Short Blocks

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

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

Unit 1 Rehearsing & understanding times tables (suggested as 3 days)

Planning and Activities

Day 1
Quickly practise revising multiples of 5. Look at a 5 by 7 array; establish four connected multiplication and division facts. Repeat for 12 × 2, modelling groups on a bead bar.
Further teaching with Y4
Investigate multiplication and division facts using an interactive ‘function machine’.
Group activities: T with Y3
Y3 -- Identify the four number facts that an array describes. Play a tables facts game.
Y4 -- Create and solve function machine problems for the 2, 3, 4, 5 and 10 times tables.

Day 2
Model and derive 3 times table facts and corresponding divisions using 12 towers of 3 cubes.
Further teaching with Y4
Generate 6 times table facts by doubling the 3 times table.
Group activities: T with Y4
Y3 -- Find multiples of 3 by hopping on a beaded line. Play a 3 times table game.
Y4 -- Play a 3 times table and 6 times table game.

Day 3
Model 4 times table facts and the corresponding divisions using a 12-section counting stick.
Further teaching with Y4
Generate 8 times table facts by doubling the 4 times table.
Group activities: T with Y4
Use the in-depth problem-solving investigation for this unit ‘Mystery age’ as today’s group activity.
Or, use these activities:
Y3 -- Find multiples of 4 by hopping on a beaded line. Practise recall of the 4 times table.
Y4 -- Recall 4 times tables facts; double to find 8s. Play a 4 and 8 times table game.

You Will Need

  • ‘5 by 7 array’ and 'Arrays' (see resources)
  • 100-bead bar
  • ITP: Function machine
  • Sets of number cards (2, 5, 10 and 3–12)
  • ‘2, 5 and 10 times tables’ (see resources)
  • Coloured pencils and sticky notes
  • ‘Mystery function machine’ (see resources)
  • Cubes, number cards 1–12 and blank cards
  • ‘0–40 beaded lines’ (see resources)
  • Set of 1–12 cards and a coin per pair
  • Set of 1–12 cards and set of 2–6 cards
  • ‘Counting stick’ (see resources)
  • ‘0–50 beaded lines’ (see resources)
  • Multiples of 4 cards and 2-minute timer

Short Mental Workouts

Day 1
Division facts: 5 times table

Day 2
Division facts: 2, 5 and 10 times tables

Day 3
Division facts: 3 and 6 times tables

Worksheets

Day 1
Y3: Recognise multiples of 2, 5 and 10.
Y4: Solve function machine problems using times tables facts.

Day 2
Y3: 3 times table practice.
Y4: 3 and 6 times tables practice.

Day 3
Y3: 4 times table practice.
Y4: 4 and 8 times tables practice.

Mastery: Reasoning and Problem-Solving

Y3

  • Write 4 number sentences to relate these 3 numbers: 5, 7 and 35.
  • We know 8 × 5 = 40. So, what is 40 ÷ 5?
    We know 24 ÷ 2 = 12. So, what is 12 × 2?
  • Write a division with an answer of 5. Now write a different division using those same three numbers.
  • Explain why you might prefer to do 5 × 9 as 9 lots of 5.
  • Write the missing numbers:
    ☐ × 4 = 28
    3 × ☐ = 21
    36 ÷ ☐ = 4

Y4

  • Write 48 in the middle of a space and circle it. Draw 10 spider legs out from it. Write 10 multiplication or division sentences using this number, e.g. 48 ÷ 6 = 8.
  • What times table is this? Explain what number ‘a’ stands for.
    6 × a = 20 + a
    8 × a = 30 + half of a
  • Always true, sometimes true or never true?
    In one times table, there are only 2 possible ones digits in the answers.
    3 times a number is an odd number.
    Answers in the 4 times table are even.
    Answers in the 3 times table are also in the 6 times table.

In-depth Investigation: Mystery Age
Y3: Children use their knowledge of the 3, 4, and 5 times tables to work out mystery numbers.
Y4: Children use their knowledge of the 5, 6, and 8 times tables to work out mystery numbers.

