Level 3 check

Method. Count back in tens by adding or taking away 10 each time.

1. Start at 960. We count from this number.
   960
2. Take 10 each time. We count back in tens.
   960 - 10 = 950; 950 - 10 = 940
3. Write the numbers in order. These are the next numbers we said.
   950, 940, 930

Check. Count on in tens from 930 to check. You reach 960.

Watch out. The step is 10. Each new number is 10 less than the last.

Method. Count back in tens by adding or taking away 10 each time.

1. Start at 180. We count from this number.
   180
2. Take 10 each time. We count back in tens.
   180 - 10 = 170; 170 - 10 = 160
3. Write the numbers in order. These are the next numbers we said.
   170, 160, 150

Check. Count on in tens from 150 to check. You reach 180.

Watch out. The step is 10. Each new number is 10 less than the last.

Method. The hundreds digit tells us how many whole hundreds there are.

1. Look at the hundreds digit in 543. The hundreds digit tells us how many hundreds.
   The hundreds digit is 5
2. Count the whole hundreds. The tens and ones are not whole hundreds, so we leave them out.
   543 is 5 hundreds and 43 more
3. Write the answer. This is the number of whole hundreds.
   5

Check. 5 hundreds is 500, which is the start of 543.

Watch out. Count the hundreds digit, not the whole number.

Method. Count back in tens by adding or taking away 10 each time.

1. Start at 770. We count from this number.
   770
2. Take 10 each time. We count back in tens.
   770 - 10 = 760; 760 - 10 = 750
3. Write the numbers in order. These are the next numbers we said.
   760, 750, 740

Check. Count on in tens from 740 to check. You reach 770.

Watch out. The step is 10. Each new number is 10 less than the last.

Method. Find the digit, then multiply it by its place value. A tens digit is worth 10.

1. Find the tens digit in 256. The tens digit is in the tens column.
   tens digit = 5
2. Multiply by the place value. Each tens digit stands for 10 at a time in this column.
   5 x 10 = 50
3. Write the answer. This is the value of the digit.
   50

Check. Check the other digits add to the number: 256 = 206 + 50.

Watch out. The value is the digit times the place. It is not just the digit.

Method. Use the hundreds first, then the tens and ones.

1. Find the hundreds word. The number before hundred tells us the hundreds.
   four hundred = 400
2. Find the tens and ones words. Read the words after and.
   twenty-six = 26
3. Add them together. The hundreds and the rest make the number.
   400 + 26 = 426
4. Write the answer.
   426

Check. Say it back: 426 is four hundred and twenty-six.

Watch out. Hundreds come first. Write the digits in the right columns: hundreds, tens, ones.

Method. Find the hundreds either side. The nearer one is the answer.

1. Find the hundreds either side of 748. These are the two hundreds the number is between.
   700 and 800
2. Find which hundred is nearer. 748 - 700 = 48, and 800 - 748 = 52.
   48 is less than 52
3. Write the nearest hundred. This is the answer.
   700

Check. 700 is 48 away from 748, and the other hundred is further away.

Watch out. Look at the tens and ones. If they are 50 or more, round up. If less than 50, round down.

Method. Change only the hundreds digit when we go less than the number.

1. Start at 563. We begin with this number.
   563
2. Change the hundreds digit. Only the hundreds digit changes. The others stay the same.
   563 - 100 = 463
3. Write the answer. This is the new number.
   463

Check. 100 more than 463 is 563. It works.

Watch out. Only the hundreds digit changes. Keep the other digits the same.

Method. Find the hundreds either side. The nearer one is the answer.

1. Find the hundreds either side of 906. These are the two hundreds the number is between.
   900 and 1000
2. Find which hundred is nearer. 906 - 900 = 6, and 1000 - 906 = 94.
   6 is less than 94
3. Write the nearest hundred. This is the answer.
   900

Check. 900 is 6 away from 906, and the other hundred is further away.

Watch out. Look at the tens and ones. If they are 50 or more, round up. If less than 50, round down.

Method. Change only the tens digit when we go more than the number.

1. Start at 868. We begin with this number.
   868
2. Change the tens digit. Only the tens digit changes. The others stay the same.
   868 + 10 = 878
3. Write the answer. This is the new number.
   878

Check. 10 less than 878 is 868. It works.

Watch out. Only the tens digit changes. Keep the other digits the same.

Method. Compare the hundreds first. If they are the same, compare the tens. Then compare the ones.

1. Start with the hundreds digits. The digit in the largest place decides first.
   3 and 2
2. The hundreds decide. 3 is more than 2 in the hundreds place.
   3 and 2
3. Write the sign. 338 is greater than 237.
   >

Check. 338 > 237 is true.

Watch out. Compare from the left. 338 is greater than 237.

Method. Change only the ones digit when we go more than the number.

1. Start at 458. We begin with this number.
   458
2. Change the ones digit. Only the ones digit changes. The others stay the same.
   458 + 1 = 459
3. Write the answer. This is the new number.
   459

Check. 1 less than 459 is 458. It works.

