Year 4: 1000 more or less, comparing and ordering
Part of the Year 4 place value chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
1000 more or less, comparing and ordering
10, 100 or 1000 more or less. Find the right column, then change that digit by 1. For 1000 more than 4,572, add 1 to the thousands digit: 4,572 becomes 5,572. Take care with 9s and 0s. 1000 more than 9,450 is 10,450, because 9 thousands + 1 thousand = 10 thousands. 100 less than 3,050 is 2,950, because there are no hundreds, so we exchange 1 thousand for 10 hundreds.
Comparing. Put the numbers in a place-value table and compare from the left. The first column that is different decides.
| Th | H | T | O | |
|---|---|---|---|---|
| 4,562 | 4 | 5 | 6 | 2 |
| 4,652 | 4 | 6 | 5 | 2 |
We use two signs: < means “is less than” and > means “is greater than”. The wide mouth opens towards the bigger number. To order numbers, compare them in pairs. Ascending means smallest first. Descending means biggest first.
Numbers on a number line. A number line can show numbers beyond 1000. First work out what each small mark is worth, then count on. You can also estimate: if an arrow points about halfway between 7,000 and 8,000, a good estimate is 7,500.
Key ideas
- To find 1000 more or less, change the thousands digit by 1. For 10 or 100, change the tens or hundreds digit.
- Watch out for 9s (carry) and 0s (exchange).
- Compare numbers from the left. The first column that is different decides.
- < means less than. > means greater than.
- A number with more digits is bigger (when no number starts with 0).
Method. To find 1,000 more, change the thousands digit by 1. Look out for 9s (carrying) and 0s (exchanging).
- Find the thousands digit. 1,000 is one thousand, so only the thousands digit (and maybe the next one) should change.
Th H T O 4 5 7 2 - Add 1 to the thousands digit. 1,000 more means 1 more thousand.4 + 1 = 5 thousands
- Write the new number. Digits in the other columns stay the same unless we carried or exchanged.4,572 + 1,000 = 5,572
Check. Do the opposite: 5,572 − 1,000 = 4,572. ✓
Watch out. Do not change every digit! Only the digit in the column you are working on changes (unless you carry or exchange).
Method. To find 100 less, change the hundreds digit by 1. Look out for 9s (carrying) and 0s (exchanging).
- Find the hundreds digit. 100 is one hundred, so only the hundreds digit (and maybe the next one) should change.
Th H T O 3 0 5 0 - Take 1 from the hundreds digit. There are 0 hundreds, so we must exchange 1 thousand for 10 hundreds. Then take 1 away.0 hundreds → take 1 from the thousands digit, then 10 − 1 = 9 hundreds
- Write the new number. Digits in the other columns stay the same unless we carried or exchanged.3,050 − 100 = 2,950
Check. Do the opposite: 2,950 + 100 = 3,050. ✓
Watch out. Do not change every digit! Only the digit in the column you are working on changes (unless you carry or exchange).
Method. To find 1,000 more, change the thousands digit by 1. Look out for 9s (carrying) and 0s (exchanging).
- Find the thousands digit. 1,000 is one thousand, so only the thousands digit (and maybe the next one) should change.
Th H T O 9 4 5 0 - Add 1 to the thousands digit. There are 9 thousands. 1 more thousand makes 10 thousands, which is 1 ten thousand and 0 thousands. So we carry.9 + 1 = 10 → write 0 in the thousands column and carry 1 to the ten thousands column
- Write the new number. Digits in the other columns stay the same unless we carried or exchanged.9,450 + 1,000 = 10,450
Check. Do the opposite: 10,450 − 1,000 = 9,450. ✓
Watch out. Do not change every digit! Only the digit in the column you are working on changes (unless you carry or exchange).
Key words. < means “less than” and > means “greater than”. The wide end of the sign faces the bigger number.
Method. Compare the digits from the left, one column at a time. The first column that is different tells you which number is bigger.
- Write both numbers in a place-value table. Lining up the columns lets us compare digit by digit.
Th H T O 4,572 4 5 7 2 4,527 4 5 2 7 - Compare the digits from the left. The first column where they are different decides which number is bigger.thousands: 4 and 4 are the same, so look at the next column.
hundreds: 5 and 5 are the same, so look at the next column.
tens: 7 and 2 are different. 7 > 2, so 4,572 is bigger. - Write the correct symbol. < means “is less than”, > means “is greater than”, = means “is equal to”.4,572 > 4,527
Check. Picture a number line: 4,527 is to the left of 4,572. ✓
Watch out. Start at the LEFT (the biggest column). Do not start with the ones.
