Step-by-step Maths Level 5 Level 5 check: check-up and practice test questions

Method. Count in 11s to find 4 groups of 11. The order of the numbers does not matter.

1. Count in 11s, 4 times. Each count adds one more group of 11.
   11, 22, 33, 44
2. The last number we said is the answer. We counted 4 groups of 11.
   11 × 4 = 44
3. Write the answer. The order of the two numbers does not change the answer.
   44

Check. Check: 4 × 11 is also 44.

Watch out. Learn the 11 times table in order, then say it in any order.

Method. Read the column, then multiply the digit by the value of that column.

1. Find the thousands column. Count the columns from the right: ones, tens, hundreds and so on.
   The digit is 2
2. Multiply the digit by the value of its column. Each place in the thousands column is worth 1,000.
   2 × 1,000 = 2,000
3. Write the value. This is the value of the digit in this number, not just the digit.
   2,000

Check. Check: 2,000 is 2 groups of 1,000.

Watch out. Say the value, such as 70,000, not only the digit 7.

Method. Add the top numbers and keep the bottom number. Simplify if you can.

1. Add the top numbers. The bottom number stays the same, because the parts are the same size.
   4 + 4 = 8
2. Keep the bottom number 10. The total is counted in the same parts.
   8/10
3. Simplify. Divide the top and bottom by the same number, which is 2.
   8/10 = 4/5
4. Write the answer. This is the simplest form.
   4/5

Check. Check: 4/5 is equal to 8/10.

Watch out. Do not add the bottom numbers too. 2/8 + 3/8 is 5/8, not 5/16.

Method. Split 12 into 10 and 2, then add the two results.

1. Split 12 into 10 and 2. Multiply each part by the number.
   12 × 12 = 10 × 12 + 2 × 12
2. Work out each part. Both parts are facts we know.
   10 × 12 = 120, and 2 × 12 = 24
3. Add the two parts. The total is the answer.
   120 + 24 = 144
4. Write the answer. This is the answer to 12 times the number.
   144

Check. Check: 144 ÷ 12 = 12.

Watch out. Do not add 12 to the number only once. Work out both parts.

Method. Divide by the bottom number to find one part, then multiply by the top number.

1. Find one 5th of 15. Share 15 into 5 equal parts.
   15 ÷ 5 = 3
2. Take 3 of those parts. The top number tells us how many parts.
   3 × 3 = 9
3. Write the answer. Keep the unit from the question.
   9 cm

Check. Check: 3 × 5 = 15, and 3 parts is 9.

Watch out. Divide first, then multiply. Do not multiply by the bottom number.

Method. Count in 11s to find 9 groups of 11. The order of the numbers does not matter.

1. Count in 11s, 9 times. Each count adds one more group of 11.
   11, 22, 33, 44, 55, 66, 77, 88, 99
2. The last number we said is the answer. We counted 9 groups of 11.
   11 × 9 = 99
3. Write the answer. The order of the two numbers does not change the answer.
   99

Check. Check: 9 × 11 is also 99.

Watch out. Learn the 11 times table in order, then say it in any order.

Method. Add the columns from the right. Carry any ten into the next column on the left.

1. Add the ones column. Write 2 and carry 1 to the tens column.
   4 + 8 = 12
2. Add the tens column. Write 2 and carry 1 to the hundreds column.
   6 + 5 + 1 carried = 12
3. Add the hundreds column. Write 2 and carry 1 to the thousands column.
   2 + 9 + 1 carried = 12
4. Add the thousands column. Write 0 and carry 1 to the ten thousands column.
   0 + 9 + 1 carried = 10
5. Add the ten thousands column. Write 7 in the ten thousands column.
   3 + 3 + 1 carried = 7
6. Add the hundred thousands column. Write 1 in the hundred thousands column.
   1 + 0 = 1
7. Write the answer. Put the digits together, with commas between groups of three.
   170,222

Check. Check: 170,222 - 39,958 = 130,264.

Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.

Method. Divide by 10 to find the whole cm; the remainder is the mm.

