Negative Numbers in Context
Negative numbers in context covers ordering, adding, subtracting and finding differences with negative numbers in real situations, such as temperature, sea level, lift floors or money owed. 11+ papers test whether a pupil can picture a number line to judge size and direction correctly, since mistakes with negative numbers usually come from a misunderstanding of direction rather than from the arithmetic itself.
Method
- Picture a number line with zero in the middle, positive numbers to the right and negative numbers to the left, to help judge size and direction.
- Remember that a negative number is always smaller than any positive number, and that -8 is smaller than -3 because it sits further to the left on the number line.
- To add a negative number, move left on the number line by that amount; to subtract a negative number, move right instead, since subtracting a negative is the same as adding a positive.
- To find the difference between two temperatures or heights, subtract the smaller value from the larger one, or count the number line steps between them.
- When multiplying or dividing, remember two negatives make a positive, and a positive multiplied or divided by a negative gives a negative.
- Read word problems carefully to identify what zero represents in the context, such as sea level, ground floor or no money owed, before setting up the calculation.
Worked example
At 6am, the temperature in a town was -4 degrees C. By 2pm, it had risen by 11 degrees C. What was the temperature at 2pm?
- Start at -4 on the number line, representing the temperature at 6am.
- A rise of 11 degrees means moving 11 steps to the right, in the positive direction.
- Work out the calculation: -4 + 11.
- Final answer: -4 + 11 = 7, so the temperature at 2pm was 7 degrees C.
Practice questions
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Q1Order these temperatures from coldest to warmest: -3, 5, -8, 0.Show answer
Answer: -8, -3, 0, 5
Q2Work out -6 + 9.Show answer
Answer: 3
Q3Work out -5 - 4.Show answer
Answer: -9
Q4Work out 3 - 10.Show answer
Answer: -7
Q5A submarine is at a depth of -120 m. It rises by 45 m. What is its new depth?Show answer
Answer: -75 m (-120 + 45)
Q6Find the difference in temperature between -7 degrees C and 6 degrees C.Show answer
Answer: 13 degrees C (6 - (-7) = 13)
Q7Explain, using a number line, why subtracting a negative number has the same effect as adding a positive number.Show answer
Answer: Subtracting normally moves you to the left on the number line, but a negative number already points to the left of zero, so subtracting it reverses that direction and moves you to the right instead, which has exactly the same effect as adding the equivalent positive number.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
The temperature at the top of a mountain is -12 degrees C. At the base of the mountain, it is 9 degrees C warmer. Work out the temperature at the base of the mountain.
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A lift starts at floor -2, two floors below ground. It travels up 7 floors, then back down 3 floors. (a) Work out which floor the lift ends on. (b) Work out how many floors the lift travelled in total, counting both the upward and downward journeys.
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Free printable worksheet
Want more practice on paper? Download the negative numbers in context worksheet pack - 6 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 41 of 11+ Maths Workbook 4, the whole course as one free printable PDF.
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