Place value to 1000

Method. Look at the hundreds place in 415.

1. Find the hundreds place. The first digit of a three-digit number is in the hundreds place.
   415: hundreds 4, tens 1, ones 5
2. Read the digit in that place. The digit is the number that the place has.
   4
3. Write the answer.
   4

Check. 400 + 10 + 5 = 415. ✓

Watch out. Count the places from the right: ones, tens, hundreds.

Method. Look at the tens place in 260.

1. Find the tens place. The middle digit of a three-digit number is in the tens place.
   260: hundreds 2, tens 6, ones 0
2. Read the digit in that place. The digit is the number that the place has.
   6
3. Write the answer.
   6

Check. 200 + 60 = 260. ✓

Watch out. Count the places from the right: ones, tens, hundreds.

Method. Look at the ones place in 739.

1. Find the ones place. The last digit of a three-digit number is in the ones place.
   739: hundreds 7, tens 3, ones 9
2. Read the digit in that place. The digit is the number that the place has.
   9
3. Write the answer.
   9

Check. 700 + 30 + 9 = 739. ✓

Watch out. Count the places from the right: ones, tens, hundreds.

Key words. A digit is one of the figures 0 to 9. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones.

Method. The value of a digit depends on its place.

1. Find the digit in the hundreds place. Look at that place in the number.
   782: the digit is 7
2. Work out its value. Each hundred is worth 100.
   7 × 100 = 700
3. Write the answer. The value is the digit times the place, not just the digit.
   700

Check. 700 + 80 + 2 = 782, so the hundreds part is 700. ✓

Watch out. The digit is 7, but its value is 700.

Key words. A digit is one of the figures 0 to 9. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones.

Method. The value of a digit depends on its place.

1. Find the digit in the tens place. Look at that place in the number.
   129: the digit is 2
2. Work out its value. Each ten is worth 10.
   2 × 10 = 20
3. Write the answer. The value is the digit times the place, not just the digit.
   20

Check. 100 + 20 + 9 = 129, so the tens part is 20. ✓

Watch out. The digit is 2, but its value is 20.

Key words. A digit is one of the figures 0 to 9. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones.

Method. Count the flats, then the bars, then the cubes, and add them.

1. Count the flats. Each flat is one hundred.
   6 flats = 600
2. Count the bars. Each bar is ten ones.
   3 bars = 30
3. Count the single cubes. Each cube is one.
   9 cubes = 9
4. Add the parts. Put the parts together.
   600 + 30 + 9 = 639
5. Write the answer.
   639

Check. 6 hundreds, 3 tens and 9 ones make 639. ✓

Watch out. Count each block once. Do not count a bar as ten separate cubes as well.

Key words. A digit is one of the figures 0 to 9. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones.

Method. Work out each place, then add the three parts.

1. Write the hundreds. Each hundred is 100.
   4 × 100 = 400
2. Write the tens. Each ten is 10. A 0 means there are no tens.
   0 × 10 = 0
3. Write the ones. Each one is 1.
   7 × 1 = 7
4. Add the parts. Put the parts together.
   400 + 0 + 7 = 407
5. Write the answer.
   407

Check. 400 + 7 = 407. ✓

Watch out. A 0 in the tens place means no tens, so do not drop it.

Key words. A digit is one of the figures 0 to 9. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones.

Method. Split the number into its hundreds, tens and ones.

1. Find the hundreds. The hundreds digit is worth 100 each.
   5 × 100 = 500
2. Find the tens. The tens digit is worth 10 each.
   6 × 10 = 60
3. Find the ones. The ones digit is worth 1 each.
   3 × 1 = 3
4. Add the parts together. This checks that the parts make the number.
   500 + 60 + 3 = 563
5. Write the answer. Leave out a place that has 0.
   500 + 60 + 3

Check. 500 + 60 + 3 = 563. ✓

Watch out. Write each part with its zeros, for example 50 and not 5.

Key words. A digit is one of the figures 0 to 9. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones.

Method. Work out each place, then add the three parts.

1. Write the hundreds. Each hundred is 100.
   2 × 100 = 200
2. Write the tens. Each ten is 10. A 0 means there are no tens.
   5 × 10 = 50
3. Write the ones. Each one is 1.
   1 × 1 = 1
4. Add the parts. Put the parts together.
   200 + 50 + 1 = 251
5. Write the answer.
   251

Check. 200 + 50 + 1 = 251. ✓

Watch out. A 0 in the tens place means no tens, so do not drop it.

Key words. A digit is one of the figures 0 to 9. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones.

Method. Read each digit from the place it is in.

1. Read the hundreds digit. The first digit is 3.
   3 hundreds
2. Read the tens digit. The middle digit is 7.
   7 tens
3. Read the ones digit. The last digit is 0.
   0 ones
4. Compare with what Tom said. Tom has the places the wrong way round.
   No. 370 has 3 hundreds, 7 tens and 0 ones.

Check. 300 + 70 + 0 = 370. ✓

Watch out. Read the digits from left to right: hundreds, tens, ones.

Key words. A digit is one of the figures 0 to 9. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones.

Method. Put the biggest digit in the hundreds place, then the next biggest in the tens place.

1. Choose the hundreds digit. The biggest digit goes in the hundreds place.
   7 in the hundreds
2. Choose the tens digit. The next biggest digit goes in the tens place.
   4 in the tens
3. Choose the ones digit. The last digit goes in the ones place.
   2 in the ones
4. Write the answer.
   742

Check. 742 is bigger than 724, 472 and 427. ✓

Watch out. Use each digit only once. The biggest hundreds digit gives the biggest number.

Key words. A numeral is a number written with digits, such as 352. A number word is a number written in words, such as three hundred and fifty-two.

Method. Say the hundreds, then "and", then the tens and ones.

