Year 3 Week 30 Lesson 1
Main Focus
Prior Knowledge
Key Vocabulary
Curriculum Objectives
Revise column written
addition for adding three
3-digit numbers, revise mental
strategies for addition and use
reasoning skills to invent
appropriate questions
Use expanded or compact
version of column addition
mental addition; column
addition; 1s; 10s; digits
N3.2A Add several 1-digit and 2-digit numbers (up to and
including 20)
N3.2C Mentally add numbers: a 3-digit number and 1s,
a 3-digit number and 10s, a 3-digit number and 100s
N3.2F Add numbers with up to three digits, using formal written
methods of column addition
Teaching Summary
Starter
Mental addition strategies
Ask each student to write a 2-digit number on a whiteboard. Explain that you are going to write some numbers on the board and that they get a cube if they can
add one of those numbers to their number to give a 2-digit or 3-digit answer with a 0 in the 1s or 10s place, such as 107 or 340 or 90. Write these numbers on the
board: 345, 86, 123, 79, 820. Give students a couple of minutes to choose a number to add to the number on their board. On a count of three, they hold up their
addition. Who gets a cube? Discuss strategies, such as: I knew that my number had a four in the ones place so I looked for a number with a six in the ones place.
For some students it will not have been possible, so give everyone another turn by asking them to write a new number on their whiteboard and writing on the
board: 536, 75, 192, 41, 380.
Main Teaching
•
On the whiteboard, write the addition: 350 + 240 + 200. Ask students if they will need to write this down to do it. Give them a minute to discuss it with a
partner and then agree that it could be possible to do this in our heads.
•
Model adding the 100s (700), then the 10s (90) and agreeing the answer of 790. Encourage some students to tell you if they did it a different way, such as
adding 350 and 240 to get 590 then adding the 200.
•
On the whiteboard, write 358 + 245 + 206. Ask students if they think they could do this in their heads. Agree that we probably could not. Ask: How would we
do this? Agree that we would write the numbers in columns, remembering to leave a space for the extra 10s or 100s digits above the line.
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•
Perform the addition, adding the 1s first (19) and writing the 1 above the line in the 10s column. Then add the 10s (10), writing the 1 in the 100s column.
Then add the 100s (8). Agree the answer of 809.
•
Look again at the first addition we did (350 + 240 + 200) and then at the second addition. Can students see any similarities? The 10s and 100s digits are the
same in each of the three numbers, so the second set of numbers should add up to 8 + 5 + 6 more (the added 1s). That is 19 more than our first answer.
Ask students if this is correct. Ask: Is the second answer nineteen more than the first? Yes!
•
On the whiteboard, write 170 + 500 + 220. Ask students to work in pairs to agree an answer. Emphasise that they can do this calculation mentally.
•
Agree that the total is 890. Discuss different ways of doing the addition.
Short Task
On the whiteboard, write 177 + 508 + 228. Ask students to write this as a column addition on their boards and add the 1s, then the 10s and finally the 100s.
Remind them to leave a space above the line for the extra 10s or 100s digits.
Teaching
•
Look at their boards and agree the answer of 913. Say: We had to write two tens in the tens column after adding the ones.
•
Now compare the numbers in this addition with the numbers added mentally in the previous addition. That addition was 170 + 500 + 220 and this addition is
177 + 508 + 228. The numbers in the second addition have different 1s from the numbers in the first addition, but the 10s and the 100s are the same, so the
second total should be 7 + 8 + 8 (23) more than the first answer. Compare the two answers. Is this true? Yes: 890 + 23 = 913.
Checkpoint
Use the following task to assess understanding of the following outcomes. You can use it in this lesson or at another time in the day that suits you.
•
Choose an appropriate strategy (mental or written) to solve addition of 3-digit numbers
•
Add numbers with up to 3 digits using column addition and using reasoning and trial and improvement
Ask the students:
1) Use a mental method to work out these additions.
240 + 350 (590)
534 + 210 (744)
420 + 200 + 140 (760)
2) Use column addition to work out these additions.
524 + 238 (762)
351 + 272 (623)
326 + 231 + 234 (791)
3) Choose a mental or written method to work out these additions.