Key words. Ascending order means smallest first. Descending order means biggest first.
Method. Put the numbers in a place-value table, then compare columns from the left. Smallest first.
- Write all the numbers in a place-value table. This lines up the digits so we can compare them.
Th H T O 6,104 6 1 0 4 6,014 6 0 1 4 6,410 6 4 1 0 1,604 1 6 0 4 6,041 6 0 4 1 - Compare the thousands, then the hundreds, then the tens, then the ones. Where the digits in a column match, move on to the next column.1,604 and 6,014: thousands: 1 and 6 are different. 1 < 6, so 1,604 is smaller.
6,014 and 6,041: tens: 1 and 4 are different. 1 < 4, so 6,014 is smaller.
6,041 and 6,104: hundreds: 0 and 1 are different. 0 < 1, so 6,041 is smaller.
6,104 and 6,410: hundreds: 1 and 4 are different. 1 < 4, so 6,104 is smaller. - Write them smallest first. Check you have used every number once.1,604, 6,014, 6,041, 6,104, 6,410
Check. Count the numbers: 5 in the question and 5 in the answer. ✓
Watch out. Do not forget a number. Tick each one off as you write it.
Method. Find out what each small mark is worth, then count on from a number you can read.
- Count the gaps between two labelled numbers. The line goes from 4,000 to 5,000 in 10 equal gaps.5,000 − 4,000 = 1,000
- Work out what one gap is worth. Share the distance equally between the gaps.1,000 ÷ 10 = 100
- Count on from the start to the arrow. The arrow is 7 gaps after 4,000.4,000 + 7 × 100 = 4,000 + 700 = 4,700
Check. Count back from 5,000: 3 gaps back is 5,000 − 300 = 4,700. ✓
Watch out. Do not read the nearest label. Count the small marks to find the exact number.
Watch out
When you find 1000 more or less, do not change the other digits. 1000 less than 3,208 is 2,208 (only the thousands digit changes), not 3,198. And when you compare, start on the left: 4,562 is smaller than 4,652 even though the ones digit 2 is the same.Exercise 1C More, less, compare and order
Non-calculatorMethod. To find 1,000 more, change the thousands digit by 1. Look out for 9s (carrying) and 0s (exchanging).
- Find the thousands digit. 1,000 is one thousand, so only the thousands digit (and maybe the next one) should change.
Th H T O 2 3 4 5 - Add 1 to the thousands digit. 1,000 more means 1 more thousand.2 + 1 = 3 thousands
- Write the new number. Digits in the other columns stay the same unless we carried or exchanged.2,345 + 1,000 = 3,345
Check. Do the opposite: 3,345 − 1,000 = 2,345. ✓
Watch out. Do not change every digit! Only the digit in the column you are working on changes (unless you carry or exchange).
Method. To find 1,000 more, change the thousands digit by 1. Look out for 9s (carrying) and 0s (exchanging).
- Find the thousands digit. 1,000 is one thousand, so only the thousands digit (and maybe the next one) should change.
Th H T O 6 9 0 8 - Add 1 to the thousands digit. 1,000 more means 1 more thousand.6 + 1 = 7 thousands
- Write the new number. Digits in the other columns stay the same unless we carried or exchanged.6,908 + 1,000 = 7,908
Check. Do the opposite: 7,908 − 1,000 = 6,908. ✓
Watch out. Do not change every digit! Only the digit in the column you are working on changes (unless you carry or exchange).
Method. To find 1,000 more, change the thousands digit by 1. Look out for 9s (carrying) and 0s (exchanging).
- Find the thousands digit. 1,000 is one thousand, so only the thousands digit (and maybe the next one) should change.
Th H T O 5 0 9 0 - Add 1 to the thousands digit. 1,000 more means 1 more thousand.5 + 1 = 6 thousands
- Write the new number. Digits in the other columns stay the same unless we carried or exchanged.5,090 + 1,000 = 6,090
Check. Do the opposite: 6,090 − 1,000 = 5,090. ✓
Watch out. Do not change every digit! Only the digit in the column you are working on changes (unless you carry or exchange).
