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An Algebra story

An Algebra story. Background. What we did !. New PLD environment Development of a diagnostic snapshot What we found: Number not a big problem No generalisations Language of algebra an issue No strategies Intervention negotiated length

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An Algebra story

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  1. An Algebra story

  2. Background

  3. What we did ! • New PLD environment • Development of a diagnostic snapshot • What we found: • Number not a big problem • No generalisations • Language of algebra an issue • No strategies • Intervention negotiated • length • what was important and therefore worth spending time on • Concentrate on the language and pedagogy using the SNP teaching model • Lesson structure

  4. The greatest enemy of understanding is coverage. As long as you are determined to cover everything, you actually ensure that most kids are not going to understand. You’ve got to take enough time to get kids deeply involved in something so they can think about it in lots of different ways and apply it – not just at school but at home and on the street and so on. (Brandt, 1993)

  5. So what did we cover? • The language • Out of language came substitution and like terms • Patterning • Expansions • Equations • Lots of revision

  6. The language of Maths Continually revisit using activities such as: • Bingo • Loopies • Addonagons • 4 in a row (number to algebra) • Simple questions in context • Reading out loud • Unscrambling maths words • Crosswords

  7. Loopies • Collecting up like terms • Using Maths language

  8. 4 in a row – number to algebra • Mult/div or add/sub. • Algebra

  9. Questions in context • Use simple knowledge questions. • T/students read qs out loud to the class • Students write the “maths” problem using correct notation. • Eg Tickets to the concert cost $58. If 4 friends want to go what is it going to cost altogether? • Eg Joel has $69 less than Marty who has $350. How much money does Joel have?

  10. Unscrambling Maths words/crosswords etc • http://puzzlemaker.discoveryeducation.com/WordSearchSetupForm.asp • www.puzzle-maker.com/CW/

  11. Patterning • Spatial patterns – drawing the next 2 shapes • Matching a spatial pattern to a number • Finding the next 3 terms in a number pattern • Finding the missing numbers in a number pattern • Making up a spatial pattern for a number pattern • How many objects are added to get the next term • Design a spatial pattern that adds: 4 matchsticks to get the next term or 1 black dot and 3 yellow dots to get next term • For the pattern 24, 20, 16, describe what is happening in words. • Find the next 2 terms - describe the rule in words • Use the number 5 and the rule to find the first 5 terms • Using tables: • “n” match stick design………..no of match sticks needed

  12. Patterning continued • Complete the table (no design given) • Now introduce some more context. Eg to hire “the coffee man” it costs $50/hr and an $80 set up fee. Construct a table to show the cost for 1 to 6 hours. • Move to using rules and formulas eg • Find first 4 terms for this rule • Find the 6th term (n=6) of the number pattern 3n + 5 • Complete the table using the rule m = 2n + 6 • Lots of these using lots of different variables. Move to across and down rules and context examples

  13. Moving towards expansions and factorising Revisit Using PV and partitioning to multiply (L4 Stage 5) Context question: 37 loaves of bread have been ordered for the tangi. There are 24 slices in each loaf . How many slices have to be buttered? Read the question What is the maths question? Record it. Provide students with a large dotty array. What is an array/ Ask them to draw a border around the array that shows this problem. Now tell them to partition(what is this?) it to help them find the total dots .Students are likely to use a variety of divisions – discuss all.

  14. Start by: • Using materials, diagrams to illustrate and solve the problem Progress to: • Developing mental images to help solve the problem Extend to: • Working abstractly with the number property

  15. 46 + = 83 46 83 Using Materials 37 10 10 10 4 3

  16. 39 + = 63 10 10 3 1 30 40 50 60 70 39 63 Encouraging Imaging 24

  17. 18 + = 62 Using Number Properties 44 From 18: add 2 to get to 20 add 40 to get to 60 add 2 to get to 62 Total: add 44

  18. 47 83 47 83 Solving Equations 47 + = 83

  19. Solving Equations 2X + 1 = X + 7 X X 1 X 7

  20. X X 1 Solving Equations 2X + 1 = 7 7

  21. Solving Equations 2(X + 1) = 18 X 1 X 1 18

  22. 9 9 Solving Equations 2(X + 1) = 18 X 1 X 1

  23. Solving Equations 2(X + 1) = 18 X X 1 1 18

  24. 27 53 Solving Equations 53 - = 27 53 27

  25. Solving Equations 2X - 1 = X + 7 X X X 7 1

  26. Solving Equations 2X - 1 = 8 - X X X X 8 1

  27. Solving Equations X - 1 = 2X - 7 7 X X X 1

  28. Solving Equations X + 3 = 2 X 3 2

  29. Key points • Present new ideas in context • Read all questions out loud • Articulate all calculations • Put calculations in words and pictures • Keep the glossary going • Ensure that students can explain their answers. • Use lots of reinforcement activities

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