Ordering Numbers
Question 1: Order these
a) In ascending order: 4572, 4578, 4571, 4575, 4579
Guidelines: Compare digit by digit from left to right. Since all start with 457_, compare the fourth digit.
Solution: 4571, 4572, 4575, 4578, 4579
b) In ascending order: 394125, 394178, 394234, 394215, 394193
Guidelines: All start with 394_, so compare the fourth and subsequent digits systematically.
Solution: 394125, 394178, 394193, 394215, 394234
c) In descending order: 2832, 2945, 2846, 2936, 2935
Guidelines: Arrange from highest to lowest. Compare first digits, then subsequent digits.
Solution: 2945, 2936, 2935, 2846, 2832
d) In descending order: 1354287, 1358123, 1359346, 1358154, 1354217
Guidelines: Compare systematically from left to right for 7-digit numbers.
Solution: 1359346, 1358154, 1358123, 1354287, 1354217
Question 2: Round
Understanding Place Value Positions
Hundreds | Tens | Units | . | Tenths | Hundredths
4 | 5 | 6 | . | 7 | 8
Question: Use the Gattegno chart to make up a 3-digit number with 2 decimal places. Round it to the nearest: a) tenth b) whole number c) ten d) hundred
Guidelines:
- If the next digit is 5 or more, round up
- If it is less than 5, leave it the same
Example number created: 456.78
Solutions:
- a) tenth: 456.8 (look at hundredths: 8 ≥ 5, so round up)
- b) whole number: 457 (look at tenths: 7 ≥ 5, so round up)
- c) ten: 460 (look at units: 6 ≥ 5, so round up)
- d) hundred: 500 (look at tens: 5 ≥ 5, so round up)
Investigate
Part 1: Make these amounts of money using the fewest number of notes and coins: a) £4.97 b) £8.13 c) £10.56 d) £17.62 e) £22.25 f) £26.12
Guidelines: Use largest denominations first (£50, £20, £10, £5, £2, £1, 50p, 20p, 10p, 5p, 2p, 1p)
Solutions:
- a) £4.97: £2 + £2 + 50p + 20p + 20p + 5p + 2p = 7 notes/coins
- b) £8.13: £5 + £2 + £1 + 10p + 2p + 1p = 6 notes/coins
- c) £10.56: £10 + 50p + 5p + 1p = 4 notes/coins
- d) £17.62: £10 + £5 + £2 + 50p + 10p + 2p = 6 notes/coins
- e) £22.25: £20 + £2 + 20p + 5p = 4 notes/coins
- f) £26.12: £20 + £5 + £1 + 10p + 2p = 5 notes/coins
Part 2: Now round them to the nearest pound. Solve these problems. Round up 1 amount to a multiple of 10 by taking what you need from the other amount.
g) Charlie bought a DVD player for £115 and a flat screen TV for £249. How much did he spend in total?
Guidelines: Add the amounts, rounding as specified.
Solution: £115 + £249 = £364 total
Question 4: Think
Question: Use the Gattegno chart to make up two 3-digit numbers with 2 decimal places. Compare them. Write down 4 ways in which they are the same. Write down 4 ways in which they are different. Repeat with another pair of 3-digit numbers with 2 decimal places.
Guidelines: Use place value understanding to identify similarities and differences systematically.
Example numbers created: 245.67 and 245.76
4 ways they are the same:
- Both have the same hundreds digit (2)
- Both have the same tens digit (4)
- Both have the same units digit (5)
- Both have exactly 2 decimal places
4 ways they are different:
- Different tenths place (6 vs 7)
- Different hundredths place (7 vs 6)
- 245.67 < 245.76 (different numerical values)
- When rounded to 1 decimal place: 245.7 vs 245.8