1. Say the hundreds. The first digit tells us the hundreds.
   2 hundreds = two hundred
2. Say the tens and ones. Read the last two digits together.
   5 tens and 8 ones = fifty-eight
3. Join them with "and". UK English puts "and" between the hundreds and the tens and ones.
   two hundred and fifty-eight
4. Write the answer.
   two hundred and fifty-eight

Check. Read the words back: two hundred and fifty-eight is 258. ✓

Watch out. Put "and" after the hundreds. Do not write "and" if there are no tens or ones.

Key words. A numeral is a number written with digits, such as 352. A number word is a number written in words, such as three hundred and fifty-two.

Method. Write the hundreds first, then the tens, then the ones.

1. Find the hundreds word. The word before "hundred" gives the hundreds digit.
   seven hundred → 7 hundreds = 700
2. Find the tens and ones. The words after "and" are the last two digits.
   six → 6
3. Put the digits in order. Write the hundreds, then the tens, then the ones. Use 0 for an empty place.
   7 0 6 → 706
4. Write the answer.
   706

Check. 700 + 6 = 706, so the digits are right. ✓

Watch out. A zero in the tens place is still a digit. Do not leave the place out.

Key words. A numeral is a number written with digits, such as 352. A number word is a number written in words, such as three hundred and fifty-two.

Method. Say the hundreds, then "and", then the tens and ones.

1. Say the hundreds. The first digit tells us the hundreds.
   9 hundreds = nine hundred
2. There are no tens or ones. The last two digits are 00, so we say nothing more.
   no tens and no ones
3. Keep it as hundreds only. Do not write "and" when there is nothing after the hundreds.
   nine hundred
4. Write the answer.
   nine hundred

Check. Read the words back: nine hundred is 900. ✓

Watch out. Put "and" after the hundreds. Do not write "and" if there are no tens or ones.

Key words. A numeral is a number written with digits, such as 352. A number word is a number written in words, such as three hundred and fifty-two.

Method. Write the hundreds first, then the tens, then the ones.

1. Find the hundreds word. The word before "hundred" gives the hundreds digit.
   three hundred → 3 hundreds = 300
2. Find the tens and ones. The words after "and" are the last two digits.
   seventy → 70
3. Put the digits in order. Write the hundreds, then the tens, then the ones. Use 0 for an empty place.
   3 7 0 → 370
4. Write the answer.
   370

Check. 300 + 70 = 370, so the digits are right. ✓

Watch out. A zero in the tens place is still a digit. Do not leave the place out.

Key words. A numeral is a number written with digits, such as 352. A number word is a number written in words, such as three hundred and fifty-two.

Method. Read the number as a thousand.

1. Look at the number. It is one thousand, which has four digits.
   1000
2. Say it in words. One thousand is ten hundreds.
   one thousand
3. Write the answer.
   one thousand

Check. 1000 is ten hundreds, which is more than 999. ✓

Watch out. One thousand has no hundreds word, so write "one thousand".

Key words. A numeral is a number written with digits, such as 352. A number word is a number written in words, such as three hundred and fifty-two.

Method. Write the hundreds first, then the tens, then the ones.

1. Find the hundreds word. The word before "hundred" gives the hundreds digit.
   three hundred → 3 hundreds = 300
2. Find the tens and ones. The words after "and" are the last two digits.
   one → 1
3. Put the digits in order. Write the hundreds, then the tens, then the ones. Use 0 for an empty place.
   3 0 1 → 301
4. Write the answer.
   301

Check. 300 + 1 = 301, so the digits are right. ✓

Watch out. A zero in the tens place is still a digit. Do not leave the place out.

Key words. A numeral is a number written with digits, such as 352. A number word is a number written in words, such as three hundred and fifty-two.

Method. Say the hundreds, then "and", then the tens and ones.

1. Say the hundreds. The first digit tells us the hundreds.
   8 hundreds = eight hundred
2. Say the tens and ones. Read the last two digits together.
   0 tens and 3 ones = three
3. Join them with "and". UK English puts "and" between the hundreds and the tens and ones.
   eight hundred and three
4. Write the answer.
   eight hundred and three

Check. Read the words back: eight hundred and three is 803. ✓

Watch out. Put "and" after the hundreds. Do not write "and" if there are no tens or ones.

Key words. A numeral is a number written with digits, such as 352. A number word is a number written in words, such as three hundred and fifty-two.

Method. Read the words and write the digits in the right places.

1. Find the hundreds. Two hundred is 200.
   200
2. Find the tens and ones. Forty is 40, and there are no ones.
   40 + 0 = 40
3. Put them together. Two hundred and forty is 240, not 204.
   200 + 40 = 240
4. Decide. Tom has put the tens and ones the wrong way round.
   No. Two hundred and forty is 240.

Check. 204 is two hundred and four. ✓

Watch out. "Forty" is the tens, so it goes before the ones.

Key words. A numeral is a number written with digits, such as 352. A number word is a number written in words, such as three hundred and fifty-two.

Method. Write the number as digits, then compare the two numbers.

1. Write three hundred and fifty as digits. Three hundreds, then 5 tens, then 0 ones.
   350
2. Write three hundred and five as digits. Three hundreds, then 0 tens, then 5 ones.
   305
3. Compare the two numbers. The tens digits are different: 5 tens and 0 tens.
   350 is not 305
4. Write the answer.
   350. No, it is not the same as 305.

Check. 350 is 45 more than 305. ✓

Watch out. The zero in 305 means there are no tens. Check the middle digit.

Key words. A count in steps jumps by the same amount each time. The numbers we say are multiples of the step: 8, 16 and 24 are multiples of 8.

Method. Count on in steps of 4.

1. Start at the number we are counting from. We start at 0.
   0
2. Add 4 to find the next number. The step is always 4.
   0 + 4 = 4
3. Add 4 to find the next number. The step is always 4.
   4 + 4 = 8
4. Add 4 to find the next number. The step is always 4.
   8 + 4 = 12
5. Add 4 to find the next number. The step is always 4.
   12 + 4 = 16
6. Add 4 to find the next number. The step is always 4.
   16 + 4 = 20
7. Write the answer. Say the numbers in order.
   4, 8, 12, 16, 20

Check. 0 + 5 × 4 = 20. ✓

Watch out. Keep the step the same every time. Each number is one step from the number before it.

