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Ministry of Education Secondary Numeracy Project

Ministry of Education Secondary Numeracy Project. Algebra in Long Multiplication. Kevin Hannah Central Auckland Airport Hotel 23-24 February 2005. Algebra in Long Multiplication. Using arrays to illustrate multiplication Exploring polynomial expansions Touching polynomial division.

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Ministry of Education Secondary Numeracy Project

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  1. Ministry of EducationSecondary Numeracy Project Algebra in Long Multiplication Kevin Hannah Central Auckland Airport Hotel 23-24 February 2005

  2. Algebra in Long Multiplication • Using arrays to illustrate multiplication • Exploring polynomial expansions • Touching polynomial division

  3. What’s the answer? 5 x 21 5 20 1

  4. What’s the answer? 14 x 21 10 4 20 1

  5. What’s the answer? 23 x 21 20 3 20 1

  6. What’s the answer? 23 x 21 20 3 20 1

  7. What’s the answer? 23 x 21 20 3 400 60 20 20 3 1 23 x 21=400+80+3=483

  8. What’s the answer? 23 x 21 20 3 400 60 20 1 20 3 So 400+80+3= 23 x 21

  9. Expanding Expressions (2x+3)(2x+1) 2x 3 4x2 6x 2x 2x 3 1 4x2 +8x +3= (2x+3)(2x+1)

  10. x 1 2x2 +5x +3 Polynomial Division (2x2+5x+3)/(x+1) =2x + 3 2x2 3x 2x 3

  11. x 4 1 4 X+1 3x2 +4x +5 + Polynomial Division (3x2+4x+5)/(x+1) =3x + 1 3x2 x 3x 1

  12. x 12 1 12 X+1 3x2 -4x +5 + Polynomial Division (3x2-4x+5)/(x+1) =3x - 7 3x2 -7x 3x -7

  13. x 1 Series expansions Expand 1/(x+1) …. -x3 +x2 -x +1 -x4 x3 -x2 x -x3 x2 -x 1 +0x3 +0x2 +0x +1

  14. Algebra in Long Multiplication • Using arrays to illustrate multiplication • Exploring polynomial expansions • Touching polynomial division • Versatile mathematical diagrams

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