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Created by: Miss Jessie Minor Use: PSSA Review For 7th Grade Sources: Common Core Standards from PDE website. Contents: Concepts with description of how to solve and practice problems. Reinforcement: Internet Websites: www.studyisland.com, www.ask.com, www.ixl.com, www.mathmaster.org, and PSSA Coach workbook EXPERIMENTAL PROBABILITY IN ORDER TO CALCULATE EXPERIMENTAL PROBABILITY OF AN EVENT USE THE FOLLOWING DEFINITION: P(Event)= LESSON 30 EXPERIMENTAL PROBABILITY A student flipped a coin 50 times. The coin landed on heads 28 times. Find the experimental probability of having the coin land on heads P(heads) = 28 = .56 = 56% 50 It is experimental because the outcome will change every time we flip the coin. http://www.ixl.com/math/grade-7/experimental-probability Theoretical Probability –The outcome is exact. When we roll a die, the total possible outcomes are 1,2,3,4,5, and 6. The set of possible outcomes is known as the sample space. Find the prime numbers---since 2,3,and 5 are the only numbers in the same space P(the number is prime) = 3 = 60% 5 LESSON 29 Rate is comparison of two numbers example: 40 feet per second or 40 ft 1 sec Unit price = price divided by the units Sales Tax= change sales tax from a percent to a decimal and the multiply it times the amount. Finally add that amount to the total to find the total price. Example 1: $1200 at 6% sales tax = 100 6 = .06 x 1200 = 72 = $1272 Example 2: Rachel bought 3 DVDs. Using the 6% sales tax rate, calculate the amount of tax she paid if each DVD costs $7.99? http://www.ixl.com/math/grade-7/unit-prices LESSON 4 Distance formula = distance = rate x time OR D = rt Example 1: A car travels at 40 miles per hour for 4 hours. How far did it travel? d=rt d=40 miles /hr x 4 hrs d = 160 miles. We can also use this formula to find time and rate. We just have to manipulate the equation. Example 2: A car travels 160 miles for 4 hours. How fast was it going? d = rt 160 miles = r (4 hours) 160 miles 4 hrs = t 40 miles/hr = t LESSON 23 Michael enters a 120-mile bicycle race. He bikes 24 miles an hour. What is Michael's finishing time, in hours, for the race? A B C D 2 5 0.2 0.5 DISTANCE = RATE X TIME WITH THIS FORMULA WE CAN FIND THE DISTANCE IF THEY GIVE US THE RATE AND THE TIME. IN FACT, AS LONG AS THEY GIVE ME ANY TWO QUANTITIES, WE CAN FIND THE THIRD. EXAMPLE: HOW FAR DID ED TRAVEL IN 7 HOURS IF HE WAS GOING 6O MILES PER/HOUR D = RT D = 60MILES/HR X 7 HRS D = 420 MILES OR IF THE DISTANCE IS GIVEN AND THE RATE OR SPEED IS ALSO GIVEN, D = RT 420MILES = 60 MILES/HR X T 420 MILES 60MILES/HR = 7 HOURS Ratio = comparison of two numbers. Example: Johnny scored 8 baskets in 4 games. The ratio is 8 = 2 4 1 2 ratios separated by an equal sign . If Johnny score 8 baskets in 4 games how many baskets will he score in 12 games? Set up the proportion--- 8 baskets = x baskets 4 games 12 games Cross multiply 4x = 8 ( 12 ) 4x = 96 X= 96 4 X= 24 baskets http://www.ixl.com/math/grade-7/compare-ratios-word-problems LESSON 7 FRACTIONS: ADDING AND SUBTRACTION ---FIND COMMON DENOMINATORS. Use factor trees, find prime factors , circle ones that are the same circle the ones by themselves. Multiply the circled numbers. Ex ample: 5 + 8 12 9 12 2 2 9 6 3 3 2 3 2 2 2 3 3 3 3 x 3 x 2 x 2 = 36 Common denominator = 36 3 x5 = 4 x 8 = 15 + 32 = 47 36 36 36 36 36 http://www.ixl.com/math/grade-7/least-common-denominator LESSON 1 Multiplying fractions : cross cancel