Maths Year 5 Spring Multiplication and Division

Each unit has everything you need to teach a set of related skills and concepts. 'Teaching for Understanding' provides whole-class teaching and fully differentiated adult-led group activities. ‘Problem-solving and Reasoning’ develops these skills, and includes questions to enable you to assess mastery. Practice sheets ensure procedural fluency. Extra support activities enable targeted work with children who are well below ARE.

‘UNIT PLAN’ gives you a text version of all parts of the unit to use in your school planning documentation. ‘DOWNLOAD ALL FILES’ gives you that unit plan plus all of associated documents.

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

Objectives

Lowest common multiples and highest common factors; mental strategies in division and multiplication
Unit 1: ID# 5531

National Curriculum
Mult/Div (i) (v) (ix)

Hamilton Objectives
12. Know and recite all times tables including division facts; identify multiples and factors, including common factors of two numbers.
14. Use efficient mental methods to multiply two or three numbers.
15. Perform divisions mentally in range of tables.
21. Solve problems involving multiplication and division, using knowledge of factors, multiples.

Teaching and Group Activities for Understanding

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 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)

Procedural Fluency

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)

Objectives

Short multiplication with four digit numbers including money
Unit 2: ID# 5557

National Curriculum
Mult/Div (iv) (ix)

Hamilton Objectives
16. Multiply 2-, 3- and 4-digit numbers by numbers ≤ 26, using short multiplication or grid method.
21. Solve problems involving multiplication and division, using knowledge of factors, multiples.

Teaching and Group Activities for Understanding

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 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)

Procedural Fluency

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)

Objectives

Short division with three and four digit numbers
Unit 3: ID# 5563

National Curriculum
Mult/Div (vi) (ix)

Hamilton Objectives
18. Divide 2-, 3- and 4-digit numbers by 1-digit numbers above tables range; choose and use efficient methods; interpret remainders appropriately according to context.
21. Solve problems involving multiplication and division, using knowledge of factors, multiples.

Teaching and Group Activities for Understanding

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 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)

Procedural Fluency

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 in this division, written as vertical chunking.
    7 8 3 ÷ 9 = ☐
    so, ? × 9 = 7 ☐ 3
    80 × 9 = 7 2 0
    ☐ 3
    ☐ × 9 = 6 3
    So answer = ☐
  • Complete the same calculation using short division.
    Which method do you find easier? Explain why.
  • (i) Is the answer to 1535 ÷ 3 treble the answer to 1535 ÷ 9?
  • (ii) 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