456 + 218 + 127 (801 (using column addition))
450 + 210 + 100 (760 (using a mental method))
Champions’ Challenge
Use the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9 to make three 3-digit numbers that add together to make the smallest total possible. (The smallest total is 774, such as
147 + 258 + 369 = 774)
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Main Activity
Core
Y3 TB3 p84 Revising 3-digit addition and subtraction
Students work through the questions and then complete the Think activity in pairs.
Linked Resources: Y3 TB3 Answers p80-89
Support
Adding 3-digit numbers using expanded column addition
Ask students to complete the five pairs of questions on Y3 TB3 p84 (Y3 TB3 Answers p80-89), but doing the second addition in each pair first. They should use
the expanded version of written column addition if appropriate. When they have all agreed the answer for this addition, look at the first mental addition. Work
together on this and agree an answer. Then compare the two answers, if necessary using a calculator to find the difference. Look at the addition of the 1s only in
the second addition. Ask: Is this the difference?
Assessment Focus
•
Can students use column addition to add 3-digit numbers?
•
Can students mentally add two or three numbers?
Extend
Y3 TB3 p84 Revising 3-digit addition and subtraction
Students work through the questions and then complete the Think activity in pairs. Challenge students to write at least five pairs of additions where the difference
between the first addition (of multiples of 10) and the second addition is 15.
Linked Resources: Y3 TB3 Answers p80-89
Further Support
Students who have difficulty with column addition will need to use the expanded version and also base-10 equipment to remind them what is happening.
Plenary
Take feedback from students. Ask students to share a pair of additions that they invented. Choose a pair and try them out. Ask: Can we predict the answer to the
written addition before we do it?
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Resources
Physical Resources
Photocopiable Resources
•
Base-10 equipment
•
•
Calculators
•
Multilink cubes
•
Whiteboards
•
Y3 TB3
Y3 TB3 Answers p80-89
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Year 3 Week 30 Lesson 2
Main Focus
Prior Knowledge
Key Vocabulary
Curriculum Objectives
Subtract 3-digit numbers
using written and mental
methods
Knowing number bonds to 10,
adding to the next 10 and 100
and understanding numbers
as positions on a line
subtraction; mental; written;
counting up
N3.2D Mentally subtract numbers: a 3-digit number and 1s,
a 3-digit number and 10s, a 3-digit number and 100s
N3.2G Subtract numbers with two digits, using formal written
methods of column subtraction
N3.2H Subtract numbers with up to three digits, using formal
written methods of column subtraction
Teaching Summary
Starter
Complements to 10 and 100
Ask students to write a number less than 10 and a multiple of 10 less than 100 on their whiteboards. Write a 2-digit number on the board, such as 26. Ask
students: What number do we add to this to get to the next multiple of ten? Write the addition on the board, such as 26 + 4 = 30. Any student who has written the
correct answer on their whiteboard gets a cube. Then point at the multiple of 10, such as 30. Ask: How much to make one hundred? (70) If any student has 70
written on their board, they get a cube. Keep writing 2-digit numbers on the board and continuing to play. Who is the first to get five cubes?
Main Teaching
•
Write 314 – 268 on the board. Discuss with students how you might do this subtraction. Agree that we will need to write it down. Take suggestions as to how
we will do this.
•
Remind students how we can draw a number line and use Frog. He counts from the smaller number to the larger.
•
Model starting on 268, jumping to the next 10 (270) and on to the next 100 (300). The final jump is to 314. Ask students to add Frog’s jump numbers:
2 + 30 + 14 = 46. Complete the subtraction on the board: 314 – 268 = 46.
•
Remind students that Frog can always help us to count up from a smaller number to a larger number if the subtraction is one we cannot do just in our heads.
•
Write on the board: 300 – 103, 243 – 185, 500 – 499. Say to students that only one of these subtractions needs to be written down.
Short Task
Students work in pairs to decide which subtraction they think they would need to write down. They then answer this subtraction, writing it out and making sure they
and their partner agree how to lay it out and what to do.
Teaching
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•
Take feedback and agree which subtraction is too hard to do in their heads. Model how we do the subtraction.
•
Add the jumps and complete the subtraction: 5 + 10 + 43 = 58; 243 – 185 = 58.
•
Look at the other two subtractions. Discuss how we can do these in our heads. (For 300 – 103, we can take off 100 to get 200 and then count back 3 to get
197, so 300 – 103 = 197. For 500 – 499, we see that 499 is only 1 less than 500.)