1. Use the rule. 1 cm is 10 mm.
   1 cm = 10 mm
2. Share 153 mm into groups of 10. Each group is one cm.
   153 ÷ 10 = 15 r 3
3. Write the answer. 15 whole cm and the mm left over.
   15 cm 3 mm

Check. Check: 15 × 10 + 3 = 153.

Watch out. Use a space between the two parts, and the unit after each: 15 cm 3 mm.

Method. Subtract each column from the right. Exchange 1 from the column on the left when the top digit is too small.

1. Subtract the ones column. 9 is at least 4, so subtract directly.
   9 - 4 = 5
2. Subtract the tens column. 1 is at least 1, so subtract directly.
   1 - 1 = 0
3. Subtract the hundreds column. 1 is less than 3, so exchange 1 thousands for 10 hundreds.
   11 - 3 = 8
4. Subtract the thousands column. 6 is less than 8, so exchange 1 ten thousands for 10 thousands.
   16 - 8 = 8
5. Subtract the ten thousands column. 2 is less than 8, so exchange 1 hundred thousands for 10 ten thousands.
   12 - 8 = 4
6. Subtract the hundred thousands column. 1 is at least 0, so subtract directly.
   1 - 0 = 1
7. Write the answer. Read the digits from the left, and put commas in.
   148,805

Check. Check: 88,314 + 148,805 = 237,119.

Watch out. When you exchange across zeros, change each zero to 9 as you pass it. Do not leave a zero in the middle.

Method. Count in 11s to find 8 groups of 11. The order of the numbers does not matter.

1. Count in 11s, 8 times. Each count adds one more group of 11.
   11, 22, 33, 44, 55, 66, 77, 88
2. The last number we said is the answer. We counted 8 groups of 11.
   11 × 8 = 88
3. Write the answer. The order of the two numbers does not change the answer.
   88

Check. Check: 8 × 11 is also 88.

Watch out. Learn the 11 times table in order, then say it in any order.

Method. Work out each missing side, then add all the sides of the shape.

1. Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.
   step = 5 - 2 = 3 cm; right side = 8 - 2 = 6 cm
2. List all six sides. The perimeter is the distance all the way round.
   2 + 6 + 3 + 2 + 5 + 8 cm
3. Add the sides. Add all the lengths together.
   26 cm
4. Write the perimeter. Give the answer with the unit cm.
   26 cm

Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (5 + 8) = 26 cm.

Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.

Method. Work out each missing side, then add all the sides of the shape.

1. Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.
   step = 12 - 10 = 2 cm; right side = 5 - 3 = 2 cm
2. List all six sides. The perimeter is the distance all the way round.
   10 + 2 + 2 + 3 + 12 + 5 cm
3. Add the sides. Add all the lengths together.
   34 cm
4. Write the perimeter. Give the answer with the unit cm.
   34 cm

Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (12 + 5) = 34 cm.

Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.

Method. Look at the digit to the right of the tens column, then decide.

1. Look at the ones digit. This digit decides whether to round up or down.
   The ones digit is 7
2. Decide: round up or down. 5 or more: round up. 4 or less: round down.
   7 is 5 or more, so round up
3. Write the rounded number. Replace the digits after the tens column with zeros.
   117,170

Check. Check: 117,170 is a multiple of 10 and is the closest one to 117,167.

Watch out. Round up only when the next digit is 5 or more. Do not round up on a 4.

Method. Add the costs, then subtract the total from the money at the start.

1. Add the two costs. Add the pounds and the pence together.
   £4.93 + £1.16 = £6.09
2. Take the total away from the money Sam has. Subtract the total cost.
   £10.29 - £6.09 = £4.20
3. Write the answer. Give the amount left with the pound sign.
   £4.20

Check. Check: £4.20 + £6.09 = £10.29.

Watch out. Keep the pence in two places: £0.85 and £2.40, not £0.85 and £2.4.

Method. The first digit after the point is the number of tenths.

1. Find the tenths digit. It is the first digit after the decimal point.
   The digit is 0
2. Write its value. 0 tenths is 0/10.
   0/10 = 0.0
3. Write the answer. The value of the tenths digit is 0.1 times the digit.
   0.0

Check. Check: the first digit after the point is 0, so the value is 0/10 = 0.0.

