Instructions
Let's put your number sense to the test! Work through the following challenges involving place value, rounding, and estimation. Think carefully and show your reasoning where needed.
1. Place Value Breakdown
Write these numbers in expanded form. This means breaking them down into their individual place values (thousands, hundreds, tens, and ones).
Example: 521 = 500 + 20 + 1
A) 3,486 = + + +
B) 29,405 = + + + +
2. Rounding Real-Life Numbers
Round each of the numbers below to the nearest 10, the nearest 100, and the nearest 1,000.
A) 6,724 steps on a pedometer
- Nearest 10:
- Nearest 100:
- Nearest 1,000:
B) 154,892 people at a stadium
- Nearest 10:
- Nearest 100:
- Nearest 1,000:
C) £2,987.65 on a shopping bill
- Nearest 10:
- Nearest 100:
- Nearest 1,000:
3. Estimation in Context
Sometimes a quick guess is more useful than a precise calculation. First, estimate the answers to the problems below by rounding the numbers to make them easier to work with.
A) 198 × 49 ≈
B) 4,892 ÷ 52 ≈
Explain one real-life situation where using an estimated answer is better or more practical than calculating an exact answer.
&-
4. Error Spotting
Someone was asked to round the number 3,465 to the nearest 100. They gave the answer 3,000.
Their answer is incorrect. What is the correct answer, and what mistake did they make?
Correct Answer: &-
5. Riddle Maths
Use the clues to figure out the mystery number.
I am a number between 2,300 and 2,400.
When you round me to the nearest 100, I become 2,300.
When you round me to the nearest 10, I am 2,345.
What number am I?
Answer Key
1. Place Value Breakdown
A) 3,486 = 3,000 + 400 + 80 + 6
B) 29,405 = 20,000 + 9,000 + 400 + 0 + 5
2. Rounding Real-Life Numbers
A) 6,724 steps
- Nearest 10: 6,720
- Nearest 100: 6,700
- Nearest 1,000: 7,000
B) 154,892 people
- Nearest 10: 154,890
- Nearest 100: 154,900
- Nearest 1,000: 155,000
C) £2,987.65
- Nearest 10: £2,990
- Nearest 100: £3,000
- Nearest 1,000: £3,000
3. Estimation in Context
(Note: Estimates can vary slightly but should be close to these answers.)
A) 198 × 49 ≈ 200 × 50 = 10,000
B) 4,892 ÷ 52 ≈ 5,000 ÷ 50 = 100 or 4,900 ÷ 50 = 98
Explanation of when estimation is useful:
- Shopping: To quickly estimate the total cost of your items to make sure you have enough money, without needing to add up the exact pence.
- Cooking: When a recipe calls for a precise amount of an ingredient like "227g of flour", you can often estimate and use a little more or less without ruining the dish.
- Travel: Estimating travel time for a journey based on distance and average speed.
4. Error Spotting
Correct Answer: 3,500
Explanation of mistake: They rounded to the nearest thousand instead of the nearest hundred. To round 3,465 to the nearest hundred, you look at the tens digit (6). Since 6 is 5 or greater, you round the hundreds digit (4) up to 5, making the answer 3,500.
5. Riddle Maths
What number am I? 2,345
(Explanation: The number must be less than 2,350 to round down to 2,300. The second clue pinpoints it exactly.)