and multiply straight across 4 X 5 5 8 = 1 2 Dividing fractions : change the sign to multiply and reciprocate the 2nd fraction 3 ÷ 5 4 8 = 3 X 8 4 5 = 24 20 •http://www.ixl.com/math/grade-7/multiply-fractions http://www.ixl.com/math/grade-7/divide-mixed-numbers LESSON 2 3 X 5 4 6 1 X 7 49 5 X 9 13 4 5 LCM = least common multiple = the smallest number that 2 or more numbers will divide into. Example: find the lcm of 24 and 32 You can multiply each number by 1,2,3,4… until you find a common multiple which is 96. Or you can use a factor tree: 24 2 12 2 2 6 2 2 2 3 24: 32: 2 2 2 3 2 2 2 2 2 32 2 16 2 2 8 2 2 2 4 2 2 2 2 2 2x2x2x3x2x2 = 96 GCF = GREATEST COMMON FACTOR = The Largest factor that will divide two or more numbers. In this case we would multiply the factors that are the same. 2x2x2 = 8, so 8 is the GCF of 24 and 32. What is the greatest common factor (GCF) of 108 and 420 ? A B C D 6 9 12 18 What is the least common multiple (LCM) of 8, 12, and 18 ? A B C D 24 36 48 72 DISTRIBUTIVE PROPERTY A(B + C) = AB + AC We distributed A TO B AND C Solving 2 step equations: 4(x + 2) = 24 4x + 8 = 24 sub 8 4x = 16 divide by 4 x = 4 Remember when solving 2 step equations do addition and subtraction first then do multiplication and division first. Just the opposite of (please excuse my dear aunt sally,) which we us on math expressions that don’t have variables http://www.ixl.com/math/grade-7/distributive-property LESSON 20 Associative and Commutative property Associative Commutative • Always has parentheses • A ( B X C) = B (C X A) • FOR MULTIPLICATION • A + (B + C) = B + (C + A) • FOR ADDITION • http://www.mathmaster.org/v ideo/associative-property-formultiplication/?id=932 • AXB=BXA • FOR MULTIPLICATION • A+B=B+A • FOR ADDITION http://www.mathmaster.org/video/com mutative-property-for-addition/?id=931 Stem and leaf plotsBox and –Whisker plots Investigation 4 http://www.ixl.com/math/grade-7/interpret-stem-and-leaf-plots LESSON 24 To organize scores or large groups of numbers, we can use stem and leaf plots. Example 40, 30, 43, 48, 26, 50, 55, 40, 34, 42, 47, 47, 52, 25, 32, 38, 41, 36, 32, 21, 35, 43, 51, 58, 26, 30, 41, 45, 23, 36, 41, 51, 53, 39, 28 Stem 2 3 4 5 Leaf 1 3 5 6 68 0022456689 001112335778 0112358 Stem 2 3 4 5 Leaf 1 3 5 6 68 0022456689 001112335778 Upper quartile 0112358 Lower quartile MODE—The number that occurs the most often—The mode of these 35 scores is 41. RANGE—The difference between the least and greatest number—is 37 MEDIAN—is the set of numbers is the middle number of the set when the numbers are arranged in order—it is 40 MEAN– another name for average is mean FIRST QUARTILE OR LOWER QUARTILE—The middle number of the lower half of scores. 32 THIRD QUARTILE OR UPPER QUARTILE—The middle number of the upper half of scores. 47 LESSON 27, 25 Make a stem and leaf plot from the following numbers. Then make a box and whiskers diagram. 25, 27, 27, 40, 45, 27, 29, 30, 26, 23, 31, 35, 39 Below are the number of points John has scored while playing the last 14 basketball games. Finish arranging John’s points in the stem and leaf plot and then find the range, mode, and median. Points: 5, 14, 21, 16, 19, 14, 9, 16, 14, 22, 22, 31, 30, 31 Stem Leaf Range: 0 Mode: 1 Median: 2 3 Lower extreme 20 Box-and –whisker plot First quartile Second Third quartile Upper quartile or or lower or upper extreme median quartile quartile 30 40 Inter quartile range 50 60 ABSOLUTE VALUE = the number itself without the sign. The symbol for