BY: MILES JUSTIS AND CAMERON WILLIAMS Equations and functions Chapter 12 BY: MILES JUSTIS AND CAMERON WILLIAMS Equations and functions

Word review chapter 12 Evaluate: You evaluate an expression by finding it’s value. To make sure everyone gets the same result, mathematicians use the order of operations. Variable: A variable is a symbol, usually a letter that represents one or more numbers. Variable Expression: A variable expression substitutes a number for each variable and evaluates the numeral expression. Equation: An equation is a mathematical sentence is formed by placing an equal sign between two expressions. Solution: A solution of an equation is a number when substituted for a variable, makes the equation true.

Prerequisite skills/pemdas Evaluate the expression then tell whether the given number is a solution of the equation. (Evaluate the expression means to solve the equation.) Evaluate: 3+9x10= 9x10 = 90 + 3 = 93 Tell whether the number is a solution of the problem 6+x=19; 11

Vocabulary 12.1 Variable expression: Equation: A variable expression substitutes a number for each variable and evaluates the numeral expression. An equation is a mathematical sentence is formed by placing an equal sign between two expressions.

example Write the phrase as a variable expression. Phrase Expression 3pieces added to x pieces in the art show 3=x The sum of 4 and a number n 4+n The difference of 12 and a number x 12-x 9 fewer than the number of boys b b-9

Writing expressions and equations Addition: Plus the sum of increased by total added to more than Subtraction: Minus the difference of decreased by fewer than subtract from Multiplication: Times the product of multiplied by of twice Division: Divided by the quotient of separate into equal parts

Reviewing Content You will write variable expressions and equations. To solve a variable expression is to read the phrase then answer it.

Lesson 2 Solving addition equations vol. Variable: Solution: Solve: To solve an equation, you find all the solutions of the equation .To solve simple equations using mental math, you can think of the equation as a question A variable is a symbol, usually a letter that represents one or more numbers A solution of an equation is a number when substituted for a variable, makes the equation true.

Solving addition equation Step 1: Represent the equation using algebra tiles Step 2: Take away two 1 tiles from each side Step3: The remaining tiles show that the value of x is 2 EXAMPLE x + 2 = +

Vocabulary 12.3 Variable: Solution: Solve: To solve an equation, you find all the solutions of the equation. A variable is a symbol, usually a letter that represents one or more numbers. A solution of an equation is a number when substituted for a variable, makes the equation true.

Solving subtraction equations 12.3 Step 1: You have to find out what x or y or any letter that’s there and see what that letter equals. Step 2: You subtract or add however much you need to. Step 3: then you look at the equation you just solved and you are done. EXAMPLE: After giving away two conch shells to find the value x you had before subtracting 2, you can add 2to undo the subtraction. You have 5 conch shells. x – 2= 5

Vocabulary 12.4 Variable: Solution: Solve: A variable is a symbol, usually a letter that represents one or more numbers A solution of an equation is a number when substituted for a variable, makes the equation true. To solve an equation, you find all the solutions of the equation .To solve simple equations using mental math, you can think of the equation as a question

Solving multiplication and division equations 12.4 Step1 : Use algebra tiles to represent the equation 2x= 6 Step2: Divide the x-tiles into two equal groups. Divide the 1-tiles into the same number of equal groups. Step3: Match a group on the left with a group on the right. Example: Solve the equation 5x=20. 5x=20 Write the original equation 5x/5=20/5 Divide each side by 5. X=4 simplify

Vocabulary 12.5 Function: A function Is a pairing of each number in one set with a number in a second set. Input and output: Starting with a number in the first set, called an input the function pairs it with exactly one number in the second set called an output.

Functions 12.5 Step 1: to solve the problem above about giant pandas , you can make an input and output table. Step 2:Use the function rule p=30d, where d is the number of days ( input ) and p is the pounds of bamboo eaten ( output ) p= 30 = 30 P= 30 =60 P= 30 = 90 bamboo eaten p= 30 =120 p= 30 =150

Vocabulary 12.6 Linear function: a linear function is a function whose graph is a straight line.

Graphing Functions 12.6 Step 1: Make an input- output table for the function y= 15x Step 2: Write the input and output values as ordered pairs: (input, output). (0,0), (1,15), (2,30), (3,45) Step 3: Graph the ordered pairs. Step 4: Draw a line through through the points. That was the example and the lessons for chapter 12