Key words. A count in steps jumps by the same amount each time. The numbers we say are multiples of the step: 8, 16 and 24 are multiples of 8.

Method. Count on in steps of 8.

1. Start at the number we are counting from. We start at 0.
   0
2. Add 8 to find the next number. The step is always 8.
   0 + 8 = 8
3. Add 8 to find the next number. The step is always 8.
   8 + 8 = 16
4. Add 8 to find the next number. The step is always 8.
   16 + 8 = 24
5. Add 8 to find the next number. The step is always 8.
   24 + 8 = 32
6. Add 8 to find the next number. The step is always 8.
   32 + 8 = 40
7. Write the answer. Say the numbers in order.
   8, 16, 24, 32, 40

Check. 0 + 5 × 8 = 40. ✓

Watch out. Keep the step the same every time. Each number is one step from the number before it.

Key words. A count in steps jumps by the same amount each time. The numbers we say are multiples of the step: 8, 16 and 24 are multiples of 8.

Method. Count on in steps of 50.

1. Start at the number we are counting from. We start at 100.
   100
2. Add 50 to find the next number. The step is always 50.
   100 + 50 = 150
3. Add 50 to find the next number. The step is always 50.
   150 + 50 = 200
4. Add 50 to find the next number. The step is always 50.
   200 + 50 = 250
5. Add 50 to find the next number. The step is always 50.
   250 + 50 = 300
6. Write the answer. Say the numbers in order.
   150, 200, 250, 300

Check. 100 + 4 × 50 = 300. ✓

Watch out. Keep the step the same every time. Each number is one step from the number before it.

Key words. A count in steps jumps by the same amount each time. The numbers we say are multiples of the step: 8, 16 and 24 are multiples of 8.

Method. Count on in steps of 100.

1. Start at the number we are counting from. We start at 200.
   200
2. Add 100 to find the next number. The step is always 100.
   200 + 100 = 300
3. Add 100 to find the next number. The step is always 100.
   300 + 100 = 400
4. Add 100 to find the next number. The step is always 100.
   400 + 100 = 500
5. Add 100 to find the next number. The step is always 100.
   500 + 100 = 600
6. Add 100 to find the next number. The step is always 100.
   600 + 100 = 700
7. Write the answer. Say the numbers in order.
   300, 400, 500, 600, 700

Check. 200 + 5 × 100 = 700. ✓

Watch out. Keep the step the same every time. Each number is one step from the number before it.

Key words. A count in steps jumps by the same amount each time. The numbers we say are multiples of the step: 8, 16 and 24 are multiples of 8.

Method. Count back in steps of 50.

1. Start at the number we are counting from. We start at 500.
   500
2. Take 50 away to find the next number. The step is always 50.
   500 − 50 = 450
3. Take 50 away to find the next number. The step is always 50.
   450 − 50 = 400
4. Take 50 away to find the next number. The step is always 50.
   400 − 50 = 350
5. Write the answer. Say the numbers in order.
   450, 400, 350

Check. 500 − 3 × 50 = 350. ✓

Watch out. Keep the step the same every time. Each number is one step from the number before it.

Key words. A count in steps jumps by the same amount each time. The numbers we say are multiples of the step: 8, 16 and 24 are multiples of 8.

Method. Count back in steps of 4.

1. Start at the number we are counting from. We start at 40.
   40
2. Take 4 away to find the next number. The step is always 4.
   40 − 4 = 36
3. Take 4 away to find the next number. The step is always 4.
   36 − 4 = 32
4. Take 4 away to find the next number. The step is always 4.
   32 − 4 = 28
5. Take 4 away to find the next number. The step is always 4.
   28 − 4 = 24
6. Write the answer. Say the numbers in order.
   36, 32, 28, 24

Check. 40 − 4 × 4 = 24. ✓

Watch out. Keep the step the same every time. Each number is one step from the number before it.

Key words. A count in steps jumps by the same amount each time. The numbers we say are multiples of the step: 8, 16 and 24 are multiples of 8.

Method. Count in eights from 0, then look for 36.

1. Count in eights from 0. Say each number in the count.
   0, 8, 16, 24, 32, 40
2. Look for 36. 36 is between 32 and 40.
   32 is less than 36, and 36 is less than 40
3. Decide. The count never says 36.
   No. The count in eights goes 32, 40, so 36 is not in it.

Check. 8 × 4 = 32 and 8 × 5 = 40. ✓

Watch out. Find the two numbers either side of the number you are checking.

Key words. A count in steps jumps by the same amount each time. The numbers we say are multiples of the step: 8, 16 and 24 are multiples of 8.

Method. Count in eights, once for each box.

1. Count in eights, once for each box. Each box holds 8 cups.
   8, 16, 24, 32, 40
2. Count the boxes. There are 5 boxes, so there are 5 steps.
   5 boxes = 5 steps of 8
3. Write the answer.
   40

Check. 5 × 8 = 40. ✓

Watch out. Count one step for each box, not one step for each cup.

Key words. A count in steps jumps by the same amount each time. The numbers we say are multiples of the step: 8, 16 and 24 are multiples of 8.

Method. Count in fours, once for each pack.

1. Count in fours, once for each pack. Each pack holds 4 pens.
   4, 8, 12, 16, 20, 24
2. Count the packs. Priya buys 6 packs, so there are 6 steps.
   6 packs = 6 steps of 4
3. Write the answer.
   24

Check. 6 × 4 = 24. ✓

Watch out. The last number you say is the total.

Key words. A count in steps jumps by the same amount each time. The numbers we say are multiples of the step: 8, 16 and 24 are multiples of 8.