Watch out. Only the ones digit changes. Keep the other digits the same.

Method. Find the digit, then multiply it by its place value. A tens digit is worth 10.

1. Find the tens digit in 630. The tens digit is in the tens column.
   tens digit = 3
2. Multiply by the place value. Each tens digit stands for 10 at a time in this column.
   3 x 10 = 30
3. Write the answer. This is the value of the digit.
   30

Check. Check the other digits add to the number: 630 = 600 + 30.

Watch out. The value is the digit times the place. It is not just the digit.

Method. Split the number by its places, then write each part.

1. Find the hundreds, tens and ones of 126. Read the place value table.
   1 hundreds, 2 tens, 6 ones
2. Write each part as a number. Each part is the digit times its place value.
   100 + 20 + 6
3. Write the answer. The parts add up to the number.
   100 + 20 + 6

Check. Add the parts: 100 + 20 + 6 = 126.

Watch out. Leave out a part that is zero. 204 is 200 + 4.

Method. Use the hundreds first, then the tens and ones.

1. Say the hundreds in words. Hundreds come first.
   539 has 5 hundreds: five hundred
2. Say the tens and ones in words. Say the number after hundred.
   thirty-nine
3. Join them with "and". British English puts and before the tens and ones.
   five hundred and thirty-nine

Check. Say it back: 539 is five hundred and thirty-nine.

Watch out. Write hundred and then and before the tens and ones, like three hundred and seven.

Method. Start at the number and count on or back, one number at a time.

1. Start at 273. We begin with this number.
   273
2. Count on 13. Say each new number as we go.
   273 + 13 = 286
3. Write the answer. This is the last number we reached.
   286

Check. Count back 13 from 286: you reach 273.

Watch out. Start from the number in the question. Do not start again from 1 or from 0.

Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.

1. Write the numbers in columns. Keep the ones under the ones and the tens under the tens.
   681 over 7
2. Exchange 1 ten for 10 ones. The ones on top (1) are fewer than the ones below (7), so we need more ones.
   8 tens become 7 tens, and the ones go from 1 to 11
3. Subtract the ones. 11 - 7 = 4.
   11 - 7 = 4
4. Subtract the tens. 7 - 0 = 7.
   7 - 0 = 7
5. Subtract the hundreds. 6 - 0 = 6.
   6 - 0 = 6
6. Write the answer. Read the columns from left to right.
   674

Check. Check: 674 + 7 = 681.

Watch out. Exchange a ten for ten ones when the ones on top are too small. Then take away.

Method. Add the ones, then the tens, then the hundreds. Carry any ten or hundred you make.

1. Write the numbers in columns. Keep the ones under the ones and the tens under the tens.
   759 over 115
2. Add the ones. The ones make 10 or more, so write the ones digit and carry 1 ten.
   9 + 5 = 14, write 4 and carry 1
3. Add the tens. Add the carried ten with the tens.
   5 + 1 + 1 carried = 7
4. Add the hundreds. Add any carried hundred too.
   7 + 1 = 8
5. Write the answer. Read the columns from left to right.
   874

Check. Check: 874 - 115 = 759.

Watch out. When the ones make 10 or more, carry a ten to the tens column. Do not forget it.

Method. Add the ones, then the tens, then the hundreds. Carry any ten or hundred you make.

1. Write the numbers in columns. Keep the ones under the ones and the tens under the tens.
   852 over 48
2. Add the ones. The ones make 10 or more, so write the ones digit and carry 1 ten.
   2 + 8 = 10, write 0 and carry 1
3. Add the tens. Add the carried ten with the tens. The tens make 10 or more, so write the tens digit and carry 1 hundred.
   5 + 4 + 1 carried = 10
4. Add the hundreds. Add any carried hundred too.
   8 + 0 + 1 carried = 9
5. Write the answer. Read the columns from left to right.
   900

Check. Check: 900 - 48 = 852.

Watch out. When the tens make 10 or more, carry a hundred to the hundreds column.

Method. Add the ones, then the tens, then the hundreds. Carry any ten or hundred you make.

1. Write the numbers in columns. Keep the ones under the ones and the tens under the tens.
   39 over 18
2. Add the ones. The ones make 10 or more, so write the ones digit and carry 1 ten.
   9 + 8 = 17, write 7 and carry 1
3. Add the tens. Add the carried ten with the tens.
   3 + 1 + 1 carried = 5
4. Write the answer. Read the columns from left to right.
   57

Check. Check: 57 - 18 = 39.

Watch out. When the ones make 10 or more, carry a ten to the tens column. Do not forget it.

Method. Add the ones, then the tens, then the hundreds. Carry any ten or hundred you make.

1. Write the numbers in columns. Keep the ones under the ones and the tens under the tens.
   837 over 27
2. Add the ones. The ones make 10 or more, so write the ones digit and carry 1 ten.
   7 + 7 = 14, write 4 and carry 1
3. Add the tens. Add the carried ten with the tens.
   3 + 2 + 1 carried = 6
4. Add the hundreds. Add any carried hundred too.
   8 + 0 = 8
5. Write the answer. Read the columns from left to right.
   864

Check. Check: 864 - 27 = 837.

