Maths Year 3/4 Summer Multiplication and Division

Day 1
Revise tables facts using a partially completed multiplication grid. Revise multiplication and division as inverses by exploring all four number sentences to link 3, 7 and 21. Practise recall using the ‘Number Dials’ ITP.
Group Activities: T with Y3
Y3 -- Ring certain times table numbers on a 1–50 grid and say the associated division fact.
-- Play division facts bingo for the 2, 3, 4, 5, 8 and 10 times tables.
Y4 -- Complete a multiplication grid up to 12 × 12.
-- Explore the calculations on a 12 × 12 multiplication grid that children often find more difficult to remember.

Day 2
Use arrays of 20 counters to model finding factors. List factors in pairs to aid finding all possibilities. Repeat for 24; note common factors of 20 and 24. Repeat for 16 and 18.
Further Teaching with Y4
Model using factors to break down and solve multiplications mentally, e.g. 20 × 36 by doubling then multiplying by 10, or 52 × 14 by finding 52 × 7, then doubling.
Group Activities: T with Y4
Y3 Use the in-depth problem-solving investigation ‘Ordering Cards’ from NRICH as today’s group activity.
Or, use these activities:
-- Find factors of 2-digit numbers; investigate common factors.
Y4 Use the in-depth problem-solving investigation ‘Race to 200’ as today’s group activity.
Or, use these activities:
-- Multiply 23 by 8, 12, 14, 16 and 18 by choosing a pair of factors to aid calculation.
-- Use a ‘broken’ calculator to multiply 379 by 6, 8, 12, 18 and 24 by choosing a pair of factors to aid the calculation.

Day 3
Model multiplying three 1-digit numbers by re-ordering in a convenient way, e.g. find 4 × 7 × 5 by re-ordering as 4 × 5 × 7 (20 × 7).
Group Activities: T with Y3
Y3 -- Multiply three numbers recognising where reordering might simplify the calculation; explain choices.
Y4 -- Multiply three numbers (2–9) recognising where reordering might simplify the calculation; explain choices.
-- Multiply three numbers, recognising where factors and reordering might simplify the calculation; explain choices.

• ‘Partially completed multiplication grid 1’ (see resources)
• Number dials ITP
• Mini-whiteboards and pens
• ‘1–50 grid’ (see resources)
• ‘1–100 grid’ (see resources)
• Colouring pencils
• ‘12 × 12 Multiplication grid’ (see resources)
• ‘Partially completed multiplication grid 2’ (see resources)
• ‘Completed ‘12 × 12 Multiplication grid’ (see resources)
• Flipchart and pens
• Cubes
• Counters
• ‘Number cards’ (see resources)
• Calculators
• Three 1–6 dice per pair
• Number cards 2–9

Day 1
Times tables

Day 2
Think of a number: division facts

Day 3
Find unit fractions

Day 1
Y3 Multiplication grid.
Y4 Multiplication and division facts.

Day 2
Y3 Find factors.
Y4 Use factors.

Day 3
Y3 Multiply 3 numbers.
Y4 Multiply 3 numbers.

Y3

• Write the missing numbers:
  ☐ × 8 = 32
  6 × ☐ = 48
  9 = 36 ÷ ☐
  ☐ × 4 = 48
  5 = ☐ ÷ 8
• Write 8 × 6 = 48 in the middle of a space and circle it. Draw 8 spider legs out from it. Write 8 related number sentences using this central fact.
• Always true, sometimes true or never true?
  -- 6 × 8 is the same as 4 × 12.
  -- Dividing a number by 3 gives an odd answer.
  -- Even numbers divide by 8 to leave no remainder

Y4

• Find three different multiplication facts that you can multiply by 10 to give an answer of 400.
• Use doubling to help you solve:
  23 × 4; 18 × 8; 141 × 4
• How could you use the factors of 12 to help multiply a number by 12?
  Try this to find:
  16 × 12; 23 × 12; 34 × 12
• Use and explain a mental method to find:
  8 × 13; 7 × 16; 12 × 13

Y3 In-depth Investigations: Ordering Cards:
Children use their knowledge of times table facts to find the order of a set of loop cards. Ordering Cards from nrich.maths.org.

