Maths Year 3/4 Summer Multiplication and Division (A)

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.