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Year 6 Maths Number Properties & Integers

Negative numbers & integers on a number line

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Theory

Integers are the whole numbers, zero and the negative whole numbers: \(\ldots, -3, -2, -1, 0, 1, 2, 3, \ldots\). Negative numbers sit to the left of zero on a number line. This Year 6 maths page shows how to place, compare and order integers, and how to count up and down past zero in real situations.

An integer is a whole number that can be positive, negative or zero. \(-4\), \(0\) and \(7\) are integers; \(-2.5\) and \(\dfrac{1}{2}\) are not.

Negative numbers are less than zero and are written with a minus sign. They describe temperatures below zero, depths below sea level and floors below ground.

On a number line, numbers get larger to the right and smaller to the left. So \(-2 > -5\): \(-2\) is to the right of \(-5\).

For negative numbers, the further from zero, the smaller the number: \(-9\) is colder than \(-4\).

Ascending order is smallest to largest; descending is largest to smallest.

Number line from minus 6 to 6 A number line marked in ones from minus 6 to 6. A point A is at minus 5, and a green jump of plus 6 goes from minus 2 to 4. −6−5−4−3−2−10123456 A +6
A is at \(-5\). Moving \(6\) to the right from \(-2\) reaches \(4\).
Thermometer showing minus 4 degrees A thermometer marked from minus 10 to 20 degrees Celsius in ones, labelled every 5. The red liquid reaches minus 4. −10−505101520°C
The thermometer shows \(-4^\circ\)C, four degrees below zero.

Comparing and moving along the number line:

\[ \ldots < -3 < -2 < -1 < 0 < 1 < 2 < 3 < \ldots \]
<−3<−2<−1<0<1<2<3<
\[ \text{up / warmer / rise} \Rightarrow \text{move right} \]
up , warmer , rise move right
\[ \text{down / colder / fall} \Rightarrow \text{move left} \]
down , colder , fall move left
Closer to zero is bigger (for negatives). \(-1\) is greater than \(-8\).
Count the steps past zero. From \(6\) down \(10\): \(6\) steps to \(0\), then \(4\) more to \(-4\).

Ordering integers

  1. Picture the number line.
  2. Start with the negative number furthest from zero (the smallest).
  3. Work right: negatives closest to zero, then \(0\), then positives.

Moving past zero

  1. Count from the start to zero.
  2. Count on the remaining steps on the other side.
Example 1 — Read the line
Use the first diagram. Which integer is at A, and which integer is \(3\) steps to the right of A?
Solution
\(-5 + 3\)\(=\)\(-2\)
−5+3=−2

A is \(-5\); \(3\) steps right is \(-2\).

Example 2 — Compare
Which is smaller, \(-3\) or \(-8\)?
Solution

\(-8\), because it is further left on the number line.

Example 3 — Order
Write \(-8, -1, 4, -6, 0\) in ascending order.
Solution

\(-8, -6, -1, 0, 4\).

Example 4 — Temperature falls
The temperature is \(6^\circ\)C and falls by \(10\) degrees. What is the new temperature?
Solution
\(6 - 10\)\(=\)\(-4\)
6−10=−4

\(-4^\circ\)C, as on the thermometer.

Example 5 — Below sea level
A diver is \(8\) m below sea level.
(i) Write this as an integer.
(ii) She rises \(3\) m. Where is she now?
Solution
\(-8 + 3\)\(=\)\(-5\)
−8+3=−5

(i) \(-8\)
(ii) \(-5\), still \(5\) m below sea level

Example 6 — Lift
A lift is at level \(1\) and goes down \(4\) levels. Which level does it reach?
Solution
\(1 - 4\)\(=\)\(-3\)
1−4=−3

Level \(-3\) (three levels below ground).

Example 7 — Clues
An integer is greater than \(-4\), less than \(-1\), and odd. What is it?
Solution

The integers between are \(-3\) and \(-2\); the odd one is \(-3\).

Example 8 — Find the mistake
Max says \(-9\) is greater than \(-4\) because \(9 > 4\). What is right?
Solution

For negatives, further from zero means smaller. \(-9 < -4\), so \(-4\) is greater.

Common pitfalls

Treating negatives like positives. \(-9\) is less than \(-4\), even though \(9 > 4\).
Forgetting zero when counting. Count the step onto zero as well.
Calling decimals integers. \(-2.5\) is negative but it is not an integer.
Ordering by the digits only. Check the sign first.

Frequently asked questions

What is an integer?

A positive or negative whole number, or zero.

Where do negative numbers go on a number line?

To the left of zero.

Which is bigger, −2 or −5?

\(-2\), because it is closer to zero (further right).

What is 2 − 7?

\(-5\): count \(2\) back to zero, then \(5\) more.

Where are negative numbers used?

Temperatures below zero, places below sea level, floors below ground and money owed.

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