Watch out. When the ones make 10 or more, carry a ten to the tens column. Do not forget it.

Method. Find the operation, then work out the total.

1. Find the operation. We are putting two amounts together, so we add.
   63 + 177
2. Work out the total. Use column addition with the ones first.
   63 + 177 = 240
3. Write the answer. This is the total in the question.
   240

Check. Check: 240 - 177 = 63.

Watch out. Look for words like more, altogether and in all. These mean add.

Method. Add the ones, then the tens, then the hundreds. Carry any ten or hundred you make.

1. Write the numbers in columns. Keep the ones under the ones and the tens under the tens.
   27 over 91
2. Add the ones. The ones make less than 10, so no ten is carried.
   7 + 1 = 8
3. Add the tens. There is no carried ten to add. The tens make 10 or more, so write the tens digit and carry 1 hundred.
   2 + 9 = 11
4. Add the hundreds. Add any carried hundred too.
   0 + 0 + 1 carried = 1
5. Write the answer. Read the columns from left to right.
   118

Check. Check: 118 - 91 = 27.

Watch out. When the tens make 10 or more, carry a hundred to the hundreds column.

Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.

1. Write the numbers in columns. Keep the ones under the ones and the tens under the tens.
   324 over 307
2. Exchange 1 ten for 10 ones. The ones on top (4) are fewer than the ones below (7), so we need more ones.
   2 tens become 1 tens, and the ones go from 4 to 14
3. Subtract the ones. 14 - 7 = 7.
   14 - 7 = 7
4. Subtract the tens. 1 - 0 = 1.
   1 - 0 = 1
5. Subtract the hundreds. 3 - 3 = 0.
   3 - 3 = 0
6. Write the answer. Read the columns from left to right.
   17

Check. Check: 17 + 307 = 324.

Watch out. Exchange a ten for ten ones when the ones on top are too small. Then take away.

Method. Find the operation, then work out what is left.

1. Find the operation. Words like left, gives and empty mean take away.
   345 - 167
2. Work out the answer. Use column subtraction, and exchange if needed.
   345 - 167 = 178
3. Write the answer. This is the number left.
   178

Check. Check: 178 + 167 = 345.

Watch out. Words like left, gone and gives away mean take away.

Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.

1. Write the numbers in columns. Keep the ones under the ones and the tens under the tens.
   825 over 549
2. Exchange 1 ten for 10 ones. The ones on top (5) are fewer than the ones below (9), so we need more ones.
   2 tens become 1 tens, and the ones go from 5 to 15
3. Exchange 1 hundred for 10 tens. The tens on top are fewer than the tens below (4 tens), so we need more tens.
   8 hundreds become 7 hundreds, and 1 tens become 11 tens
4. Subtract the ones. 15 - 9 = 6.
   15 - 9 = 6
5. Subtract the tens. 11 - 4 = 7.
   11 - 4 = 7
6. Subtract the hundreds. 7 - 5 = 2.
   7 - 5 = 2
7. Write the answer. Read the columns from left to right.
   276

Check. Check: 276 + 549 = 825.

Watch out. When a column is too small, exchange one from the column to its left. Ten ones make one ten, ten tens make one hundred.

Method. Find the operation, then work out the total.

1. Find the operation. We are putting two amounts together, so we add.
   395 + 48
2. Work out the total. Use column addition with the ones first.
   395 + 48 = 443
3. Write the answer. This is the total in the question.
   443

Check. Check: 443 - 48 = 395.

Watch out. Look for words like more, altogether and in all. These mean add.

Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.

1. Write the numbers in columns. Keep the ones under the ones and the tens under the tens.
   458 over 9
2. Exchange 1 ten for 10 ones. The ones on top (8) are fewer than the ones below (9), so we need more ones.
   5 tens become 4 tens, and the ones go from 8 to 18
3. Subtract the ones. 18 - 9 = 9.
   18 - 9 = 9
4. Subtract the tens. 4 - 0 = 4.
   4 - 0 = 4
5. Subtract the hundreds. 4 - 0 = 4.
   4 - 0 = 4
6. Write the answer. Read the columns from left to right.
   449

Check. Check: 449 + 9 = 458.

Watch out. Exchange a ten for ten ones when the ones on top are too small. Then take away.

Method. Add the ones, then the tens, then the hundreds. Carry any ten or hundred you make.

1. Write the numbers in columns. Keep the ones under the ones and the tens under the tens.
   589 over 9
2. Add the ones. The ones make 10 or more, so write the ones digit and carry 1 ten.
   9 + 9 = 18, write 8 and carry 1
3. Add the tens. Add the carried ten with the tens.
   8 + 0 + 1 carried = 9
4. Add the hundreds. Add any carried hundred too.
   5 + 0 = 5
5. Write the answer. Read the columns from left to right.
   598

Check. Check: 598 - 9 = 589.