this is----- The absolute value of -5 The absolute value of 5 Is 5 Is 5 http://www.ixl.com/math/grade-7/integer-inequalities-with-absolute-values ORDER OF OPERATIONS Please, Excuse, My, Dear, Aunt, Sally 3(4 + 4) ÷ 3-2 3(8) ÷ 3-2 24 ÷ 3-2 8 - 2 =6 Note that there are not any variables is the statement. This is why we use order of operation instead of the Distributive property. LESSON 5 3 + 2(4 x 3) 12 - 15 - 3 (22 + 14) – 6 64 – 8 + 8 http://www.mathmaster.org/video/exponent-properties-involving-products/?id=1889 2³ 3⁴ = 2x2x2 144 = 3x3x3x3 64 4² = 4x4 http://www.ixl.com/math/grade-7/exponents-with-decimal-and-fractional-bases Finding the missing side of a triangle. Since the sum of the degrees of a triangle is 180 degrees we subtract the sum of 65 + 50 = 115 from 180 - 115 = 65 So b = 65 a 50° 65° b c If b = 65 to find c we know that a straight line is 180 so if we subtract 65 from 180 we get 115. Angle c = 115 To find L a we do the same thing. 180 – 50 = 130 so a = 130 degrees. http://www.ixl.com/math/grade-7/find-measures-of-complementary-supplementaryvertical-and-adjacent-angles Pythagorean Theorem To find the missing hypotenuse of a right triangle, we use the formula c² = A² + B² Hypotenuse Height = 6 in c² = A² + B² C² = 6²in + 8²in C² = 36 sq in + 64 sq in C² = 100 sq in = C sq in = 10 sq in Base = 8 inches http://www.mathmaster.org/video/pythagorean-theorem/?id=1922 AREA OF A TRIANGLE A + base x height 2 Area = base x height 2 A = 10in x 8 in 2 Height= 8 in A = 80 sq in 2 A = 40 sq in Base= 10 in Definition of height is a line from the opposite vertex perpendicular to the base. http://www.ixl.com/math/grade-7/area-of-triangles-and-trapezoids LESSON 12 FINDING AREA OF A TRIANGLE AREA = ½ (BASE X HEIGHT) A = ½ bh 2 ft height Area = ½ bh A = ½ (4ft)(2ft) A = ½ 8ft A =4 ft² base 4 ft Finding area of a parallelogram h b Area = b x h Area of a rectangle = length x width Area of a square = side x side 2ft 4ft 2ft 2ft http://www.ixl.com/math/grade-7/area-of-rectangles-and-parallelograms FINDING PERIMETER AND AREA OF COMPOUND FIGURES PERIMETER IS THE DISTANCE AROUND A FIGURE. 9 FT 3FT P = a + b + c + ….. P = 9FT + 9FT + 3FT + 3FT P = 24 FT TO FIND THE AREA OF A COMPOUND FIGURE, ALL WE HAVE TO DO IS FIND THE AREA OF BOTH FIGURES AND ADD THEM. 6FT 3FT 7FT 2FT AREA = LENGTH X WIDTH A = 3FT X 6FT A = 18FT² AREA = LENGTH X WIDTH A = 4FT X 4FT A = 16 FT² Volume of a quadrilateral Volume = Length x Width x Height 3 ft 4 ft 5 ft http://www.ixl.com/math/grade-7/volume Parallel lines = lines that never touch--- symbol Perpendicular lines = lines that intersect---symbol Skew lines = lines in different planes that never intersect Plane = many points that are next to each other extending in the same direction Vertical angles = angles that share a point and are equal--- Adjacent angles = are angles that are 180 degrees and share a side. Lesson 18 ADJACENT ANGLES ARE ANGLES THAT SHARE A COMMON SIDE. ANGLES 3 AND 4 ARE ADJACENT ANGLES ANGLES 2 AND 3 ARE ALSO ADJACENT ANGLES. 