Method. To find 1,000 more, change the thousands digit by 1. Look out for 9s (carrying) and 0s (exchanging).
- Find the thousands digit. 1,000 is one thousand, so only the thousands digit (and maybe the next one) should change.
Th H T O 8 9 9 9 - Add 1 to the thousands digit. 1,000 more means 1 more thousand.8 + 1 = 9 thousands
- Write the new number. Digits in the other columns stay the same unless we carried or exchanged.8,999 + 1,000 = 9,999
Check. Do the opposite: 9,999 − 1,000 = 8,999. ✓
Watch out. Do not change every digit! Only the digit in the column you are working on changes (unless you carry or exchange).
Method. To find 1,000 less, change the thousands digit by 1. Look out for 9s (carrying) and 0s (exchanging).
- Find the thousands digit. 1,000 is one thousand, so only the thousands digit (and maybe the next one) should change.
Th H T O 6 4 3 2 - Take 1 from the thousands digit. 1,000 less means 1 less thousand.6 − 1 = 5 thousands
- Write the new number. Digits in the other columns stay the same unless we carried or exchanged.6,432 − 1,000 = 5,432
Check. Do the opposite: 5,432 + 1,000 = 6,432. ✓
Watch out. Do not change every digit! Only the digit in the column you are working on changes (unless you carry or exchange).
Method. To find 1,000 less, change the thousands digit by 1. Look out for 9s (carrying) and 0s (exchanging).
- Find the thousands digit. 1,000 is one thousand, so only the thousands digit (and maybe the next one) should change.
Th H T O 9 0 7 5 - Take 1 from the thousands digit. 1,000 less means 1 less thousand.9 − 1 = 8 thousands
- Write the new number. Digits in the other columns stay the same unless we carried or exchanged.9,075 − 1,000 = 8,075
Check. Do the opposite: 8,075 + 1,000 = 9,075. ✓
Watch out. Do not change every digit! Only the digit in the column you are working on changes (unless you carry or exchange).
Method. To find 1,000 less, change the thousands digit by 1. Look out for 9s (carrying) and 0s (exchanging).
- Find the thousands digit. 1,000 is one thousand, so only the thousands digit (and maybe the next one) should change.
Th H T O 4 0 0 8 - Take 1 from the thousands digit. 1,000 less means 1 less thousand.4 − 1 = 3 thousands
- Write the new number. Digits in the other columns stay the same unless we carried or exchanged.4,008 − 1,000 = 3,008
Check. Do the opposite: 3,008 + 1,000 = 4,008. ✓
Watch out. Do not change every digit! Only the digit in the column you are working on changes (unless you carry or exchange).
Method. To find 1,000 less, change the thousands digit by 1. Look out for 9s (carrying) and 0s (exchanging).
- Find the thousands digit. 1,000 is one thousand, so only the thousands digit (and maybe the next one) should change.
Th H T O 7 0 0 0 - Take 1 from the thousands digit. 1,000 less means 1 less thousand.7 − 1 = 6 thousands
- Write the new number. Digits in the other columns stay the same unless we carried or exchanged.7,000 − 1,000 = 6,000
Check. Do the opposite: 6,000 + 1,000 = 7,000. ✓
Watch out. Do not change every digit! Only the digit in the column you are working on changes (unless you carry or exchange).
Method. To find 10 more, change the tens digit by 1. Look out for 9s (carrying) and 0s (exchanging).
- Find the tens digit. 10 is one ten, so only the tens digit (and maybe the next one) should change.
Th H T O 3 4 9 5 - Add 1 to the tens digit. There are 9 tens. 1 more ten makes 10 tens, which is 1 hundred and 0 tens. So we carry.9 + 1 = 10 → write 0 in the tens column and carry 1 to the hundreds column
- Write the new number. Digits in the other columns stay the same unless we carried or exchanged.3,495 + 10 = 3,505
Check. Do the opposite: 3,505 − 10 = 3,495. ✓
Watch out. Do not change every digit! Only the digit in the column you are working on changes (unless you carry or exchange).
Method. To find 100 more, change the hundreds digit by 1. Look out for 9s (carrying) and 0s (exchanging).
- Find the hundreds digit. 100 is one hundred, so only the hundreds digit (and maybe the next one) should change.