•
Remind students that it is a good idea to look carefully at a subtraction, even if the numbers are quite big, just to check whether you have to write it down.
Say: Some subtractions may have big numbers, but we can still do them mentally.
Key Questions
•
How do we know if a subtraction needs to be written down?
•
Where does Frog jump to first? Then where does he jump?
Watch out for
•
Students who have difficulty identifying the mental strategies they can use to help subtract
•
Students who cannot quickly recall number bonds
•
Students who have difficulty relating counting up to subtraction
Main Activity
Core
Y3 TB3 p86 Revising 3-digit addition and subtraction
Linked Resources: Y3 TB3 Answers p80-89
Support
Y3 TB3 p85 Revising 3-digit addition and subtraction
Linked Resources: Y3 TB3 Answers p80-89
Extend
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Subtracting 3-digit numbers using counting up
Students work through the subtractions on Y3 TB3 p86 (Y3 TB3 Answers p80-89). When they have completed them, they explain what they have found.
Encourage students to discuss this and to give reasons why this pattern occurs. They then work through a new set of subtractions with a similar pattern. What
pattern do they see? How does it relate to the earlier pattern? Can students explain it? Work with students and encourage them to do the subtractions in just two
jumps.
Work with students to use this shortcut and encourage any students who can use this method with just two jottings to do the subtractions mentally.
Assessment Focus
•
Can students subtract 3-digit numbers?
•
Can students use mathematical reasoning to explain patterns?
Further Support
Use bead strings or landmarked lines (RS 337 Landmarked line, multiples of 10 and 100, 0-1000 (0-500) and RS 338 Landmarked line, multiples of 10 and 100,
0-1000 (500-1000)) to help students to count up to the next 10 and then to the next 100.
Plenary
Discuss the fact that all four calculations on Y3 TB3 p86 had the same answer. (91) Ask: What happens to the tens and ones digit when the digits are reversed?
(The 10s digit is always one less in the first number and the 1s digit is always one more in the first number.) Can students offer explanations? Share the patterns
that Support group found when working on Y3 TB3 p85. Can we explain these?
Resources
Physical Resources
Photocopiable Resources
•
Bead strings of 100 beads
•
RS 337 Landmarked line, multiples of 10 and 100, 0-1000 (0-500)
•
Multilink cubes
•
RS 338 Landmarked line, multiples of 10 and 100, 0-1000 (500-1000)
•
Whiteboards
•
Y3 TB3 Answers p80-89
•
Y3 TB3
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Year 3 Week 30 Lesson 3
Main Focus
Prior Knowledge
Key Vocabulary
Curriculum Objectives
Find change by subtracting
using counting up and check
subtraction using addition
Add to the next 10p and to the
next whole pound and
understand money notation
subtraction; change; count up;
pound; pence
N3.2B Recognise and work out bonds for numbers to 100
N3.2K Understand when to add and when to subtract and the
relationship between addition and subtraction
N3.4A Solve simple problems in contexts, deciding which of
the four operations to use
G3.1K Add and subtract amounts of money to give change
G3.1L Solve problems in a practical context involving money
(integer money amounts only)
Teaching Summary
Starter
Bonds to 100
Put the students in pairs. Roll two dice and use these to create a 2-digit number which you write on the board. Ask each pair to write the bond to the next 100. The
first student says how much to the next 10 and the second student then says how much to the next 100. For example, if the number is 67, the first student says 3
and the second student says 30. They add these two numbers to get the bond to 100. 30 + 3 = 33, so 67 + 33 = 100. Model this first example on a bead string,
identifying 67, then adding 3 more (to 70) and then 30 more to 100. Remind students that the first number takes us to the next 10 (70) so we are then adding from
there to get to 100 (we add 33, not 43, to 67 to make 100). Repeat, giving students at least six 2-digit numbers, with students taking turns to make the next 10 or
100 and checking that they can add to 100.
Main Teaching
•
Write the following meal prices on the board: pizza, £6.75; meatballs, £4.69; burger and chips, £5.32.
•
Explain that a group of three superheroes went out for a meal and this is what they had. Show students a real or pretend £10 note and say that each
superhero paid for their meal with a £10 note, but unfortunately their super powers do not include working out their change, so we are going to help them.
