Websink Prep UKKS2 MathsYear 5 chaptersMaths textbooksYear 1Year 2Year 4Year 5Year 6GCSEBrowse allPast papersFind a tutorBecome a tutor
Primary Maths · Year 5Chapter 1 · Place value to 1,000,000
Year 5 · Place Value to 1,000,000 · Lesson 1.4

Year 5: Negative numbers: temperatures, depths and bank balances

Part of the Year 5 place value to 1,000,000 chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)

Download worksheet (PDF)Answers (PDF)
1.4

Negative numbers: temperatures, depths and bank balances

Year 5
Negative numbers in context, Counting through zero, Differences across zero

Numbers below zero are called negative numbers. We use them in real life. When it is very cold, the temperature can go below zero: 5 degrees below zero is written −5°C. When we measure heights and depths, sea level is zero. A diver 15 metres under the sea is at −15 m. In a bank account, a balance of −£30 means the account is overdrawn: you owe the bank £30. In a building, floors below the ground floor can be −1, −2 and so on.

−15−10−5051015Leeds−15−10−5051015Bath−15−10−5051015Cork
Three thermometers: −12°C, 3°C and 9°C. Each small mark is 1 degree.
sea level (0 m)−50−40−30−20−100102030Lighthouse topBoatDiverWreck
Sea level is 0 m. Heights above it are positive. Depths below it are negative.

On a number line, zero is in the middle. Numbers to the right are bigger. Numbers to the left are smaller, so the further left a number is, the smaller it is. −20 is smaller than −5.

−25−20−15−10−50510152025−20−512
−20 < −5 < 12. The numbers increase as you go right.

Counting through zero. If you count back in 4s from 10, you say 6, 2, −2, −6… When a jump goes past zero, split it into two parts. To work out 2 − 4, go down 2 to reach 0, then 2 more: that is −2. Going up works the same way: −3 + 7 is 3 up to reach 0, then 4 more, which is 4.

The difference across zero. To find how far apart a negative and a positive number are, add their distances from zero. From −9 up to 6 is 9 + 6 = 15. If both numbers are below zero, take the smaller distance from the bigger: from −9 to −2 is 9 − 2 = 7.

Key words. A negative number is less than zero. Overdrawn means the bank balance is below zero. The difference between two numbers is how far apart they are on a number line.

Key ideas

  • Negative numbers are less than zero: −1, −2, −3… Used for temperatures, depths below sea level, overdrawn bank balances and floors below ground.
  • On a number line, the further left, the smaller. −20 < −5.
  • Counting through zero: split the jump into the part that reaches 0 and the part that goes past it.
  • Difference across zero: add the distances from zero (−9 to 6 is 9 + 6 = 15).
  • Difference when both are below zero: subtract the distances (−9 to −2 is 9 − 2 = 7).
Worked example 1.4.1
What temperature does this thermometer show?
−10−505101520

Method. Find the numbered mark nearest the top of the red liquid, then count the small marks to the top.

  1. Look at the numbers on the scale. The scale is numbered every 5 degrees. The small marks are 1 degree each.
    Big numbers: ..., −5, 0, 5, 10, ...
  2. Find the numbered mark just below the top of the red. The top of the red is between −10 and −5.
    The mark below is −10.
  3. Count the small marks above it. Each small mark is 1 degree.
    3 small marks above −10: −10 + 3 = −7

Check. Count from 0 instead: the top of the red is 7 small marks below 0, so the temperature is −7°C. ✓

Watch out. Going up the scale the numbers get bigger. Below zero, the number nearest the bottom is the smallest.

Worked example 1.4.2
Count back in 4s from 14. Write the next six numbers.

Key words. A negative number is less than zero. It has a minus sign in front, like −4.

Method. Counting back in 4s means taking away 4 each time. A number line helps when we go through zero.

  1. Draw a number line. Numbers to the left of 0 are negative (below zero). Numbers to the right are positive.
    −12−8−40481216
  2. Jump back 4 each time, starting from 14. When a jump goes past zero, split it into the part that reaches zero and the part that goes beyond.
    14 − 4 = 10
    10 − 4 = 6
    6 − 4 = 2
    2 down 4: go down 2 to reach 0, then 2 more below zero → −2
    −2 down 4: start at or below zero and go down 4 more → −6
    −6 down 4: start at or below zero and go down 4 more → −10
  3. Write the numbers in order.
    10, 6, 2, −2, −6, −10

Check. Go the other way from the last number: −10 + 4 = −6. ✓

Watch out. After 0 comes −1, not 1. Below zero the numbers count down: −1, −2, −3…

Worked example 1.4.3
Count on in 10s from −35. Write the next five numbers.

Key words. A negative number is less than zero. It has a minus sign in front, like −4.

Method. Counting on in 10s means adding 10 each time. A number line helps when we go through zero.