Th H T O 4 9 5 0 - Add 1 to the hundreds digit. There are 9 hundreds. 1 more hundred makes 10 hundreds, which is 1 thousand and 0 hundreds. So we carry.9 + 1 = 10 → write 0 in the hundreds column and carry 1 to the thousands column
- Write the new number. Digits in the other columns stay the same unless we carried or exchanged.4,950 + 100 = 5,050
Check. Do the opposite: 5,050 − 100 = 4,950. ✓
Watch out. Do not change every digit! Only the digit in the column you are working on changes (unless you carry or exchange).
Method. To find 10 less, change the tens digit by 1. Look out for 9s (carrying) and 0s (exchanging).
- Find the tens digit. 10 is one ten, so only the tens digit (and maybe the next one) should change.
Th H T O 6 0 0 5 - Take 1 from the tens digit. There are 0 tens, so we must exchange 1 hundred for 10 tens. Then take 1 away.0 tens → take 1 from the hundreds digit, then 10 − 1 = 9 tens
- Write the new number. Digits in the other columns stay the same unless we carried or exchanged.6,005 − 10 = 5,995
Check. Do the opposite: 5,995 + 10 = 6,005. ✓
Watch out. Do not change every digit! Only the digit in the column you are working on changes (unless you carry or exchange).
Method. To find 100 less, change the hundreds digit by 1. Look out for 9s (carrying) and 0s (exchanging).
- Find the hundreds digit. 100 is one hundred, so only the hundreds digit (and maybe the next one) should change.
Th H T O 7 0 4 0 - Take 1 from the hundreds digit. There are 0 hundreds, so we must exchange 1 thousand for 10 hundreds. Then take 1 away.0 hundreds → take 1 from the thousands digit, then 10 − 1 = 9 hundreds
- Write the new number. Digits in the other columns stay the same unless we carried or exchanged.7,040 − 100 = 6,940
Check. Do the opposite: 6,940 + 100 = 7,040. ✓
Watch out. Do not change every digit! Only the digit in the column you are working on changes (unless you carry or exchange).
Method. To find 100 more, change the hundreds digit by 1. Look out for 9s (carrying) and 0s (exchanging).
- Find the hundreds digit. 100 is one hundred, so only the hundreds digit (and maybe the next one) should change.
Th H T O 9 9 0 0 - Add 1 to the hundreds digit. There are 9 hundreds. 1 more hundred makes 10 hundreds, which is 1 thousand and 0 hundreds. So we carry.9 + 1 = 10 → write 0 in the hundreds column and carry 1 to the thousands column
- Write the new number. Digits in the other columns stay the same unless we carried or exchanged.9,900 + 100 = 10,000
Check. Do the opposite: 10,000 − 100 = 9,900. ✓
Watch out. Do not change every digit! Only the digit in the column you are working on changes (unless you carry or exchange).
Method. Use the opposite (inverse) operation to find the missing number. Then check it in the number sentence.
- Look at the number sentence. The box stands for the number we want.? + 1,000 = 7,368
- Choose the subtract operation. The opposite operation undoes the sum and finds the box.7,368 − 1,000 = 6,368
- Check it in the number sentence. Put the answer back in the box.6,368 + 1,000 = 7,368 ✓
Check. Look at the digits: only one column changes between the two numbers, and it changes by the amount in the number sentence. ✓
Watch out. The box is not always at the start. Think about what the sum is asking before you choose + or −.
Method. Use the opposite (inverse) operation to find the missing number. Then check it in the number sentence.
- Look at the number sentence. The box stands for the number we want.5,120 − ? = 4,120
- Choose the subtract operation. The opposite operation undoes the sum and finds the box.5,120 − 4,120 = 1,000
- Check it in the number sentence. Put the answer back in the box.5,120 − 1,000 = 4,120 ✓
Check. Look at the digits: only one column changes between the two numbers, and it changes by the amount in the number sentence. ✓
Watch out. The box is not always at the start. Think about what the sum is asking before you choose + or −.
Method. Use the opposite (inverse) operation to find the missing number. Then check it in the number sentence.
- Look at the number sentence. The box stands for the number we want.? − 100 = 3,950
- Choose the add operation. The opposite operation undoes the sum and finds the box.3,950 + 100 = 4,050
- Check it in the number sentence. Put the answer back in the box.4,050 − 100 = 3,950 ✓
Check. Look at the digits: only one column changes between the two numbers, and it changes by the amount in the number sentence. ✓
Watch out. The box is not always at the start. Think about what the sum is asking before you choose + or −.