Method. Check the numbers in the count in fifties against the count in fours.

1. Write the counts in fifties up to 150. These are the numbers we check.
   50, 100, 150
2. Check which are in the count in fours. A number is in the count in fours if it divides by 4 with no remainder.
   50 ÷ 4 = 12 remainder 2; 100 ÷ 4 = 25; 150 ÷ 4 = 37 remainder 2
3. Write the answer. 100 is 4 times 25 and 50 times 2.
   100

Check. 4 × 25 = 100 and 50 × 2 = 100. ✓

Watch out. Multiples of both 4 and 50 are multiples of 100 here.

Key words. More means add. Less means take away. When you change a number by 10 or 100, the number changes in one place value.

Method. 10 more changes the tens place, and the other places stay the same.

1. Write the number in place-value columns. Hundreds, tens and ones.
   4 hundreds, 1 tens, 7 ones
2. Change the tens digit. 10 more changes the tens place.
   1 tens + 1 ten = 2 tens
3. Keep the other places the same. Only the place that changed moves.
   4 hundreds, 2 tens, 7 ones
4. Write the answer.
   427

Check. 427 − 10 = 417. ✓

Watch out. Only change the place that is named. Watch for a change that crosses a hundred.

Key words. More means add. Less means take away. When you change a number by 10 or 100, the number changes in one place value.

Method. 10 less changes the tens place, and the other places stay the same.

1. Write the number in place-value columns. Hundreds, tens and ones.
   2 hundreds, 6 tens, 3 ones
2. Change the tens digit. 10 less changes the tens place.
   6 tens − 1 ten = 5 tens
3. Keep the other places the same. Only the place that changed moves.
   2 hundreds, 5 tens, 3 ones
4. Write the answer.
   253

Check. 253 + 10 = 263. ✓

Watch out. Only change the place that is named. Watch for a change that crosses a hundred.

Key words. More means add. Less means take away. When you change a number by 10 or 100, the number changes in one place value.

Method. 100 more changes the hundreds place, and the other places stay the same.

1. Write the number in place-value columns. Hundreds, tens and ones.
   2 hundreds, 8 tens, 6 ones
2. Change the hundreds digit. 100 more changes the hundreds place.
   2 hundreds + 1 hundred = 3 hundreds
3. Keep the other places the same. Only the place that changed moves.
   3 hundreds, 8 tens, 6 ones
4. Write the answer.
   386

Check. 386 − 100 = 286. ✓

Watch out. Only change the place that is named. Watch for a change that crosses a hundred.

Key words. More means add. Less means take away. When you change a number by 10 or 100, the number changes in one place value.

Method. 100 less changes the hundreds place, and the other places stay the same.

1. Write the number in place-value columns. Hundreds, tens and ones.
   6 hundreds, 5 tens, 0 ones
2. Change the hundreds digit. 100 less changes the hundreds place.
   6 hundreds − 1 hundred = 5 hundreds
3. Keep the other places the same. Only the place that changed moves.
   5 hundreds, 5 tens, 0 ones
4. Write the answer.
   550

Check. 550 + 100 = 650. ✓

Watch out. Only change the place that is named. Watch for a change that crosses a hundred.

Key words. More means add. Less means take away. When you change a number by 10 or 100, the number changes in one place value.

Method. 10 more changes the tens place, and the other places stay the same.

1. Write the number in place-value columns. Hundreds, tens and ones.
   2 hundreds, 9 tens, 8 ones
2. Change the tens digit. 10 more changes the tens place.
   9 tens + 1 ten = 10 tens, and 10 tens make 1 hundred. So 0 tens and 1 more hundred
3. Keep the other places the same. Only the place that changed moves.
   3 hundreds, 0 tens, 8 ones
4. Write the answer.
   308

Check. 308 − 10 = 298. ✓

Watch out. Only change the place that is named. Watch for a change that crosses a hundred.

Key words. More means add. Less means take away. When you change a number by 10 or 100, the number changes in one place value.

Method. 10 less changes the tens place, and the other places stay the same.

1. Write the number in place-value columns. Hundreds, tens and ones.
   3 hundreds, 0 tens, 0 ones
2. Change the tens digit. 10 less changes the tens place.
   0 tens − 1 ten: exchange 1 hundred for 10 tens, then 10 tens − 1 ten = 9 tens
3. Keep the other places the same. Only the place that changed moves.
   2 hundreds, 9 tens, 0 ones
4. Write the answer.
   290

Check. 290 + 10 = 300. ✓

Watch out. Only change the place that is named. Watch for a change that crosses a hundred.

Key words. More means add. Less means take away. When you change a number by 10 or 100, the number changes in one place value.

Method. Start with 340. Add 100 first, then take 10 away.

1. Add 100 first. Her friend gives her 100 more stickers.
   340 + 100 = 440
2. Take 10 away. Priya gives 10 stickers to her brother.
   440 − 10 = 430
3. Write the answer.
   430

Check. 430 + 10 = 440, and 440 − 100 = 340. ✓

Watch out. Do the changes in the order the story gives them.

Key words. More means add. Less means take away. When you change a number by 10 or 100, the number changes in one place value.

Method. Add 10 books for each week.

1. Add 10 for the first week. Ten more books arrive.
   480 + 10 = 490
2. Add 10 for the second week. Ten more books arrive again.
   490 + 10 = 500
3. Add 10 for the third week. Ten more books arrive a third time.
   500 + 10 = 510
4. Write the answer.
   510

Check. 480 + 3 × 10 = 510. ✓

Watch out. Crossing 500 changes the hundreds digit, so check that place carefully.

Key words. More means add. Less means take away. When you change a number by 10 or 100, the number changes in one place value.

Method. Work out 10 more than 195.

1. Look at the tens digit of 195. The tens digit is 9.
   9 tens
2. Add 10. Nine tens plus one ten makes ten tens, which is one hundred.
   195 + 10 = 205
3. Decide. Ravi took 10 away instead of adding it.
   No. 10 more than 195 is 205.

