1. Division in all its aspects
Dr Jenni Back
Host Schools Project Lead

2. Key thresholds in mathematical development in arithmetic
KS1 entry: conservation and counting
KS2 entry: addition/subtraction, number bonds to 20, place value
KS3 entry: multiplication/division, multiplication tables
KS4 entry: proportional reasoning

3. The issues in years 3 and 4 Securing conservation and counting
Additive reasoning, fluent recall and application of number bonds to 20, understanding place value
Developing ideas of multiplication and division
Intuitive understanding of proportional reasoning

4. The Big Ideas in arithmetic in Y3 & 4
Doing and undoing
The number system and place value
Securing and deepening understanding of addition and subtraction
Building repertoire of known facts
Developing understanding of multiplication and division

5. Some questions to explore
Imagine a party scenario.
Look at the question and think about the meaning of division that it relates to
Consider the resources that might support an investigation of the problem
Be ready to share your ideas with others

6. Party scenarios
How many apricots will we each have if 1kg is shared between 12 of us? There are roughly 30 apricots in one kilogram. Sharing by counting out and cutting
There are 40 sandwiches and 12 people at the party. How many will each guest be able to have? What shall we do with the spares? Sharing by counting out and cutting
Here is a cake, we need to share it between the 12 people at the party. How do we do it? Sharing by cutting into congruent shapes    

7. Party Scenarios continued
There are 5 pizzas. How can we share them between the 12 people? Sharing by cutting successively into congruent shapes
We have 3 litres of juice for a party of 12 people. How many 120ml glasses will it fill? How many glasses each will that give everyone? Sharing by pouring liquids
I am making invitations for a party and want them to be 10cm by 12cm. How many will I be able to cut out of each A4 sheet of card that I have? How many sheets of card will I need to make 12 invitations? Sharing by fitting into a shape

8. Party Scenarios continued
I am making bunting to hang across the room. How many flags will I need to make to reach across the diagonal of the hall measuring 6m by 7m? You will need to think about the size of the flags, their shape, the tape or string they are fixed to and the gaps between them. To put them across both diagonals and along all four of the sides, how many more will I need? Finding out how many lengths x there are in y
I have a bag of 30 balloons to decorate the hall. How many groups of 4 can I make? Grouping in 4s

9. Party scenarios continued
If 12 people come to the party, how can I divide them into teams? What would be the best way to do this? Grouping in 2s, 3s, 4s etc or using multiplication facts
If 12 people come to the party and they all go bowling by car from the hall, how many cars will be needed if each car can take 5 people? How many cars will be needed if each car has to have an adult to drive it in addition to the party guests? Successive subtraction or grouping and rounding up

10. Division: what does it mean?
Children need to make sense of it
Crucial to focus on communicating ideas
How would you explain it?
Sharing
Grouping
Inverse of multiplication
Successive subtraction
What other concepts is it dependent on?
Addition, subtraction and multiplication

11. How can we support children’s understanding of it?
Easy access to a range of appropriate and useful representations
Support them in applying their ideas to new problems and eventually new concepts

12. Carousel of activities
Division as the inverse of multiplication
Exploring Factors – Maths Out Loud 5 lesson 15
Considering remainders
Susie the Snake & Maisie the Mouse – Mathematical Challenges Able pupils at Key Stages 1 & 2
Division as repeated subtraction
Dan the Dragon Slayer - Beam’s Big Book of Word Problems for Years 5 & 6 Unit 22
Division as sharing
Party Time - Beam’s Big Book of Word Problems for Years 5 & 6 Unit 21
Division as grouping
Cinderella -Beam’s Big Book of Word Problems for Years 3 & 4 Unit 22

13. Focus of engagement with activities
Try the activity together – do the mathematics
Identify the potential learning and progression of learning through the task
Consider support and extension
Identify the practical resources that might support the learning
Develop an outline lesson plan using the task for your Y3 & 4 pupils
Be prepared to feedback and share

14. Developing fluency in division calculations
Building on know facts and inverses – mental methods and jottings
Written methods
Chunking up or down
The ‘bus stop’ method for short division
Using Dienes as a supporting resource
The ultimate goal of long division
Division of three-digit numbers – Maths Out Loud 6 lesson 15

15. Next Steps Where do you plan to take the work we have done today?
Try some activity within the next week
Feedback on the NCETM website about what you have done
Share your experiences with your colleagues in school

16. Thank you for listening
Dr Jenni Back
Telephone