3. WHAT ARE OPERATIONS ??? ALTHOUGH NUMBERS ARE THE MOST IMPORTANT PART OF MATH, WE WOULDN’T BE ABLE TO DO ANYTHING WITH THEM WITHOUT OPERATIONS! + - x ÷+ - x ÷ + - x ÷ + - x ÷ + - x ÷ SYMBOLS THAT CONNECT NUMBERS TO FORM MATHEMATICAL EXPRESSIONS ARE REPRESENT THESE OPERATIONS. THE FOUR MOST BASIC OPERATIONS ARE ADDITION, SUBTRACTION, MULTIPLICATION, AND DIVISION

4. OPERATIONS AND KEY TERMS OPERATIONSYMBOLKEY TERMS ADDITION + ADD, PLUS, TOTAL, SUM SUBTRACTION − SUBTRACT, MINUS, LESS THAN, GREATER THAN, DIFFERENCE MULTIPLICATION x MULTIPLY, MULTIPLE, TIMES, DOUBLE, TRIPLE, TWICE, PRODUCT DIVISION ÷ DIVIDE, DIVIDEND, DIVISOR, HALF, PER, EACH, QUOTIENT OTHER IMPORTANT OPERATIONS IN MIDDLE SCHOOL MATHEXPONENTS# EXPONENT, POWER, SQUARED, CUBED SQUARE ROOTS √# SQUARE ROOT WHEN SOLVING WORD PROBLEMS, THE FOLLOWING KEY TERMS WILL INDICATE WHICH OPERATION WILL HELP YOU FIND A SOLUTION

5. EXPONENTS WHEN A SINGLE NUMBER IS MULTIPLIED BY ITSELF REPEATEDLY, EXPONENTS CAN BE USED TO SIMPLIFY THE WAY THE EXPRESSION LOOKS. THE NUMBER ITSELF IS CALLED A BASE NUMBER AND THE AMOUNT OF TIMES IT APPEARS IS REPRESENTED BY THE EXPONENT, SMALL TO THE UPPER RIGHT CORNER 3 x 3 x 3 x 3 x 3 x 3 ≈ 3, SIX TIMES ≈ 3 6

6. SQUARE ROOTS PERFECTSQUARE‘WORK’ROOT √1 1 ÷ 1 = 1 1 √4 4 ÷ 2 = 2 2 √9 9 ÷ 3 = 3 3 √16 16 ÷ 4 = 4 4 √25 25 ÷ 5 = 5 5 √36 36 ÷ 6 = 6 6 √49 49 ÷ 7 = 7 7 √64 64 ÷ 8 = 8 8 √81 81 ÷ 9 = 9 9 √100 100 ÷ 10 = 10 10 A SPECIAL KIND OF DIVISION, IN WHICH THE DIVISOR AND QUOTIENT ARE THE SAME NUMBER, IS CALLED A SQUARE ROOT. SQUARE ROOTS ARE THE INVERSE OF SQUARING A NUMBER (EXPONENTS OF 2) A NUMBER WHOSE SQUARE ROOT IS A WHOLE NUMBER IS CALLED A PERFECT SQUARE – SINCE WHOLE NUMBERS ARE RATIONAL, PERFECT SQUARES HAVE RATIONAL ROOTS. ALL TH E NUMBERS ‘SKIPPED’ ON THE LIST OF PERFECT SQUARES (2,3,5,6,7,8,10, 11…) HAVE DECIMAL ROOTS, WHICH MAKES THEM IRRATIONAL

7. THE ORDER OF OPERATIONS EXPRESSIONS CONTAINING MANY OPERATIONS MUST BE SOLVED IN AN ORGANIZED WAY. THE ACRONYM IS USED TO REPRESENT THE CORRECT ORDER OF PERFORMING OPERATIONSP.E.M.D.A.S. …IT STANDS FOR: PARENTHESIS, EXPONENTS, MULTIPLICATION & DIVISION, ADDITION & SUBTRACTION * *PARENTHESIS IS NOT AN OPERATION, IT MEANS THAT ANY OPERATIONS INSIDE PARENTHESIS SHOULD BE DONE FIRST * *SINCE EXPONENTS AND SQUARE ROOTS ARE INVERSES, THEY SHOULD BE DONE SECOND IN EVALUATING AN EXPRESSION * *MULTIPLICATION AND DIVISION SHOULD BE DONE AS THEY APPEAR IN A MATHEMATIC SENTENCE FROM LEFT TO RIGHT

