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Step-by-step practice: Maths · Level 5Chapter 10 · Level 5 check
Level 5 · Chapter 10

Level 5 check

By the end of this chapter you will be able to

  • Answer a mix of Level 5 questions
  • Show secure place value to a million and decimals to tenths
  • Show secure column methods for adding, subtracting, multiplying and dividing
  • Show secure fractions, decimals and measures
  • Show secure perimeter, time and money problems

You should already know

  • Chapters 1 to 9 of Level 5

Where this leads

  • Level 6: long division with two-digit divisors, and remainders as fractions or decimals

Step-by-step practice: maths (Level 5). Small steps, repeated until fluent. Content: Read, write, order and compare numbers to 1,000,000, and know place value (chapter 1), Add and subtract whole numbers to a million in columns (chapter 2), Recall the times tables to 12 times 12, and multiply by 11 and 12 (chapter 3), Multiply a two-digit number by a one-digit number with the written method (chapter 4), Divide a two-digit number by a one-digit number with remainders (chapter 5), Add and subtract fractions with the same denominator (chapter 6), Decimals to hundredths, and rounding decimals (chapter 7), Convert metric measures and solve measure problems (chapter 8), Perimeter, time and money problems (chapter 9).

Exercise P  Do you remember?

Non-calculator
1
FWhat is the value of the 6 in 2,645? (Hint: the 6 is in the hundreds column.)
2
FWork out 4,375 + 2,819.
3
FWhat is 4 × 6?
4
FWork out 38 × 4.
5
FWhich is greater: 5/8 or 3/8?
10.1

Numbers to a million, and decimals to tenths

Level 5
Know place value to a million, and round and compare numbers, Read and compare decimals to tenths
Video lesson: Numbers to a million, and decimals to tenthsComing soon

This section mixes the skills from chapters 1 and 7. Read each question, then write the answer.

Name the column first when you find the value of a digit. Round by looking at the digit on the right.

Key ideas

  • Name the column, then multiply the digit by its value.
  • Adding 10,000 changes the ten thousands digit.
  • Round by looking one column to the right.
Worked example 10.1.1
What is the value of the digit in the ten thousands column of 472,893?

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

  1. Find the ten thousands column. Count the columns from the right: ones, tens, hundreds and so on.
    The digit is 7
  2. Multiply the digit by the value of its column. Each place in the ten thousands column is worth 10,000.
    7 × 10,000 = 70,000
  3. Write the value. This is the value of the digit in this number, not just the digit.
    70,000

Check. Check: 70,000 is 7 groups of 10,000.

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

Worked example 10.1.2
What is 10,000 more than 295,000?

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 9
  2. Change that digit by one. Carry or borrow if the digit goes past 9 or below 0.
    9 + 1 = 10, so write 0 and carry 1 into the hundred thousands
  3. Write the answer. All the other digits stay the same.
    305,000

Check. Check: 305,000 take away 10,000 gives back 295,000.

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

Worked example 10.1.3
Round 472,893 to the nearest 1,000.

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

  1. Look at the hundreds digit. This digit decides whether to round up or down.
    The hundreds digit is 8
  2. Decide: round up or down. 5 or more: round up. 4 or less: round down.
    8 is 5 or more, so round up
  3. Write the rounded number. Replace the digits after the thousands column with zeros.
    473,000

Check. Check: 473,000 is a multiple of 1,000 and is the closest one to 472,893.

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

Watch out

Watch out. The 7 in 472,893 is worth 70,000, not 7. Say the value with its column.

Exam tip

Grown-up tip. Ask the child to explain how they found the answer, not only to say it.