Y4 In-depth Investigations: Race to 200
Children apply knowledge of factors within the 2, 3, 4, 5, 9 and 10 times tables.

Y3: Factor Bugs
Adapt the Group Activity from Day 2 to practise systematically finding pairs of factors for numbers less than 30. Record as ‘Factor Bugs’.

Y4: Creepy Crawlies
Learning the 6 times table.

Sleeping Spiders
Learning the 8 times table.

Day 1
Model using a completed multiplication grid to solve missing number division problems, e.g. 24 ÷ [_] = 6; [_] ÷ 8 = 6.
Further Teaching with Y4
Use times tables facts to solve divisions of multiples of 10 and 100.
Group Activities: T with Y4
Y3 -- Write division questions with a given answer.
Y4 -- List the factors of a 2-digit ‘tables answer’, e.g. 36, 20, 32, 18, 45, 28, 42, etc., then write divisions beginning with 10 × that number.

Day 2
Model division above the times tables using ‘chunking’ on an empty number line (ENL), e.g. 65 ÷ 5, 54 ÷ 3, 43 ÷ 3.
Further Teaching with Y4
Introduce a vertical layout for dividing 2-digit by 1-digit numbers, a precursor to the ‘bus shelter’ method, e.g. 48 ÷ 3, 72 ÷ 3.
Group Activities: T with Y3
Y3 Use the in-depth problem-solving investigation ‘Threes and Fours’ as today’s group activity.
Or, use these activities:
-- Investigate numbers that will divide by 3 or 4 or both without leaving a remainder.
-- Play division mini-bingo with divisions that are just beyond the times tables (no remainders).
Y4 -- Calculate 10 ×, 20 × and 30 × 3, 4, 5, 6, 7 and 8. Use this to estimate answers when dividing 2-digit numbers by 1-digit numbers, with answers less than 20, then 30.
-- Divide 2-digit numbers by 1-digit numbers, with answers between 30 and 40.

Day 3
Model further divisions using an empty number line, this time with examples that leave remainders, e.g. 46 ÷ 3, 78 ÷ 5, 115 ÷ 8. Children solve 51 ÷ 4 on their whiteboards.
Further Teaching with Y4
Reason about the relative size of dividends. Further consolidate using the ‘bus shelter’ layout, e.g. for 85 ÷ 3, 85 ÷ 4, 85 ÷ 5; 134 ÷ 5/ 6/ 7.
Group Activities: T with Y3
Y3 -- Play a game choosing and calculating divisions then collecting counters for the remainders.
-- Play a division with remainders card game.
Y4 Use the in-depth problem-solving investigation ‘Arranging the Tables’ from NRICH as today’s group activity.
Or, use these activities:
-- Play a game to discover 2-digit by 1-digit divisions that have answers between 10 and 20.
-- Play a game to discover 2-digit by 1-digit divisions that have answers between 20 and 30, or between 30 and 40.

• Mini-whiteboards and pens
• ‘12 × 12 Multiplication grid’ (see resources)
• Number cards 1–12
• Counters
• ‘Recording table’ (see resources)
• ‘Division questions for mini-bingo’ (see resources),
• ‘Division practice’ (see resources)
• ‘Division calculations’ (see resources)
• ‘Blue and red cards’ (see resources)
• Flipchart and pens

Day 1
Double and halve 2-digit numbers

Day 2
Division facts for the 3 and 4 times tables

Day 3
8 times table

Day 1
Y3 Solve division problems.
Y4 Use times tables to divide.

Day 2
Y3 Divide beyond the times tables.
Y4 Division practice.

Day 3
Y3 Find remainders.
Y4 Division with remainders.