8. LESSON 2 VOCABULARY REVIEW TERMDEFINITION OPERATION NON-NUMERIC SYMBOLS INDICATING HOW TO COMBINE OR SEPARATE THE VALUES IN A MATHEMATICAL EXPRESSION (ADDITION AND SUBTRACTION ARE OPERATIONS, REPRESENTED BY THE SYMBOLS ‘+’ AND ‘–‘ ) SUM SOLUTION TO AN ADDITION PROBLEM (4 +3 IS 7, OR THE SUM OF 4 AND 3 IS 7) DIFFERENCE SOLUTION TO A SUBTRACTION PROBLEM (8 – 2 = 6 OR THE DIFFERENCE OF 8 AND 2 IS 6) PRODUCT SOLUTION TO A MULTIPLICATION PROBLEM (4X7 IS 28 OR THE PRODUCT OF 4 AND 7 IS 28) QUOTIENT SOLUTION TO A DIVISION PROBLEM (10÷5=2 OR THE QUOTIENT OF 10 AND 5 IS 2) EXPONENT A SMALL NUMBER LOCATED TO THE UPPER RIGHT OF A BASE NUMBER; IT INDICATES THE AMOUNT OF TIMES TO MULTIPLY THE BASE TIMES ITSELF (IN 4 3, THE EXPONENT IS 3…IT TELLS US TO MULTIPLY 4 TIMES ITSELF 3 TIMES)

9. TERMDEFINITION BASE NUMBER LARGE NUMBER WITH EXPONENT TO THE UPPER RIGHT; IT WILL BE MULTIPLIED TIMES ITSELF BASED ON THE NUMBER IN THE EXPONENT (IN 7 3, THE BASE NUMBER IS SEVEN) SQUARE ROOT “SPECIAL DIVISION” IN WHICH THE DIVISOR AND QUOTIENT ARE THE SAME NUMBER (64 DIVIDED BY 8 IS 8, SO THE SQUARE ROOT OF 64 IS 8)’√’IS THE SYMBOL TO REPRESENT THIS OPERATION PERFECT SQUARE ANY NUMBER WHOSE SQUARE ROOT IS A COUNTING NUMBER (1, 4, 9, 16, AND 25 ARE THE FIRST FIVE PERFECT SQUARES IN THE REAL NUMBER SYSTEM, THEIR SQUARE ROOTS ARE 1, 2, 3, 4, AND 5) EXPRESSION ANY MATHEMATICAL SENTENCE CONTAINING OPERATIONS, NUMBERS, AND/OR VARIABLES (3+7 IS AN EXPRESSION; SO IS 5n – 13) ORDER OF OPERATIONS THE PROCEDURE FOR PERFOMING OPERATIONS WHEN A MATHEMATICAL EXPRESSION CONTAINS MORE THAN ONE OPERATION: ANYTHING INSIDE OF PARENTHESIS, FOLLOWED BY ANY EXPONENTS (OR SQUARE ROOTS), THEN MULTIPLICATION AND/OR DIVISION AS IT APPEARS FROM LEFT TO RIGHT, AND FINALLY ANY ADDITION OR SUBTRACTION FROM LEFT TO RIGHT PEMDAS THIS ACRONYM REPRESENTS THE ORDER OF OPERATIONS: ‘P’ IS PARENTHESIS, ‘E’ IS EXPONENTS, ‘M’ AND ‘D’ ARE MULTIPLICATION AND DIVISION, ‘A’ AND ‘S’ ARE ADDITION AND SUBTRACTION LESSON 2 VOCABULARY REVIEW