Short Blocks

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

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 Strategies for division (suggested as 4 days)

Objectives

Strategies for division
Unit 3: ID# 34286

Y3: Dividing using multiplication facts, with remainders.
Y4: Divide numbers above the 10th multiple using chunking/written method.

National Curriculum
Y3: Num/Mult/Div (i) (ii) (iii)
Y4: Num/Mult/Div (i) (ii) (iv)

Y3 Hamilton objectives
16. Understand that division is the inverse of multiplication.
17. Know the 2×, 3×, 4×, 5× and 10× times tables, including division facts.

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.

Planning and Activities

Day 1
Explore division by 5 by grouping. Use numbers that facilitate introduction of remainders, e.g. 21 ÷ 5.
Further teaching with Y4
Division on an Empty Number Line (no remainders)
Group activities: T with Y3 or Y4
Y3 -- Explore how to calculate and record ‘left overs’ when dividing by 5.
Y4 -- Make a poster showing how to divide using ‘chunking’ on a number line.

Day 2
Y4s show Y3s how they use an Empty Number Line for solving division questions.
Further teaching with Y3
Divide by 3, 4, 5 and 10 using the Grouping ITP.
Group activities: T with Y3
Y3 -- Create a range of number stories that show how groups can be formed from different numbers of children (including with left overs).
Y4 -- Improve fluency with dividing by chunking.

Day 3
Consider how to tell if a division question will have a remainder; check division by multiplication.
Further teaching with Y4
Model vertical layout for division.
Group activities: T with Y3 or Y4
Use the in-depth problem-solving investigation ‘Rocking remainders’ as today’s group activity.
Or, use these activities:
Y3 -- Divide a range of 2-digit numbers by 3, 4, 5 and 10; check division by multiplication.
Y4 -- Divide 2-digit numbers to give answers with remainders.

Day 4
Use multiples of 10 times the divisor to estimate answers to divisions. Reason about which will have the largest/smallest answer.
Further teaching with Y3
Estimating answers to divisions, which will have the largest/smallest answer? (further examples).
Group activities: T with Y3 or Y4
Y3/ Y4 -- Play a game to create divisions of 2-digit numbers, resulting in answers within a given range and with a remainder.

You Will Need

  • ITP: Grouping
  • ‘0–50 beaded lines’ (see resources)
  • Cubes, poster paper and pens
  • ‘Story cards’ (see resources)
  • ‘Images to use for grouping’ (see resources)
  • Sticky notes
  • ‘Chunking Champ’ division cards (see resources)
  • Blank cards, bag and stopwatch
  • ‘3×, 4× and 5× tables’ (see resources)
  • Mini whiteboards and pens
  • 1–6 dice and 0–9 dice (or spinners)

Short Mental Workouts

Day 1
Multiplication patterns

Day 2
I spy a 3 times table fact

Day 3
Doubles and halves

Day 4
Division facts: 3 and 6 times tables

Procedural Fluency

Day 1
Y3 Dividing by 3, 4, and 5 with remainders.
Y4 Use chunking on a number line to divide by 3, 4, 5, 6 and 8 with no remainders.

Day 2
Y3 Dividing by 2, 3, 4, 5, and 10 with remainders.
Y4 Use chunking on a number line to divide by 3, 4, 5, 6 and 8 with no remainders.

Day 3
Y3 Reason about remainders; check division by multiplication.
Y4 Divide 2-digit numbers by 1-digit numbers - beyond tables - with remainders.

Day 4
Y3 Odd one out: Division with remainders.
Y4 Use division in real-life contexts to solve word problems.

Mastery: Reasoning and Problem-Solving

Y3

  • What is the remainder when 34 divides by 4?
  • Divide 29 by 2 then by 3, then by 4, then by 5. What will the remainder be if you divide it by 10?
  • What number will divide into 34 and leave a remainder of 4?
  • Which number between 30 and 40 can be divided by the most numbers leaving no remainders?

Y4

  • Correct Amit’s number line divisions. He has made the same mistake twice. Explain what the mistake is. Show the correct calculations (see download).
  • What is similar about these two calculations?
    57 ÷ 3 = ?
    76 ÷ 4 = ?
    Challenge: Write a similar calculation where we divide by 5.

In-depth Investigation: Rocking Remainders
Children divide 11, 22, 33 ... 99 by 3, 4, 5... and look for patterns in the remainders.