Y3

• How many 3s in each number?
  45
  52
  39
• Will the remainder be the same in these divisions?
  (i) 53 ÷ 4
  (ii) 66 ÷ 5
  (iii) 40 ÷ 3
  Estimate first, then calculate each to check.

Y4

• Write the missing number in each calculation.
  26 ÷ ☐ = 3 r 5
  55 ÷ ☐ = 18 remainder 1
• Fill in the missing numbers on the number lines (see download).
• Charlie has 95 pound coins. She makes six equal piles of coins as high as she can. Does she have any left over? If so, how many?
• Taking a taxi home from the cinema, 5 friends equally shared the cost of £12. How much did each passenger pay?
• True or False?
  An odd number divided by an odd number always gives an odd answer.
  An even number divided by an odd number always leaves a remainder.

Y3 In-depth Investigation: Threes and Fours
Children explore multiples of 3 and 4 to find divisibility patterns.

Y4 In-depth Investigation: Arranging the Tables
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places. Arranging the Tables from nrich.maths.org.

Y3: Flip-flops
Dividing within tables by 3, 4 and 5 (no remainders).

Y4: Remainders Rule
Using ‘chunking’ to divide numbers just beyond the times tables, including with remainders.

Day 1
Use place value cards as a supporting model to revise doubling and halving 2-digit numbers by partitioning and recombining.
Group Activities: T with Y3
Y3/4 Whole class -- Play a ‘chain’ game, halve numbers if even; add 1 when numbers are odd.
Y3 -- Play a 4-in-a-row grid game, doubling 2-digit numbers.
Y4 Use the in-depth problem-solving investigation ‘Set Square’ as today’s group activity.
Or, use this activity:
-- Play a 4-in-a-row grid game, halving 2-digit numbers.

Day 2
Model the grid method for multiplying 2-digit by 1-digit numbers: 14 × 2, 14 × 3, 14 × 6.
Further Teaching with Y4
Model the ladder method and compare to the grid method for 3-digit by 1-digit multiplication, e.g. 786 × 4.
Group Activities: T with Y3
Y3 Use the in-depth problem-solving investigation ‘18 Times Table – Wow!’ as today’s group activity.
Or, use these activities:
-- Describe stepping stones in developing use of the grid method. Rehearse use of preferred image(s) to begin using the grid method.
-- Practise multiplying smaller 2-digit numbers by 1-digit numbers.
Y4 -- Solve 3-digit by 1-digit multiplication challenges.

Day 3
Further shared learning of the grid method to build the 24 times table from 1 × 24 to 10 × 24. Link repeated addition to multiplication.
Further Teaching with Y4
Estimate and solve multiplications: 4 × 782 618 × 6 5 × 579.
Group Activities: T with Y4
Y3 -- Investigate multiplying odd and even 2-digit numbers by 1-digit numbers using the grid method.
Y4 -- Use a written method for 3-digit by 1-digit multiplications, finding answers in a number of given ranges.

• ITP Place Value
• Mini-whiteboards and pens
• ‘Doubling numbers’ Sheets 1 and 2 (see resources)
• Coloured pencils
• Sets of 100s, 10s and 1s place value cards
• ‘Halving numbers’ Sheets 1 and 2 (see resources)
• ‘Steps towards using the grid method for 14 × 5’ Sheets 1 and 2 (see resources)
• ‘Using the grid method’ (see resources)
• Flipchart and pens
• Squared paper
• Number cards 1–9, 11–30 and 21–40

Day 1
Times tables bingo

Day 2
30 times table

Day 3
Multiply and divide by 10 and 100

Day 1
Y3 Double and halve 2-digit numbers.
Y4 Halve 2 and 3-digit numbers.

Day 2
Y3 Grid multiplication.
Y4 Written multiplication.

Day 3
Y3 Grid multiplication.
Y4 Written multiplication.

