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. '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. These bulk downloads are added value for Hamilton Friends and School Subscribers.

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.

Teaching and Group Activities for Understanding

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 Division with remainders.
Y4 Divide 2-digit numbers by 1-digit numbers to get answers with remainders.

Day 4
Y3 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.