Watch out. When the ones make 10 or more, carry a ten to the tens column. Do not forget it.

Method. Find the operation, then work out what is left.

1. Find the operation. Words like left, gives and empty mean take away.
   127 - 87
2. Work out the answer. Use column subtraction, and exchange if needed.
   127 - 87 = 40
3. Write the answer. This is the number left.
   40

Check. Check: 40 + 87 = 127.

Watch out. Words like left, gone and gives away mean take away.

Method. Add the ones, then the tens, then the hundreds. Carry any ten or hundred you make.

1. Write the numbers in columns. Keep the ones under the ones and the tens under the tens.
   961 over 9
2. Add the ones. The ones make 10 or more, so write the ones digit and carry 1 ten.
   1 + 9 = 10, write 0 and carry 1
3. Add the tens. Add the carried ten with the tens.
   6 + 0 + 1 carried = 7
4. Add the hundreds. Add any carried hundred too.
   9 + 0 = 9
5. Write the answer. Read the columns from left to right.
   970

Check. Check: 970 - 9 = 961.

Watch out. When the ones make 10 or more, carry a ten to the tens column. Do not forget it.

Method. Add the ones, then the tens, then the hundreds. Carry any ten or hundred you make.

1. Write the numbers in columns. Keep the ones under the ones and the tens under the tens.
   24 over 79
2. Add the ones. The ones make 10 or more, so write the ones digit and carry 1 ten.
   4 + 9 = 13, write 3 and carry 1
3. Add the tens. Add the carried ten with the tens. The tens make 10 or more, so write the tens digit and carry 1 hundred.
   2 + 7 + 1 carried = 10
4. Add the hundreds. Add any carried hundred too.
   0 + 0 + 1 carried = 1
5. Write the answer. Read the columns from left to right.
   103

Check. Check: 103 - 79 = 24.

Watch out. When the tens make 10 or more, carry a hundred to the hundreds column.

Method. Count in 10s to find 10 groups of 9. The order of the two numbers does not matter.

1. Count in 10s, 9 times. Each count adds one more group of 10.
   10, 20, 30, 40, 50, 60, 70, 80, 90
2. The last number we said is the answer. We counted in equal groups.
   10 × 9 = 90
3. Write the answer. The order of the numbers does not change the answer.
   90

Check. Check: 9 × 10 is also 90.

Watch out. Say the 10 times table in order until you reach the fact you need.

Method. Change to cm, work it out, then change back.

1. Change both to the smaller unit. 100 cm make one bigger unit.
   2 m 45 cm = 245 cm, 1 m 25 cm = 125 cm
2. Add the cm. Work with the numbers in cm.
   245 + 125 = 370
3. Change back to the bigger units. 370 cm is written with 100 cm as one bigger unit.
   370 cm = 3 m 70 cm
4. Write the answer. This is the answer.
   3 m 70 cm

Check. Check: 3 m 70 cm - 1 m 25 cm = 2 m 45 cm.

Watch out. Work in cm to avoid mistakes. Change back at the end.

Method. Repeated addition: add the same number once for each group.

1. Write one 3 for each group. There are 6 groups, so there are 6 lots of 3.
   3 + 3 + 3 + 3 + 3 + 3
2. Add them up. Add the groups one after another, or count in steps of the group size.
   3 + 3 + 3 + 3 + 3 + 3 = 18
3. Write the answer. This is the total altogether.
   18

Check. Count in 3s 6 times and you reach 18.

Watch out. Add 3 6 times. Do not add 6 3 times.

Method. Count in 5s to find 5 groups of 11. The order of the two numbers does not matter.

1. Count in 5s, 11 times. Each count adds one more group of 5.
   5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55
2. The last number we said is the answer. We counted in equal groups.
   5 × 11 = 55
3. Write the answer. The order of the numbers does not change the answer.
   55

Check. Check: 11 × 5 is also 55.

Watch out. Say the 5 times table in order until you reach the fact you need.

Method. Choose the unit that fits the size of the object.

1. Think about how big or heavy it is. A strawberry is about the size of a thing we can check easily.
   a strawberry
2. Choose the unit that fits. Heavy things are weighed in kilograms. Light things are weighed in grams.
   g
3. Write the answer. This is the unit to use.
   g

Check. Think of a thing that is about the same size, so you can picture the unit.

Watch out. Metres and kilograms are large. Centimetres and grams are small.

Method. A unit fraction has a 1 on top. The bottom number is the number of equal parts.

1. Count the equal parts. The bottom number is the number of equal parts.
   9 equal parts
2. One part is 1 of them. A unit fraction has 1 on top.
   1 part out of 9
3. Write the fraction. The top number is 1 for one part.
   1/9

Check. Check: 9 of these parts make the whole.

Watch out. One part of a shape split into four is 1/4.

Method. Use the 2, 5 or 10 facts. Count in steps of the number to find the missing number.