•
Point at the first meal, which cost £6·75. Say: It is easy to work out the change if we use Frog to help us count up to ten pounds. Remind students how we
can count to the next 10p and then to the pound and on to £10. Model using Frog on a line.
•
Consult the class. Who can add Frog’s jumps? (This superhero receives £3·25 change when he buys his meal with £10.)
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•
Ask: How can we check our answer? Agree that since addition and subtraction undo each other (are inverse operations), we can check subtraction using
addition. Demonstrate adding £6·75 and £3·25. Say: The answer is ten pounds, so our subtraction is correct!
•
Point at the second superhero’s meal, which cost £4.69. Ask: How much change will she get from ten pounds? Say that this time, we are going to see if we
can help Frog do this in just two jumps. Model drawing the line and writing the meal price at the start of the line and £10 at the end. Discuss how we can
work out how far Frog has to jump to get to the next pound: it is not that hard to combine the two smaller jumps. A jump of 1p would take him to 70p, then a
jump of 30p would take him to the next pound. Model this on the line.
•
(This superhero gets £5·31 change.)
•
Again use addition to check the answer. £4·69 + £5·31 = £10·00, so £5·31 is correct.
Short Task
Challenge students to work in pairs to work out the change that the third superhero gets when they pay for their meal costing £5·32 with £10. Encourage a few
students to calculate this using only two jumps, going to the next pound in one jump.
Teaching
Take feedback about how they worked this out. Agree that the answer is £4·68 and check using addition. Say: It does not matter whether we do three jumps or
two jumps, as long as we get the correct answer.
Checkpoint
Use the following task to assess understanding of the following outcomes. You can use it in this lesson or at another time in the day that suits you.
•
Add and subtract amounts of money to give change, using both £ and p in practical contexts
•
Estimate the answer to a calculation and use inverse operations to check answers (use addition to check subtraction)
Ask the students:
It is summer!
1) Find the change from £10 for each of these beach toys.
beach ball: £3·49 (£6·51)
cricket set: £8·25 (£1·75)
bucket and spade: £2·19 (£7·81)
inflatable dolphin: £7·85 (£2·15)
bat and ball set: £5·45 (£4·55)
rubber ring: £4·30 (£5·70)
2) Choose two subtractions to check using addition. (Answers will vary, but additions should give a total of £10.)
Champions’ Challenge
1) Which two items do you think you could buy for a total of less than £10? Find the exact total and the change from £10. (Any from: £3·49 + £2·19 = £5·68
(£4·32 change); £5·45 + £2·19 = £7·64 (£2·36 change); £3·49 + £5·45 = £8·94 (£1·06 change); £5·45 + £4·30 = £9·75 (25p change);
£3·49 + £4·30 = £7·79 (£2·21 change); £2·19 + £4·30 = £6·49 (£3·51 change).)
2) Can you buy three items for less than £10? (Yes, £3·49 + £2·19 + £4·30 = £9·98 with 2p change.)
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Main Activity
Core
Finding change
Work with students on GP 3.30.3. Encourage students to work out the change using two jumps rather than three if they can. Support them in working out the
amount to the next pound in their heads, making sure they clearly say the next ten as they do so, such as: Forty-seven pence and three pence makes fifty pence
and then fifty pence more to the next pound. That is a jump of fifty-three pence. Encourage students to use addition to check their answers.
Assessment Focus
•
Can students use Frog to help them work out change from £10?
•
Can students count up to £10 using two jumps instead of three?
Support
Finding change
Ask students to find change for the first six meals on GP 3.30.3. Provide RS 856 Empty number lines – change from £10 showing six empty number lines, all with
£10 at the end and two landing places marked on the line. Students write the meal price at the start of each line and then draw in the jumps, first to the next 10p
and then to the next pound.
They use addition to check three of their answers.
Extend
Y3 TB3 p87 Finding change from £10 and £20
Linked Resources: Y3 TB3 Answers p80-89
Further Support
Use real 1p and 10p coins to show counting up to the next 10p and then to the next £1.
Plenary
Write £87·35 on the board. This was the cost of the meal for all the superheroes together. Can we help them work out how much change they will get from one
hundred pounds? Draw an empty number line to help and use Frog to jump to £88 (65p) and then to £100 (£12). Say: That is twelve pounds sixty-five pence
change. Wow! Everyone in this class is a maths superhero!
