest
Order these from longest to shortest: \(2\) m \(5\) cm, \(192\) cm, \(2\) m, \(215\) cm. How much longer is the longest than the shortest?
Solution
\(2\text{ m }5\text{ cm}\)\(=\)\(205\text{ cm}\)
\(2\text{ m}\)\(=\)\(200\text{ cm}\)
\(215 > 205 > 200\)\(>\)\(192\)
\(215 - 192\)\(=\)\(23\text{ cm}\)
215, 205, 200, 192; 215 - 192 = 23 cm

Longest to shortest: \(215\) cm, \(2\) m \(5\) cm, \(2\) m, \(192\) cm. The longest is \(23\) cm longer than the shortest.

Example 7 — Add a length on
A shelf is \(1\) m \(35\) cm high. A box \(25\) cm tall sits on top. How high is the top of the box? Answer in metres and centimetres.
Solution
\(1\text{ m }35\text{ cm}\)\(=\)\(135\text{ cm}\)
\(135 + 25\)\(=\)\(160\text{ cm}\)
\(160\text{ cm}\)\(=\)\(1\text{ m }60\text{ cm}\)
135 + 25 = 160 cm = 1 m 60 cm

Going higher means adding. The top of the box is \(1\) m \(60\) cm from the floor.

Example 8 — Difference across a metre
Tom's rope is \(2\) m \(30\) cm long. Ana's rope is \(185\) cm long. How much longer is Tom's rope?
Solution
\(2\text{ m }30\text{ cm}\)\(=\)\(230\text{ cm}\)
\(230 - 185\)\(=\)\(45\)
\(\text{longer by}\)\(=\)\(45\text{ cm}\)
230 - 185 = 45 cm

Write both in centimetres, then subtract. Tom's rope is \(45\) cm longer.

Common pitfalls

Compare the units, not just the numbers. Watch out for comparing lengths in different units. \(190\) cm is not longer than \(2\) m, because \(2\) m \(=200\) cm and \(200 > 190\).
Mind the zero in metres and centimetres. \(1\) m \(7\) cm is \(107\) cm, not \(170\) cm. Only \(1\) m \(70\) cm is \(170\) cm.
A bigger number can be a shorter length. \(99\) looks bigger than \(1\), but \(1\) m \(=100\) cm, so \(1\) m is longer than \(99\) cm. Change to the same unit first.
Line lengths up at the same end. When you read a picture, start both lengths from the same line before you decide which one reaches furthest.

Frequently asked questions

How do you compare two lengths in different units?

Change both lengths to the same unit first, then compare the numbers. For example, \(3\) m \(=300\) cm, so \(3\) m is longer than \(270\) cm.

How do you put lengths in order from shortest to longest?

Put every length in the same unit, then write the smallest number first and the largest number last. That gives the order from shortest to longest.

How many centimetres are in a metre?

There are \(100\) cm in \(1\) m. So \(2\) m \(=200\) cm, and \(1\) m \(45\) cm \(=145\) cm.

Is 2 m longer than 190 cm?

Yes. \(2\) m \(=200\) cm, and \(200 > 190\), so \(2\) m is longer than \(190\) cm.

How do you find how much longer one length is than another?

Put both lengths in the same unit, then subtract the smaller length from the longer length. The answer is how much longer one is.

How do you write metres and centimetres as centimetres?

Change the metres to hundreds of centimetres, then add the extra centimetres. \(1\) m \(55\) cm \(=100+55=155\) cm, and \(2\) m \(7\) cm \(=207\) cm.

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