2 3 1 4 http://www.ixl.com/math/grade-7/identify-complementary-supplementary-verticaland-adjacent-angles Complementary angles : angles whose sum =‘s 90 degrees Supplementary angles: angles whose sum =‘s 180 degrees Right angle: angle measures 90 degrees ---symbol--Acute angle: angle less than 90 Obtuse angle: angle greater than 90 degrees Congruent: when two figures are exactly the same Similar: when two figures are the same shape but not the same size Regular: when a figure has all = sides Line of symmetry: when a line can cut a figure in two symmetrical sides LESSON 17 SUPPLEMENTARY ANGLES SUPPLEMENTARY ANGLES ARE ANGLES WHOSE SUM IS 180 DEGREES. COMPLEMENTARY ANGLES ARE ANGLES WHOSE SUM IS 90 DEGREES. A STRAIGHT ANGLE IS EQUAL TO 180 DEGREES CLASSIFY LINES INTERSECTING LINES---OCCUPY THE SAME PLANE. THEY MEET AT ONLY ONE POINT. PERPENDICULAR LINES WHEN TWO LINES INTERSECT AND FORM4 RIGHT ANGLES. THE SYMBOL IS ∏ PARALLEL LINES EXTEND FOREVER IN BOTH DIRECTIONS IN THE SAME PLANE AND NEVER INTERSECT. THES SYMBOL IS // SKEW LINES ARE A PAIR OF LINES THAT ARENOT PARALLEL BUT NEVER INTERSECT. THEY OCCUPY TWO DIFFERENT PLANES. Congruent angles and sides mean that they have the same measure. http://www.ixl.com/math/grade-7/identify-complementary-supplementary-vertical-andadjacent-angles Similar figures Two figures are similar if they have exactly the same shape, but may or may not have the same size. The symbol ≈ Points on a coordinate grid Quadrant ll Point of Origin [0, 0] y 6 5 4 3 2 1 Quadrant I -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -1 -2 -3 Quadrant lll Quadrant lV -4 -5 -6 [2, 6] Ordered pair: 2 is x value and 6 is y value x axis LESSON 16 What is the total number of lines of symmetry that can be drawn on the trapezoid below? A B C D 4 3 2 1 Which figure below correctly shows all the possible lines of symmetry for a square? A Figure 1 B Figure 2 C Figure 3 D Figure 4 http://www.ixl.com/math/grade-7/symmetry Chord = line that cuts the circle and doesn’t go through the center of the circle. Diameter = distance across the center of the circle Radius = the distance half way across the circle. Central angles = angles that are in the center of the circle Inscribed angle = the angle on the inside of the circle Area = ∏ x r Circumference = distance around the outside of the circle 2 Circumference= 2∏r LESSON 15 CIRCUMFERENCE IS THE DISTANCE AROUND -------------------------------- ----------------- DIAMETER- CUTS THE CIRCLE IN HALF IN THE MIDDLE OF THE CIRCLE CHORD CUTS THE CIRCLE ANYWHERE ELSE OTHER THAN THE MIDDLE RADIUS– GOES FROM THE CENTER OF THE CIRCLE TO THE OUTER MOST EDGE http://www.ixl.com/math/grade-7/identify-complementary-supplementary-verticaland-adjacent-angles CIRCUMFERENCE AND AREA OF A CIRCLE CIRCUMFERENCE IS THE DISTANCE AROUND -------------------------------- ----------------- RADIUS– GOES FROM THE CENTER OF THE CIRCLE TO THE OUTER MOST EDGE DIAMETER- CUTS THE CIRCLE IN HALF IN THE MIDDLE OF THE CIRCLE CHORD CUTS THE CIRCLE ANYWHERE ELSE OTHER THAN THE MIDDLE C = ∏ X D A = ∏ X R² http://www.ixl.com/math/grade-7/identify-complementary-supplementary-verticaland-adjacent-angles LESSON 13 A duck swims from the edge of a circular pond to a fountain in the center of the pond. Its path is represented by the dotted line in the diagram below. What term describes the duck's path? A chord B radius C diameter D central angle Functions: inserting a value in for x to find y Example: f(x) = 2x + 4 If x = 2 Then f(x) = 2 (2) + 4 f( x) = 4 + 4 f(x) = 8 So y = 8 Another explanation is-- a function is when we put a value in and get an answer out. http://www.ixl.com/math/grade-7/evaluate-a-function LESSON 20 Scientific notation -- 4.057 x 10⁶ Means we are going to move the decimal 6 places to the right 4.057 x 10⁶ becomes 4057000 Expanded notation --- numbers written using powers of 10 Example -----4234 = (4 x 10³) + (2 x 10²) + (3 x 10¹) + (4 x 10⁰) 4000 + 200 + 30 + 4 = 4234 