Short Blocks

Maths Year 5/6 Autumn Multiplication and Division (A)

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

Properties of numbers, including primes (suggested as 3 days)

Planning and Activities

Day 1 Teaching
Identify multiples of given numbers on a grid. Discuss divisibility tests. Identify common multiples of two numbers. Identify the lowest common multiple.
Group Activities
Y5 -- Explore common multiples, either using a Venn diagram for sorting, or by playing a 4-in-a-row dice game.
Y6 -- Explore common multiples, either by playing a 4-in-a-row dice game or a card game.

Day 2 Teaching
Find factors of 2-digit numbers. Play a game to help children understand that bigger numbers don’t necessarily have more factors.
Further Teaching with Y6
Find common factors; then the highest common factor.
Group Activities
Use the ‘Long as you like’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
Y5 -- Investigation: Find the number less than 50 with the greatest number of factors; explore numbers which have an even or odd number of factors.
Y6 -- Play games finding common factors and then highest common factors.

Day 3 Teaching
Play a game which encourages children to think which numbers have fewest factors, introduce prime and composite numbers.
Group Activities
Y5 -- Investigation: Find all the prime numbers to at least 50.
Y6 -- Investigation: Find which numbers from 10 to 50 can be made by multiplying two prime numbers together.

You Will Need

  • ITP: Number Grid
  • Whiteboards and pens
  • IWB calculator
  • Flipchart and pen
  • Sticky notes
  • 12 × 12 multiplication grid (see resources)
  • 0–9 dice
  • Coloured pencils
  • Several sets of number cards 2–12
  • Large number cards 1–10
  • ‘Common factors’ grid (see resources, enlarge to A3)
  • ‘Common factors’ grid (see resources)
  • 1–6 dice

Short Mental Workouts

Day 1
Divisibility

Day 2
Stand up – sit down squares

Day 3
Times tables

Worksheets

Day 1
Y5: Place numbers into a Carroll diagram, depending on divisibility by 3 and 4.
Y6: Find common multiples.

Day 2
Y5: Find factors of 2-digit numbers.
Y6: Find common factors of 2-digit numbers.

Day 3
Y5: Identify prime numbers to 100.
Y6: List prime numbers in a given range. Identify numbers with a pair of prime factors. Reduce a composite number to a list of its prime factors.

Mastery: Reasoning and Problem-Solving

Y5

  • Are there more or fewer common multiples of 2 and 3 under 30 than of 3 and 5? Explain your answer.
  • Write the common multiples of 2, 3 and 4 up to 50. Write the common multiples of 3, 4 and 5 up to 200. Which is the bigger group?
  • True or false?
    5 is a factor of 20 and a factor of 40.
    3 is a factor of 7 numbers less than 20.
    15 is a factor of 100.
  • Prime numbers are often one more or less than a multiple of 6. Write two prime numbers for which this is not true.
  • Write the following as the product of 2 or more prime numbers: 30, 35, 42, 56.

Y6

  • Which pair of numbers under 20 have the largest number of common factors? What is the highest common factor of these numbers?
  • Write common multiples of 4 and 6 up to 60. What is the lowest common multiple? Use this information to find the lowest common multiple of 8 and 12.
  • True or false?
    The lowest common multiple of two prime numbers, a and b is always a × b.
    The highest common factor of two multiples of 6 is always 6.

In-depth Investigation: Long as You Like
Children create chains of numbers by finding factors and multiples. Their aim is to create the longest chain possible.

Extra Support

Y5: Array or Disarray
Making different arrays using a given number as an introduction to factors.

Y6: Factor Hunt
Finding factors of numbers within times tables.