Algebra Maths 8 May 2013

Curriculum Outcomes B14 add and subtract algebraic terms concretely, pictorially, and symbolically to solve simple algebraic problems B15 explore addition and subtraction of polynomial expressions, concretely and pictorially B16 demonstrate an understanding of multiplication of a polynomial by a scalar, concretely, pictorially, and symbolically

Vocabulary… variable: a symbol that represents an unknown value For example: x, y, a, b, r, h, etc. coefficient: A number that precedes a variable in an expression. The coefficient multiplies by the variable. For example if we write 3 times w like 3w. 3 is the coefficient.

vocabulary… constant: a quantity that does not change. example: ½, -3, 6,  term: A term consists of a constant, a variable, a coeffieient which is multiplied by the variable, or two or more variables are possible. For example: 3, 4x, 4xy 2, and x 3 are some terms.

vocabulary… An algebraic expression: An expression with one or more terms. There is no solution to an expression. Example:3x – 2 -4x 3 – 2y + 3xy -5

vocabulary… An algebraic equation: Two expressions separated by an equal sign. Example:3x – 2 = 6 -4x 3 – 2y + 3xy -5 = 4x – 3y

Think and reflect 4x 2 – 3x = 1 Expression or equation? 3y 2 + 5x – 7z + 32c -2 Expression or equation? 3y 2 + 5x – 7z + 32c -2 Combine the terms? 3x – 5y 3 – 8  Identify the numerical coefficients 3x – 5y 3 – 8 Identify the variables 3x –  – 8 Identify the constants

A little more vocabulary Monomial: An algebraic expression which contains only one term. Example:x Binomial: An algebraic expression the contains only two terms. Example:3x – 2 Polynomial: An algebraic expression with more than one term. Example :5x 2 + 2x + 3

Yet more vocabulary Like terms: Terms where the coefficients are different, but have the same variable. Examples: 3x and 2x are like 4x and 5y are not like x 2 and x are not like

ALGETILES 1 x -x x x x2x2 -x 2 y-y y y y2y2 -y 2 x y xy -xy Algetiles are pieces used to represent algebraic terms concretely.

Represent these expressions with Algetiles x 2 + 4x + 3 x x x2x2 xxxx 1 11

Practice Represent the following expressions with algetiles then draw them onto a paper to hand in to your teacher. 2x - 3 -x x 2 + 3x + 1 x 2 + (-2x) + 1

Practice 2x – 3 2x 2 + 3x + 1 -x 2 – 2 x 2 + (-2x) + 1 xx x x x2x2 x x x2x2 xxx 1 -x 2 x x x2x2 -x 1

Combining Like Terms If you know a certain distance is 2m and another is 30 cm, then you know the total distance is = 32 units? NO – You must express the distances with the same units. 2m m = 2.3 m Can you add 2 dozen and 5 units to get 7? NO - 2 dozen plus 5 units = 29 Can you add 5 apples and 3 orages to get 8 appleorages? NO! You must combine like units and/or objects (like terms)

Combining like terms If the terms are the same variable and have the same exponent, you can combine them. But, if the exponents are different, you cannot combine them. x x x2x2 xxxxx 2x3x + = xxxxxxx 2x x2x2 + = x x x2x2 xx x2x2 + 5x

Combining like terms If the terms are positive or negative it will not affect combining like terms. x x x2x2 x x x2x2 -x 2

« zeros » If you combine a positive term and a negative term you get « zero » x x x2x2 -x 2 + = 0 x -x + = 0 1 += 0

Combine like terms to simplify the expressions x x x2x2 x x x2x2 xxx -x 1 y y y2y2 y y y2y2 y y y2y x 2 Regroupe the terms of the same shape and make « zero» when its possible.

Combine like terms and simplify x x x2x2 x x x2x2 xxx -x 1 y y y2y2 y y y2y2 y y y2y x 2 Identify the « zeros » and regroup the rest. 3y 2 + x + 2