Extra Support

Y3
Hops, Skips and Jumps

Counting in 2s from 0 to 20 and counting in 5s from 0 to 50

and/ or

Monster Multiplications
Counting in 3s - 'Clever Counting' and multiplication

Y4
Clever Counting

3 and 4 times tables. Linking multiplication and division

Unit 2 Partitioning in multiplication and division (suggested as 3 days)

Planning and Activities

Day 1
Identify and reason about patterns across the 1, 2 and 4 times tables. Use this as a basis for modelling multiplying by 4 by doubling twice, using the strategy of partitioning, doubling and recombining.
Further teaching with Y4
Introduce the grid method for multiplying 2-digit by 1-digit numbers, beginning with comparison of partitioning/recombining and grid for 23 × 2.
Group activities: T with Y4
Use the in-depth problem-solving investigation ‘Doubling forever’ as today’s group activity.
Or, use these activities:
Y3 -- Multiply a range of 2-digit numbers by 4.
Y4 -- Multiply 23 by 1-digit numbers using the grid method. Some children will find the 36 times table using the grid method.

Day 2
Model dividing by 4 by halving twice, linking with Day 1’s strategy of multiplying by 4 by doubling twice.
Further teaching with Y4
Use grid multiplication with larger 2-digit numbers.
Group activities: T with Y4
Y3 -- Divide numbers on cards by 4 by halving twice.
Y4 -- Use grid multiplication to find which arrangement of digits produces the greater answer.

Day 3
Year 4 explain grid multiplication to Y3, for 6 × 13, then 7 × 14.
Further teaching with Y3
Look at the multiplication and division facts that an array describes.
Group activities: T with Y3 or Y4
Y3 -- Investigate arrays.
Y4 -- Investigate grid multiplication, finding different numbers that produce the same products.

You Will Need

  • ‘Multiples of 1, 2 and 4’ (see resources)
  • Set of 2–9 cards and sets of 1–10 cards
  • ‘Multiplying and Dividing by 4’ (see resources)
  • ‘Multiples of 4 number cards’ (see resources, 1 set per pair)
  • Calculators
  • Place value cards (arrow cards): tens (10–50) and ones (1–9)
  • 1–6 dice and counters

Short Mental Workouts

Day 1
4 and 8 times tables

Day 2
3 and 6 times tables

Day 3
Multiply and divide by 10

Worksheets

Day 1
Y3: Multiply by 4 by doubling twice.
Y4: Complete multiplication grids for multiplying 2-digit by 1-digit numbers.

Day 2
Y3: Halve twice to divide by 4.
Y4: Grid method multiplication.

Day 3
Y3: Linking multiplication and division within tables.
Y4: Matching grids – find different multiplications with the same partial products.

Mastery: Reasoning and Problem-Solving

Y3

  • Start at 3 and keep doubling until your answer is close to 100 but NOT over. How many doubles did you write? Repeat, starting at 4. How many this time?
  • Write the missing numbers in these diagrams:
    Diagram 1:
3636

Diagram 2:

52
??
  • What mistake has Fred made in his work?
    13 × 4 = 26
    21 × 4 = 42
    56 ÷ 4 = 28
    64 ÷ 4 = 32
  • Divide 128 by 4. Can you divide the answer by 4? Can you divide that answer by 4?

Y4

  • Use the grid method to complete each of these:
    24 × 6 = ☐
    ☐ = 3 × 48
    Say why the missing numbers are the same.
  • Write the missing numbers:
x30
424= ☐
  • Say how much bigger the answer to (ii) will be than the answer to (i). Answer both using the grid method to find out if you were right.
    (i) 6 × 43
    (ii) 5 × 43

In-depth Investigation: Doubling Forever
Children double numbers up to 10 (Y3) or 20 (Y4) and look for duplicate sequences.

Extra Support

Y3

Double your Money
Doubling 2-digit numbers (answers less than 100)

and/or

Fair Friends
Halving even 2-digit numbers, with even 10s digits

Y4

Double or Halve?
Doubling and halving 2-digit numbers using partitioning (whole number answers only)

and/or

Double Trouble
Doubling 2-digit numbers using partitioning (including answers over 100)