Algebra I Teacher Notes Expressions, Equations, and Formulas Unit 01 Review

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1 Big Ideas Write and evaluate algebraic expressions Use expressions to write equations and inequalities Solve equations Represent functions as verbal rules, equations, tables and graphs Review concepts of algebra throughout the course. This material has been taught in previous courses, but it is important to help students remember it. The student will identify and apply real number properties using variables, including distributive, commutative, associative, identity, inverse, and absolute value to expressions or equations. Real Number Properties For a Review of Real Numbers, see Unit 00a Real Numbers Review A.SSE.1 Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity. A.REI.1 Understand solving equations as a process of reasoning and explain the reasoning 1. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. A.CED.1 Create equations and inequalities in one variable and use them to solve problems. N.NQ.1 Use units as a way to understand problems and to guide the solution of multi-step problems. SNRPDP Alg I Unit 01 notes ExpEqFormulasb 1 5/16/013

2 Skill: Simplify algebraic expressions by adding and subtracting like terms. Terms: algebraic expressions separated by a + or a sign Constant Term: a term that is a real number (no variable part) Coefficient: the numerical factor of a term Like Terms: terms that have the exact same variable part (must be the same letter raised to the same exponent) Note: Only like terms can be added or subtracted (combined). To add or subtract like terms, add or subtract the coefficients and keep the variable part. Ex: Simplify This means we are adding 3 smiley faces plus 4 smiley faces. Therefore, we have a total of 7 smiley faces, which we can write as 7. Ex: Use the expression 1 3x 4xy x 5y to answer the following questions. 1. How many terms are in the expression? Solution: There are 5 terms.. Name the constant term(s). Solution: There is one constant term, How many like terms are in the expression? Solution: There are like terms. 3 x and x 4. What is the coefficient of the xy term? What is the coefficient of the fourth term? Solution: The xy term has a coefficient of 4. The third term has a coefficient of Simplify the algebraic expression. Solution: Combine like terms. 1 3x 1x 4xy 5y 1 x 4xy 5y 6. How many terms are in the simplified form of the algebraic expression? Solution: There are 4 terms. Simplifying an Algebraic Expression 4 x 8 5x 1. Ex: Simplify the expression Step One: Eliminate the parentheses using the distributive property. 4x 3 5x 1 4x 5x 3 1 Step Two: Combine like terms. 5 n 3n 8 4n Ex: Simplify the expression 1x 33 x 33 Step One: Eliminate the parentheses using the distributive property. 5 6n 16n 4n Note: The expression in parentheses is being multiplied by n, which is what was distributed. 5 6n 4n 16n Step Two: Combine like terms. 5 10n 16n Note: The answer may be written as 10n 16n 5 by the commutative property. SNRPDP Alg I Unit 01 notes ExpEqFormulasb 5/16/013

3 Ex: Write a simplified expression for the perimeter of a rectangle with length 7 x. Note: The formula for the perimeter of a rectangle is x and width P l w. Substitute the length and width into the formula. x 7 x x14 x 4 Simplify using the distributive property and combining like terms. 4x 10 You Try: 1. Simplify the expression x x Write a simplified expression for the area of a triangle with a base of 4x and a height of x 1. QOD: Explain in your own words why only like terms can be added or subtracted. SNRPDP Alg I Unit 01 notes ExpEqFormulasb 3 5/16/013

4 Sample Practice Question(s): 1. Simplify the expression: 5 3 x 4 x A. 7x 4 B. 7x 3 C. x + 1 D. x 7. Simplify the expression: 5x x 6 4x 6x 1 A. B. C. D. x x 6 5 3x 10x 5 11x x 5 11x 6x 5 3. Write an expression for the perimeter of the rectangle: y x A. xy B. 6xy C. 4x + y D. 4x y SNRPDP Alg I Unit 01 notes ExpEqFormulasb 4 5/16/013

5 *These two-column notes are designed to be used for study. The left side or the right side can be covered for self-check or buddy-check support and are meant to be developed throughout each unit. For example, certain vocabulary words may not be defined until that concept is covered/discussed/developed during the unit. Vocabulary Definition/Meaning/Example Expression Constant Variable Order of Operations Numerical expression Evaluate Algebraic expression Open sentence Equation Literal equation Solution of an equation Power, exponent, base *Properties of Equality SNRPDP Alg I Unit 01 notes ExpEqFormulasb 5 5/16/013

6 A.SSE.1 Variables and Expressions Give two ways to write each algebraic expression in words 1. n-5. 8x 3. t 1 4 Translate from words to algebraic expressions 1. Sam is years less than three times the age of his younger brother Evaluate each, given x=5, y=8, z=4 1. x+y. y/z 3. z /y +x Write an expression for: 1. area of a rectangle if the length of the rectangle is 9 inches. SNRPDP Alg I Unit 01 notes ExpEqFormulasb 6 5/16/013

7 A.REI.1 A.REI.1 A.REI.1 Solving equations by adding or subtracting Solving equations by multiplying or dividing Solving multi-step equations Solve each equation 1. x m b 4. b k 0.75 Write an equation to represent: 1. Ten less than a number is equal to 1. The sum of 5 and a number is 5 3. The difference of a number and 4 is 9 Solve: 4. -4=k/ x= /9v= =-1p 8. q/15-1/5=3/5 9. 4a=3= x/6+4=14 SNRPDP Alg I Unit 01 notes ExpEqFormulasb 7 5/16/013

8 11. 5(h-4)=8 Write an equation, then solve: 1. Seven less that twice a number equals 19. The sum of two times a number and 5 is 11. Solve the equation5x 9 6. Write a reason for each numbered step. 5x 9 6 Given 9 9 5x 35 [1] Simplify 5x x 7 [] Simplify SNRPDP Alg I Unit 01 notes ExpEqFormulasb 8 5/16/013