Year 4 · Numbers to 10,000
Counting back past zero
Count backwards through zero to include negative numbers
Lesson overview
What you'll learn in this lesson
Count backwards through zero to include negative numbers
Key learning points
- • The line keeps going
- • Which is colder?
- • Counting across zero
- • Where you meet them
This lesson at a glance
- 20 minutes
- 19 parts to scroll through
- 4 quick checks
- No marked quiz yet
- Gentle pace: short sittings with pauses
Words to know
Scroll down — the lesson carries on below
Watch & discover
Part 1 of 19
Watch first
Counting back past zero
Watch how ones build into tens, hundreds, thousands and beyond.
Do it for real
The practicals below use what the film shows, with a full method you can follow at home.
In a nutshell
Count backwards through zero to include negative numbers
What you already know
Part 2 of 19
Before we start
What you already know
You can count forwards and backwards in ones and tens.
Key words
Part 3 of 19
Key words
Words you'll need today
- negative number
- A number less than zero, written with a minus sign like −3.
- zero
- Not a negative or a positive number — the point in between.
- difference
- How far apart two numbers are on the line.
Learning cycle
Part 4 of 19
Learning cycle 1 of 2
Part 1 — Below zero
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 5 of 19
Learn
The line keeps going
Count back from 3: 3, 2, 1, 0, then −1, −2, −3. The minus sign tells you the number is below zero. We read −4 as 'negative four'. On a thermometer, −4°C is four degrees colder than freezing.
Explore the idea
Part 6 of 19
Learn
Which is colder?
With negative numbers, the bigger the digit, the lower the number. −9 is colder than −2, because it is further below zero. This catches everyone out at first, so picture the thermometer: −9 sits lower down than −2.
Quick check
Part 7 of 19
Quick check
Count back: 2, 1, 0, ...
Quick check
Part 8 of 19
Quick check
Which temperature is colder?
Reset break
Part 9 of 19
Pause
That's sitting 1 of 2 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Learning cycle
Part 10 of 19
Learning cycle 2 of 2
Part 2 — Counting across zero
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 11 of 19
Learn
Counting across zero
From 2 down to −3 you step: 1, 0, −1, −2, −3. That is 5 steps. To go from −3 up to 4, count the steps to zero (3) then the steps up from zero (4), which is 7 altogether. Splitting the jump at zero keeps it simple.
Explore the idea
Part 12 of 19
Learn
Where you meet them
Weather forecasts (−2°C overnight), freezers (−18°C), lift buttons (−1 for the basement) and bank accounts all use negative numbers. If a temperature rises from −5°C to 3°C, it has gone up 8 degrees.
Quick check
Part 13 of 19
Quick check
How many steps from 1 down to −4?
Quick check
Part 14 of 19
Quick check
A freezer is −18°C. Is that above or below freezing?
Common mix-ups
Part 15 of 19
Common mix-ups
Things people often get wrong
- Thinking −9 is bigger than −2 because 9 is bigger than 2.
- Counting zero as a step when you jump across it.
- Writing negative four as 4− instead of −4.
Challenge round
Part 16 of 19
Game · Sort it
Which of these are true?
Drag each card into the right column. Tap a card first if dragging is fiddly.
True
Not true
Challenge round
Part 17 of 19
Game · Fill the gaps
Finish the sentences
Choose the word that belongs in each gap.
We read −4 as '____ four'.
On a thermometer, −4°C is four degrees ____ than freezing.
With negative ____, the bigger the digit, the lower the number.
Mastery quiz
Part 18 of 19
No quiz for this one
This lesson has no marked quiz attached yet.
Lesson round-up
Part 19 of 19
Lesson round-up
Ready when you are
Quiz score
Not sat
Games
Not played
Points this lesson
0
Best run
0 in a row
Luna: 0 out of 4 on the practice checks. Only if you feel up to it — one more?
Ask LunaDo the work
Your written work for this lesson
This is the part you'd do in your book at school. Pick the pieces below, write here or on paper, and photograph anything you draw or work out.
The cost of a school trip
A school is planning a trip to a wildlife park. The coach costs £480 however many people go. Entry costs £9.50 for each pupil and each adult goes free. The school says every pupil must pay the same amount, and the trip must not lose money.
If 60 pupils go, the coach works out at £8 each, so the total for each pupil is £17.50. If only 40 pupils go, the coach works out at £12 each, so the price rises to £21.50. The teacher explains that the coach is a fixed cost and the entry is a cost per person — which is why the price per pupil changes when the number changes.
The school decides to charge £20 and to use anything left over for a second trip later in the year.
Written for Good Learning Co.
Reading questions
- Work out the total cost of the trip if 50 pupils go.
- Show why the price per pupil falls when more pupils go, using numbers.
- At £20 each, how many pupils must go before the trip makes money? Show your working.
Working out
Working outDo the practice questions on paper, showing every step — not just the answer. Mark them yourself and circle anything you got wrong.
10–15 questions
Worked example, explained
WritingCopy one question out and write underneath, in words, why each step works.
1 question, 4–5 sentences
Problem in words
Working outWrite your own real-life problem that uses today's method, then solve it.
1 problem + solution
Saved as you type.
Part 1 of 19 · Watch & discover