  1. Draw a number line. Numbers to the left of 0 are negative (below zero). Numbers to the right are positive.
    −40−30−20−1001020
  2. Jump on 10 each time, starting from −35. When a jump goes past zero, split it into the part that reaches zero and the part that goes beyond.
    −35 up 10: start below zero and go up 10 → −25
    −25 up 10: start below zero and go up 10 → −15
    −15 up 10: start below zero and go up 10 → −5
    −5 up 10: go up 5 to reach 0, then 5 more → 5
    5 + 10 = 15
  3. Write the numbers in order.
    −25, −15, −5, 5, 15

Check. Go the other way from the last number: 15 − 10 = 5. ✓

Watch out. After 0 comes −1, not 1. Below zero the numbers count down: −1, −2, −3…

Worked example 1.4.4
The temperature is 5°C. It falls by 12°C. What is the new temperature?

Method. Draw a number line, start at 5 and jump down 12. When you pass 0 the numbers change between positive and negative.

  1. Show the start on a number line. This lets us see where zero is.
    −8−6−4−202465−12
  2. Go down 12. Split the jump into two parts if it crosses zero: the part that reaches 0, then the part that goes past it.
    5 down 12: go down 5 to reach 0, then 7 more below zero → −7
  3. Write the answer. This is the new temperature.
    −7°C

Check. Do the opposite: −7 + 12 = 5. ✓

Watch out. Going down past zero gives a negative number. Going up from a negative number gets closer to zero.

Worked example 1.4.5
At night the temperature is −9°C. By midday it has risen by 14°C. What is the temperature at midday?

Method. Draw a number line, start at −9 and jump up 14. When you pass 0 the numbers change between positive and negative.

  1. Show the start on a number line. This lets us see where zero is.
    −10−8−6−4−20246−9+14
  2. Go up 14. Split the jump into two parts if it crosses zero: the part that reaches 0, then the part that goes past it.
    −9 up 14: go up 9 to reach 0, then 5 more → 5
  3. Write the answer. This is the new temperature.
    5°C

Check. Do the opposite: 5 − 14 = −9. ✓

Watch out. Going down past zero gives a negative number. Going up from a negative number gets closer to zero.

Worked example 1.4.6
How many degrees warmer is 6°C than −9°C?

Method. The difference between two numbers is how far apart they are on a number line.

  1. Mark both numbers on a number line. Seeing the gap helps.
    −10−8−6−4−202468−9615
  2. Count the gap. One number is below zero and one is above. Count up to zero first, then on to the other number.
    −9 up to 0 is 9.
    0 up to 6 is 6.
    9 + 6 = 15
  3. Write the answer.
    15°C

Check. Start at −9 and go up 15: −9 + 15 = 6. ✓

Watch out. Do not just subtract the digits when one number is negative. Go through zero: −4 and 5 are 9 apart, not 1.

Worked example 1.4.7
Write these numbers in order, smallest first:   −12,   5,   −3,   0,   −20,   8

Method. On a number line, numbers further to the left are smaller. Mark each number, then read them off from left to right.

  1. Put the numbers on a number line. The line shows which are below zero.
    −20−16−12−8−4048
  2. Read from left to right. Left is smallest, right is biggest.
    −20, −12, −3, 0, 5, 8
  3. Write them smallest first. Check you have used every number once.
    −20, −12, −3, 0, 5, 8

Check. The numbers below zero are the smallest. Of those, the one with the biggest digit (like −9) is furthest from zero, so it is the smallest. ✓

Watch out. −9 is smaller than −2. The further below zero, the smaller the number.

Worked example 1.4.8
Dev’s bank balance is −£45. He pays in £120. What is his new balance?

Key words. The balance is how much money is in a bank account. Overdrawn means the balance is below zero.

Method. A positive balance means the account has money in it. A negative balance means the bank is owed money (overdrawn). Paying in adds money.

  1. Write the balance as a positive or negative number. Money owed is below zero.
    Balance now: −£45
  2. Add £120. Split the move if it crosses zero.
    −£45 up £120: go up £45 to reach 0, then £75 more → £75
  3. Write the new balance. If it is negative, the account is overdrawn.
    £75

Check. Do the opposite: £75 − £120 = −£45. ✓

Watch out. Being −£40 means you owe £40. Paying in £40 only gets you back to £0.

Worked example 1.4.9
A submarine is at −120 m (120 m below sea level). It rises 45 m. Where is it now?

Method. Draw a number line, start at −120 and jump up 45. When you pass 0 the numbers change between positive and negative.

  1. Show the start on a number line. This lets us see where zero is.
    −120−100−80−60−40−200−120+45
  2. Go up 45. Split the jump into two parts if it crosses zero: the part that reaches 0, then the part that goes past it.
    −120 up 45: start below zero and go up 45 → −75
  3. Write the answer. This is the new depth.
    −75 m

Check. Do the opposite: −75 − 45 = −120. ✓

Watch out. Going down past zero gives a negative number. Going up from a negative number gets closer to zero.

