Place Value Extension Mastery

Name:

Date:

🧮 Part 1: Complex Multi-Step Word Problems

1. A school is organising a charity event. They have collected £3,847 so far. They need to report this amount to the nearest £100 for the local newspaper and to the nearest £1000 for the council records. How much will they report to each organisation? Explain why different rounding might be needed.

2. A cinema has 4,263 seats. On Saturday, 3,789 people attended. The manager needs to round both numbers to the nearest 100 to estimate how many empty seats there were. Show your working and explain if this gives an accurate estimate.

3. A factory produces 8,456 toys in January, 7,892 toys in February, and 9,147 toys in March. Round each month's production to the nearest 1000, then estimate the total production for the quarter. How does this compare to rounding the exact total?

🤔 Part 2: Reasoning and Justification

4. Sarah says "6,500 rounded to the nearest 1000 is 6000." Tom says "6,500 rounded to the nearest 1000 is 7000." Who is correct and why? What rule helps you decide?

5. A town's population is 5,739. Compare what happens when you round this to the nearest 10, 100, and 1000. Which rounding would be most useful for:

a) Planning school places: _____________ because _________________________________

b) Ordering a town map: _____________ because ___________________________________

c) National census data: _____________ because __________________________________

6. Explain why 4,999 and 5,001 both round to the same number when rounded to the nearest 1000, even though they are very different numbers.

✨ Part 3: Create and Challenge

7. Create your own word problem involving a 4-digit number that needs to be rounded to two different place values. Include why each type of rounding is needed.

8. Choose a number between 7,000 and 8,000. Show what happens when you round it to the nearest 10, 100, and 1000. Explain which rounding loses the most information about the original number.

My chosen number: ___________

9. Challenge: A number rounds to 6,000 when rounded to the nearest 1000 and to 6,200 when rounded to the nearest 100. What could the original number be? Give three possibilities and explain your reasoning.