Method. Use the opposite (inverse) operation to find the missing number. Then check it in the number sentence.
- Look at the number sentence. The box stands for the number we want.2,406 + ? = 3,406
- Choose the subtract operation. The opposite operation undoes the sum and finds the box.3,406 − 2,406 = 1,000
- Check it in the number sentence. Put the answer back in the box.2,406 + 1,000 = 3,406 ✓
Check. Look at the digits: only one column changes between the two numbers, and it changes by the amount in the number sentence. ✓
Watch out. The box is not always at the start. Think about what the sum is asking before you choose + or −.
Key words. < means “less than” and > means “greater than”. The wide end of the sign faces the bigger number.
Method. Compare the digits from the left, one column at a time. The first column that is different tells you which number is bigger.
- Write both numbers in a place-value table. Lining up the columns lets us compare digit by digit.
Th H T O 4,562 4 5 6 2 4,652 4 6 5 2 - Compare the digits from the left. The first column where they are different decides which number is bigger.thousands: 4 and 4 are the same, so look at the next column.
hundreds: 5 and 6 are different. 5 < 6, so 4,562 is smaller. - Write the correct symbol. < means “is less than”, > means “is greater than”, = means “is equal to”.4,562 < 4,652
Check. Picture a number line: 4,562 is to the left of 4,652. ✓
Watch out. Start at the LEFT (the biggest column). Do not start with the ones.
Key words. < means “less than” and > means “greater than”. The wide end of the sign faces the bigger number.
Method. Compare the digits from the left, one column at a time. The first column that is different tells you which number is bigger.
- Write both numbers in a place-value table. Lining up the columns lets us compare digit by digit.
Th H T O 7,009 7 0 0 9 7,090 7 0 9 0 - Compare the digits from the left. The first column where they are different decides which number is bigger.thousands: 7 and 7 are the same, so look at the next column.
hundreds: 0 and 0 are the same, so look at the next column.
tens: 0 and 9 are different. 0 < 9, so 7,009 is smaller. - Write the correct symbol. < means “is less than”, > means “is greater than”, = means “is equal to”.7,009 < 7,090
Check. Picture a number line: 7,009 is to the left of 7,090. ✓
Watch out. Start at the LEFT (the biggest column). Do not start with the ones.
Key words. < means “less than” and > means “greater than”. The wide end of the sign faces the bigger number.
Method. Compare the digits from the left, one column at a time. The first column that is different tells you which number is bigger.
- Write each side as one number. We can only compare numbers when each is written the usual way.3,200 = 3,200
3,000 + 200 = 3,200 - Write both numbers in a place-value table. Lining up the columns lets us compare digit by digit.
Th H T O 3,200 3 2 0 0 3,200 3 2 0 0 - Compare the digits from the left. The first column where they are different decides which number is bigger.Every column is the same.
- Write the correct symbol. < means “is less than”, > means “is greater than”, = means “is equal to”.3,200 = 3,200
Check. Both are 3,200. ✓
Watch out. Start at the LEFT (the biggest column). Do not start with the ones.
Key words. < means “less than” and > means “greater than”. The wide end of the sign faces the bigger number.
Method. Compare the digits from the left, one column at a time. The first column that is different tells you which number is bigger.
- Count the digits. A number with more digits is bigger (if neither starts with 0).8,451 has 4 digits and 845 has 3 digits.
- Write the correct symbol. < means “is less than”, > means “is greater than”, = means “is equal to”.8,451 > 845
Check. Picture a number line: 845 is to the left of 8,451. ✓
Watch out. Start at the LEFT (the biggest column). Do not start with the ones.
Key words. < means “less than” and > means “greater than”. The wide end of the sign faces the bigger number.
Method. Compare the digits from the left, one column at a time. The first column that is different tells you which number is bigger.
- Write both numbers in a place-value table. Lining up the columns lets us compare digit by digit.
Th H T O 6,730 6 7 3 0 6,073 6 0 7 3 - Compare the digits from the left. The first column where they are different decides which number is bigger.thousands: 6 and 6 are the same, so look at the next column.
hundreds: 7 and 0 are different. 7 > 0, so 6,730 is bigger. - Write the correct symbol. < means “is less than”, > means “is greater than”, = means “is equal to”.6,730 > 6,073
Check. Picture a number line: 6,073 is to the left of 6,730. ✓
Watch out. Start at the LEFT (the biggest column). Do not start with the ones.