Watch out. Read the digit after the point as tenths. 4 tenths is 0.4, not 4.

Method. Only the ten thousands digit changes when we add or take away 10,000.

1. Look at the ten thousands digit. Adding or taking away 10,000 changes this digit by one.
   The ten thousands digit is 8
2. Change that digit by one. Carry or borrow if the digit goes past 9 or below 0.
   8 - 1 = 7
3. Write the answer. All the other digits stay the same.
   875,464

Check. Check: 875,464 add 10,000 gives back 885,464.

Watch out. Do not change the thousands digit. 10,000 is not 1,000.

Method. Count in 12s to find 7 groups of 12. The order of the numbers does not matter.

1. Count in 12s, 7 times. Each count adds one more group of 12.
   12, 24, 36, 48, 60, 72, 84
2. The last number we said is the answer. We counted 7 groups of 12.
   12 × 7 = 84
3. Write the answer. The order of the two numbers does not change the answer.
   84

Check. Check: 7 × 12 is also 84.

Watch out. Learn the 12 times table in order, then say it in any order.

Method. The second digit after the point is the number of hundredths.

1. Find the hundredths digit. It is the second digit after the decimal point.
   The digit is 0
2. Write its value. 0 hundredths is 0/100.
   0/100 = 0.00
3. Write the answer. The value is a decimal with the digit in the second place.
   0.00

Check. Check: in 7.10 the second digit after the point is 0, so the value is 0/100 = 0.00.

Watch out. The value is 0.0 with the digit after it: 0.07, not 0.7.

Method. Multiply the hours by 60 to change them into minutes.

1. Use the rule. There are 60 minutes in 1 hour.
   1 h = 60 min
2. Multiply the hours by 60. Each hour has 60 minutes.
   4 × 60 = 240
3. Write the answer. The unit is minutes.
   240 minutes

Check. Check: 240 ÷ 60 = 4.

Watch out. Going from hours to minutes gives a bigger number. Multiply by 60.

Method. Compare the digits from the left: whole numbers, then tenths, then hundredths.

1. Compare the whole numbers. The bigger whole number is the bigger decimal.
   1 and 1
2. Compare the tenths. If the whole numbers match, the tenths decide.
   8 and 1 tenths
3. Compare the hundredths. If the tenths also match, the hundredths decide.
   7 and 3 hundredths
4. Choose the greater number. This is the number with the larger digit in the first place they differ.
   1.87

Check. Check: 1.87 is 187 hundredths and 1.13 is 113 hundredths.

Watch out. Do not think 0.45 is bigger than 0.5 because 45 is bigger than 5. Compare the tenths first.

Method. Count on in steps from the start to the arrival time: first to the next hour, then whole hours, then minutes.

1. Count the minutes to the next hour. Go from the start time to the next full hour.
   08:45 to 09:00 is 15 min
2. Count the whole hours. Count each full hour after that.
   0 whole hours
3. Count the minutes after the last whole hour. Count on to the arrival time.
   58 min
4. Add the parts. Add all the parts for the total time.
   15 min + 0 h + 58 min = 1 h 13 min
5. Write the answer. Give the journey time in hours and minutes.
   1 h 13 min

Check. Check: 1 h 13 min added to 08:45 gives 09:58.

Watch out. Do not subtract the times as if they were ordinary numbers. Count on across the hour.

Method. Add the columns from the right. Carry any ten into the next column on the left.

1. Add the ones column. Write 8 in the ones column.
   2 + 6 = 8
2. Add the tens column. Write 7 and carry 1 to the hundreds column.
   9 + 8 = 17
3. Add the hundreds column. Write 4 and carry 1 to the thousands column.
   4 + 9 + 1 carried = 14
4. Add the thousands column. Write 3 in the thousands column.
   1 + 1 + 1 carried = 3
5. Add the ten thousands column. Write 8 in the ten thousands column.
   3 + 5 = 8
6. Add the hundred thousands column. Write 4 in the hundred thousands column.
   3 + 1 = 4
7. Write the answer. Put the digits together, with commas between groups of three.
   483,478

Check. Check: 483,478 - 151,986 = 331,492.

Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.