1. Think of the multiplication: 10 × ? = 60. Division asks how many groups.
   10 × ? = 60
2. Count in 10s until you reach 60. Count the steps as you go.
   10, 20, 30, 40, 50, 60
3. Write the answer. This is the number of groups.
   6

Check. Check: 10 × 6 = 60, so 60 ÷ 10 = 6.

Watch out. The times table of 10 is the key. Division is the opposite of multiplication.

Method. Count the equal parts for the bottom number, and the shaded parts for the top number.

1. Count the equal parts. The shape is split into 4 equal parts.
   4 equal parts
2. Count the shaded parts. 2 of the 4 parts are shaded.
   2 shaded
3. Write the fraction. The shaded parts go on top. The number of equal parts goes underneath.
   2/4

Check. Check: 2 shaded parts out of 4 equal parts.

Watch out. The bottom number counts all the equal parts, shaded or not.

Method. Repeated addition: add the same number once for each group.

1. Write one 3 for each group. There are 3 groups, so there are 3 lots of 3.
   3 + 3 + 3
2. Add them up. Add the groups one after another, or count in steps of the group size.
   3 + 3 + 3 = 9
3. Write the answer. This is the total altogether.
   9

Check. Count in 3s 3 times and you reach 9.

Watch out. Add 3 3 times. Do not add 3 3 times.

Method. Use the ruler: find the start and the end of the line, then the difference.

1. Find where the line starts. The line starts at this mark.
   start = 6 cm
2. Find where the line ends. The line ends at this mark.
   end = 15 cm
3. Subtract the start from the end. The length is the distance between the two marks.
   15 - 6 = 9
4. Write the length. This is how long the line is.
   9 cm

Check. Add the length to the start: 6 + 9 = 15 cm.

Watch out. Put the 0 of the ruler at the start of the line, then read the end.

Method. Use the 2, 5 or 10 facts. Count in steps of the number to find the missing number.

1. Think of the multiplication: 10 × ? = 20. Division asks how many groups.
   10 × ? = 20
2. Count in 10s until you reach 20. Count the steps as you go.
   10, 20
3. Write the answer. This is the number of groups.
   2

Check. Check: 10 × 2 = 20, so 20 ÷ 10 = 2.

Watch out. The times table of 10 is the key. Division is the opposite of multiplication.

Method. Use repeated addition, or count in steps of the group size.

1. Write 5 groups of 2 as repeated addition. Each pack or group has the same number.
   2 + 2 + 2 + 2 + 2
2. Add them up, or count in steps. Count in 2s, 5 times.
   2, 4, 6, 8, 10
3. Write the answer. This is the total altogether.
   10

Check. Count in 2s 5 times and you reach 10.

Watch out. Multiply 5 by 2: each group is 2.

Method. Two fractions are the same when they cover the same part of a shape.

1. Look at 1/5. We want a fraction with the same value.
   1/5
2. Compare each option with the target. 2/10 covers the same part of a shape as 1/5.
   2/10
3. Write the answer. This fraction is the same as the target.
   2/10

Check. Shade 1/5 and 2/10 on two shapes. They cover the same part.

Watch out. 2/4 and 1/2 are the same. Both mean the shape is split into halves.

Method. Count in 5s to find 5 groups of 12. The order of the two numbers does not matter.

1. Count in 5s, 12 times. Each count adds one more group of 5.
   5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60
2. The last number we said is the answer. We counted in equal groups.
   5 × 12 = 60
3. Write the answer. The order of the numbers does not change the answer.
   60

Check. Check: 12 × 5 is also 60.

Watch out. Say the 5 times table in order until you reach the fact you need.

Method. Use the ruler: find the start and the end of the line, then the difference.

1. Put the 0 at the start of the line. Line up the ruler so the line begins at 0.
   0 cm
2. Read where the line ends. The end of the line is on this number.
   The end is at 6
3. Write the length. The length is the end number, because we started at 0.
   6 cm

Check. Count the centimetres from 0 to 6: 6 cm.

Watch out. Put the 0 of the ruler at the start of the line, then read the end.

Method. Compare the hundreds first. If they are the same, compare the tens. Then compare the ones.

1. Start with the hundreds digits. The digit in the largest place decides first.
   8 and 7
2. The hundreds decide. 8 is more than 7 in the hundreds place.
   8 and 7
3. Write the sign. 896 is greater than 755.
   >

Check. 896 > 755 is true.

Watch out. Compare from the left. 896 is greater than 755.

Method. Add the ones, then the tens, then the hundreds. Carry any ten or hundred you make.

1. Write the numbers in columns. Keep the ones under the ones and the tens under the tens.
   71 over 55
2. Add the ones. The ones make less than 10, so no ten is carried.
   1 + 5 = 6
3. Add the tens. There is no carried ten to add. The tens make 10 or more, so write the tens digit and carry 1 hundred.
   7 + 5 = 12
4. Add the hundreds. Add any carried hundred too.
   0 + 0 + 1 carried = 1
5. Write the answer. Read the columns from left to right.
   126

Check. Check: 126 - 55 = 71.