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Resources
Physical Resources
Photocopiable Resources
•
1p and 10p coins
•
GP 3.30.3
•
£10 note (real or pretend)
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RS 856 Empty number lines – change from £10
•
Bead string of 100 beads
•
Y3 TB3 Answers p80-89
•
Dice × 2
•
Y3 TB3
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Year 3 Week 30 Lesson 4
Main Focus
Prior Knowledge
Key Vocabulary
Curriculum Objectives
Multiply numbers between 10
and 40 by 1-digit numbers
using grid method
Know number bonds to 10,
add to the next 10 and 100
and understand numbers as
positions on a line
multiplication; total; product;
times; pounds; pence; digit;
10s; 1s; grid method; partition
N3.3A Recall and use multiplication and division facts for the 2,
5 and 10 multiplication tables; recognise and work out
multiplication and division for the 3 and 4 multiplication tables
(up to and including 10 × ... )
N3.3B Know doubles up to and including 20; know their related
halves
N3.3D Read, write and interpret mathematical statements
involving multiplication and division using the multiplication (×),
division (÷) and equals (=) signs, for the 3 and 4 multiplication
tables
N3.4A Solve simple problems in contexts, deciding which of
the four operations to use
N4.3H Multiply 2-digit and 3-digit numbers by a 1-digit number
using a formal written method
Teaching Summary
Starter
2, 3, 4, 5 and 8 times-tables
Students work in pairs. Each pair chooses two tables from their known tables (that is, 2, 3, 4, 5 and 8 times-tables). Make sure that different pairs choose different
pairs of tables. They are not allowed to choose the same pair of tables as any pair next to them. Then each student in the pair writes out one of the tables. Then
they compare tables and make a list of all the numbers that are in both tables. Give them 3 minutes to do this, so they must work fast. Now take feedback. Which
numbers were common multiples? That is, which were in both tables? Are any numbers common multiples for three tables? Four tables? Write 24 and 40 on the
board because 24 is a multiple of 2, 3, 4 and 8 and 40 is a multiple of 2, 4, 5, 8 and 10.
Main Teaching
•
Write 5 × 17p = on the board. Use 10p and 1p coins to make 17p. Ask: How much will five lots of seventeen pence be? Discuss whether the total here will
be more or less than a pound. Ask students to give reasons for their estimate. For example, five times 20p is £1, so five times 17p will be less.
•
Say to students that it is easiest to multiply these numbers by partitioning 17p into a 10p and some 1ps. Say: This means that we will be using the grid
method. Draw out the empty grid. Talk through how to set up the grid, writing the numbers in the cells as you go.
•
Perform the multiplications (5 × 10 = 50 and 5 × 7 = 35). Point out that we need to know 5 × 7, but that we can turn this around to do 7 × 5 as we know our
5 times-tables facts.
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•
Use coins to make the two products: five 10p coins for 50p and three 10p coins and five 1p coins for 35p. Ask students to add the two amounts:
50 + 35 = 85p. Write the final answer on the board.
Short Task
Now write 4 × 23p on the board. Ask students to use the grid method to work out the answer to this multiplication. Work with those who are struggling to support
them in splitting the 23p into 20 and 3 and then multiplying each part by 4.
Teaching
•
Discuss how students laid out their grid. Work through the answer on the board, first drawing the grid, then filling in the two products, 80 and 12. Ask: Who
knew their three times-table and so knew four threes? The two products add to give us ninety-two pence, so four times twenty-three pence is less than a
pound.
•
Demonstrate how we can do a multiplication that will total more than a pound. Write 8 × 24p on the board and then work through the grid method to find the
answer. Stress that 8 × 20p is 160p and 8 × 4p is 32p. This totals 192p. Ask: Is this more than one pound? Yes, definitely. It is one pound and ninety-two
pence. Show how we write this as £1·92.
Key Questions
•
What can we partition a two-digit amount into? (ten ps and one ps)
•
What do we do first when using the grid method? Then what next?
•
What facts can we use to help us?
