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Planning a Sequence of Learning in Mathematics

This session is designed to help facilitators plan a sequence of learning in mathematics, incorporating TLAC techniques for effective working routines. Participants will give and receive feedback on using TLAC within a short-term plan.

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Planning a Sequence of Learning in Mathematics

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  1. INFORMATION FOR SESSION FACILITATOR Length: 3.5 hours Subject specific 8.1 Planning a sequence of learning in mathematics • Session Outcomes: • By the end of this session participants will:  • Use a medium-term plan to plan a sequence of learning over 4-6 lessons • Incorporate TLAC techniques in their planning to establish effective working routines • Give and receive feedback on using TLAC within a short-term plan. • Supernumerary Participant Development Framework: • Theme 2 Plan effectively • Theme 3 Instruction • Links to other sessions or Subject Knowledge Enhancement: • Planning • Questioning and Feedback • Resources and references: • TLAC placemats • Textbooks to support planning • Supernumerary Planning proforma • A medium term plan from participants’ schools

  2. Do Now A house is worth £175,000 in 2018. If it increases in value by 10% per year, how long until it doubles in value? What about if it increased in value by 5% per year?

  3. Planning a sequence of learning in mathematics

  4. Session Outcomes By the end of this session you will be able to: • Use a medium-term plan to plan a sequence of learning over 4-6 lessons • Incorporate TLAC techniques into planning to establish effective working routines • Give and receive feedback on using TLAC within a short-term plan

  5. Long-term plan       Principles of effective planning Medium-term plan Short-term plan

  6. Long-term plan       Levels of planning Medium-term plan Short-term plan

  7. Calculations with Percentages Subject Content Ratio, proportion and rates of change • Solve problems involving percentage change, including: • Percentage increase • Decrease • Original value problems • Simple interest in financial mathematics Number • Define percentage as “number of parts per hundred” • Interpret percentages and percentage change as a fraction or a decimal and interpret these multiplicatively • Express one quantity as a percentage of another • Compare two quartiles using percentages • Work with percentages greater than 100%

  8. Working mathematically Develop Fluency • Consolidate their numerical and mathematical capability from KS2 and extend their understanding of the number system and place value to include decimals and fractions. Reason mathematically • Extend their understanding of the number system; make connections between number relationships and their algebraic and graphical representations. Solve problems • Begin to model situations mathematically and express the results using a range of formal mathematical representations.

  9. Key Concepts • A percentage is a fraction out of 100, so 52% is the same as 52/100, which has the decimal equivalent of 0.52. • Finding a percentage of an amount without the use of a calculator can be done by halving, dividing by 10 or dividing by 100. Another method could be to change the percentage to a decimal and multiply the decimal by the quantity • If something increases by 20% the total percentage is 120%.  This has an equivalent decimal multiplier of 1.2. • If something decreases by 20% the total percentage is 80%.  This has an equivalent decimal multiplier of 0.8. • The original amount is 100%.  To find the original amount students should use equivalent ratios. • The word 'of' means to multiply.

  10. Prerequisite knowledge • Work interchangeably with terminating decimals and their corresponding fractions. • Define percentage as ‘number of parts per hundred’, interpret percentages and percentage changes as a fraction or a decimal • Interpret fractions and percentages as operators

  11. Efficient use of a calculator Incl. Recap FDP from Y7 Calculations with Percentages Financial Literacy Opportunity for a rich activity. Developing written methods Non-calc methods & mental arithmetic

  12. Calculations with Percentages

  13. Calculations with Percentages

  14. Expressing One Number as a Percentage of Another Short-term planning: a lesson plan Where are learners at coming into this lesson?

  15. How could we use TLAC in this lesson? Randomly pick a TLAC number from the middle of the desk 2 minutes to discuss how to include in this lesson (be specific) Repeat x 4

  16. Planning time • Working in pairs • Use the model from this morning • Get all lessons planned in short-term before beginning to resource • Plan in ~2 foci TLACs per lesson • Prepare to share 1 TLAC use in front of peers

  17. Giving Feedback • We will use the criteria of the relevant Teach Like a Champion Technique • …..only! • This way we ensure we give fair, relevant, and constructive feedback to develop in using this technique well

  18. A few final thoughts on planning www- ebi -

  19. References ‘Principles of Instruction’, (2012) Barak Rosenshine.  https://www.aft.org/sites/default/files/periodicals/Rosenshine.pdf Make Every Lesson Count: Six principles to support great teaching and learning (2015) Shaun Allison and Andy Tharby, Crown House (Foreword by Doug Lemov)  Teach Like A Champion 2.0, (2015) Doug Lemov, San Francisco: Jossey-Bass 

  20. Questions?

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