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SATs practice · Year 6Chapter 1 · Place value and the four operations
Year 6 Arithmetic (SATs) · Place value and the four operations · Lesson 1.2

Year 6 Arithmetic (SATs): Negative numbers in context

Part of the Year 6 Arithmetic (SATs) place value and the four operations chapter. Chapter overview · whole chapter on one page

1.2

Negative numbers in context

Year 6
Interpret negative numbers in context, and count forwards and backwards through zero (Year 6)
Story. On a cold morning the thermometer outside the bakery reads -4°C. By lunchtime it has risen by 3 degrees.

Rule

A negative number is less than zero. On a number line, -1 is one step below 0 and -5 is five steps below.

Counting up moves towards zero and then into the positives. Counting down moves further below zero.

The bigger the negative number ignoring its minus sign, the smaller the number: -9 is less than -2.

Key ideas

  • Negative numbers are below zero: -1, -2, -3 ...
  • Going up from -4 by 3 gives -1: the count stops at -1, not at 1.
  • Less than means further left on the number line.
  • Counting up from a negative number moves towards zero.
Worked example 1.2.1
The temperature is -4°C and rises by 3°C. What is the new temperature?

Method. Count up 3 steps from -4 on a number line.

  1. Start at -4. The thermometer starts at -4°C.
    -4°C
  2. Count up 3 steps. Each step adds 1: -3, -2, -1.
    -4 → -3 → -2 → -1
  3. Read the answer. Three steps up from -4 is -1.
    -4 + 3 = -1
  4. Write the answer.
    -1°C

Check. -1 + 1 = 0, so -1 is one step below zero. ✓

Watch out. Do not go up past zero: -4 + 3 is -1, not 1.

Worked example 1.2.2
A diver is 12 m below the surface, which we write as -12 m. She swims up 9 m. Where is she now?

Method. Move up 9 metres from -12 by counting up through the negatives.

  1. Start at -12. The diver is 12 m below the surface.
    -12 m
  2. Count up 9 metres. Going up adds to the number: -12 + 9 = -3.
    -12 + 9 = -3
  3. Read the answer in the context. She is 3 m below the surface.
    -3 m
  4. Write the answer.
    -3 m

Check. She is still below the surface, so the answer is negative. ✓

Worked example 1.2.3
Which is colder: -9°C or -2°C?

Method. The further a negative number is from zero, the colder it is.

  1. Compare the two temperatures. Both are below zero.
    -9 and -2
  2. Think about the number line. -9 is further left than -2, so it is less.
    -9 < -2
  3. Say which is colder. The smaller temperature is colder.
    -9°C is colder
  4. Write the answer.
    -9°C

Check. -9 is less than -2. ✓

Watch out. -9 is less than -2, even though 9 is bigger than 2.

Exercise 1B  Practice: negative numbers in context

Non-calculator
1
FWhat is 2 more than -5?
2
FCount from -3 up to 2. How many steps is that?
3
FWhich temperature is the coldest? Choose one: -7°C, -2°C, 0°C or 3°C.
4
FThe temperature at night is -6°C. What is it after it gets 6 degrees warmer?
5
FWrite the number that is 4 less than 1.
6
FThe temperature is 1°C at noon and falls by 4 degrees. What is the temperature now?
7
PSA bank balance is -£35. A payment of £60 goes in. What is the new balance?
8
PSA diver is at -12 m. He swims up 9 m. Where is he?
9
PSThe temperature falls from 3°C to -5°C. How many degrees does it fall?
10
PSA lift starts in the basement at floor -2. It goes up 5 floors. Which floor is it on now?
11
RWhich is greater: -15 or -9? Choose one: -15 or -9.
12
RAli says -2 is bigger than -7 because 2 is smaller than 7. Is he right? Explain.

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