Watch out for
•
Students who do not use known number facts to help
•
Students who cannot partition into 10s and 1s
Main Activity
Core
Y3 TB3 p88 Multiplying numbers between 10 and 25
Linked Resources: Y3 TB3 Answers p80-89
Support
Multiplying numbers between 10 and 25
In pairs, students work out 4 × 16p. They partition 16p using 10p and 1p coins. One student in the pair takes the 1p coins and works out what four lots of that
amount is. The other student does the same with the 10p coins. Each pair records their calculations in a grid and together they work out and write the total. Do a
few more of these multiplications, keeping the 2-digit numbers ‘friendly’ and less than 40, with the totals less than £1. When students are confident, move on to
multiplications with a total of more than £1, such as 8 × 25p. Point out that 8 × 20p is 160p and when we add 40p we get 200p. Encourage students to realise that
200p is the same as £2, so they should write their final answer as £2. Ask them to do other examples, such as 5 × 22p (= 110p = £1·10), 8 × 15p
(= 120p = £1·20). Support them in writing 3-digit numbers of pence using £ and p notation.
Assessment Focus
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•
Can students use partitioning to multiply numbers between 10 and 25 by 1-digit numbers?
•
Are they beginning to use the grid method?
Extend
Y3 TB3 p89 Multiplying numbers between 10 and 25
Linked Resources: Y3 TB3 Answers p80-89
Further Support
Continue to use coins to multiply friendly 2-digit amounts by 3 or 4 or 5. Encourage students to see how partitioning the amount into 10ps and 1ps helps us
perform the multiplication.
Plenary
Write 3 × 42 and 4 × 32 on the board. Ask: Which do you think will give the bigger answer? Take a quick class vote. Divide the class into two halves. Ask one half
to do the first multiplication using a grid and the other half to do the second multiplication using a grid. Each half should agree answers; show on the board how to
complete the grids and the answers: 126 and 128. So four times thirty-two gives a bigger answer than three times forty-two. Can anyone explain why? Now write
5 × 34 and 3 × 54 on the board. Ask: Which do you think will give the bigger answer? Take a quick class vote. Again, ask each half of the class to do a calculation
and then check their answers together on the board using grids. Say: So five times thirty-four gives a bigger answer than three times fifty-four. Can anyone
explain why?
Resources
Physical Resources
Photocopiable Resources
•
1p and 10p coins
•
•
Whiteboards
•
Y3 TB3
Y3 TB3 Answers p80-89
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Year 3 Week 30 Lesson 5
Main Focus
Prior Knowledge
Key Vocabulary
Curriculum Objectives
Solving division problems just
beyond the range of known
tables facts
Know multiples of 10 of the
divisor and subtract mentally
multiples of 10 and 1-digit
numbers from 2-digit numbers
division; remainder;
times-table; double; facts;
calculation; multiplication;
subtract; divisor
N3.3A Recall and use multiplication and division facts for the 2,
5 and 10 multiplication tables; recognise and work out
multiplication and division for the 3 and 4 multiplication tables
(up to and including 10 × ... )
N3.3D Read, write and interpret mathematical statements
involving multiplication and division using the multiplication (×),
division (÷) and equals (=) signs, for the 3 and 4 multiplication
tables
N3.3E Solve 1-step problems involving multiplying and dividing
by 2, 3, 4, 5 and 10
N3.3F Solve missing number problems for multiplication and
division facts for the 2, 3, 4, 5 and 10 multiplication tables
N5.3F Divide numbers up to and including four digits by 1-digit
numbers with remainders written as integers, and interpret
remainders appropriately for the context
Teaching Summary
Starter
Divide by 10 with a remainder
1
9
1
9
Ask each pair of students to write a number of tenths between and inclusive on their whiteboard (they could write , or any number of tenths in between).
10
10
10 10
When they have done this, say that we are going to divide a 2-digit number by 10. If the remainder can be written as their number of tenths, they get a cube. Write
34 ÷ 10 on the board. Ask students to write the answer, such as 3 r4. Demonstrate using a number line on the board that three jumps of 10 is 30 and we have four
4
4
left over. Remind students that we can divide the remainder by 10, giving us or 4 divided by 10. Does anyone have on their board? They get a cube. Repeat,
10
10
writing different 2-digit numbers (change the 1s digit each time). Which students get cubes?
Main Teaching
Explain to students that today they will be solving division problems that use numbers a bit bigger than the tables they know. Say: This might sound hard, but you
will be able to use facts you know, so I think you will be able to do them!
