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Teaching Mathematics at St Michael’s Junior School

Teaching Mathematics at St Michael’s Junior School. The approach to teaching calculation methods. Do it your way!. 25x19 5% of 86 248-99 103-98 ½ of 378 1+2+3+4+5+6+7+8+9+10+11=. Key features of the strategy for mathematics. An emphasis on the development of mental calculation

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Teaching Mathematics at St Michael’s Junior School

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  1. Teaching Mathematics at St Michael’s Junior School The approach to teaching calculation methods SDe'Athe, Maths Subject Leader

  2. Do it your way! • 25x19 • 5% of 86 • 248-99 • 103-98 • ½ of 378 • 1+2+3+4+5+6+7+8+9+10+11= SDe'Athe, Maths Subject Leader

  3. Key features of the strategy for mathematics • An emphasis on the development of mental calculation • A greater focus on the development of number skills and knowledge SDe'Athe, Maths Subject Leader

  4. Expanded Written Methods Standard Written Methods Calculator Mental Calculations with jottings Informal Methods Mental Recall The calculating continuum SDe'Athe, Maths Subject Leader

  5. The calculating repertoire • Children constantly move up and down the continuum • Learning a new method of calculating does not mean other ways are no longer relevant • Children should always be looking for calculations they can do wholly or partly mentally SDe'Athe, Maths Subject Leader

  6. A structured approach to calculation An approach based on the skills of mental calculation: • Remembering number facts • Using known facts to derive new ones • Familiarity with the number system and relationships between numbers • Having a repertoire of mental calculation strategies • Understanding of the four operations and how they are related SDe'Athe, Maths Subject Leader

  7. Addition and subtraction • Partitioning is an important strategy children must learn • A number line is a method of informal calculation that works for any size of number, for both operations. • Knowing 33 + 25 = 58 leads to the following: 25 + 33 = 58, 58 - 33 = 25, 58 - 25 = 33 And being able to manipulate them to work out 25+ ? = 58 SDe'Athe, Maths Subject Leader

  8. Addition - Informal Mental method, using partitioning: 47 + 76 = (40 + 70) + (7 + 6) or 47 + 76 = (47 + 70) + 6 Introduction to vertical layout, using partitioning SDe'Athe, Maths Subject Leader

  9. Addition – Expanded Written Vertical layout, expanded working, moving to adding the least significant digit first: SDe'Athe, Maths Subject Leader

  10. Addition – Standard Written Vertical layout, working towards a compact efficient method: SDe'Athe, Maths Subject Leader

  11. + 20 - 20 + 4 -4 + 4 - 4 56 56 60 60 80 80 84 84 Subtraction - Informal Use of a number line to count up. TU - TU. Use of a number line to count back. TU - TU. SDe'Athe, Maths Subject Leader

  12. Subtraction – Expanded Written Partitioned vertical form using TU – TU, e.g. 84 - 42 SDe'Athe, Maths Subject Leader

  13. Subtraction – Expanded to Standard Written Method Then, 563 - 241 leading to SDe'Athe, Maths Subject Leader

  14. Multiplication and division • Multiplication is repeated addition, division is repeated subtraction • Doubling, halving, partitioning, and multiplying by 10, 100, 1000 are essential mental strategies • 3 x 4=12 leads to 4 x 3, 12 ÷ 3, 12 ÷ 4, 6 x 4, etc, 30 x 4, 300 x 4, 120 ÷ 4 etc SDe'Athe, Maths Subject Leader

  15. Multiplication – The Grid Method Mental method using partitioning multiplying tens first: 38 x 7 38 x 7 = (30 x 7) + (8 x 7) = 210 + 56 = 266 Grid layout 38 x 7 SDe'Athe, Maths Subject Leader

  16. Multiplication – Standard Written Expanded short multiplication Standard short multiplication SDe'Athe, Maths Subject Leader

  17. Standard Long Multiplication SDe'Athe, Maths Subject Leader

  18. 2 2 2 2 0 2 4 6 8 Division - Informal Number lines & grouping 8÷2 SDe'Athe, Maths Subject Leader

  19. Division – Expanded Written Informal methods using ‘chunking’ TU  U SDe'Athe, Maths Subject Leader

  20. Short Division - Standard Standard method HTU  U SDe'Athe, Maths Subject Leader

  21. Moving from informal to formal methods • At every stage, teachers first use examples that children can easily do mentally • Children then see how the steps in a written procedure link to what they do in their heads • They then move to using numbers that cannot easily be dealt with mentally, including money and decimal numbers • Partitioning and place value are crucial concepts and estimation of size of answers is essential. SDe'Athe, Maths Subject Leader

  22. What else is changing? • Raising the Profile of Maths • ½ termly assessments on the targets • Maths Week • Monitoring SDe'Athe, Maths Subject Leader

  23. Any Questions? • Please ask one of my lovely assistants to demonstrate any of the methods you would like to see again • Please look through the resources and see what we are using • Please come and find me at any time if you have any questions SDe'Athe, Maths Subject Leader

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