Watch out. When the tens make 10 or more, carry a hundred to the hundreds column.

Method. Add the ones, then the tens, then the hundreds. Carry any ten or hundred you make.

1. Write the numbers in columns. Keep the ones under the ones and the tens under the tens.
   57 over 18
2. Add the ones. The ones make 10 or more, so write the ones digit and carry 1 ten.
   7 + 8 = 15, write 5 and carry 1
3. Add the tens. Add the carried ten with the tens.
   5 + 1 + 1 carried = 7
4. Write the answer. Read the columns from left to right.
   75

Check. Check: 75 - 18 = 57.

Watch out. When the ones make 10 or more, carry a ten to the tens column. Do not forget it.

Method. Find the total, then look at its last digit.

1. Work out the total. Use repeated addition or multiplication.
   3 + 3 + 3 + 3 = 12
2. Look at the last digit. Even numbers end in 0, 2, 4, 6 or 8. Odd numbers end in 1, 3, 5, 7 or 9.
   12 ends in 2
3. Write the answer. 12 is even.
   even

Check. Share 12 into two equal groups: yes, with none left.

Watch out. An even number can be shared into two equal groups with none left over.

Method. Use repeated addition, or count in steps of the group size.

1. Write 9 groups of 10 as repeated addition. Each pack or group has the same number.
   10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10
2. Add them up, or count in steps. Count in 10s, 9 times.
   10, 20, 30, 40, 50, 60, 70, 80, 90
3. Write the answer. This is the total altogether.
   90

Check. Count in 10s 9 times and you reach 90.

Watch out. Multiply 9 by 10: each group is 10.

Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.

1. Write the numbers in columns. Keep the ones under the ones and the tens under the tens.
   452 over 363
2. Exchange 1 ten for 10 ones. The ones on top (2) are fewer than the ones below (3), so we need more ones.
   5 tens become 4 tens, and the ones go from 2 to 12
3. Exchange 1 hundred for 10 tens. The tens on top are fewer than the tens below (6 tens), so we need more tens.
   4 hundreds become 3 hundreds, and 4 tens become 14 tens
4. Subtract the ones. 12 - 3 = 9.
   12 - 3 = 9
5. Subtract the tens. 14 - 6 = 8.
   14 - 6 = 8
6. Subtract the hundreds. 3 - 3 = 0.
   3 - 3 = 0
7. Write the answer. Read the columns from left to right.
   89

Check. Check: 89 + 363 = 452.

Watch out. When a column is too small, exchange one from the column to its left. Ten ones make one ten, ten tens make one hundred.

Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.

1. Write the numbers in columns. Keep the ones under the ones and the tens under the tens.
   23 over 15
2. Exchange 1 ten for 10 ones. The ones on top (3) are fewer than the ones below (5), so we need more ones.
   2 tens become 1 tens, and the ones go from 3 to 13
3. Subtract the ones. 13 - 5 = 8.
   13 - 5 = 8
4. Subtract the tens. 1 - 1 = 0.
   1 - 1 = 0
5. Write the answer. Read the columns from left to right.
   8

Check. Check: 8 + 15 = 23.

Watch out. Exchange a ten for ten ones when the ones on top are too small. Then take away.

Method. Use the ruler: find the start and the end of the line, then the difference.

1. Find where the line starts. The line starts at this mark.
   start = 4 cm
2. Find where the line ends. The line ends at this mark.
   end = 6 cm
3. Subtract the start from the end. The length is the distance between the two marks.
   6 - 4 = 2
4. Write the length. This is how long the line is.
   2 cm

Check. Add the length to the start: 4 + 2 = 6 cm.

Watch out. Put the 0 of the ruler at the start of the line, then read the end.

Method. Use the 2, 5 or 10 facts. Count in steps of the number to find the missing number.

1. Count in 5s until you reach 45. Each count is one group.
   5, 10, 15, 20, 25, 30, 35, 40, 45
2. Count the numbers you said. There are 9 numbers, so there are 9 groups.
   9 groups
3. Write the answer. This is the number of groups.
   9

Check. Check: 5 × 9 = 45.

Watch out. The times table of 5 is the key. Division is the opposite of multiplication.

Method. Count in 5s to find 5 groups of 10. The order of the two numbers does not matter.

1. Count in 5s, 10 times. Each count adds one more group of 5.
   5, 10, 15, 20, 25, 30, 35, 40, 45, 50
2. The last number we said is the answer. We counted in equal groups.
   5 × 10 = 50
3. Write the answer. The order of the numbers does not change the answer.
   50

Check. Check: 10 × 5 is also 50.

Watch out. Say the 5 times table in order until you reach the fact you need.

Method. Groups of is multiply. Write the sentence, then find the total.

1. Read it as 2 groups of 2. The first number tells how many groups.
   2 groups of 2
2. Write the repeated addition. Add the group size once for each group.
   2 + 2 = 4
3. Write the answer in the box. This is the missing number.
   4

Check. Check: 2 + 2 gives 4.

