Entry Task Find the next three numbers 101,92,83,74….. Now create your own pattern, see if you can stump me.
Entry Task
Find the next three numbers
101,92,83,74…..
Now create your own pattern, see if you can stump me.
Expressions & Formulas
ORDER OF OPERATIONS• Parentheses • Exponents • Multiply/Divide from left to right• Add/Subtract from left to right
Review
Order of Operations
• Simplify: [9 ÷ (42 - 7)] - 8• Exponents [9 ÷ (16 - 7)] - 8• Parentheses [9 ÷ (9)] - 8• Divide [ 1 ] - 8• Subtract -7
Review
Algebraic Expressions
An expression that is a number, a variable or the product of a number and one or more variables is a term.
An algebraic expression is an expression that contains at least one variable.
-4ax + 7w - 6 constant has no
variablesCoefficient is the
numerical factor of a term
Modeling words with algebraic expressions
Seven fewer than a number yy – 7
two times the sum of a and b2(a + b)
Modeling a situation
Savings You start with $20 and save $6 each
week. What algebraic expressions models the total amount you save?
relate (write using words), define (assign variables), write (use numbers, operations and
variables)20 + 6w
Algebraic Expressions
How do you evaluate expressions?
You can evaluate an algebraic expression by replacing each variable with a value and then applying the Order of Operations.
Example: Evaluate a(5a + 2b) if a=3 and b=-2 Substitute the values into the expression. 3[5(3) + 2(-2)] Now apply the Order of Operations:
Inside the brackets, perform multiplication and division before addition and subtraction
5(3) = 15 and 2(-2)= -4 3[15 + -4] then 15 + -4 = 11 3[11] = 33
Expressions
Evaluate: a[b2(b + a)] if a = 12 and b= 1• Substitute: 12[12(1 + 12)]• Parentheses: 12[12(13)]• Exponents: 12[1(13)]• Parentheses: 12[13]• Multiply: 156
Expressions – like terms
Like terms have the same variable raised to the same power.
3x2 + 5x2 + 9y3x + 2 – 4y3x
Simplify Algebraic Expressions
1. 7x2 + 3y2 + 2y2 – 4x2 =3x2 + 5y2
2. -(3k + m) + 2(k – 4m)= - k – 9m
Solving Equations
• To solve an equation, find replacements for the variables to make the equation true.
• Each of these replacements is called a solution of the equation.
• Equations may have {0, 1, 2 … solutions.
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