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Brighton CTP: Division in Y5&6

Brighton CTP: Division in Y5&6. Jenni Back Associate Director for Primary. 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

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Brighton CTP: Division in Y5&6

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  1. Brighton CTP: Division in Y5&6 Jenni Back Associate Director for Primary

  2. 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

  3. 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

  4. Sharing or Grouping • What does each mean? • Model each with some counters for 8  2 • What’s the same? What’s different?

  5. How do grouping and sharing relate to repeated addition and scaling?

  6. Two Main Structures • Addition and Subtraction • Multiplication and Division • What key models and images support • conceptual understanding?

  7. The aims of the new National Curriculum • Fluency • Problem solving • Reasoning

  8. Progression in Y 5 & 6 • Knowing and being able to apply all multiplication and division facts to 12x12 • Moving from mental calculation to formal written methods • Solving problems involving division and being able to interpret remainders

  9. What are the key facts? • Tables expressed 4 ways • Deep understanding of place value • ‘Mega’ tables

  10. Party scenarios • How many apricots will we each have if 1.5kg is shared between 12 of us? There are roughly 30 apricots in one kilogram. Sharing by counting and cutting • There are 30 cocktail sausages. How many will each guest be able to have? What shall we do with the spares? Sharing by counting out • 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

  11. 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

  12. 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 • 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

  13. 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

  14. 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 Y5 & 6 pupils • Be prepared to feedback and share

  15. 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

  16. An image for 56  7 8 7 5 6 • Either: • How many 7s can I see? (grouping) • Or: • If I put these into 7 groups how many in each group? (sharing) The array is an image for division too

  17. An image for 56  7 8 7 5 6 • How many 7s can I see?

  18. 8 • How many 7s can I see? 7 5 6 • 18

  19. 8 • How many 7s can I see? 7 5 6 • 19

  20. 120  3 40 3 120 The power of the place value: counters for larger numbers • 20

  21. 1200  3 400 3 1200 Similarly for 100s • 21

  22. 3 0 23 138 6 20 1 1 6 1 3 8 • 22

  23. Task Explore some division calculations using the different manipulatives. • How well do the manipulatives help you to solve the calculation problems? • How well do the manipulatives help to move pupils towards written methods? • Reflect on your own practice about how a written method for division can be taught.

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