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Mastery Unlocked

Mastery Unlocked. Session 4: Fluency. The 5 big ideas. Fluency is more than memorisation. Fluency rests on a well-built mathematical foundation with three parts:

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Mastery Unlocked

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  1. Mastery Unlocked Session 4: Fluency

  2. The 5 big ideas

  3. Fluency is more than memorisation Fluency rests on a well-built mathematical foundation with three parts: • an understanding of the meaning of the operations and their relationships to each other -- for example, the inverse relationship between multiplication and division; • the knowledge of a large repertoire of number relationships, including the addition and multiplication "facts" as well as other relationships, such as how 4 × 5 is related to 4 × 50; and • a thorough understanding of the base ten number system, how numbers are structured in this system, and how the place value system of numbers behaves in different operations -- for example, that 24 + 10 = 34 or 24 × 10 = 240. • (Russell 2000)

  4. Why Facts and Procedures? In teaching procedural and factual knowledge, ensure the students get to automaticity. Explain to students that automaticity with procedures and facts is important because it frees their minds to think about concepts. Daniel Willingham Is it true that some people just cant do math?

  5. Fluency involves: • 18 + 14 = + 15 • 32 – 27 = • = 25 x 9 • 42 ÷ 3 = • 2.4 – 0.7 = Discuss the knowledge & strategies which make you fluent answering these questions.

  6. What does mastery of number facts mean? • Recall facts out of sequence: 3 + 4 = 7 • Use the fact to derive other facts: • 8 + 2 = 10, so 8 + 3 = 11 • Apply laws and principles – inverse relationships, commutative and associative laws: • 3 + 5 = 5 + 3 • 7 + 5 + 3 = 7 + 3 + 5 = 10 + 5

  7. Number sense v memorisation 18 x 5 Jo Boaler video https://www.youcubed.org/what-is-number-sense/

  8. Number talks • Ruth Parker and Kathy Richardson • Pose an abstract problem eg 18 x 5 and ask the children to solve it mentally. • Teacher collects different methods and the class looks at why they work.

  9. www.insidemathematics.org

  10. Y1 facts Adding 1 Bonds to 10 Adding 10 Bridging/ compensating Y2 facts Doubles Adding 0 Adding 2 Near doubles

  11. Progression in teaching addition facts. Group A: Year 1 • Adding 1 (e.g. 7 + 1 and 1 + 7) • Doubles of numbers to 5 (e.g. 4 + 4) • Adding 2 (e.g. 4 + 2 and 2 + 4) • Number bonds to 10 (e.g. 8 + 2 and 2 + 8) • Adding 10 to a number (e.g. 5 + 10 and 10 + 5) • Adding 0 to a number (e.g. 3 + 0 and 0 + 3) • The ones without a family: 5 + 3, 3 + 5, 6 + 3, 3 + 6 • Knowing these facts by the end of Year 1 will mean children will know 87 of the 121 addition facts in the grid. • (Could also teach ‘5 and a bit’ facts as a family)

  12. Progression in teaching addition facts:Group B: Year 2 (those that bridge 10) • Know or derive a quick strategy (not counting): • Doubles: 7 + 7 • Near doubles: 8 + 9 = 8 + 8 + 1 • Bridging: 8 + 9 = 8 + 2 + 7 • Compensation 8 + 9 = 8 + 10 – 1

  13. Mid attaining Y3

  14. High attaining Y4

  15. The Impact of Factual &Procedural Fluency • “In the course of this year, I have come to realise that the procedural gap in my Y6 class was much bigger than the conceptual gap.” • (Tom, Cohort 1 Mastery Specialist)

  16. Some Reflections • Outcomes are stronger where there is a combination of recall and strategies • The route to memorisation is recognising relationships and making connections • Need to move away as quickly as we can from counting strategies • The best way to develop fluency with numbers is to work with numbers in different ways not to blindly memorise without number sense. • Don’t let children switch off from maths because they can’t memorise facts

  17. Activities to develop fluency • Make it fun! • If the activities are meaningful children will begin to commit maths facts to heart at the same time as developing number sense • Don’t think that timed testing is the only way to achieve rapid recall

  18. Snap it Children make a train of blocks of a specified length. On the signal “snap” they break their train and hid one part behind their back. The other children have to work out how many blocks are hidden.

  19. Strike it Out - nrich 6 + 4 = 10 10 take away 9 makes 1 1 add 17 is 18 18…… Competitive aim – stop your partner from going Collaborative aim – cross off as many as possible

  20. What whole numbers between 0 and 12 do the shapes represent?

  21. Solution: Purple square = 2 Yellow semicircle = 8 Orange oval = 4 Blue rectangle = 3 Red circle = 12 Green triangle = 6 Green star = 9 Purple star = 5 Blue hexagon = 10 Red triangle = 0 Yellow diamond = 1

  22. The 5 big ideas

  23. Strike it out - nrich

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