Mathematics

Numerical Operations Essential Questions After completing this lesson, you will be able to answer the following questions: How are expressions rewritten in simplified form based on the mathematical operations in the expression? What is the correct order for performing mathematical operations in simplifying expressions? Main Idea (page #) DEFINITION OR SUMMARY EXAMPLE Real Numbers(P.1) Natural Number: _______________ integers ____________ Numbers: A member of the set of positive integers or zero Integers: A number that can be written without a fraction or _______________ Rational Numbers: Can include positive/negative fractions and decimals. Irrational Number: Any real number that can not be expressed as a ratio. Adding and Subtracting Integers(P.2)

02.06 Compound Inequalities Essential Questions How can you create inequalities in one variable and use them to solve problems? How can you represent constraints by inequalities? How can you interpret solutions as viable or nonviable options in a modeling context? Absolute Value Inequalities: Absolute Value Inequalities are problems that involve ranges. For example: On public stairs, handrails must be installed. The height of the handrails must be within a 3 inch range of 35 inches. Compound inequality Key words ?and? / ?or? Scenario 1 A fish has to measure between 18 and 24 inches in length. b>= 18 and b<=24 Writing the compound inequality like this makes it easier to understand that the solutions for b must fall between 18 and 24 inches Scenario 2

02.03 Absolute Value Equations Essential Questions How can you represent constraints by absolute value equations? How can you interpret solutions as viable or nonviable options in a model? Absolute value equations can have: Examples One solution |x|= ________ Two solutions |x|= ______________________ No solutions |x| = _____________________ To solve an advance absolute value equation e.g. |2x-3|=11 Make two equations to solve by eliminating the absolute signs and making them equal opposite sign answers: Solve below: ___________________ ___________________ Check answers by substituting both into original equation. Check answers below: ____________________________________________ ____________________________________________ You can show constraints in real world problems by:

02.01 One-Variable Equations Essential Questions How can we create equations in one variable and use them to solve problems? How can we solve linear equations in one variable? KEEP IT ___________________. The goal is to figure out how much each x weight weighs. You do this by getting one x on one side and its value on the other side. STEPS TO SOLVING AN EQUATION Simplify each side of the __________________. Get the __________________ on one side of the ___________________. Get the _____________ by ___________________. (Solve for the variable) ___________ your solution. Follow along on page 3, Example 1. ?2(x + 1) = 5x + 4 ? x Simplify each side of the equation. Get the variable on one side of the equation.