Watch out. The number in front is the number of groups. The number after is the size of each group.

Method. Find the total, then look at its last digit.

1. Work out the total. Use repeated addition or multiplication.
   6 + 6 + 6 = 18
2. Look at the last digit. Even numbers end in 0, 2, 4, 6 or 8. Odd numbers end in 1, 3, 5, 7 or 9.
   18 ends in 8
3. Write the answer. 18 is even.
   even

Check. Share 18 into two equal groups: yes, with none left.

Watch out. An even number can be shared into two equal groups with none left over.

Method. Count back in twos by adding or taking away 2 each time.

1. Start at 89. We count from this number.
   89
2. Take 2 each time. We count back in twos.
   89 - 2 = 87; 87 - 2 = 85
3. Write the numbers in order. These are the next numbers we said.
   87, 85, 83

Check. Count on in twos from 83 to check. You reach 89.

Watch out. The step is 2. Each new number is 2 less than the last.

Method. Split the amount into equal parts, then take the parts the fraction asks for.

1. Split the 16 beads into 2 equal groups. Each group is one part of the whole.
   16 ÷ 2 = 8
2. Take 1 of the groups for the box. 1/2 is 1 of the 2 equal parts.
   1 × 8 = 8
3. Write the answer. This is the number in the box.
   8

Check. Check: 8 is 1 of the 2 equal groups of 8.

Watch out. Work out one part first, then take the number of parts.

Method. Put the numbers in order, largest to smallest. Compare hundreds first, then tens, then ones.

1. Compare the hundreds of each number. The number with fewer hundreds is smaller.
   338: 3 hundreds, 235: 2 hundreds, 718: 7 hundreds, 819: 8 hundreds, 517: 5 hundreds
2. Find the first number in the order. It is the smallest, or the largest if we go the other way.
   819
3. Write all the numbers in order. Check each one fits between the ones next to it.
   819, 718, 517, 338, 235

Check. Read the list again. Each number is smaller than the one before it.

Watch out. Compare hundreds first. 508 is less than 521, because 5 hundreds is the same but 0 tens is less than 2 tens.

Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.

1. Write the numbers in columns. Keep the ones under the ones and the tens under the tens.
   91 over 18
2. Exchange 1 ten for 10 ones. The ones on top (1) are fewer than the ones below (8), so we need more ones.
   9 tens become 8 tens, and the ones go from 1 to 11
3. Subtract the ones. 11 - 8 = 3.
   11 - 8 = 3
4. Subtract the tens. 8 - 1 = 7.
   8 - 1 = 7
5. Write the answer. Read the columns from left to right.
   73

Check. Check: 73 + 18 = 91.

Watch out. Exchange a ten for ten ones when the ones on top are too small. Then take away.

Method. Use repeated addition, or count in steps of the group size.

1. Write 5 groups of 2 as repeated addition. Each pack or group has the same number.
   2 + 2 + 2 + 2 + 2
2. Add them up, or count in steps. Count in 2s, 5 times.
   2, 4, 6, 8, 10
3. Write the answer. This is the total altogether.
   10

Check. Count in 2s 5 times and you reach 10.

Watch out. Multiply 5 by 2: each group is 2.

Method. Count in 2s to find 2 groups of 11. The order of the two numbers does not matter.

1. Count in 2s, 11 times. Each count adds one more group of 2.
   2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22
2. The last number we said is the answer. We counted in equal groups.
   2 × 11 = 22
3. Write the answer. The order of the numbers does not change the answer.
   22

Check. Check: 11 × 2 is also 22.

Watch out. Say the 2 times table in order until you reach the fact you need.

Method. Add the ones, then the tens, then the hundreds. Carry any ten or hundred you make.

1. Write the numbers in columns. Keep the ones under the ones and the tens under the tens.
   628 over 5
2. Add the ones. The ones make 10 or more, so write the ones digit and carry 1 ten.
   8 + 5 = 13, write 3 and carry 1
3. Add the tens. Add the carried ten with the tens.
   2 + 0 + 1 carried = 3
4. Add the hundreds. Add any carried hundred too.
   6 + 0 = 6
5. Write the answer. Read the columns from left to right.
   633

Check. Check: 633 - 5 = 628.

Watch out. When the ones make 10 or more, carry a ten to the tens column. Do not forget it.

Method. Count in 10s to find 10 groups of 5. The order of the two numbers does not matter.

1. Count in 10s, 5 times. Each count adds one more group of 10.
   10, 20, 30, 40, 50
2. The last number we said is the answer. We counted in equal groups.
   10 × 5 = 50
3. Write the answer. The order of the numbers does not change the answer.
   50

Check. Check: 5 × 10 is also 50.

Watch out. Say the 10 times table in order until you reach the fact you need.

Method. Split the number by its places, then write each part.

1. Find the hundreds, tens and ones of 263. Read the place value table.
   2 hundreds, 6 tens, 3 ones
2. Write each part as a number. Each part is the digit times its place value.
   200 + 60 + 3
3. Write the answer. The parts add up to the number.
   200 + 60 + 3

Check. Add the parts: 200 + 60 + 3 = 263.

