Maths Year 5 Spring Multiplication and Division

Each unit has everything you need to teach a set of related skills and concepts.

Unit 1 Multiples & factors; mental x/÷ strategies (suggested as 3 days)

Planning and Activities

Day 1 Teaching
Use the ITP Number grid to highlight multiples of 2 and 3. Point out that 6 is the lowest common multiple of 2 and 3. Repeat for LCM of 3 and 4, then of 3 and 6, then 6 and 9. Now find highest common factor of 32, 16 and 24, then 12, 20 and 32.
Group Activities
Use the ‘LCM Squares’ in-depth problem-solving investigation below as today’s group activity.
Or, use this activity:
-- Derive highest common factors and/or lowest common multiples.

Day 2 Teaching
Write 23 × 10 and 23 × 5 and show how we can use the former to solve the latter – it’s a lot more efficient than counting in 5s! Repeat for 23 × 20 and 23 × 19. Then model 23 × 6 as 23 × 3 doubled. Discuss strategies for 23 × 8 by repeated doubling.
Group Activities
-- Explore mental methods based on doubling and halving to multiply by 5, 20, 6, 4 and 8.

Day 3 Teaching
Use 240 ÷ 10 to solve 240 ÷ 5 and 240 ÷ 20. Ensure children realise when they need to double to give a bigger answer (÷5) and when they need to halve it to give a smaller answer (÷20). Ask children to work out 270 ÷ 3, and use this to find 270 ÷ 6. Use repeated halving to divide by 4 and 8.
Group Activities
-- Explore mental strategies to divide by 5, 20, 6, 4 and 8. Articulate strategies to make generalisations.

You Will Need

Mental/Oral Maths Starters

Day 1
Divisibility by 2, 3 or 5 (pre-requisite skills)
Click on Random Number Bingo Generator from www.primaryresources.co.uk

Suggested for Day 2
Double 2-digit numbers (simmering skills)

Suggested for Day 3
‘Fizz-Buzz-Whizz: Common multiples’ (simmering skills)

Worksheets

Day 1
Finding highest common factor and lowest common multiple of sets of numbers.

Day 2
Using mental strategies (in particular doubling and halving) to multiply by 5, 20, 6, 4 and 8.

Day 3
Using mental strategies (in particular doubling and halving) to divide by 5, 20, 6, 4 and 8; articulate strategies.

Mastery: Reasoning and Problem-Solving

  • Is the lowest common multiple of 6 and 4 smaller than the highest common factor of 30 and 45?
  • Write common factors of 24 and 48.
    Write common multiples of 3 and 5 up to 60.
    Are any numbers in both sets?
  • True or false?
    There are exactly four 2-digit, common multiples of 3 and 7.
    4 and 5 are common factors of all 2-digit multiples of 10.
    15 is a factor of 100.
  • If 350 ÷ 5 is 70, calculate 350 ÷ 10, 350 ÷ 20 and 350 ÷ 70.
    So can you have a try at 350 ÷ 2.5?


In-depth Investigation: LCM Squares
Children use trial and improvement to find the smallest possible total on a square of lowest common multiples.

Extra Support

Mammoth Multiplications
Using known times tables and place value to multiply, e.g. 4 × 3, 4 × 30, 4 × 300.

Unit 2 Short multiplication: 4-digit nos & money (suggested as 3 days)

Planning and Activities

Day 1 Teaching
Use the grid method to work out 3 × 235. Then model the same calculation using short multiplication. Having first discussed estimating answers, use both methods to solve 3 × 4235, 6 × 3241 and 5734 × 4.
Group Activities
-- Estimate products. Multiply 4-digit numbers by 1-digit numbers: some with money.

Day 2 Teaching
Write 2137 × 6. Children discuss a good estimate for this product. Take feedback: 13,000 would be a good estimate. Children use the grid method or short multiplication to find the exact answer. Repeat with 7 × 6423.
Group Activities
Use the in-depth problem-solving investigation ‘Domino multiplication’ from NRICH as today’s group activity.
Or, use this activity:
-- Investigate to solve puzzles, using multiplication of 4-digit numbers by 1-digit numbers.

Day 3 Teaching
Show children four cards, e.g. 3, 5, 7 and 8. Ask them to each create a 4-digit number using these digits. Choose one of the numbers made by a child. Write this number × 7. Choose some children to use the grid method, whilst you model short multiplication. Compare answers.
Model short multiplication with money, e.g. 6 × £25.79 using both the grid method and short multiplication, emphasising care with place value.
Group Activities
-- Estimate products, then multiply 4-digit money amounts by 1-digit numbers.

