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TANGRAM

TANGRAM. About Tangram. Tangrams come from China. They are thousands of years old. The Tangram is made by cutting a square into seven pieces. The puzzle lies in using all seven pieces of the Tangram to make birds, houses, boats, people and geometric shapes.

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TANGRAM

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  1. TANGRAM

  2. About Tangram Tangrams come from China. They are thousands of years old. The Tangram is made by cutting a square into seven pieces. The puzzle lies in using all seven pieces of the Tangram to make birds, houses, boats, people and geometric shapes. In each case you have to use all the seven pieces - no more, no less. Tangrams have fascinated mathematicians and lay people for years. You might be wondering why only the solutions are given. Well, you could just blacken the white lines to create problems! Watch out as Tangrams are known to be addictive. With these Seven Little Wonders the whole family can have hours of fun!

  3. Polauntuk tangram

  4. Polauntuk tangram

  5. | • Dari tangram tersebutbuatmenjadibentuk-bentuk yang memungkinkan.

  6. The Algebra Grid SumberdariDr.CresenciaLaguerta Ateneo de Naga University Philippines

  7. The Algebra grid visualizes • Concept of • Algebraic expression • Similar terms • Product of • A monomial and binomial • Two binomials with similar terms • Factoring/Factorizing a • Product with a common monomial factor (CMF) • Quadratic trinomials

  8. Some preliminary concepts • Unit of length • Unit of area

  9. Unit of length x y a b

  10. Length of segments x y x + y 2x

  11. Length of segments a b 2b + 3a a + 2b

  12. Unit of area : • Let and y x xy y2 x2

  13. Area of squares y2 x2 (2x)2 (x+2y)2

  14. Area of rectangels 2x2 3xy (2x2+3xy)

  15. Challenge. What geometric figure can visualize the following algebraic expressions? • 2x + 3y • 8y2 • 10y2 • 6xy • X+5y • 9xy • 6y+3x

  16. Challenge.. • 4x2 + 2xy • 5xy + 6y2 • X2 +5xy +6y2 • 10y2 + 17xy + 3x2 • 3x2 + 5xy + 2y2

  17. Area of Rectangels X2 + 2xy+y2 x2 + 4xy+3y2 2x2 + 4xy+4y2

  18. Challenge.. • 4x2 + 2xy • 12 xy+ 6x2 • 4x2 +12xy+9y2 • 10y2 + 17xy+3x2

  19. The Algebra Grid

  20. The Algebra Grid

  21. The Algebra Grid

  22. Uses of the algebra grid • Finding product of • a monomial and a binomial • 2x(3x+2y) • 4x(5x-3y) • Two binomials with similar term • (2x+3y)(4x-2y) • (x+2y)(3x+y) • (x-4)(2x-3y)

  23. …. 2. Factorizing/factoring • Polynomial with a common monomial factor • 2xy-3x2 • 6xy + 12 y2 • 5y2– 15xy • Quadratic trinomial • X2 +5xy+6y2 • 5x2+11xy+2y2 • X2 – 4xy – 5y2 • 2x2 + 3xy – 2y2

  24. … 3. Proving algebraic identities • (x+y)2 =x2 + 2xy + y2 • (x+y)2 + (x-y)2 =2x2 + 2y2

  25. Example 1 Finding product : 2x (3x + 2y) Consider : • The factor 2x as the width and 3x+2y as the length of a rectangle • The product 2x(3x+2y) as the area of the recangle

  26. Finding product of two polynomials is finding the area of a rectangle

  27. 2x(3x+2y) =

  28. (4x+y)(2x-3y) =

  29. (x-4y)(2x-3y) =

  30. Practice : Product of a monomial and a polynomial

  31. Practice : Product of two binomial with similar term

  32. Practice

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