Year 4 · Column methods and times tables
Estimating and checking with the inverse
Estimate and use inverse operations to check answers to a calculation
Lesson overview
What you'll learn in this lesson
Estimate and use inverse operations to check answers to a calculation
Key learning points
- • Round, then add
- • Estimates spot big mistakes
- • Undoing with the inverse
- • Checking a subtraction
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
Estimating and checking with the inverse
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
Estimate and use inverse operations to check answers to a calculation
What you already know
Part 2 of 19
Before we start
What you already know
You can add and subtract four-digit numbers in columns.
Key words
Part 3 of 19
Key words
Words you'll need today
- estimate
- A sensible near-answer, worked out quickly by rounding.
- inverse
- The opposite operation — subtraction undoes addition.
- approximately (≈)
- Roughly equal to.
Learning cycle
Part 4 of 19
Learning cycle 1 of 2
Part 1 — Estimate first
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 5 of 19
Learn
Round, then add
For 3,812 + 2,190, round both to the nearest hundred: 3,800 + 2,200 = 6,000. So the real answer should be close to 6,000. When you work it out properly you get 6,002 — close to your estimate, so it is believable.
Explore the idea
Part 6 of 19
Learn
Estimates spot big mistakes
If your column answer came out as 60,002 or 602, the estimate tells you instantly that something has gone wrong — usually a column that slipped. An estimate does not need to be exact; it needs to be quick.
Quick check
Part 7 of 19
Quick check
Best estimate for 4,187 + 2,905?
Quick check
Part 8 of 19
Quick check
Which check undoes 3,400 + 1,250 = 4,650?
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 — Check with the inverse
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 11 of 19
Learn
Undoing with the inverse
Subtraction undoes addition. If 4,271 + 1,538 = 5,809, then 5,809 − 1,538 should take you back to 4,271. If it does not, one of the two calculations is wrong and you can look again.
Explore the idea
Part 12 of 19
Learn
Checking a subtraction
Addition undoes subtraction too. If 8,400 − 2,650 = 5,750, then 5,750 + 2,650 should make 8,400. This check is especially worth doing when you had to exchange several times.
Quick check
Part 13 of 19
Quick check
A pupil says 5,000 − 1,980 = 3,020. Checking:
Quick check
Part 14 of 19
Quick check
Estimate 6,940 − 3,120.
Common mix-ups
Part 15 of 19
Common mix-ups
Things people often get wrong
- Rounding one number but not the other, so the estimate is useless.
- Thinking the estimate is the answer.
- Checking by redoing the same calculation the same way, which repeats the same slip.
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.
When you work it out properly you get 6,002 — close to your ____, so it is believable.
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