Key words. < means “less than” and > means “greater than”. The wide end of the sign faces the bigger number.
Method. Compare the digits from the left, one column at a time. The first column that is different tells you which number is bigger.
- Write each side as one number. We can only compare numbers when each is written the usual way.5,000 + 40 = 5,040
5,400 = 5,400 - Write both numbers in a place-value table. Lining up the columns lets us compare digit by digit.
Th H T O 5,040 5 0 4 0 5,400 5 4 0 0 - Compare the digits from the left. The first column where they are different decides which number is bigger.thousands: 5 and 5 are the same, so look at the next column.
hundreds: 0 and 4 are different. 0 < 4, so 5,040 is smaller. - Write the correct symbol. < means “is less than”, > means “is greater than”, = means “is equal to”.5,040 < 5,400
Check. Picture a number line: 5,040 is to the left of 5,400. ✓
Watch out. Start at the LEFT (the biggest column). Do not start with the ones.
Key words. Ascending order means smallest first. Descending order means biggest first.
Method. Put the numbers in a place-value table, then compare columns from the left. Smallest first.
- Write all the numbers in a place-value table. This lines up the digits so we can compare them.
Th H T O 4,385 4 3 8 5 4,358 4 3 5 8 4,835 4 8 3 5 4,538 4 5 3 8 - Compare the thousands, then the hundreds, then the tens, then the ones. Where the digits in a column match, move on to the next column.4,358 and 4,385: tens: 5 and 8 are different. 5 < 8, so 4,358 is smaller.
4,385 and 4,538: hundreds: 3 and 5 are different. 3 < 5, so 4,385 is smaller.
4,538 and 4,835: hundreds: 5 and 8 are different. 5 < 8, so 4,538 is smaller. - Write them smallest first. Check you have used every number once.4,358, 4,385, 4,538, 4,835
Check. Count the numbers: 4 in the question and 4 in the answer. ✓
Watch out. Do not forget a number. Tick each one off as you write it.
Key words. Ascending order means smallest first. Descending order means biggest first.
Method. Put the numbers in a place-value table, then compare columns from the left. Smallest first.
- Write all the numbers in a place-value table. This lines up the digits so we can compare them.
Th H T O 6,014 6 0 1 4 6,104 6 1 0 4 6,041 6 0 4 1 6,410 6 4 1 0 1,604 1 6 0 4 - Compare the thousands, then the hundreds, then the tens, then the ones. Where the digits in a column match, move on to the next column.1,604 and 6,014: thousands: 1 and 6 are different. 1 < 6, so 1,604 is smaller.
6,014 and 6,041: tens: 1 and 4 are different. 1 < 4, so 6,014 is smaller.
6,041 and 6,104: hundreds: 0 and 1 are different. 0 < 1, so 6,041 is smaller.
6,104 and 6,410: hundreds: 1 and 4 are different. 1 < 4, so 6,104 is smaller. - Write them smallest first. Check you have used every number once.1,604, 6,014, 6,041, 6,104, 6,410
Check. Count the numbers: 5 in the question and 5 in the answer. ✓
Watch out. Do not forget a number. Tick each one off as you write it.
Key words. Ascending order means smallest first. Descending order means biggest first.
Method. Put the numbers in a place-value table, then compare columns from the left. Smallest first.
- Write all the numbers in a place-value table. This lines up the digits so we can compare them.
Th H T O 2,999 2 9 9 9 3,001 3 0 0 1 2,990 2 9 9 0 3,010 3 0 1 0 - Compare the thousands, then the hundreds, then the tens, then the ones. Where the digits in a column match, move on to the next column.2,990 and 2,999: ones: 0 and 9 are different. 0 < 9, so 2,990 is smaller.
2,999 and 3,001: thousands: 2 and 3 are different. 2 < 3, so 2,999 is smaller.
3,001 and 3,010: tens: 0 and 1 are different. 0 < 1, so 3,001 is smaller. - Write them smallest first. Check you have used every number once.2,990, 2,999, 3,001, 3,010
Check. Count the numbers: 4 in the question and 4 in the answer. ✓
Watch out. Do not forget a number. Tick each one off as you write it.
Key words. Ascending order means smallest first. Descending order means biggest first.