Y3

• Write the missing numbers in each diagram (see download).
• How many odd numbers between 50 and 100, when halved, give an answer ending 4¹/2?
• Write the missing numbers in this grid (see download).
• Now complete the addition to find the total of the partial products:
  ☐ + ☐ = ☐

Y4

• Calculate: 154 × 7; 6 × 289; 4 × 5 × 9 × 3
• This calculation has the same number missing from each box. Write the missing number in the boxes. ☐ × ☐ – ☐ = 72
• A shop sells some boxes of ‘Triple-Chocs’ that cost £3.58 each, and makes £32.22. How many boxes did they sell?

Y3 In-depth Investigation: 18 Times Table – Wow!
Children use the grid method to derive the 18 times table, then look for patterns in the answers.

Y4 In-depth Investigation: Set Square
Use digits 1–9 once only to complete a calculation grid with given answers for each row and column.

Y3: Doubles Decisions
Doubling numbers up to 50.

Harder Halves
Halving even numbers to 100.

Y4: Multiplication Mix
Using the grid method to multiply 2-digit numbers by 1-digit numbers.

Day 1
Model and share examples of scaling, e.g. with a flapjack recipe and increasing the size of furniture. Discuss use of scaling in everyday life, e.g. maps, toys, model villages, furniture assembly instructions.
Group Activities: T with Y4
Y3 -- Scale down Lego™ houses to 1/4 of their original number of bricks
Scale up rectangles by × 4 and × 10.
Y4 -- Calculate the scaled-up dimensions for a giant’s furniture, converting cm to m (most children multiply by 4; some multiply by 5).

Day 2
Combine numbers of main courses and desserts. Find how many possible combinations. Establish links to tables facts.
Whole class activity: T with Y3
Y3/4 -- Investigate how many different combinations of two-scoop ice creams there are from a choice of four flavours.

Day 3
Revise how to find several multiplication and division facts from one known fact; investigate patterns on a multiplication grid.
Group Activities: T with Y4
Y3 -- Play multiplication/division ‘Ping Pong’ by writing a multiplication or division from the 2, 3, 4, 5, 8 or 10 times tables while a partner writes a related multiplication or division fact.
Practise multiplication and division facts games online.
Y4 -- Investigate patterns on a multiplication grid.

• Tape measures
• Mini-whiteboards and pens
• Lego bricks
• Rulers
• cm2 paper
• Chairs, bowls, spoons and mugs
• ‘12 × 12 Multiplication grid’ (see resources)
• Internet access

Day 1
Double numbers to 50

Day 2
Halve even numbers to 100

Day 3
3 and 4 times tables; 5 and 8 times tables

Day 1
Y3 Scaling problems.
Y4 Scaling problems.

Day 2
Y3 Combinations.
Y4 Combinations.

Day 3
Y3 Related multiplication and division facts.
Y4 Times tables practice.

Y3

• The postcards in the art gallery measure 15cm by 10cm.
  One is of a painting which is 4 times bigger.
  One is of a painting which is 10 times bigger.
  One is of a painting which is 5 times bigger.
  Write the measurements of each painting.
• A painting in the museum measures 160cm by 100cm. The gift shop sells posters of the painting at 1/4 full size and postcards at 1/10 full size. How big are posters and postcards?

Y4

• Write at least six divisions beginning with 3600, e.g. 3600 ÷ 4 = 900.
• Mr Jones’ rectangular garden measures 5m by 8m. His neighbour, Mr Payne, says, ‘My garden is twice as wide and double the length of your garden, so yours is half the size of mine.’ Do you agree with Mr Payne?
• The top-seller at Giovanni’s café is the ‘Quad-Choc-Challenge’ which is a dessert with 4 different flavours of chocolatey ice cream in a long thin dish. Here is one arrangement of flavours (see download). How many others are there?

In-depth investigation: Ice Cream Flavours
Y3/4 Day 2 Group Activity

Y3: Double Double
Multiplying by 4 by doubling twice; Dividing by 4 by halving twice.

Y4: Revisit the Group Activity from Unit 2 Day 1, creating Factor Bugs for a wide range of 2-digit numbers.