Worked example 1.4.10
A cliff top is 35 m above sea level. A cave is 18 m below sea level. How far is it from the cliff top to the cave?

Method. The difference between two numbers is how far apart they are on a number line.

  1. Mark both numbers on a number line. Seeing the gap helps.
    −20−10010203040−183553
  2. Count the gap. One number is below zero and one is above. Count up to zero first, then on to the other number.
    −18 up to 0 is 18.
    0 up to 35 is 35.
    18 + 35 = 53
  3. Write the answer.
    53 m

Check. Start at −18 and go up 53: −18 + 53 = 35. ✓

Watch out. Do not just subtract the digits when one number is negative. Go through zero: −4 and 5 are 9 apart, not 1.

Watch out

A negative number with a bigger digit is a smaller number: −20 is less than −5, because it is further below zero. And do not just subtract the digits when a number is negative. The gap between −4 and 5 is 9, not 1. Always go through zero.

Exercise 1D  Negative numbers

Non-calculator
1
PSThe thermometers show the temperature in four cities one morning.
−15−10−5051015Edinburgh−15−10−5051015Cardiff−15−10−5051015Reykjavik−15−10−5051015Madrid
(a)Which city is the coldest?
(b)Which city is the warmest?
(c)How many degrees warmer is Cardiff than Edinburgh?
(d)What is the difference in temperature between Madrid and Reykjavik?
(e)Write the cities in order, coldest first.
2
FWhat temperature does the thermometer show?
−10−505101520
3
FWrite the missing numbers in the boxes on the number line.
−40?−20?0?20?40
4
FCount on or back. Write the next five numbers each time.
(a)Count back in 3s from 10.
(b)Count on in 5s from −22.
(c)Count back in 10s from 25.
(d)Count on in 4s from −18.
5
FWrite < or > in each box.
(a)−3  [ ? ]  2
(b)−17  [ ? ]  −7
(c)0  [ ? ]  −1
(d)−25  [ ? ]  −52
(e)−100  [ ? ]  10
(f)−6  [ ? ]  −60
6
FWrite each set of numbers in order.
(a)−14,  6,  −2,  −20,  9,  0  (smallest first)
(b)−35,  −3,  −53,  5,  35  (biggest first)
7
FWhat is the new temperature?
(a)It is 6°C. It falls by 11°C.
(b)It is −3°C. It rises by 9°C.
(c)It is −12°C. It rises by 5°C.
(d)It is 4°C. It falls by 15°C.
8
FFind the difference between the two temperatures.
(a)−4°C and 9°C
(b)−13°C and −2°C
(c)−21°C and 6°C
(d)5°C and −17°C
(e)−30°C and −5°C
9
PSZainab’s bank statement is shown below.
What happenedMoney inMoney outBalance
Opening balance−£30
Birthday money paid in£85£55
Bought a book£60−£5
Pocket money paid in£20?
Bought a game£45?
(a)What is her balance after the pocket money is paid in?
(b)What is her balance after she buys the game?
(c)How much must she pay in to get her balance back to £0?
10
PSThe picture shows a lighthouse, a boat, a diver and a wreck.
sea level (0 m)−50−40−30−20−100102030Lighthouse topBoatDiverWreck
(a)How far is the wreck below the boat?
(b)How far is it from the top of the lighthouse to the diver?
(c)The diver dives another 12 m. What is her position now?
11
PSA building has floors numbered from −2 (the car park) to 8.
(a)A lift starts on floor 5 and goes down 8 floors. Which floor is it on now?
(b)A cleaner goes from floor −2 up to floor 6. How many floors does she go up?
12
PSA freezer at −18°C is switched off. The temperature inside rises by 3°C every hour. After how many hours is it first above 0°C?
13
PSAt midnight the temperature is −9°C. By 6 a.m. it has risen by 4°C. By noon it has risen by another 11°C. By 6 p.m. it has fallen by 8°C.
(a)What is the temperature at noon?
(b)What is the temperature at 6 p.m.?
(c)What is the difference between the lowest and the highest temperatures of the day?
14
RThe temperature rises from −6°C to 4°C. Aisha says it has risen by 2°C. What mistake has she made? What is the correct answer?
15
RIs this always, sometimes or never true?
“If you take a number away from 5, the answer is positive.”
16
RWhich one is different?   −7°C    7°C below zero    minus seven degrees    7°C above zero
17
RTwo temperatures are 14 degrees apart. One of them is −5°C. What could the other temperature be? Find both answers.

Websink Prep UK is an independent site. It is not affiliated with, endorsed by or sponsored by AQA, Pearson Edexcel, OCR, WJEC, Eduqas, CCEA, SQA, GL Assessment, CEM or the Department for Education. All exam board names and trademarks belong to their owners. Past papers are linked from the exam boards' own websites and are not hosted here.

About Websink Prep UK · Find a tutor · Privacy · Terms · Cookie settings