Method. Put the numbers in a place-value table, then compare columns from the left. Biggest first.
- Write all the numbers in a place-value table. This lines up the digits so we can compare them.
Th H T O 7,280 7 2 8 0 7,028 7 0 2 8 7,208 7 2 0 8 782 7 8 2 - Compare the thousands, then the hundreds, then the tens, then the ones. Where the digits in a column match, move on to the next column.782 and 7,028: 7,028 has 4 digits and 782 has 3 digits, so 7,028 is bigger.
7,028 and 7,208: hundreds: 0 and 2 are different. 0 < 2, so 7,028 is smaller.
7,208 and 7,280: tens: 0 and 8 are different. 0 < 8, so 7,208 is smaller. - Write them biggest first. Check you have used every number once.7,280, 7,208, 7,028, 782
Check. Count the numbers: 4 in the question and 4 in the answer. ✓
Watch out. Do not forget a number. Tick each one off as you write it.
Key words. Ascending order means smallest first. Descending order means biggest first.
Method. Put the numbers in a place-value table, then compare columns from the left. Biggest first.
- Write all the numbers in a place-value table. This lines up the digits so we can compare them.
Th H T O 9,099 9 0 9 9 9,909 9 9 0 9 9,090 9 0 9 0 9,990 9 9 9 0 9,009 9 0 0 9 - Compare the thousands, then the hundreds, then the tens, then the ones. Where the digits in a column match, move on to the next column.9,009 and 9,090: tens: 0 and 9 are different. 0 < 9, so 9,009 is smaller.
9,090 and 9,099: ones: 0 and 9 are different. 0 < 9, so 9,090 is smaller.
9,099 and 9,909: hundreds: 0 and 9 are different. 0 < 9, so 9,099 is smaller.
9,909 and 9,990: tens: 0 and 9 are different. 0 < 9, so 9,909 is smaller. - Write them biggest first. Check you have used every number once.9,990, 9,909, 9,099, 9,090, 9,009
Check. Count the numbers: 5 in the question and 5 in the answer. ✓
Watch out. Do not forget a number. Tick each one off as you write it.
Method. Find out what each small mark is worth, then count on from a number you can read.
- Count the gaps between two labelled numbers. The line goes from 7,000 to 8,000 in 10 equal gaps.8,000 − 7,000 = 1,000
- Work out what one gap is worth. Share the distance equally between the gaps.1,000 ÷ 10 = 100
- Count on from the start to the arrow. The arrow is 6 gaps after 7,000.7,000 + 6 × 100 = 7,000 + 600 = 7,600
Check. Count back from 8,000: 4 gaps back is 8,000 − 400 = 7,600. ✓
Watch out. Do not read the nearest label. Count the small marks to find the exact number.
Method. Find the numbers on each side of the arrow and decide how far along it is.
- Find the labelled numbers either side of the arrow. The arrow is between 7,000 and 8,000.7,000 < arrow < 8,000
- Find the number halfway between them. Halfway between two numbers is the number in the middle: add them and halve.7,000 + 8,000 = 15,000 and 15,000 ÷ 2 = 7,500
- Choose the best estimate. The arrow looks about halfway along the gap, so it is close to 7,500.The best estimate is B (7,500).
Check. 7,100 would be very close to 7,000, and 7,900 would be very close to 8,000. 8,500 is past 8,000. So only 7,500 fits. ✓
Watch out. An estimate is a sensible guess. You do not need the exact number.
Method. A four-digit number cannot start with 0. The smallest digit for the thousands column is 1, and the other columns are all 0.
- Choose the thousands digit. It cannot be 0, so the smallest choice is 1.Th = 1
- Make the other columns as small as possible. 0 is the smallest digit.H = 0, T = 0, O = 0
- Write the number. 1,000
Check. 999 has only three digits, and 1,000 is one more than 999. ✓
Method. Use the biggest digit, 9, in every column.
- Choose the biggest digit for every column. 9 is the biggest digit.Th = 9, H = 9, T = 9, O = 9
- Write the number. 9,999
Check. One more is 10,000, which has five digits. ✓
Method. Add 1 to 9,999 and carry from the ones to the thousands.
