You can picture this on a number line. The numbers increase from left to right. 4, 6,0, 2 in order from least to greatest.

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2 COMPARING AND ORDERING NUMBERS Objective: To compare and order numbers. Eample Compare the numbers 689 and 698 by using,, or. Reminder: The alligator (>) eats the bigger number!!! You can picture this on a number line. The numbers increase from left to right. 689 is less than 698 because 689 is to the left of 698 Therefore Eample Write the numbers, 6,0, in order from least to greatest. Again think of the number line. Therefore the order from least to greatest would be 6,,,0. Eample Write the numbers,,, 6 in order from least to greatest. The least common multiple (LCM) of,, 6, and is. Rewrite each fraction using the LCM Now simply compare the new fraction s numerators. Since 6 9 then 6 9. Therefore the order from least to greatest would be 6 9,,,. Compare the two numbers using,, or , 6, Put the numbers in order from least to greatest. 6. {0, -, -8, -}.,,, ,,,.

3 FRACTIONS (Adding and Subtracting) Objective: To add and subtract fractions using a common denominator. Eample a. Add Eample Add 6 When the denominators are the same, add or subtract the numerators and keep the same denominator First find the LCM of and 6 which is b. Subtract Eample Add 8 Rewrite each fraction using the LCM Add the numerators, keeping the same denominator First find the LCM of 8 and which is 8 Rewrite each fraction using the LCM 6 6 or 6 Add the whole numbers and then add the fractions, keeping the same denominator Reduce fraction to lowest terms Add or subtract the fractions. Write each answer in simplest form. Show ALL work

4 FRACTIONS (Multiplying and Dividing) Objective: To multiply and divide fractions. Reminder: Eample Multiply Multiply the numerators together and then multiply the denominators together The top number in a fraction is called the numerator and the number in the bottom of the fraction is called the denominator. Eample Divide 8 8 Notice that the first fraction stays the same the whole way through Change division to multiplication and flip the second fraction Multiply the numerators together and the denominators together Eample Multiply Rewrite each fraction as an improper fraction Multiply the numerators and denominators Reduce the improper fraction completely Multiply or divide the fractions. Reduce final answers where possible. Show ALL work

5 ORDER OF OPERATIONS Objective: To evaluate epressions using the order of operations. Eample Simplify 9 0 Solution (9 ) 0 Divide 9 by ( ) 0 Multiply and 8 (0 ) Divide 0 by ( 8) Add and 8 Subtract from Reminder: Please Ecuse My Dear Aunt Sally Eample Simplify 8 [( ) ]. Solution 8 [ ] 8 Simplify the innermost parentheses first Then the [ ] grouping Subtract Find the value of each epression. Show ALL work.. 8 [(6 6) ]. 6 9 ( ). [( 8) 6]. (8 6) ( 9). 0 ( ) 6. [( ) ]

6 EVALUATING EXPRESSIONS Objective: To evaluate an algebraic epression. Eample Evaluate the epression c b if c and b 6. Solution c b 6 Substitute the given values for the variables Simplify by adding and 6 8 Subtract from Eample Evaluate the epression ( y z ) if, y, and z. Solution ( y z ) ( ) Substitute the given values into the epression (6 ) Simplify by following the correct order of operations 0 Multiply times and subtract from 6 9 Add Evaluate each epression if and y. Show ALL work.. y. y ( ). ( )( y ) Evaluate each epression if r 6 and t 8. Show ALL work.. ( r ) t. [0 ( r )] t 6. [ ( t )] r

7 INTEGERS (Adding and Subtracting) Objective: To add and subtract integers. Eample a. Add ( ) b. Add 9 ( ) or To add integers with same signs, add their absolute values and keep their original sign To add integers with different signs, subtract their absolute values and use the sign of the greater absolute value Eample a. Subtract 8 b. Subtract ( 8) 8 ( ) To subtract integers, add the opposite ( 8) 8 c. Subtract 6 d. Subtract ( ) To subtract integers, add the opposite 8 ( 9) Add or subtract the integers. Show ALL work.. ( ) ( ) ( 6) ( ) ( 00) 0. 6 ( 8). 0 ( )

8 INTEGERS (Multiplying and Dividing) Objective: To multiply and divide integers. Eample a. Multiply 9 b. Multiply ( 6)( ) 8 0 Multiplying two integers with the same sign will produce a positive integer c. Multiply (0) d. Multiply ( 0) 0 60 Multiplying two integers with different signs will produce a negative integer Eample a. Divide 8 b. Divide 90 ( ) 9 6 Different signs negative Same signs positive Multiply or divide the integers. Show ALL work.. ( )( ). (8). (6)(0). 0( ) ( 9). 6 ( 8) ( 8)( 8)(). 6. ( )( 6)()