Check. 205 − 10 = 195. ✓

Watch out. Adding 10 makes the number bigger, so the answer must be bigger than 195.

Key words. > means greater than. < means less than. = means equal to. The wide end of the sign faces the bigger number.

Method. Compare the hundreds first, then the tens, then the ones.

1. Compare the hundreds digits. Start on the left. The bigger hundreds digit gives the bigger number.
   380 has 3 hundreds, 308 has 3 hundreds
2. The hundreds are the same, so compare the tens. Look at the middle digit next.
   8 tens and 0 tens
3. Choose the sign. The wide end of the sign faces the bigger number.
   380 > 308
4. Write the answer.
   >

Check. 380 is the bigger number, so the sign points to it. ✓

Watch out. Do not compare the ones first. Start with the hundreds.

Key words. > means greater than. < means less than. = means equal to. The wide end of the sign faces the bigger number.

Method. Compare the hundreds first, then the tens, then the ones.

1. Compare the hundreds digits. Start on the left. The bigger hundreds digit gives the bigger number.
   415 has 4 hundreds, 415 has 4 hundreds
2. The hundreds are the same, so compare the tens. Look at the middle digit next.
   1 tens and 1 tens
3. The tens are the same, so compare the ones. Look at the last digit.
   5 ones and 5 ones
4. Choose the sign. The wide end of the sign faces the bigger number.
   415 = 415
5. Write the answer.
   =

Check. 415 is the bigger number, so the sign points to it. ✓

Watch out. Do not compare the ones first. Start with the hundreds.

Key words. > means greater than. < means less than. = means equal to. The wide end of the sign faces the bigger number.

Method. Compare the hundreds first, then the tens, then the ones.

1. Compare the hundreds digits. Start on the left. The bigger hundreds digit gives the bigger number.
   527 has 5 hundreds, 572 has 5 hundreds
2. The hundreds are the same, so compare the tens. Look at the middle digit next.
   2 tens and 7 tens
3. Choose the sign. The wide end of the sign faces the bigger number.
   527 < 572
4. Write the answer.
   <

Check. 572 is the bigger number, so the sign points to it. ✓

Watch out. Do not compare the ones first. Start with the hundreds.

Key words. > means greater than. < means less than. = means equal to. The wide end of the sign faces the bigger number.

Method. Compare the hundreds first, then the tens, then the ones.

1. Compare the hundreds digits. Start on the left. The bigger hundreds digit gives the bigger number.
   600 has 6 hundreds, 599 has 5 hundreds
2. Choose the sign. The wide end of the sign faces the bigger number.
   600 > 599
3. Write the answer.
   >

Check. 600 is the bigger number, so the sign points to it. ✓

Watch out. Do not compare the ones first. Start with the hundreds.

Key words. > means greater than. < means less than. = means equal to. The wide end of the sign faces the bigger number.

Method. Compare the hundreds first, then the tens, then the ones.

1. Compare the hundreds digits. Start on the left. The bigger hundreds digit gives the bigger number.
   614 has 6 hundreds, 641 has 6 hundreds
2. The hundreds are the same, so compare the tens. Look at the middle digit next.
   1 tens and 4 tens
3. Choose the greater number. The number with the bigger place values is greater.
   641 is greater
4. Write the answer.
   641

Check. 641 is the bigger number, so the sign points to it. ✓

Watch out. Do not compare the ones first. Start with the hundreds.

Key words. > means greater than. < means less than. = means equal to. The wide end of the sign faces the bigger number.

Method. Compare the hundreds digits, then the tens and ones if needed.

1. Look at the hundreds digits. Two of the numbers have 2 hundreds. One has 7 hundreds.
   207: 2; 270: 2; 702: 7
2. Choose the biggest hundreds digit. 702 has the most hundreds, so it is the largest number.
   702 is the largest
3. Write the answer.
   702

Check. 702 is more than 270, and 270 is more than 207. ✓

Watch out. Compare the hundreds first. The 7 is the biggest digit in the hundreds place.

Key words. > means greater than. < means less than. = means equal to. The wide end of the sign faces the bigger number.

Method. Compare the hundreds, then the tens, then the ones.

1. Look at the hundreds digit of each number. The hundreds digit gives the first clue.
   503 has 5 hundreds, 530 has 5 hundreds, 305 has 3 hundreds, 350 has 3 hundreds
2. Put the numbers in order. If two hundreds digits are the same, compare the tens. Then compare the ones.
   305 → 350 → 503 → 530
3. Write the answer. The numbers go from smallest to largest.
   305, 350, 503, 530

Check. The first number is the smallest, and the last is the largest. ✓

Watch out. Compare the tens and ones only when the hundreds are the same.

Key words. > means greater than. < means less than. = means equal to. The wide end of the sign faces the bigger number.

Method. Compare the tens digits, because the hundreds are the same.

1. Compare the hundreds. Both numbers have 3 hundreds.
   349 has 3 hundreds, and 352 has 3 hundreds
2. Compare the tens. Five tens is more than four tens.
   5 tens is more than 4 tens
3. Decide. The tens are compared before the ones, so 352 is greater.
   No. 352 is bigger, because 5 tens is more than 4 tens.

Check. 349 is less than 352. ✓

Watch out. The 9 in 349 is in the ones place. It is worth less than the 5 tens in 352.

Key words. > means greater than. < means less than. = means equal to. The wide end of the sign faces the bigger number.

Method. Compare the hundreds, then the tens of any bags that have the same hundreds.

1. Look at the hundreds. Bag C has 3 hundreds, and bags A and B have 2 hundreds.
   C: 3 hundreds; A and B: 2 hundreds
2. Bag C has the most hundreds. So Bag C has more beads than Bag A and Bag B.
   306 is greater than 286 and 268
3. Write the answer.
   Bag C

Check. 286 and 268 are both less than 306. ✓

Watch out. Compare the hundreds first. You do not need to look at the ones here.