Exercise 10A  Mixed practice: numbers and decimals

Non-calculator
1
FWhat is the value of the digit in the hundred thousands column of 132,262?
2
FWhich is greater: 9.2 or 3.9?
3
FWhat is 10,000 less than 261,850?
4
FRound 821,656 to the nearest 1,000.
5
FRound 128,473 to the nearest 100,000.
6
FWhich number is greater: 561,644 or 535,634?
7
FPut these in order, smallest first: 4.9, 7.1, 8.9, 1.1.
8
FWhat is the value of the tenths digit in 4.5?
9
FPut these in order, smallest first: 9.6, 6.1, 4.5, 6.5.
10
FWhat is 10,000 more than 585,397?
11
FWhat is 10,000 more than 562,618?
12
FWhat is the value of the digit in the hundred thousands column of 563,601?
13
FWrite 370,543 as an addition of the value of each digit.
14
FRound 902,770 to the nearest 10,000.
15
FRound 158,297 to the nearest 10,000.
16
FWhat is the value of the tenths digit in 9.8?
10.2

Adding, subtracting, multiplying and dividing

Level 5
Add and subtract to a million in columns, Multiply two-digit numbers by one-digit numbers, and divide with remainders
Video lesson: Adding, subtracting, multiplying and dividingComing soon

Line up the digits in columns. Carry when you add; exchange when you subtract; carry the tens when you multiply.

In short division, share the tens first, then the ones, and write any remainder after the answer.

Key ideas

  • Work from the right in columns.
  • Carry or exchange as you go.
  • Check each answer with the inverse.
Worked example 10.2.1
Work out 265,384 + 48,973.

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

  1. Add the ones column. Write 7 in the ones column.
    4 + 3 = 7
  2. Add the tens column. Write 5 and carry 1 to the hundreds column.
    8 + 7 = 15
  3. Add the hundreds column. Write 3 and carry 1 to the thousands column.
    3 + 9 + 1 carried = 13
  4. Add the thousands column. Write 4 and carry 1 to the ten thousands column.
    5 + 8 + 1 carried = 14
  5. Add the ten thousands column. Write 1 and carry 1 to the hundred thousands column.
    6 + 4 + 1 carried = 11
  6. Add the hundred thousands column. Write 3 in the hundred thousands column.
    2 + 0 + 1 carried = 3
  7. Write the answer. Put the digits together, with commas between groups of three.
    314,357

Check. Check: 314,357 - 48,973 = 265,384.

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.

Worked example 10.2.2
Work out 500,000 - 273,468.

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. 0 is less than 8. The tens and hundreds and thousands and ten thousands are 0, so exchange across them: take 1 hundred thousands and make each zero a 9, which gives 10 ones.
    10 - 8 = 2
  2. Subtract the tens column. 9 is at least 6, so subtract directly.
    9 - 6 = 3
  3. Subtract the hundreds column. 9 is at least 4, so subtract directly.
    9 - 4 = 5
  4. Subtract the thousands column. 9 is at least 3, so subtract directly.
    9 - 3 = 6
  5. Subtract the ten thousands column. 9 is at least 7, so subtract directly.
    9 - 7 = 2
  6. Subtract the hundred thousands column. 4 is at least 2, so subtract directly.
    4 - 2 = 2
  7. Write the answer. Read the digits from the left, and put commas in.
    226,532

Check. Check: 273,468 + 226,532 = 500,000.

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

Worked example 10.2.3
Work out 38 × 6.

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

  1. Multiply the ones digit by 6. Write 8 in the ones column and carry 4 to the tens column.
    8 × 6 = 48
  2. Multiply the tens digit by 6. Write 2 in the tens column and carry 2 to the hundreds column.
    3 × 6 = 18, plus 4 carried = 22
  3. Write the carried number in front. The carried number is the next digit on the left.
    2 in the hundreds column
  4. Write the answer. Read the digits from the bottom of each column, from the left.
    228

Check. Check: 228 ÷ 6 = 38.

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

Watch out

Watch out. Do not forget a carried 1 or an exchange. Check the answer with the inverse operation.

Exam tip

Grown-up tip. Ask: “Did you carry, exchange or add the carried number? Does your check work?”