Short Task
Ask students to work in pairs to divide 100 by 5. They can do this any way they like but must be prepared to explain their method.
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Teaching
•
Take feedback and give lots of praise. Say: One hundred is bigger than the facts you know for the five times-table, but you could do it using facts you do
know. Share different ways of doing this, encouraging the use of mathematical language. For example, say: We knew that ten fives are fifty. Since one
hundred is double fifty, then we thought that twenty fives must be one hundred…
•
Write ☐ × 5 = 100 on the whiteboard. Show that we can draw a line and ask Chunky Chimp to help.
•
Agree the answer. Say: Yes, there are twenty fives in one hundred. 20 × 5 = 100 and 100 ÷ 5 = 20.
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Write 45 ÷ 3 = on the whiteboard and ask students how Chunky Chimp can help us here. Point out that this calculation can be read as: How many threes in
forty-five? Write this as ☐ × 3 = 45. Then draw the line and record a jump of 10 × 3 and another jump of 5 × 3. Encourage students to agree that there are
15 lots of 3 in 45. Complete the division. 45 ÷ 3 = 15. Remind students that they have used facts they do know to work out the answer to a problem using
numbers bigger than their known tables.
Short Task
Write 76 ÷ 4 = ⬜ on the whiteboard and ask students to work in pairs to solve this. They re-write this as ☐ × 4 = 76, draw the
empty number line and use Chunky Chimp to help them work out the answer. Support those who need it by reminding them to do one jump of 10 × 4 and a
second jump to get to 76.
Teaching
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Ask some pairs to share their working. Rehearse how to re-write the division as a multiplication with a hole in and drawing the number line. Then do 10 × 4
(jumping to 40) and 9 × 4 (jumping to 76) to get 10 + 9 = 19, so 19 × 4 = 76 and 76 ÷ 4 = 19. Again, emphasise how students have used known facts to help
solve problems with bigger numbers.
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Remind students that we can always use Chunky Chimp to help us divide these large numbers. Say: Sometimes we have some left over and we call this a
remainder. Write 47 ÷ 3 on the whiteboard. Remind students that we have just worked out 45 ÷ 3, so this should be easy for them. Draw the line to model
finding the remainder.
Key Questions
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How can we divide a number above our known tables facts?
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How do we re-write a division to make it easy to work out?
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How many lots of the divisor do we subtract first?
Watch out for
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Students who do not understand that division is the inverse of multiplication
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Students who have forgotten or cannot quickly recall their tables facts
Main Activity
Core
Y3 TB3 p90 Dividing on a number line
Linked Resources: Y3 TB3 Answers p90-95
Support
Solve division problems using chunking
Support students in working through the questions on RS 858 Solve division problems using chunking. Ask questions such as: What numbers do we label the
ends of the line? What fact do we use first? (10 lots of the divisor.) How do we draw this on our line? Ensure that students know we are always jumping 10 lots
first, so we can see how far we still have to jump.
Assessment Focus
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Can students use chunking to divide numbers just above the multiple of 10 of the divisor?
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Can students say 10 times the divisor, then subtract this from the dividend?
Extend
Y3 TB3 p91 Dividing on a number line
Linked Resources: Y3 TB3 Answers p90-95
Further Support
Provide copies of 3 and 4 times-tables (RS 124 3 times-table poster and RS 125 4 times-table poster). Encourage students to spot relevant multiples on these.
Plenary
Write 48 ÷ 4 = ⬜ on the board. Can students say what the answer is? Give them two minutes to talk to a partner. They can
either draw a number line and use Chunky Chimp or just remember the table fact for 12 × 4 = 48. Now write 49 ÷ 4 = ⬜.
Ask: Do we know what the answer to this will be without doing any more work? How do we know? Encourage students to explain. What about 50 ÷ 4?
Additional Activity
Students can have a go at the additional activity Divide It Out from the NRICH website.
Linked with kind permission of NRICH, nrich.maths.org
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Resources
Physical Resources
Photocopiable Resources
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Multilink cubes
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RS 124 3 times-table poster
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Whiteboards
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RS 125 4 times-table poster
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Y3 TB3
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RS 858 Solve division problems using chunking
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Y3 TB3 Answers p90-95
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