Key words. > means greater than. < means less than. = means equal to. The wide end of the sign faces the bigger number.

Method. Make the largest number with the biggest digit first, and the smallest with the smallest digit first.

1. Make the largest number. Put the biggest digit in the hundreds place, then the next biggest.
   853
2. Make the smallest number. Put the smallest digit in the hundreds place, then the next smallest.
   358
3. Find the difference. Subtract the smaller number from the larger one.
   853 − 358 = 495
4. Write the answer.
   495

Check. 358 + 495 = 853. ✓

Watch out. The smallest three-digit number cannot start with 0.

Key words. On a number line the numbers get bigger as you move to the right. An estimate is a sensible guess that is close to the true value.

Method. Count the steps from a mark you know, then work out the value.

1. Find the two marks the arrow is between. The marks go up by 10.
   500 and 510 are the first two marks
2. Count the steps from the start mark. Each step is 10.
   540 is 4 steps from 500
3. Work out the value. Multiply the steps by the step size, then add the start.
   500 + 4 × 10 = 540
4. Write the answer.
   540

Check. 4 steps of 10 from 500 is 540. ✓

Watch out. Check that the value is between the two marks on either side of it.

Key words. On a number line the numbers get bigger as you move to the right. An estimate is a sensible guess that is close to the true value.

Method. Count the steps from a mark you know, then work out the value.

1. Find the two marks the arrow is between. The marks go up by 20.
   200 and 220 are the first two marks
2. Count the steps from the start mark. Each step is 20.
   260 is 3 steps from 200
3. Work out the value. Multiply the steps by the step size, then add the start.
   200 + 3 × 20 = 260
4. Write the answer.
   260

Check. 3 steps of 20 from 200 is 260. ✓

Watch out. Check that the value is between the two marks on either side of it.

Key words. On a number line the numbers get bigger as you move to the right. An estimate is a sensible guess that is close to the true value.

Method. Find the middle of 700 and 800.

1. Find the two marks. The arrow is between 700 and 800.
   700 and 800
2. Find the middle. Halfway is the average of the two marks.
   (700 + 800) ÷ 2 = 750
3. Write the answer.
   750

Check. 750 − 700 = 50, and 800 − 750 = 50. ✓

Watch out. Halfway between two marks is half the distance between them.

Key words. On a number line the numbers get bigger as you move to the right. An estimate is a sensible guess that is close to the true value.

Method. Find the two hundreds that 450 is between.

1. Look at the marks. The marks are 100 apart.
   0, 100, 200, 300, 400, 500
2. Find where 450 sits. 450 is more than 400 and less than 500.
   400 is less than 450, and 450 is less than 500
3. Write the answer.
   400 and 500

Check. 450 is halfway between 400 and 500. ✓

Watch out. 450 is exactly halfway, so it is between the two marks.

Key words. On a number line the numbers get bigger as you move to the right. An estimate is a sensible guess that is close to the true value.

Method. Compare the distance from 500 to each number.

1. Find the distance from 500 to 430. Count the steps from 500 down to 430.
   500 − 430 = 70
2. Find the distance from 500 to 580. Count the steps from 500 up to 580.
   580 − 500 = 80
3. Compare. The smaller distance is the nearer number.
   70 is less than 80
4. Write the answer.
   430

Check. 430 is 70 away from 500, and 580 is 80 away. ✓

Watch out. Find the distance from 500 to each number, not just the number itself.

Key words. A count in steps jumps by the same amount each time. The numbers we say are multiples of the step: 8, 16 and 24 are multiples of 8.

Method. Count on in tens from 320, one step for each ten.

1. Start at 320. The first mark is 320.
   320
2. Count on 5 tens. Each step is 10, and we need 5 steps.
   330, 340, 350, 360, 370
3. Write the answer. The last number you say is the arrow.
   370

Check. 320 + 5 × 10 = 370. ✓

Watch out. Each step is 10, so 5 tens is 50.

Key words. A digit is one of the figures 0 to 9. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones.

Method. Work out the value of the bags, then add the loose beads.

1. Count the bags. Each bag holds 100 beads.
   4 bags = 4 × 100 = 400
2. Add the loose beads. The 27 loose beads are added to the bags.
   400 + 27 = 427
3. Write the answer.
   427

Check. 427 = 4 hundreds, 2 tens and 7 ones. ✓

Watch out. Each bag is a hundred, so do not count it as 4 beads.

Key words. More means add. Less means take away. When you change a number by 10 or 100, the number changes in one place value.

Method. Take the apples away first, then add the new apples.

1. Take away the apples sold. The shop sells 10 apples.
   580 − 10 = 570
2. Add the new apples. 100 more apples arrive.
   570 + 100 = 670
3. Write the answer.
   670

Check. 670 − 100 = 570, and 570 + 10 = 580. ✓

Watch out. Check that the answer makes sense: more apples arrived than were sold.

Key words. On a number line the numbers get bigger as you move to the right. An estimate is a sensible guess that is close to the true value.

Method. Use the bar model. Take the balcony seats away from the total.

1. Read the total. The hall has 400 seats in all.
   400 seats
2. Take away the balcony seats. The 150 balcony seats are not on the ground floor.
   400 − 150 = 250
3. Check. Add the two parts to see if you get the total.
   250 + 150 = 400
4. Write the answer.
   250

Check. 250 + 150 = 400. ✓

Watch out. Check your answer by adding the two parts back to the total.

Key words. A digit is one of the figures 0 to 9. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones.

Method. Work out the value of 1 hundred and 3 tens, then check the digits.

1. Work out 1 hundred. One hundred is 100.
   1 hundred = 100
2. Work out 3 tens. Three tens is 30.
   3 tens = 30
3. Add them. The number is 100 + 30.
   100 + 30 = 130
4. Write the answer. Ravi put the 3 in the ones place by mistake.
   Ava is right. It is 130.