Any number raised to the zero power = 10 ⁰ = 1 Any number raised to the 1st power = that number METRIC SYSTEM KILO DEKA METER LITER GRAM HECTO MILLI DECI CENTI START where your at and move the decimal to where you want to go. Example: 4 kilometers = 400 meters LESSON 11 METRIC CONVERSION KING HENERY DIED DRINKING KILO HECTO DEKA (BASIC ) DECI UNIT EXAMPLE 24 KILOGRAMS = _______GRAMS CHOCOLATE CENTI MILK MILLI IN 24, THE DECIMAL IS AFTER THE 4 –WE WILL MOVE IT 3 PLACES TO THE RIGHT AND GET 24,000 GRAMS http://www.ixl.com/math/grade-7/evaluate-a-function Weight Unit Conversions: USE THE CHART AND MOVE THE DECIMAL POINT. GRAM = WEIGHT METER = DISTANCE LITER = VOLUME FOR U.S. CUSTOMARY MEASUREMENT, CONVERSIONS ARE ON CHARTS. The flower box in front of the main city library weighs 124 ounces. What does the flower box weigh in pounds? Unit multipliers Always list the conversion. For example: change 240 feet to yards First we list the conversions There are 3 ft 1 yard or 1 yard 3 feet Because I want to go to yards I am going to multiply by 1 yard 3 feet So 240 feet X 1 yard 240 feet X 1 yard 1 3 feet = 1 3 feet = 80 yards LESSON 9 Irrational Numbers: Which of these is an irrational number? Inequalities: is a mathematical sentence with one of these symbols <, >, <, > < < > > Is less than Is less than or equal to Is greater than Is greater than or equal to http://www.ixl.com/math/grade-7/solve-one-step-linear-inequalities Scaling: A SCALE IS THE RATIO OF THE MEASUREMENTS OF A DRAWING,A MODEL,A MAP OR A FLOOR PLANTO THE ACTUAL SIZE OF THE OBJECTS OR DISTANCES EXAMPLE: AN ARCHITECT’S FLOOR PLAN FOR A MUSEUM EXHIBIY HALF USES A SCALE OF 0.5 INCH : 2 FEET. On this drawing, a passageway between exhibits is represented by a rectangle 3.75 inches long. What is the actual length of the passageway? To find an actual length from a scale drawing, identify and solve a proportion. Drawing = Drawing Actual Actual Let p = the actual length in feet of the passageway .5 inch 2 feet .5 = 3.75 .5 x p = 2 x 3.75 2 p p = 15 http://www.mathmaster.org/video/scale-and-indirectmeasurement/?id=1858 Use cross products to solve the proportion LESSON 14 RATIO IS A COMPARISON BETWEEN TWO NUMBERS. TWO RATIOS SEPERATED BY AN = SIGN IS CALLED A PROPORTION. ⅘ = 2/X TO SOLVE A PROPORTION WE CROSS MULTIPLY AND WE GET 4X = 10 X = 10/4 http://www.ixl.com/math/grade-7/understanding-ratios LESSON 7 Use proportions to enlarge or reduce Mindy and her sisters want to make an enlargement of photograph of their parents. The original photograph is 5 inches long and 3 inches wide. They would like the enlargement to be 35 inches long. What is the scale factor of the enlargement? The original length is 5 inches and the enlargement length is 35 inches. As a ratio: Enlargement length /35 inches, 7/original length or 5 inches / 1 Use a proportion to find the width of the enlargement. Let x represent the width of the enlargement. 1 ∙ x=7 ∙ 3 Scale factor X = 21 7/1 = x/3 http://www.ixl.com/math/grade-7/solve-proportions LESSON 8 Scaling Scaling is the ratio of the measurements of a drawing, a model, a map, or a floor plan to the actual size of the objects or distances. A scale drawing is similar in shape to the object it represents. Problem—an architect’s floor plan for a museum exhibit hall uses a scale of .5 inch : 2 feet. On this drawing, a passageway between exhibits is represented by a rectangle 3.75 inches long. What is the actual length of the passageway? To find the actual