Exercise 10B  Mixed practice: adding, subtracting, multiplying and dividing

Non-calculator
1
FUse 10 and 2 to work out 12 × 11.
2
PSSam has 53 stamps. Lee has 4 times as many stamps as Sam. How many stamps does Lee have?
3
RIs 918,021 the correct answer to 746,477 + 171,544? Check it and answer Yes or No.
4
FWork out 585,073 - 413,677.
5
PS27 children go on a trip. Each bus holds 5 children. How many buses are needed?
6
FWork out 96 × 9.
7
RIs 882,437 the correct answer to 597,023 + 275,414? Check it and answer Yes or No.
8
FUse the 7 times table to find the largest multiple of 7 that is not more than 51.
9
FWork out 215 × 3.
10
FWork out 10 × 7.
11
FWork out 30 ÷ 9.
12
F___ - 84,766 = 207,536. What is the missing number?
13
RWork out 15 ÷ 5. Check your answer with multiplication and addition.
14
FWhat is 11 × 6?
15
PSA shop has 108 cups. They are packed into boxes of 12. How many boxes are there?
16
RIs 5 the correct answer to 30 ÷ 6? Check it and write Yes or No.
10.3

Fractions, measures, perimeter, time and money

Level 5
Add and subtract fractions with the same denominator, Work with decimals, metric measures, perimeter, time and money
Video lesson: Fractions, measures, perimeter, time and moneyComing soon

To add fractions with the same denominator, add the top numbers and keep the bottom number. Simplify when you can.

For time and money, count on in steps and keep the units and the decimal points in line.

Key ideas

  • Add the top numbers; keep the bottom number.
  • Change measures to the same unit first.
  • Count on across the hour or midnight.
Worked example 10.3.1
Work out 3/4 + 2/4. Write your answer as a mixed number if it is more than 1.
3/42/4

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

Check. Check: 1 1/4 is more than 1, as 5/4 is more than 4/4.

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

Worked example 10.3.2
Work out £3.46 + £2.85.

Method. Line up the decimal points and add in columns. Keep the pound sign and two places for pence.

  1. Line up the decimal points. Write the pounds and pence in columns.
    3.46 + 2.85
  2. Add the pence first. Carry any ten pence into the pounds.
    46 + 85 = 131 pence
  3. Add the pounds. Include any carried pounds.
    3 + 2 = 6 pounds
  4. Write the answer with the pound sign. Always write two places for the pence.
    £6.31

Check. Check: £6.31 - £2.85 = £3.46.

Watch out. Always write two digits for the pence: £5.00, not £5.

Worked example 10.3.3
A train leaves at 10:45 and arrives at 12:20. How long is the journey?

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.
    10:45 to 11:00 is 15 min
  2. Count the whole hours. Count each full hour after that.
    1 whole hours
  3. Count the minutes after the last whole hour. Count on to the arrival time.
    20 min
  4. Add the parts. Add all the parts for the total time.
    15 min + 1 h + 20 min = 1 h 35 min
  5. Write the answer. Give the journey time in hours and minutes.
    1 h 35 min

Check. Check: 1 h 35 min added to 10:45 gives 12:20.

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

Watch out

Watch out. 5/4 is 1 1/4, and 10:45 to 12:20 is 1 h 35 min. Check your answer makes sense.

Exam tip

Grown-up tip. Make a short list of the key rules: fractions, decimals, units and time. Practise one list each day.

Exercise 10C  Mixed practice: fractions, measures, time and money

Non-calculator
1
PSA train leaves at 14:24 and arrives at 16:06. How long is the journey?
2
FWork out 3/8 + 2/8. Write the answer in its simplest form.
3/82/8
3
FWrite 4.8 with two decimal places.
4
FRound 4.814 to the nearest tenth.
5
FWrite 59/100 as a decimal.
6
PSA ribbon is 1 m 91 cm long. Sam buys 3 ribbons of this length. What is the total length?
7
FWork out 2/4 - 1/4. Write the answer in its simplest form.
2/41/4
8
FChange 4 km to metres.
9
FWork out 4/5 - 3/5. Write the answer in its simplest form.
4/53/5
10
PSWork out 2 l 703 ml + 916 ml.
11
PSA bag of rice weighs 3 kg 557 g. Sam buys 3 bags. What is the total mass?
12
FChange 14 cm to mm.
13
PSA ribbon is 15 cm long. Ayo uses 2/5 of it. How many cm does Ayo use?
14
FWrite 2 + 1/10 + 1/100 as a decimal.
15
FWhich is greater: 1/8 or 4/8?
16
FWrite 46/100 as a decimal.

