Step-by-step Maths Level 3 Level 3 check: check-up and practice test questions

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.