9 GREATEST COMMON FACTOR Objective: To find the greatest common factor or GCF for two or more integers or monomials. Eample Find the GCF of 6 and Find the prime factorization of each number 8 Then find the common factors of each number 6 8 The greatest common factor of 6 and 8 is or 8 Eample Find the GCF of y and 8 y y y y Find the prime factorization of each number and write out the variables 8 y y Then find the common factors of each number and variable The GCF of y and 8 y is y or 6 y Find the greatest common factor or GCF of each set of integers or monomials. Show ALL work.. and., 8, and 96. ab and 0ac. am and 8a m. 60 zw and 0w 6. np,6 n, and 9n p 8

10 COMBINING LIKE TERMS Objective: To simplify an algebraic epression by combining like terms. Eample Simplify the epression ( 9) ( ) Solution ( ) ( 9) Rewrite the epression so that like terms are together Eample Combine the like terms Simplify the epression 6 ( 8) Solution 6 ( 8) Rewrite the epression so that like terms are together Combine 6- and --(-8) Simplify each epression. Show ALL work. Remember ( 8) ( 8) ( ). ( ) ( 8) 9. 9 ( ) 9

11 DISTRIBUTIVE PROPERTY Objective: To simplify an algebraic epression by using the distributive property. Eample Simplify the epression ( ) Solution Eample ( ) Distribute the by multiplying it by the and 6 Simplify the epression ( y ) ( ) Solution ( y ) ( ) Distribute the and then distribute the 6 y 0 Combine like terms 8 y Simplify each epression. Show ALL work.. ( ). ( ). 8( ). ( ). ( ) 6. ( 8) y. ( y ) 8. 6 ( ) 9. 6( ) 0( ) 0

12 SOLVING ONE STEP EQUATIONS Objective: To solve equations using one transformation. Eample Remember to solve an equation you must perform the inverse operation to both sides of the equation a. Solve for b. Solve for c. Solve for 0 Subtract from both sides () () Multiply both sides by = 6 Multiply both sides by the reciprocal Solve for. Circle your final answer. Show ALL work

13 INEQUALITIES AND GRAPHING Objective: To solve an inequality and graph the solution on a number line. Eample Solve 6 and graph the solution on a number line Solution Subtract 6 from both sides 9 Divide both sides by To graph, plot a solid dot on and shade everything less than or to the left of Reminder: use a solid dot. < > use an open dot. Eample Solve 0 and graph the solution on a number line Solution 0 + Add to both sides Divide both sides by - Remember when you multiply or divide by a negative you must reverse the inequality symbol To graph, plot an open circle on - and shade everything greater than - or to the right of - Solve for and graph the solution on the number line. Show ALL work

14 SOLVING PROPORTIONS Objective: To solve a proportion using cross-multiplication. Eample Solve for Cross-multiply Reminder: Cross-multiplying creates an equation that you already know how to solve! 8 8 Divide both sides by Solve each proportion for using cross multiplication. Circle your final answer. Show ALL work

15 PLOTTING POINTS ON THE COORDINATE PLANE Objective: To plot points on a coordinate plane. Eample Plot the points A(, ) and B(, ) on the coordinate plane. Label the points using their coordinates. Points can be located on the plane using an ordered pair (,y) A( -, ) (-coordinate, y-coordinate) left or right, up or down (-) (+) (+) (-) B(, -) For (, ) you must travel LEFT and UP For (, ) you must travel RIGHT and DOWN Plot the points on the coordinate plane and label the points.. A (, ) 6. F (, ). B (, ). G ( 6, ). C (0,) 8. H (, ). D (, ) 9. I (0, ). E (,) 0. J ( 8, 9)

16 TABLE OF VALUES Objective: To complete a table of values for an equation and graph the solutions. Eample Complete a table of values for y and graph your solutions y y ( ) 0 (0) () () These solutions can be written as ordered pairs (, ),(0,),(,),(,). Graph and label these ordered pairs on the coordinate plane (0,) (, ) (,) (,) Connect the points with a line Complete a table of values and graph the equation. Connect the points to make a line. Show ALL work.. y.. y y y 0 0

17 MEAN, MEDIAN, MODE, and RANGE Objective: To find the mean, median, mode, and range of a set of data. Eample The top speeds in miles per hour of ten animals are listed:, 8, 0,,,,, 0, 6, Find the mean, median, mode, and the range of the data. Solution: First put the numbers in order from least to greatest, 8,,,,,, 0, 6, Mean = average = Median = middle. Since is the score that occurs the most frequently, is the Mode Range = largest value smallest value = 0 69 For each set of data find the mean, median, mode, and range. Show ALL work.., 0,, 9,, 6. 8, 6,,, 6,, Mean = Median = Mode = Range = Mean = Median = Mode = Range =. In seven football games, the Tigers scored 8,,, 8,,, and points. Mean = Median = Mode = Range =. In a class of students, the test scores were 8, 98, 00, 9, 68, 8, 96, 88, 8, 8, 8, and 9. Mean = Median = Mode = Range = 6

