Year 4 · Column methods and times tables
Multiplying and adding: splitting and scaling
Solve problems involving multiplying and adding, including using the distributive law and integer scaling problems
Lesson overview
What you'll learn in this lesson
Solve problems involving multiplying and adding, including using the distributive law and integer scaling problems
Key learning points
- • Split, multiply, add
- • Splitting the other way
- • Scaling problems
- • Matching problems
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
Multiplying and adding: splitting and scaling
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
Solve problems involving multiplying and adding, including using the distributive law and integer scaling problems
What you already know
Part 2 of 19
Before we start
What you already know
You can multiply a two-digit number by a one-digit number and know your tables.
Key words
Part 3 of 19
Key words
Words you'll need today
- distributive law
- Splitting a number up before multiplying: 6 × 23 = 6 × 20 + 6 × 3.
- scaling
- Making something a number of times bigger.
- correspondence
- Matching each of one thing to several of another.
Learning cycle
Part 4 of 19
Learning cycle 1 of 2
Part 1 — Splitting to multiply
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 5 of 19
Learn
Split, multiply, add
6 × 23 is hard in one go, so split the 23: 6 × 20 = 120 and 6 × 3 = 18, then add to get 138. This is the distributive law, and it is exactly what short multiplication does on paper — just written differently.
Explore the idea
Part 6 of 19
Learn
Splitting the other way
You can also split the multiplier: 7 × 18 = 7 × 20 − 7 × 2 = 140 − 14 = 126. Rounding up and taking a bit off is often quicker than splitting into tens and ones, especially with 9s and 19s.
Quick check
Part 7 of 19
Quick check
6 × 23 =
Quick check
Part 8 of 19
Quick check
7 × 19 using rounding:
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 — Scaling and matching
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 11 of 19
Learn
Scaling problems
A ribbon is 24 cm. Another is three times as long, so it is 24 × 3 = 72 cm. 'Times as long', 'times as heavy' and 'times as many' all mean multiply. If something is three times smaller, you divide instead.
Explore the idea
Part 12 of 19
Learn
Matching problems
Three shirts and four pairs of shorts make 3 × 4 = 12 different outfits. Each shirt matches with every pair of shorts, so you multiply rather than add. Draw a few lines if you are not sure — the pattern appears quickly.
Quick check
Part 13 of 19
Quick check
A 15 cm stick is 4 times shorter than a pole. The pole is
Quick check
Part 14 of 19
Quick check
4 hats and 5 scarves make how many pairs?
Common mix-ups
Part 15 of 19
Common mix-ups
Things people often get wrong
- Splitting the 23 into 20 and 3 but forgetting to add the two answers.
- Adding when a problem says 'times as many'.
- Multiplying only the tens: 6 × 23 = 120.
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.
This is the ____ law, and it is exactly what short multiplication does on paper — just written differently.
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