Maths shelf · Class 6
The temperature diary
One winter morning in Leh it is −8 °C. By the afternoon it is 4 °C. How many degrees did it warm up?
What you will learn: Read, order and compare negative numbers on a number line, find a rise or fall that crosses zero, and tell a reading from a prediction.
What should I know first?
If this feels new, try this first. It is fine to go back.
- Large Numbers and Place Value Topic ladder, Classes 4–7
Small test at the end: scroll down to the end of this page for five short questions that check what you have learnt. Tap an answer, then press Check answer. Go to the questions ↓
Jump to: Check yourself · For grown-ups · For teachers
Safety first
Use the readings on this page. Never go out in the cold to measure.
Keep it safe:
- Use the made-up readings on this page. Do not go out in cold or bad weather to measure.
- If you read a real thermometer, use a digital room thermometer. A grown-up handles any glass thermometer; never use a mercury one.
- If you use counters on a paper number line, keep them away from babies: nothing goes in the mouth.
You will need
- Paper and a rulerTo draw a number line from −12 to 12.
- A pencil and two coloursFor cold and warm readings.
- A digital room thermometer (optional)To see a real scale. A grown-up handles any glass one.
Time: About 35 minutes.
What do you think?
Monday morning is −8 °C. The afternoon is 4 °C. Tanmay says it warmed up by 4 degrees. Is he right?
Make a prediction and write one reason for it. Then tap the guess closest to yours to see how to test it. It is fine to change your mind after checking.
Yes, 4 degrees
Count it on a number line. Start at −8. How many steps to reach zero? How many more to reach 4?
No, more than 4
How many more? Count the steps from −8 to 4 on a number line.
It went down, not up
Which is warmer, −8 or 4? Find both on a number line. Which side is warmer?
Not sure
That is fine. Draw a number line from −10 to 5 and count the steps from −8 to 4.
Need a hint?
Split the jump at zero: from −8 up to 0, then from 0 up to 4.
The story
Dadi's chai stall has a small radio. One winter morning it reads out the weather for Leh: "minus eight degrees". "Minus?" says Tanmay. "How can it be less than nothing?" Tara looks at the thermometer on the wall. "Zero is not nothing here. It is where water freezes. Leh is eight degrees colder than that." Dhruv starts a diary of the readings for a week.
The idea
Negative numbers are numbers less than zero, written with a minus sign: −8 is read "minus eight" or "negative eight".
On a number line, numbers grow to the right. So −11 < −3 < 0 < 2, even though 11 is bigger than 3.
To find a change across zero, count to zero and then on: from −8 up to 4 is 8 + 4 = 12. As a sum, 4 − (−8) = 12.
A reading records what the thermometer showed. A prediction estimates what may happen later. Working out a difference from two readings gives us more information, but it is still not a prediction.
Worked example
Wednesday in Leh
Wednesday morning was −11 °C. By afternoon it was −2 °C. How much did it warm up?
- Both are below zero, so the jump does not cross zero.
- Count on from −11 to −2: that is 9 steps to the right.
- Check with a sum: −2 − (−11) = −2 + 11 = 9.
It warmed up by 9 degrees, but it was still below freezing.
Try it
Draw the number line.
Draw a line from −12 to 12, with zero in the middle. Mark every whole number.
Plot the mornings.
Mark the five morning readings from the diary with one colour.
Put them in order.
Write the mornings from coldest to warmest. Check: the coldest is furthest to the left.
Find each rise.
For each day, count from the morning to the afternoon reading. Split the jump at zero when it crosses it.
Reading or prediction?
Dhruv writes "Sunday will be about −6 °C". Is Sunday's temperature already measured, or is Dhruv predicting it? What information might support his prediction? How could you check it later?
Make your diary.
Copy the table and fill in the rises. Add a line saying which day warmed up most.
What you make (paper or offline)
Your temperature diary
Make the diary table and fill in the rise for each day.
Say which morning was coldest and which day warmed up most.
Add one prediction for tomorrow, and label it "prediction".
Make it on paper. Keep it with you. Nothing to upload.
What did we find out?
Read this after you have tried it. Look back at your guess and your reason first.
Numbers below zero are negative. On a number line they sit to the left of zero; the further left, the colder.
From −8 to 0 is 8 degrees, and from 0 to 4 is 4 more: a rise of 12 degrees. As a sum: 4 − (−8) = 12.
−3 is warmer than −11, even though 11 is bigger than 3. Below zero, closer to zero means warmer. On the whole number line, further right means warmer.