- Add 1 to the ones. 9 + 1 = 10, so write 0 and carry 1.9,999 + 1
- Keep carrying. Every column is 9, so every column becomes 0 and a 1 is carried into a new column.10 tens, then 10 hundreds, then 10 thousands
- Write the number. It is called ten thousand.10,000
Check. 10,000 = 10 thousands = 1 ten thousand. ✓
Method. To find 1,000 more, change the thousands digit by 1. Look out for 9s (carrying) and 0s (exchanging).
- Find the thousands digit. 1,000 is one thousand, so only the thousands digit (and maybe the next one) should change.
Th H T O 6 4 5 0 - Add 1 to the thousands digit. 1,000 more means 1 more thousand.6 + 1 = 7 thousands
- Write the new number. Digits in the other columns stay the same unless we carried or exchanged.6,450 + 1,000 = 7,450
Check. Do the opposite: 7,450 − 1,000 = 6,450. ✓
Watch out. Do not change every digit! Only the digit in the column you are working on changes (unless you carry or exchange).
Method. To find 100 less, change the hundreds digit by 1. Look out for 9s (carrying) and 0s (exchanging).
- Find the hundreds digit. 100 is one hundred, so only the hundreds digit (and maybe the next one) should change.
Th H T O 6 4 5 0 - Take 1 from the hundreds digit. 100 less means 1 less hundred.4 − 1 = 3 hundreds
- Write the new number. Digits in the other columns stay the same unless we carried or exchanged.6,450 − 100 = 6,350
Check. Do the opposite: 6,350 + 100 = 6,450. ✓
Watch out. Do not change every digit! Only the digit in the column you are working on changes (unless you carry or exchange).
Method. Use what you know about 1000 more and 100 less. Compare the three populations at the end.
- Brookley has 1000 more people than Elmby. Change the thousands digit of 6,450.6,450 + 1,000 = 7,450
- Oakton has 100 fewer people than Elmby. Change the hundreds digit of 6,450.6,450 − 100 = 6,350
- Compare the three towns. Compare from the left.Thousands: 7, 6, 6. Brookley is biggest.
Hundreds of the other two: 4 and 3. Oakton is smallest.
Check. Order: 6,350 < 6,450 < 7,450. ✓
Watch out. Read the question carefully. “More” means add, “fewer” means take away.
Method. Check what Leo did. Work out 1000 less properly and compare.
- Work out 1000 less than 3,208. Change the thousands digit.3,208 − 1,000 = 2,208
- Work out what Leo did. He wrote 3,198. Compare it with 3,208.3,208 − 3,198 = 10
- Say what went wrong. He took away 10, not 1000. He changed the tens digit instead of the thousands digit.The correct answer is 2,208.
Check. 2,208 + 1,000 = 3,208. ✓
Watch out. Check which column you need to change before you start.
“The number with the bigger digit total is the bigger number.”
Method. Try some pairs of numbers. If you find one pair where it works and one where it does not, the answer is “sometimes”.
- Try 4,500 and 1,200. Add the digits of each, then compare the numbers.4 + 5 + 0 + 0 = 9 and 1 + 2 + 0 + 0 = 3
The bigger digit total (9) is the bigger number (4,500 > 1,200). It works here. - Try 3,111 and 2,999. Add the digits of each.3 + 1 + 1 + 1 = 6 and 2 + 9 + 9 + 9 = 29
The bigger digit total (29) belongs to 2,999, but 3,111 > 2,999. It does not work here. - Write the answer. It works for some pairs and not for others.Sometimes
Check. Place value tells us why: the thousands digit matters most, so compare from the left, not by adding the digits. ✓
Watch out. One example that works does not prove “always”. You need to look for a pair that breaks the rule.
Method. Work in an organised way. An even number must end in an even digit, and a number greater than 6,000 must start with 6 or 9.
- Which digit can go in the ones column? Even numbers end in 0, 2, 4, 6 or 8. Here that means 4 or 6.Ones digit: 4 or 6
- Which digits can go in the thousands column? The number must be greater than 6,000, so the first digit is 6 or 9 (1 and 4 are too small).Thousands digit: 6 or 9
- List every number that fits. Try each pair, then arrange the two remaining digits in both ways.6,194
6,914
9,146
9,164
9,416
9,614 - Write them in order. 6,194, 6,914, 9,146, 9,164, 9,416, 9,614
Check. There are 6 numbers. Each uses 1, 4, 6 and 9 once, ends in 4 or 6, and starts with 6 or 9. ✓
Watch out. Be systematic: fix the first and last digits, then swap the middle two. Do not miss any!