18 BOX AND WHISKER PLOTS Objective: a. To create a bo and whisker plot given a set of data. Eample Draw the bo-and-whisker plot for the following data set. 9,, 8, 86, 99, 8, 80, 9 Solution: Start by putting the data in numerical order., 9, 80, 86, 8, 8, 9, 99 Find the median, or the middle. Since there are eight data points, the median will be the average of the two middle values: (86 + 8) = 86. = Q This splits the list into two halves:, 9, 80, 86 and 8, 8, 9, 99. Find the median, or middle of each half. Since the halves of the data set each contain an even number of values, the sub-medians will be the average of the middle two values. Q = (9 + 80) = 9. Q = (8 + 9) = 90. The minimum value is and the maimum value is 99, so you have: min:, Q : 9., Q : 86., Q : 90., ma: 99 Plot each of these five numbers on a number line. The "bo" part of the plot goes from Q to Q And then the "whiskers" are drawn to the endpoints.

19 Use the space provided to create a bo and whisker plot for the set of test scores and answer the questions that follow. Show ALL work. 6, 6, 89, 8,, 68,,, 6, 66, 8. Find the mean for this set of data.. Find the median for this set of data.. Find the mode for this set of data.. Find the range for this set of data. 8

20 STEM-AND-LEAF PLOT Objective: To find the mean, median, mode, and range of a stem-and-leaf plot. Eample Find the mean, median, mode, and range of the following stem-and-leaf plot: The number 8 would be represented as Stem Leaf 8 Math Test Scores (out of 0 pts) Stem 6 8 Leaf Therefore the scores represented in this stem-and-leaf are:, 6, 8, 0,,,,,,, 8, 9, 0, 0, 0 Solution Mean = Median = (middle) Since 0 is the score that occurs the most frequently, 0 is the Mode. Range = 0 6 Definitions: Mean the average of all the numbers Median the middle number of a set of numbers in order from smallest to largest Mode the number that appears most often Range the difference between the largest and smallest numbers 9

21 Create your own stem-and-leaf plot with the following temperatures for June. Show ALL work. Find the mean, median, mode, and range of the following stem-and-leaf plot:, 80, 8, 68, 6, 9, 0, 69, 6, 6, 0, 6, 9,, 6, 8, 8, 8, 9, 6. Mean =. Median =. Mode =. Range = 0

22 PROBABILITY Objective: To find the probability that an event will occur. EXAMPLE Solve. Show ALL work. A glass bowl contains red marbles, blue marbles, and white marble. A marble is drawn at random from the bowl. Find the probability of each event. a. Event A: The marble drawn is red. b. Event B: The marble drawn is either red or blue. c. Event C: The marble drawn is not red. d. Event D: The marble drawn is green. Solution: a. Since there are red marbles, Event A has equally likely outcomes. So P (A).. A jar contains blue marbles, 6 red marbles, green marbles, and black marble. A marble is drawn at random from the jar. Find the probability of each event. 8 b. Since there are red marbles and blue marbles, Event B has 8 equally likely outcomes. So P (B). c. If a marble is not red, then it must be either blue or white. Since there are blue marbles and white marble, Event C has equally likely 8 outcomes. So P (C). d. Since there aren t any green marbles, Event D is an impossible event so P (D) 0. a. The marble is blue. b. The marble is green. c. The marble is not green. d. The marble is black. e. The marble is either red or blue.. A cube whose sides are numbered,,,,, and 6 is rolled. Find the probability of the event that the number on the cube is: a. b. or c. greater than d. greater than but less than

23 . One card is drawn at random from a standard deck of hearts, diamonds, clubs, and spades. Find the probability of the event that the card is: a. an ace. b. a black c. a spade d. the jack of clubs e. a or f. an ace, king, or queen. A spinner has si equal sections numbered,,,,, and 6. The pointer on the spinner is spun. Find the probability of each event. a. The pointer stops on an odd number. b. The pointer stops on a number greater than. 6 c. The pointer stops on a multiple of. d. The pointer stops on a prime number.

24 AREA AND PERIMETER Objective: To find the area and perimeter of different polygons. Reminder: Here are some formulas: Asquare/rec tangle l w Eample Find the area of the figure below. Atriangle b h cm cm Asquare l w cm cm Asquare 6 cm A circle r Eample Find the area of the figure below. in. Since this is a circle with a inch radius, use the circle formula. ( Use. ) A circle r (.)( in.) Acircle.6 in Eample Find the area of the figure below. Since this is a triangle with a base of. cm and a height of cm, use the triangle formula. cm. cm A triangle b h Atriangle 6. (. cm)(cm) cm Eample Find the perimeter of the following figure. cm cm cm cm Perimeter is the distance around the outside of an object. To find it, simply add up all of the sides. P cm cm cm cm P cm

25 Find the area of each figure. Label with correct units. Show ALL work... in. cm in.... mm 6. mm. m Find the perimeter of each figure. Label with correct units. Show ALL work.. 6. cm ft. in in