Short Blocks

Maths Year 3/4 Spring Division

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

First time using Hamilton Maths?
Open Unit 1 and download the PowerPoint from 'Planning and Group Activities': a brilliant and ready-to-use maths lesson for your white board!

The PowerPoint incorporates step-by-step teaching, key questions, an in-depth mastery investigation, problem-solving and reasoning questions - in short, everything you need to get started.

All the other resources are there to support as-and-when required. Explore at your leisure - and remember that we are always here to answer your questions.

Unit 1 Division (suggested as 4 days)

Objectives

Division
Unit 3: ID# 34618

Y3: Connecting multiplication and division facts; remainders; finding unit and non-unit fractions.
Y4: Division using vertical layout; finding unit and non-unit fractions.

National Curriculum
Y3: Multiplication and Division (i) (ii) (iii); Fractions (ii)
Y4: Multiplication and Division (i) (iii); Fractions (iii)

Y3 Hamilton objectives
17. Know the 2, 3, 4, 5, 8 and 10 times tables, including division facts.
23. Recognise, find and write unit and non-unit fractions of 'convenient' amounts, e.g. 1/10 of 100 or 1/3 of 60.

Y4 Hamilton objectives
20. Know how to use ‘efficient chunking’ for division above the range of the tables facts, e.g. 84 ÷ 6 = ? Begin to extend this to 3-digit numbers.
24. Use times tables to find unit and non-unit fractions of amounts, e.g. 1/6 of 48, 3/8 of 64.

Planning and Activities

Day 1
Model using multiplication grid to find division facts including remainders, i.e. by tracing along 3s row to find 18 ÷ 3 then 20 ÷ 3.
Further Teaching with Y4
Divide 47 ÷ 3 using an ENL then using a vertical layout. Discuss links between the methods; then repeat for further examples, e.g. 68 ÷ 5, 67 ÷ 3 and 91 ÷ 4.
Group Activities: T with Y4
Y3 -- Division card game, using dice to generate random divisors.
Y4 -- Play a game or investigate dividing 2-digit numbers by 1-digit numbers (with remainders). Reason about patterns of remainders.

Day 2
Recap of vertical division layout – Y4 model for Y3, show how it draws on division facts.
Further Teaching with Y3
Complete blank divisions table – dividing numbers from 19 upwards by 2, 3, 4, 5, etc. and looking for patterns.
Group Activities: T with Y4
Y3 -- Complete blank divisions table, exploring patterns.
Y4 -- Divide 2-digit numbers by 1-digit numbers (with remainders). Some children will divide 3-digit numbers by 1-digit numbers.

Day 3
Find unit fractions. Use a visual model using a strip of 12 objects to find a half, a quarter and a third of 12. Make the connection to division facts then record as a bar model.
Group Activities: T with Y3
Y3 -- Find quarters or eighths using times table facts.
Y4 -- Find unit fractions of quantities using division facts including larger numbers.

Day 4
Recap from previous day then extend to non-unit fractions, i.e. if 1/3 of 18 is 6 what is 2/3? Use a visual model of a 5 × 5 grid of stars to find fifths and also record in a bar model. Also for eighths of 24.
Group Activities: T with Y3
Use the in-depth problem-solving investigation ‘Andy's Marbles’ from NRICH as today’s group activity.
Or, use these activities:
Y3 -- Write multiplication, division and fraction sentences about arrays.
Y4 -- Using bar models, write fraction sentences to go with multiplication sentences for 24 and 40. Some children create a poster to explain how to find non-unit fractions.

You Will Need

  • ‘Multiplication grid’ (see resources)
  • Number cards 1–100
  • 1–6 dice, labelled with handwritten stickers 2, 3, 4, 5, 8, 10
  • 1-100 grid
  • Day 2 Y4 practice sheets
  • Counters, Cubes
  • Large multiplication grid
  • ‘Blank divisions table 1’ and ‘Blank divisions table 2’ (see resources)
  • ‘Strips of 12 objects’ (see resources)
  • ‘Bar models’ (see resources)
  • ‘Finding non-unit fractions 1’ and ‘Finding non-unit fractions 2’ (see resources)

Short Mental Workouts

Day 1
Division facts for 3 times table

Day 2
Place value subtraction chains

Day 3
Practise the 8 times table

Day 4
Finding fractions of numbers

Procedural Fluency

Day 1
Y3: Divide 2-digit numbers by 2, 3, 4, 5, 8, and 10.
Y4: Divide 2-digit numbers to give remainders.

Day 2
Y3: Function machines to divide by 2, 3, 4, 5, 8, and 10.
Y4: Divide 2- and 3-digit numbers by 1-digit numbers.

Day 3
Y3: Find unit fractions, using a bar model for support. Find unit fractions of numbers to 40.
Y4: Find unit fractions of 3-digit multiples of 10.

Day 4
Y3: Find unit, then non-unit fractions of numbers. Find non-unit fractions of numbers.
Y4: Find non-unit fractions of 2-digit numbers; then 3-digit multiples of 10.

Mastery: Reasoning and Problem-Solving

Y3

  • Mystery number Which ONE number makes this sentence true?
    ☐ ÷ 6 = 24 ÷ ☐
  • Which number between 30 and 40 can be divided by the most numbers leaving no remainders?

Y4

  • Find 1/8, then 3/8 and then 5/8 of 24.
  • Write the missing numbers.
    ___ of 15 is 5
    2/3 of ___ = 14
    3/5 of 20 = ____
    ___ of 10 = 4
  • Which is bigger, 2/5 of 35 or 3/8 of 32?

In-depth investigation: Andy's Marbles
Calculate fractions of numbers to help Andy work out how many of his marbles have been lost or given away. Andy's Marbles from nrich.maths.org.

Extra Support

Y3
Fruit Strips
Find 1/4 of numbers by folding strips.

Y4
Leftovers
Use ‘chunking’ to divide numbers just beyond the times tables, including with remainders.