Check. Ravi's number 103 has 3 ones, not 3 tens. ✓

Watch out. The 3 must go in the tens place, not the ones place.

Key words. A digit is one of the figures 0 to 9. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones.

Method. Divide the number by 10 to find how many tens it has.

1. Look at the number. The question asks for the tens in the whole number, not one digit.
   470
2. Divide by 10. Each ten is 10 ones, so divide by 10.
   470 ÷ 10 = 47
3. Write the answer.
   47

Check. 47 × 10 = 470. ✓

Watch out. The digit 7 is in the tens place, but there are 47 tens altogether.

Key words. A digit is one of the figures 0 to 9. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones.

Method. The value of a digit depends on its place.

1. Find the digit in the tens place. Look at that place in the number.
   596: the digit is 9
2. Work out its value. Each ten is worth 10.
   9 × 10 = 90
3. Write the answer. The value is the digit times the place, not just the digit.
   90

Check. 500 + 90 + 6 = 596, so the tens part is 90. ✓

Watch out. The digit is 9, but its value is 90.

Key words. A numeral is a number written with digits, such as 352. A number word is a number written in words, such as three hundred and fifty-two.

Method. Say the hundreds, then "and", then the tens and ones.

1. Say the hundreds. The first digit tells us the hundreds.
   4 hundreds = four hundred
2. Say the tens and ones. Read the last two digits together.
   0 tens and 6 ones = six
3. Join them with "and". UK English puts "and" between the hundreds and the tens and ones.
   four hundred and six
4. Write the answer.
   four hundred and six

Check. Read the words back: four hundred and six is 406. ✓

Watch out. Put "and" after the hundreds. Do not write "and" if there are no tens or ones.

Key words. A numeral is a number written with digits, such as 352. A number word is a number written in words, such as three hundred and fifty-two.

Method. Write the hundreds first, then the tens, then the ones.

1. Find the hundreds word. The word before "hundred" gives the hundreds digit.
   nine hundred → 9 hundreds = 900
2. Find the tens and ones. The words after "and" are the last two digits.
   twenty → 20
3. Put the digits in order. Write the hundreds, then the tens, then the ones. Use 0 for an empty place.
   9 2 0 → 920
4. Write the answer.
   920

Check. 900 + 20 = 920, so the digits are right. ✓

Watch out. A zero in the tens place is still a digit. Do not leave the place out.

Key words. A count in steps jumps by the same amount each time. The numbers we say are multiples of the step: 8, 16 and 24 are multiples of 8.

Method. Count on in steps of 50.

1. Start at the number we are counting from. We start at 200.
   200
2. Add 50 to find the next number. The step is always 50.
   200 + 50 = 250
3. Add 50 to find the next number. The step is always 50.
   250 + 50 = 300
4. Add 50 to find the next number. The step is always 50.
   300 + 50 = 350
5. Write the answer. Say the numbers in order.
   250, 300, 350

Check. 200 + 3 × 50 = 350. ✓

Watch out. Keep the step the same every time. Each number is one step from the number before it.

Key words. A count in steps jumps by the same amount each time. The numbers we say are multiples of the step: 8, 16 and 24 are multiples of 8.

Method. Count back in steps of 4.

1. Start at the number we are counting from. We start at 40.
   40
2. Take 4 away to find the next number. The step is always 4.
   40 − 4 = 36
3. Take 4 away to find the next number. The step is always 4.
   36 − 4 = 32
4. Take 4 away to find the next number. The step is always 4.
   32 − 4 = 28
5. Write the answer. Say the numbers in order.
   36, 32, 28

Check. 40 − 3 × 4 = 28. ✓

Watch out. Keep the step the same every time. Each number is one step from the number before it.

Key words. More means add. Less means take away. When you change a number by 10 or 100, the number changes in one place value.

Method. 100 less changes the hundreds place, and the other places stay the same.

1. Write the number in place-value columns. Hundreds, tens and ones.
   8 hundreds, 4 tens, 5 ones
2. Change the hundreds digit. 100 less changes the hundreds place.
   8 hundreds − 1 hundred = 7 hundreds
3. Keep the other places the same. Only the place that changed moves.
   7 hundreds, 4 tens, 5 ones
4. Write the answer.
   745

Check. 745 + 100 = 845. ✓

Watch out. Only change the place that is named. Watch for a change that crosses a hundred.

Key words. More means add. Less means take away. When you change a number by 10 or 100, the number changes in one place value.

Method. 10 more changes the tens place, and the other places stay the same.

1. Write the number in place-value columns. Hundreds, tens and ones.
   6 hundreds, 9 tens, 9 ones
2. Change the tens digit. 10 more changes the tens place.
   9 tens + 1 ten = 10 tens, and 10 tens make 1 hundred. So 0 tens and 1 more hundred
3. Keep the other places the same. Only the place that changed moves.
   7 hundreds, 0 tens, 9 ones
4. Write the answer.
   709

Check. 709 − 10 = 699. ✓

Watch out. Only change the place that is named. Watch for a change that crosses a hundred.

Key words. > means greater than. < means less than. = means equal to. The wide end of the sign faces the bigger number.

Method. Compare the hundreds first, then the tens, then the ones.

1. Compare the hundreds digits. Start on the left. The bigger hundreds digit gives the bigger number.
   480 has 4 hundreds, 408 has 4 hundreds
2. The hundreds are the same, so compare the tens. Look at the middle digit next.
   8 tens and 0 tens
3. Choose the sign. The wide end of the sign faces the bigger number.
   480 > 408
4. Write the answer.
   >

Check. 480 is the bigger number, so the sign points to it. ✓

Watch out. Do not compare the ones first. Start with the hundreds.

Key words. > means greater than. < means less than. = means equal to. The wide end of the sign faces the bigger number.

