Look at this shopping receipt. The total at the bottom says €38.95. You hand over two €20 notes. Roughly how much change should you get back? Would rounding the total to €40 be close enough to check the change is right, before you count every cent?

You will see four estimates worked one at a time. You have the numbers here, so you can try each one yourself before it is shown:

• 487 + 312: a sum to round to the nearest hundred.
• 6,180 ÷ 3: a division where you pick a friendlier number first.
• 23,742 people at a match: a crowd, where the sensible place to round is bigger than you might expect.
• 19.8 × 4: a multiplication where one number is nearly a round number.

For each one, notice what gets rounded and to which place, then check that the exact answer looks sensible sitting next to the estimate.

Look at the jar of counters on the teacher's desk. Before anyone counts a single one, decide roughly how many you think are inside. Put your hand up to share your estimate out loud, and say whether each estimate you hear sounds sensible, before the real count is shown. Afterwards, ask yourself two things: was your number a sensible rough guess, and how far off the real total did it land?

Here are three estimation problems to work through together, then a stretch question. In your copy work each one: round to a sensible place, write the estimate, then find the exact answer and compare.

1. The school orders 1,180 copybooks to split evenly among 6 classes. Estimate first, then work out how many each class gets.
2. A concert sells 47,300 tickets across 4 nights. Estimate the tickets per night, then find the exact figure.
3. A farmer harvests 2,985 kg of potatoes over 5 days. Estimate the daily harvest, then calculate it exactly.
4. Stretch: Which of your three estimates would you trust enough to plan with, and why?