Check yourself
Five questions about what this page teaches. Choose an answer and press Check answer, or open "See the answer and why". Nothing is saved or sent: your choices stay on this screen and disappear when you leave or reload the page.
How do you want to answer? You choose, and you can change at any time.
See the answer and why
- A. Thursday, −3 °C Not this one. −3 is closer to zero than −11, so it is warmer.
- B. Saturday, 2 °C Not this one. 2 is above zero: that was the warmest morning.
- C. Monday, −8 °C Not this one. −8 is colder than −3, but −11 is colder still.
- D. Wednesday, −11 °C Correct. It is furthest to the left of zero on the number line.
See the answer and why
- A. 4 degrees Not this one. That only counts from zero up to 4. The 8 degrees below zero are missing.
- B. 8 degrees Not this one. That only counts from −8 up to zero.
- C. 12 degrees Correct. From −8 up to 0 is 8, then 4 more: 12.
- D. −4 degrees Not this one. That adds −8 and 4. A rise is the distance between the two readings.
See the answer and why
- A. 2, 0, −3, −11 Not this one. This goes from warmest to coldest.
- B. −11, −3, 0, 2 Correct. Left to right on the number line.
- C. 0, −3, −11, 2 Not this one. Zero is warmer than every negative number.
- D. −3, −11, 0, 2 Not this one. This treats −3 as colder because 3 is smaller than 11. Below zero, it is the other way round.
See the answer and why
- A. −8 °C Not this one. That adds the 2 to the fall. Only 4 degrees go below zero.
- B. 8 °C Not this one. That is a rise of 6, not a fall.
- C. −4 °C Correct. Down 2 to zero, then 4 more below zero.
- D. 4 °C Not this one. That is 6 − 2. A fall of 6 from 2 goes below zero.
See the answer and why
- A. The thermometer showed −5 °C on Tuesday Not this one. That records what was measured: a reading.
- B. Wednesday morning was 6 degrees colder than Tuesday Not this one. This is a comparison worked out from two past readings (−11 is 6 below −5), not a prediction.
- C. Tomorrow will be about −6 °C Correct. Nobody has measured tomorrow yet. It is a careful guess.
- D. On Friday, the thermometer displayed 0 °C Not this one. That records what the thermometer showed: a reading.
Think back
Why is −3 warmer than −11, when 11 is bigger than 3?
When does a jump need splitting at zero?
Investigate further
- A bird is directly above a diver. The diver is 5 m below the surface and the bird is 12 m above it. What is their vertical separation?
- In an atlas, find the average January temperature of two cold places. Which is colder, and by how much?
Can you use it here?
A freezer is at −18 °C and the kitchen is at 30 °C. How many degrees warmer is the kitchen?
Ask someone at home
Ask someone at home where they have seen numbers below zero: a freezer, a lift going to the basement, a bank balance?
No one free to join in? That's fine. You can do it by yourself with drawings, and ask a grown-up to help with the materials.
For grown-upsTap a heading to open it. The safety notes are at the top of the page.
Before you start
- Paper, a ruler and two colours. Keep counters away from babies; nothing in the mouth.
- If you show a real thermometer, use a digital one. Handle any glass thermometer yourself, and never use a mercury one.
Questions that help
- "Which side of zero is colder?"
- "How many steps to zero? How many after?"
- "Was that measured, or guessed?"
What's really going on
Children often think −3 is smaller than −11 "because 3 is smaller". A number line fixes it: further left is smaller.
Crossing zero is where mistakes happen. Counting to zero first, then on, makes the jump visible.
Temperatures are a friendly first use of negative numbers. Later the same rules work for money owed and heights below sea level.
Other ways to do it
- Use a lift: ground floor is 0, basements are −1, −2.
- Draw the number line on the floor with chalk and walk the jumps.
For teachersLearning aims, classroom ideas and what to look for.
Learning aims
- Place, order and compare negative numbers on a number line.
- Find a change across zero by counting through zero.
- Tell a measured reading from a prediction.
Subject links
- Maths: integers (confirm the chapter in the current edition of your textbook).
- Science: temperature and thermometers.
- Class 9 "Map the fair": negative numbers on a coordinate grid.
These links are general. They have not been checked against a specific board syllabus.
In the classroom
- A human number line: children holding cards stand in order, then "warm up" by given amounts.
- Give each group a week of made-up readings to plot and ask them to find the biggest rise.
What to look for
- Orders negative numbers correctly without prompting.
- Splits a jump at zero.
- Labels a guess as a prediction.