Chapter summary

SkillMethod
Numbers to a millionValue = digit × column value; round by looking one column to the right
Column methodsWork from the right; carry or exchange; check with the inverse
Times tables and divisionUse the 11 and 12 patterns; short division with a remainder written after the answer
Fractions and decimalsSame denominator: add or subtract the top numbers; decimals line up on the point
Measures, time and moneyChange to the same unit; count on across the hour or midnight; keep two places for pence

Can you…?

  • I can say the value of each digit in a number to 1,000,000, and round and compare numbers
  • I can add and subtract whole numbers to a million in columns
  • I can recall the times tables to 12 times 12, and use the 11 and 12 patterns
  • I can multiply a two-digit number by a one-digit number, and divide with remainders
  • I can add and subtract fractions with the same denominator, and write mixed numbers
  • I can work with decimals to hundredths, metric measures, perimeter, time and money

Key terms

column
a place in a number, such as hundreds or tens
remainder
the amount left over in a division
perimeter
the distance all the way round a shape
mixed number
a whole number and a fraction, such as 1 1/4

Exercise 10Z  Check-up

Non-calculator
1
What is 11 × 4?
2
What is the value of the digit in the thousands column of 472,779?
3
Work out 4/10 + 4/10. Write the answer in its simplest form.
4/104/10
4
Use 10 and 2 to work out 12 × 12.
5
A ribbon is 15 cm long. Ayo uses 3/5 of it. How many cm does Ayo use?
6
What is 11 × 9?
7
Work out 130,264 + 39,958.
8
Change 153 mm to cm and mm.
9
Work out 237,119 - 88,314.
10
What is 11 × 8?

Total 39 marks. Allow about 39 minutes.

Exercise 10X  Level 5 check

Non-calculator
1
PSFind the perimeter of the shape. The sides marked ? are not given, so work them out first.[1 mark]
2 cm??2 cm5 cm8 cm
2
PSFind the perimeter of the shape. The sides marked ? are not given, so work them out first.[1 mark]
10 cm??3 cm12 cm5 cm
3
FRound 117,167 to the nearest 10.[1 mark]
4
PSSam has £10.29. He buys a book for £4.93 and a pen for £1.16. How much money is left?[1 mark]
5
FWhat is the value of the tenths digit in 1.07?[1 mark]
6
FWhat is 10,000 less than 885,464?[1 mark]
7
FWhat is 7 × 12?[1 mark]
8
FWhat is the value of the hundredths digit in 7.10?[2 marks]
9
FChange 4 hours to minutes.[2 marks]
10
FWhich is greater: 1.87 or 1.13?[2 marks]
11
PSA train leaves at 08:45 and arrives at 09:58. How long is the journey?[2 marks]
12
FWork out 331,492 + 151,986.[2 marks]
13
PSOne pen costs 80p. How much do 4 pens cost? Give the answer in pence.[2 marks]
14
FPut these in order, smallest first: 5.80, 7.02, 1.19, 6.00.[2 marks]
15
PSSam buys 4 cups at £1.15 each and a cake for £1.32. He pays with £10.00. How much change should he get?[3 marks]
16
F442,385 + ___ = 659,059. What is the missing number?[3 marks]
17
PSThere are 2 bags. Each bag has 6 sweets. How many sweets are there altogether?[3 marks]
18
FWrite 7 + 4/10 as a decimal.[3 marks]
19
PSWork out 3/6 + 5/6. Write your answer as a mixed number if it is more than 1.[3 marks]
3/65/6
20
FWork out 86 × 8.[3 marks]
← Chapter 9: Perimeter of rectilinear shapes, time and money problems

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