About Tangram Tangrams come from China. They are thousands of years old. The Tangram is made by...
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Transcript of About Tangram Tangrams come from China. They are thousands of years old. The Tangram is made by...
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!
The Algebra grid visualizes1. Concept of– Algebraic expression– Similar terms
2. Product of– A monomial and binomial– Two binomials with similar terms
3. Factoring/Factorizing a– Product with a common monomial factor (CMF)– Quadratic trinomials
Challenge.
What geometric figure can visualize the following algebraic expressions?• 2x + 3y• 8y2
• 10y2
• 6xy• X+5y• 9xy• 6y+3x
Uses of the algebra grid
1. 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)
….
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
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
Practice : Product of a monomial and a polynomial
X (x+y) X(x-y) -x(x-y)
2x(x+y) 2x(x-y) -2x(x-y)
3x(2x+5y) 3x(2x-4y) -3x(2x+y)
2x(3x+2y) 2x(3x-2y) -2x(-3x+2y)
5y(2x+3y) 5y(2x-3y) -6y(2x-5y)
Practice : Product of two binomial with similar term
(x+y)(x+2y) (X-y)(x-2y) (x-y)(x+2y)
(2x+2y)(2x+3y) (x-2y)(x-3y) (x+2y)(x-3y)
(2x+3y)(3x+2y) (2x-y)(3x-2y) (2x+y)(3x-2y)
(2x+3y)(3x+4y) (3x-2y)(x-4y) (3x+2y)(x-4y)
(3y+x)(7y+3x) (2x-3y)(3x-4y) (2x-3y)(3x+4y)
Practice
X (x+y) X(x-y) -x(x-y)
2x(x+y) 2x(x-y) -2x(x-y)
3x(2x+5y) 3x(2x-4y) -3x(2x+y)
2x(3x+2y) 2x(3x-2y) -2x(-3x+2y)
5y(2x+3y) 5y(2x-3y) -6y(2x-5y)