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Chapter 12

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

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Chapter 12

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

  2. 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.

  3. 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

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

  5. 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

  6. 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

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

  8. 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.

  9. 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 = • +

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

  11. 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

  12. Vocabulary 12.4 A variable is a symbol, usually a letter that represents one or more numbers • Variable: • Solution: • Solve: 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

  13. 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

  14. 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.

  15. 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

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

  17. 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

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