Ordering positive and negative numbers | Year 6

01 / LEARN

Understand the idea.

Further right means greater

On a number line, greater values are farther right. To order integers, place the negative values first, then zero, then the positives. Within each group, keep following the line from left to right.

For negative values, a larger distance from zero means a smaller value. For example, $- 8$ is left of $- 2$ , so $- 8 < - 2$ . Comparing only the digits would ignore the meaning of the minus signs.

Compare the quantity asked for

Connect the comparison to the question. A greater temperature is warmer and a smaller one is colder. A greater signed height is higher. Decide whether the question asks for the greatest value or the least value.

The symbol $<$ means less than and $>$ means greater than. Its open side faces the greater value. Read the completed statement in words, then check it against the positions on the number line.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Worked example 1

Order −4, 3, 0, −1 and 2 from least to greatest.

Worked solution

1
Order the negative numbers.
$- 4 < - 1$
Negative four is farther left than negative one.
2
Place zero between negative and positive values.
$- 4 < - 1 < 0$
Zero is greater than every negative value.
3
Append the positive numbers in increasing order.
$- 4 < - 1 < 0 < 2 < 3$
The complete order from least to greatest follows the number line to the right.

Answer

−4, −1, 0, 2, 3.

EXAMPLE 02

Worked example 2

Which is warmer: −6°C or −2°C?

Worked solution

1
Compare the signed temperatures.
$- 6 < - 2$
Negative two lies to the right of negative six.
2
Interpret the greater temperature.
$- 2^{\circ} C > - 6^{\circ} C$
The greater temperature is warmer, so minus two degrees Celsius is warmer.

Answer

−2°C.

03 / YOUR TURN

Try it yourself.

Check your understanding

Complete −5 __ −1 with < or >.

Show answer & reasoning

−5<−1.

$- 5 < - 1$ because $- 5$ is farther left. Moving from $- 5$ towards $- 1$ increases the value.

Keep practising

6 worksheet questions · 9 marks

Open worksheet Worked solutions

Read the questions online

Which is greater: $- 7$ or $- 2$ ?
1 mark
Order 4, $- 3$ , 1, $- 8$ and 0 from least to greatest.
2 marks
Complete $- 4$ __ 2 with $<$ or $>$ .
1 mark
Morning temperatures are $- 1^{\circ} C$ , $- 5^{\circ} C$ and $2^{\circ} C$ . Which is coldest?
1 mark
Write all integers greater than $- 3$ and less than 2.
2 marks
Explain why $- 10 < - 1$ .
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Which is greater: $- 7$ or $- 2$ ?
1 mark
It lies to the right of $- 7$ .
$- 2$ .
Order 4, $- 3$ , 1, $- 8$ and 0 from least to greatest.
2 marks
Use left-to-right positions.
$- 8$ , $- 3$ , 0, 1, 4.
Complete $- 4$ __ 2 with $<$ or $>$ .
1 mark
Any negative number is less than any positive number.
$- 4 < 2$ .
Morning temperatures are $- 1^{\circ} C$ , $- 5^{\circ} C$ and $2^{\circ} C$ . Which is coldest?
1 mark
It is the least temperature.
$- 5^{\circ} C$ .
Write all integers greater than $- 3$ and less than 2.
2 marks
Do not include the endpoints.
$- 2$ , $- 1$ , 0, 1.
Explain why $- 10 < - 1$ .
2 marks
Compare positions, not just digits.
$- 10$ is further left: ten units below zero rather than one.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Positive/negative contexts; ordering; number lines; connection to coordinates.

Official curriculum source ↗

In this lesson

Understand the idea.

Further right means greater

Compare the quantity asked for

See the method in action.

Worked example 1

Order the negative numbers.

Place zero between negative and positive values.

Append the positive numbers in increasing order.

Worked example 2

Compare the signed temperatures.

Interpret the greater temperature.

Try it yourself.

Check your understanding

Keep practising