Method. Multiply the number in each group by the number of groups, or the amount by the number of times.

1. Find the cost of one pen and the number of pens. Each pen costs the same amount.
   80p for each of 4 pens
2. Multiply the cost of one pen by the number of pens. The total cost is the cost of each times the number.
   80p × 4 = 320p
3. Write the answer. Give the cost in pence, as the question asks.
   320p

Check. Check: 320p is more than the first number, because we multiplied by 4.

Watch out. Check the units: the answer should be in the same unit as the question (pencils, pence, stamps).

Method. Compare the whole numbers, then the tenths, then the hundredths.

1. Compare the whole numbers. Put the smallest whole number first.
   5, 7, 1, 6
2. Compare the tenths and hundredths. Use the next places to put the rest in order.
   5.80, 7.02, 1.19, 6.00
3. Write the list smallest first. Check each pair in order.
   1.19, 5.80, 6.00, 7.02

Check. Check: each number is smaller than the one after it.

Watch out. Do not order by the number of digits. Compare the places from the left.

Method. Find the total of all the items, then take it from the money paid.

1. Work out the cost of the cups. Multiply the price by the number of cups.
   4 × £1.15 = £4.60
2. Add the cost of the cake. Add all the items to find the total.
   £4.60 + £1.32 = £5.92
3. Work out the change. Change is what is left from the money paid.
   £10.00 - £5.92 = £4.08
4. Write the answer. Give the change with the pound sign.
   £4.08

Check. Check: £5.92 + £4.08 = £10.00.

Watch out. Add all the items before you take anything away.

Method. Use the inverse operation to find the missing number.

1. Think about the total. The missing number is what is left when we take the known number away.
   659,059 - 442,385
2. Subtract to find the missing number. Use the column method.
   659,059 - 442,385 = 216,674
3. Check by adding. The missing number and the known number must make the total.
   442,385 + 216,674 = 659,059
4. Write the missing number. This is the number in the box.
   216,674

Check. Check: put 216,674 into the sum and it works.

Watch out. To find a missing number in a sum, subtract. To find it in a difference, add.

Method. Multiply the number of groups by the number in each group.

1. Find the number of bags and the number in each. Multiply the number of equal groups by the size of each group.
   2 bags of 6
2. Work out the multiplication. Use the times table for this number.
   2 × 6 = 12
3. Write the answer. This is the total number of sweets.
   12

Check. Check: 12 ÷ 2 = 6, so each bag has 6.

Watch out. If you are not sure of the fact, count in the times table, one group at a time.

Method. Write the whole number, then a decimal point, then the tenths digit.

1. Write the whole number first. This is the part before the decimal point.
   7
2. Write the tenths after a decimal point. 4/10 is 4 tenths, so the digit 4 goes after the point.
   7.4
3. Write the answer. A decimal point separates the whole number from the tenths.
   7.4

Check. Check: 4/10 is 0.4, and 7 + 0.4 = 7.4.

Watch out. The tenths digit is one place after the decimal point.

Method. More than one whole: add the top numbers, then write the whole ones out.

1. Add the top numbers. Keep the bottom number the same.
   3 + 5 = 8
2. Write the total. 8 parts of size 1/6.
   8/6
3. Write as a mixed number. There are 1 whole one and 1/3 left over.
   4/3 = 1 1/3
4. Write the answer. This is the answer in its simplest form.
   1 1/3

Check. Check: 1 1/3 is more than 1, as 8/6 is more than 6/6.

Watch out. A top number bigger than the bottom is more than one whole. Write it as a mixed number.

Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.

1. Multiply the ones digit by 8. Write 8 in the ones column and carry 4 to the tens column.
   6 × 8 = 48
2. Multiply the tens digit by 8. Write 8 in the tens column and carry 6 to the hundreds column.
   8 × 8 = 64, plus 4 carried = 68
3. Write the carried number in front. The carried number is the next digit on the left.
   6 in the hundreds column
4. Write the answer. Read the digits from the bottom of each column, from the left.
   688

Check. Check: 688 ÷ 8 = 86.

Watch out. Add any carried number before you write the digit of that column. Carry the tens; do not write them as a digit.