Year 4 · Column methods and times tables
Factor pairs and swapping the order
Recognise and use factor pairs and commutativity in mental calculations
Lesson overview
What you'll learn in this lesson
Recognise and use factor pairs and commutativity in mental calculations
Key learning points
- • Listing factor pairs
- • Factor pairs show up in real life
- • Order does not matter
- • Splitting a factor to go faster
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
Factor pairs and swapping the order
A catchy song that helps you learn your 8 times table fast.
Do it for real
The practicals below use what the film shows, with a full method you can follow at home.
In a nutshell
Recognise and use factor pairs and commutativity in mental calculations
What you already know
Part 2 of 19
Before we start
What you already know
You know your times tables up to 12 × 12 reasonably well.
Key words
Part 3 of 19
Key words
Words you'll need today
- factor
- A number that divides into another exactly.
- factor pair
- Two numbers that multiply to make a given number.
- commutative
- You can swap the order: 4 × 7 = 7 × 4.
Learning cycle
Part 4 of 19
Learning cycle 1 of 2
Part 1 — Finding factor pairs
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 5 of 19
Learn
Listing factor pairs
For 24: 1 × 24, 2 × 12, 3 × 8, 4 × 6. That is every pair. Work up in order — 1, then 2, then 3 — and stop when the pairs start repeating. Being systematic is what stops you missing one.
Explore the idea
Part 6 of 19
Learn
Factor pairs show up in real life
24 chairs can be set out as 4 rows of 6, 3 rows of 8, or 2 rows of 12 — each factor pair is a different arrangement. Prime numbers like 13 only have 1 × 13, so they make one very long row.
Quick check
Part 7 of 19
Quick check
Which is a factor pair of 36?
Quick check
Part 8 of 19
Quick check
How many factor pairs does 16 have?
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 — Swapping and splitting
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 11 of 19
Learn
Order does not matter
12 × 5 is the same as 5 × 12. If the 12 times table is shaky, count in 5s twelve times instead, or do 10 × 5 then 2 × 5. Swapping the order is always allowed in multiplication, but never in subtraction or division.
Explore the idea
Part 12 of 19
Learn
Splitting a factor to go faster
For 6 × 15, split the 6 into 2 × 3: 15 × 2 = 30, then 30 × 3 = 90. For 8 × 25, use 4 × 25 = 100, then double it to 200. Choosing a friendly route is real mathematical thinking.
Quick check
Part 13 of 19
Quick check
7 × 12 is the same as
Quick check
Part 14 of 19
Quick check
Quickest route to 4 × 25 × 3?
Common mix-ups
Part 15 of 19
Common mix-ups
Things people often get wrong
- Missing a factor pair by jumping around instead of counting up in order.
- Thinking 15 ÷ 3 is the same as 3 ÷ 15.
- Believing 1 and the number itself are not factors.
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.
24 chairs can be set out as 4 rows of 6, 3 rows of 8, or 2 rows of 12 — each ____ pair is a different arrangement.
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