Expressions Equations and Inequalities Unit Test Date Monday

Expressions, Equations and Inequalities Unit Test Date: Monday: September 15 th Unit Objectives: • Model real-world situations with variables • Evaluate and simplify algebraic expressions • Solve algebraic equations and inequalities, including absolute values. Today’s Objective: Patterns, Real Numbers, Algebraic Expressions

Identify & Describe Patterns You are playing a video game. You reach a locked gate. The lock is a square with 9 sections. Near the gate is a carving of a pattern of squares. The key to the gate is the eighth image in the pattern. Draw the key. How many toothpicks for 20 th figure? Variable: symbol that represents a number Numerical Expression: Phrase with numbers & operations Algebraic Expression: Phrase with numbers, variables & operations Fig. number of # Process toothpicks input Output 1 1(4) 2 2(4) 4 8 3 3(4) 12 n 4(n) 4 n

Properties of Real Numbers You use emoticons in text messages. How can you describe a set of that includes five of the emoticons but not the sixth? Addition Multiplication Closure a + b is real ab is real Commutative a+b=b+a ab = ba Associative (a+b)+c=a+(b+c) (ab)c=a(bc) Identity a+0=a Inverse a+(− a)=0 Distributive: a(b + c) = ab + ac

Algebraic Expressions During summer vacation, you work two jobs. You walk three dogs several times a week, and you work part time as a receptionist at a hair studio. You earn $8 per hour as a receptionist and $20 per week per dog. Your weekly schedule (shown below) is the same each week. How much will you earn in 10 weeks? Explain. $2, 200 Write an algebraic expression for each. Seven fewer than a number t two times the sum of a and b

Algebraic Expressions Evaluate: Substitute a number for each variable and simplify Term: Product of a number and one or more variables Coefficient: Numerical factor of a term Constant Term: Term with no variables Like Terms: Terms with same variables raised to the same powers