You Will Need

  • Whiteboards and pens
  • Six large blank cards
  • Number cards 1–10

Mental/Oral Maths Starters

Suggested for Day 1
Times table bingo (simmering skills)

Suggested for Day 2
Factors and multiples (simmering skills)
Factors and multiples from nrich.maths.org

Suggested for Day 3
Addition and subtraction chains (simmering skills)

Worksheets

Day 1
Multiply 1-digit by 4-digit numbers using the grid method or short multiplication.

Day 2
Estimate and solve multiplication calculations; create puzzles.

Day 3
Estimate and solve multiplication problems with money.

Mastery: Reasoning and Problem-Solving

  • Does 2340 × 8 give the same answer as 4320 × 4? Explain how you are certain that your answer is correct.
  • Choose a strategy for each of these three multiplications. Explain why it is not sensible to use the same method for all three.
    (i) 340 × 5 =
    (ii) 421 × 7 =
    (iii) 350 × 9 =
  • ☐☐☐☐☐ x ☐
    Using the digits 3, 5, 6, 7 and 9, how close can you get to 20,000?


In-depth Investigation: Domino Multiplication
Lay out four dominoes in a pattern that shows an accurate multiplication calculation. Domino Multiplication from nrich.maths.org.

Extra Support

Multiplication Splits
Using the grid method to multiply 3-digit numbers by 1-digit numbers

Unit 3 Short division with 3- & 4-digit numbers (suggested as 4 days)

Planning and Activities

Day 1 Teaching
Today we are going to learn a ‘traditional’ method of division called short division (sometimes nicknamed the ‘bus shelter’ method). Use the PowerPoint and base-10 equipment to model this method of division for 678 ÷ 3.
Group Activities
-- Solve short division calculations and investigate remainders.

Day 2 Teaching
Use the PowerPoint, alongside base-10 equipment, to demonstrate using short division to solve 281 ÷ 3. Discuss whether the answer we get seems about right. Together, use vertical chunking to check it. Repeat for 281 ÷ 6 and 281 ÷ 5.
Group Activities
-- Solve short division calculations and investigate remainders, including examples where the first digit is less than the divisor.

Day 3 Teaching
Children use short division to solve 742 ÷ 4. Support conceptual understanding, modelling with base-10 equipment. Agree answer as 185 r2. But what does ‘remainder 2’ mean? It is 2 left over from trying to make a group of four… two out of four… or 2/4. We can simplify 2/4 to 1/2, so the exact answer is 185 1/2. Repeat for 742 ÷ 8 (92 3/4) and 742 ÷ 6 (123 2/3).
Group Activities
-- Explore division, expressing remainders as fractions.

Day 4 Teaching
Use short division or the ‘bus shelter’ layout to show 4281 ÷ 3, using base-10 equipment to model each stage (see below plan) and/or PowerPoint (see resources). Repeat for 2537 ÷ 3. Remind children that we can divide the remainder 2 by 3 to give an answer of 8452/3. Ask children to try 3341 ÷ 4 and 4281 ÷ 5.
Group Activities
Use the ‘Division remainder patterns’ in-depth problem-solving investigation below as today’s group activity.
Or, use this activity:
-- Divide 4-digit money amounts by 1-digit numbers; Explore division, expressing remainders as fractions.

You Will Need

  • Base-10 equipment
  • Whiteboards and pens
  • Flipchart
  • Number cards 1–9
  • PowerPoint Resource 1 (see resources)
  • PowerPoint Resource 2 (see resources)
  • PowerPoint Resource 3 (see resources)

Mental/Oral Maths Starters

Suggested for Day 1
Times tables (simmering skills)

Suggested for Day 2
Find highest common factors (simmering skills)

Suggested for Day 3
Doubles and halves (simmering skills)

Suggested for Day 4
Times table bingo (simmering skills)

Worksheets

Day 1
Divide 3-digit by 1-digit numbers, including answers with remainders.

Day 2
Divide 3-digit by 1-digit numbers, including word problems.

Day 3
Divide 3-digit by 1-digit numbers; write remainders as fractions in their simplest form.

Day 4
Divide 4-digit by 1-digit numbers, including word problems.

Mastery: Reasoning and Problem-Solving

  • Fill in the missing digits (see download) in this vertical chunking division calculation:
    7 8 3 ÷ 9 = ☐
  • Complete the same calculation using short division.
    Which method did you find easier? Explain why.
  • (i) Is the answer to 1539 ÷ 3 treble the answer to 1539 ÷ 9? Now use short division to find an answer to both calculations. Was your answer to (i) correct?


In-depth Investigation: Division Remainder Patterns
Children look at patterns of remainders in 4-digit numbers when dividing by numbers 3 to 6. Can they establish a rule?

Extra Support

Any Left?
Using chunking to divide, answers between 10 and 20, with remainders