Method. Compare the hundreds, then the tens, then the ones.

1. Look at the hundreds digit of each number. The hundreds digit gives the first clue.
   317 has 3 hundreds, 371 has 3 hundreds, 137 has 1 hundreds, 713 has 7 hundreds
2. Put the numbers in order. If two hundreds digits are the same, compare the tens. Then compare the ones.
   137 → 317 → 371 → 713
3. Write the answer. The numbers go from smallest to largest.
   137, 317, 371, 713

Check. The first number is the smallest, and the last is the largest. ✓

Watch out. Compare the tens and ones only when the hundreds are the same.

Key words. A digit is one of the figures 0 to 9. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones.

Method. The value of a digit depends on its place.

1. Find the digit in the tens place. Look at that place in the number.
   436: the digit is 3
2. Work out its value. Each ten is worth 10.
   3 × 10 = 30
3. Write the answer. The value is the digit times the place, not just the digit.
   30

Check. 400 + 30 + 6 = 436, so the tens part is 30. ✓

Watch out. The digit is 3, but its value is 30.

Key words. A numeral is a number written with digits, such as 352. A number word is a number written in words, such as three hundred and fifty-two.

Method. Say the hundreds, then "and", then the tens and ones.

1. Say the hundreds. The first digit tells us the hundreds.
   5 hundreds = five hundred
2. Say the tens and ones. Read the last two digits together.
   3 tens and 0 ones = thirty
3. Join them with "and". UK English puts "and" between the hundreds and the tens and ones.
   five hundred and thirty
4. Write the answer.
   five hundred and thirty

Check. Read the words back: five hundred and thirty is 530. ✓

Watch out. Put "and" after the hundreds. Do not write "and" if there are no tens or ones.

Key words. A numeral is a number written with digits, such as 352. A number word is a number written in words, such as three hundred and fifty-two.

Method. Write the hundreds first, then the tens, then the ones.

1. Find the hundreds word. The word before "hundred" gives the hundreds digit.
   six hundred → 6 hundreds = 600
2. Find the tens and ones. The words after "and" are the last two digits.
   four → 4
3. Put the digits in order. Write the hundreds, then the tens, then the ones. Use 0 for an empty place.
   6 0 4 → 604
4. Write the answer.
   604

Check. 600 + 4 = 604, so the digits are right. ✓

Watch out. A zero in the tens place is still a digit. Do not leave the place out.

Key words. A count in steps jumps by the same amount each time. The numbers we say are multiples of the step: 8, 16 and 24 are multiples of 8.

Method. Count on in steps of 8.

1. Start at the number we are counting from. We start at 56.
   56
2. Add 8 to find the next number. The step is always 8.
   56 + 8 = 64
3. Add 8 to find the next number. The step is always 8.
   64 + 8 = 72
4. Add 8 to find the next number. The step is always 8.
   72 + 8 = 80
5. Write the answer. Say the numbers in order.
   64, 72, 80

Check. 56 + 3 × 8 = 80. ✓

Watch out. Keep the step the same every time. Each number is one step from the number before it.

Key words. More means add. Less means take away. When you change a number by 10 or 100, the number changes in one place value.

Method. 100 less changes the hundreds place, and the other places stay the same.

1. Write the number in place-value columns. Hundreds, tens and ones.
   5 hundreds, 4 tens, 0 ones
2. Change the hundreds digit. 100 less changes the hundreds place.
   5 hundreds − 1 hundred = 4 hundreds
3. Keep the other places the same. Only the place that changed moves.
   4 hundreds, 4 tens, 0 ones
4. Write the answer.
   440

Check. 440 + 100 = 540. ✓

Watch out. Only change the place that is named. Watch for a change that crosses a hundred.

Key words. More means add. Less means take away. When you change a number by 10 or 100, the number changes in one place value.

Method. Change the tens digit, then check the answer.

1. Look at the tens digit of 386. Ten more changes the tens digit only.
   8 tens
2. Add 10. Eight tens plus one ten is nine tens.
   386 + 10 = 396
3. Decide. Ben is right: only the tens digit changed.
   Yes. 386 + 10 = 396, and only the tens digit changed.

Check. 396 − 10 = 386. ✓

Watch out. Adding 10 does not change the hundreds or the ones.

Key words. > means greater than. < means less than. = means equal to. The wide end of the sign faces the bigger number.

Method. Compare the hundreds, then the tens, then the ones.

1. Look at the hundreds digit of each number. The hundreds digit gives the first clue.
   402 has 4 hundreds, 420 has 4 hundreds, 240 has 2 hundreds
2. Put the numbers in order. If two hundreds digits are the same, compare the tens. Then compare the ones.
   420 → 402 → 240
3. Write the answer. The numbers go from largest to smallest.
   420, 402, 240

Check. The first number is the largest, and the last is the smallest. ✓

Watch out. Compare the tens and ones only when the hundreds are the same.

Key words. A digit is one of the figures 0 to 9. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones.

Method. Work out how many beads she has, then take away the 10 she gives away.

1. Write the number of beads. 3 bags of 100, 4 tens and 6 ones.
   300 + 40 + 6 = 346
2. Take away the 10 beads she gives away. She has 10 fewer now.
   346 − 10 = 336
3. Write the answer.
   336

Check. 336 + 10 = 346. ✓

Watch out. Work out the number first, then take away the beads.

Key words. A digit is one of the figures 0 to 9. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones.

Method. Read each digit from the place it is in.

1. Read the hundreds digit. The first digit of 709 is 7.
   7 hundreds
2. Read the tens digit. The middle digit is 0, so there are no tens.
   0 tens
3. Read the ones digit. The last digit is 9.
   9 ones
4. Decide. Leo has mixed up the tens and hundreds.
   No. 709 has 7 hundreds, 0 tens and 9 ones.

Check. 700 + 0 + 9 = 709. ✓

Watch out. The 7 is in the hundreds place. The tens place is empty.