Watch out. Leave out a part that is zero. 204 is 200 + 4.

Method. Groups of is multiply. Write the sentence, then find the total.

1. Write the repeated addition. There are 5 groups of 6.
   6 + 6 + 6 + 6 + 6
2. Use the multiplication sign. Groups of is the same as multiply, written with the × sign.
   5 × 6
3. Write the answer after the = sign. The total is the answer.
   5 × 6 = 30

Check. Check: 6 + 6 + 6 + 6 + 6 gives 30.

Watch out. The number in front is the number of groups. The number after is the size of each group.

Method. Add the ones, then the tens, then the hundreds. Carry any ten or hundred you make.

1. Write the numbers in columns. Keep the ones under the ones and the tens under the tens.
   68 over 57
2. Add the ones. The ones make 10 or more, so write the ones digit and carry 1 ten.
   8 + 7 = 15, write 5 and carry 1
3. Add the tens. Add the carried ten with the tens. The tens make 10 or more, so write the tens digit and carry 1 hundred.
   6 + 5 + 1 carried = 12
4. Add the hundreds. Add any carried hundred too.
   0 + 0 + 1 carried = 1
5. Write the answer. Read the columns from left to right.
   125

Check. Check: 125 - 57 = 68.

Watch out. When the tens make 10 or more, carry a hundred to the hundreds column.

Method. Change every measurement to the same unit, then order the numbers.

1. Change them all to the same unit. Use the smallest unit so the numbers are easy to compare.
   1 m 20 cm = 120 cm, 2 m 20 cm = 220 cm, 20 cm = 20 cm
2. Put the numbers in order. Compare the numbers, then write the measurements in that order.
   220, 120, 20
3. Write the order. Write the original measurements in order.
   2 m 20 cm, 1 m 20 cm, 20 cm

Check. Read the list again: each one is bigger or smaller than the one before, as the question asks.

Watch out. Change to the same unit before you order. 2 m is bigger than 150 cm.

Method. A shape is split into halves only when there are 2 equal parts.

1. Count the parts. We need 2 equal parts to be halves.
   2 parts
2. Check the parts are the same size. Equal parts must be the same size.
   the parts are not equal
3. Write the answer. The parts are not all the same size, so it is not split into equal parts.
   no

Check. Check the size of each part by eye: all must match.

Watch out. Equal parts are the same size. Count the parts and check each one.

Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.

1. Write the numbers in columns. Keep the ones under the ones and the tens under the tens.
   70 over 65
2. Exchange 1 ten for 10 ones. The ones on top (0) are fewer than the ones below (5), so we need more ones.
   7 tens become 6 tens, and the ones go from 0 to 10
3. Subtract the ones. 10 - 5 = 5.
   10 - 5 = 5
4. Subtract the tens. 6 - 6 = 0.
   6 - 6 = 0
5. Write the answer. Read the columns from left to right.
   5

Check. Check: 5 + 65 = 70.

Watch out. Exchange a ten for ten ones when the ones on top are too small. Then take away.

Method. Use the rule: 100 cm make 1 m, and 1000 g make 1 kg.

1. Find the number of whole kilograms. 1000 g make 1 kg.
   2250 ÷ 1000 = 2 rem 250
2. Write the grams that are left. The rest are grams.
   2 kg and 250 g
3. Write the answer. Use kilograms and grams.
   2 kg 250 g

Check. Add back: 2 kg + 250 g = 2250 g.

Watch out. The number of metres is the number of hundreds of centimetres. Check the rule before you change.

Method. Start at the number and count on or back, one number at a time.

1. Start at 929. We begin with this number.
   929
2. Count on 6. Say each new number as we go.
   929 + 6 = 935
3. Write the answer. This is the last number we reached.
   935

Check. Count back 6 from 935: you reach 929.

Watch out. Start from the number in the question. Do not start again from 1 or from 0.

Method. Find the digit, then multiply it by its place value. A ones digit is worth 1.

1. Find the ones digit in 133. The ones digit is in the ones column.
   ones digit = 3
2. Multiply by the place value. Each ones digit stands for 1 at a time in this column.
   3 x 1 = 3
3. Write the answer. This is the value of the digit.
   3

Check. Check the other digits add to the number: 133 = 130 + 3.

Watch out. The value is the digit times the place. It is not just the digit.

Method. Put the numbers in order, smallest to largest. Compare hundreds first, then tens, then ones.

1. Compare the hundreds of each number. The number with fewer hundreds is smaller.
   889: 8 hundreds, 803: 8 hundreds, 804: 8 hundreds
2. Find the first number in the order. It is the smallest, or the largest if we go the other way.
   803
3. Write all the numbers in order. Check each one fits between the ones next to it.
   803, 804, 889

Check. Read the list again. Each number is bigger than the one before it.

Watch out. Compare hundreds first. 508 is less than 521, because 5 hundreds is the same but 0 tens is less than 2 tens.