length from a scale drawing, identify and solve a proportion, Identify two ratios in the same order Drawing = Drawing Actual Actual .5/2 = 3.75/p .5p = 3.75(2) .5P = 7.2 P = 15 feet http://www.ixl.com/math/grade-7/scale-drawings-and-scale-factorshttp Adding negative numbers Rules http://www.ixl.com/math/grade-7/add-and-subtract-integers RULES FOR MULTIPLYING POSITIVE AND NEGATIVE NUMBERS NEGATIVE TIMES A NEGATIVE = POSITIVE POSITIVE TIMES A POSITIVE = POSITIVE POSITIVE TIMES A NEGATIVE = NEGATIVE -2 X -4 = 8 2 X 2 = 4 2 X -3 = -6 http://www.ixl.com/math/grade-7/integer-multiplication-and-division-rules WHEN WE HAVE A SITUATION LIKE -(- 2 ) OUR ANSWER IS POSITIVE 2 BECAUSE A NEGATIVE TIMES A NEGATIVE IS A POSITIVE. MULTIPLYING AND DIVIDING MIXED NUMBERS WHENEVER WE MULTIPLY OR DIVIDE MIXED NUMBERS, ALWAYS CHANGE THEM TO IMPROPER FRACTIONS 1 3/4 X 11/2 = 7 X 3 = 21 4 2 8 WE DO NOT HAVE TO CHANGE THEM WHEN WE ADD OR SUBTRACT. http://www.ixl.com/math/grade-7/dividemixed-numbers Histogram = is a bar graph without the spaces between the bars 6 5 4 3 2 1 4-5 6-7 8-9 10-11 Bar graph looks like this Spaces between the bars to show difference in data. http://www.ixl.com/math/grade-7/interpret-histograms LESSON 26 SOLVE PROBLEMS USING PATTERNS EXAMPLE: ERIN IS COLLECTING PLASTIC BOTTLES. ON MONDAY SHE HAS 7 BOTTLES, ON TUESDAY SHE HAS 14 BOTTLES, ON WEDNESDAY SHE HAS 21 BOTTLES, AND ON THURSDAY SHE HAS 28 BOTTLES. IF THE PATTERN CONTINUES, HOW MANY BOTTLES WILL SHE HAVE ON FRIDAY? 1 FIND THE PATTERN TO SOLVE THE PATTERN 2 7,14,21,28 3 WRITE THE DIFFERERENT OPERATIONS THAT YOU CAN PERFORM ON 7 TO GET 14 4 CHECK THESE OPERATIONS WITH THE NEXT TERM IN THE PATTERN 5 14 + 7 =21 6 14 X 2 = 28 7 FIND THE NEXT TERM IN THE PATTERN TO DETERMINE HOW MANY BOTTLES ERIN WILL HAVE ON FRIDAY 8 28 + 7 = 35 LESSON 19 SOLVING ONE STEP EQUATIONS TO SOLVE AN EQUATION, YOU NEED TO GET THE VARIABLE ALONE ON ONE SIDE OF THE EQUALS SIGN, YOU CAN USE A MODEL OR AN INVERSE OPERATION TO SOLVE A ONE STEP EQUATION. DIVIDE BY 3 3X = 24 3X = 24 3 3 DO IT TO BOTH SIDES X = 8 LESSON 21 http://www.ixl.com/math/grade-7/solve-two-step-linear-equations DIVIDING FRACTIONS RULE---- CHANGE THE SIGN TO MULTIPLY AND RECIPROCATE THE SECOND FRACTION. 3 4 ÷ 3 4 X 1 1 X 2 2 6 8 = 8 6 2 2 = 1 http://www.ixl.com/math/grade-7/divide-fractions A square has 4 angles which each measure 90 degrees A D 45 45 45 45 C B Find the measure of <A in the triangle ABC A 30 B C M<A + 90 + 30 = 180 M<A = 60 Modeling Mathematical Situations Translate “five more than” means 5 plus a quantity Translate “three times a number” means 3 x n, or 3n When you combine both you get 5 + 3n or 3n +5 Lesson 22 Comparing and Ordering Integers NEGATIVE -6 -5 -4 -3 -2 -1 POSITIVE 0 1 2 3 4 5 -4 IS GREATER THAN -6 LESSON 3 Rational Numbers On a Number Line Fraction 3 4 Decimal Percent .75 4 3 .75 x 100 = 100% Rational numbers are numbers that can be expressed as fractions that can be formed from Integers. Lesson 4 Estimation = Find compatible numbers and divide. There are 52 weeks in a year. Leo’s salary is $51,950. $51,950 is about $52,000. Divide the compatible numbers. $52,000 divided 52 = $1,000 Lesson 10 Double and Triple Bar Graphs and Double and Triple Line Graphs are used to show two sets of related data 6 5 4 Series 1 3 Series 2 Series 3 2 1 0 Category 1 Category 2 Category 3 Category 4 Lesson 25 Making Predictions– You can use trends or patterns you see in graphs to make predictions. 6 5 4 Series 1 3 Series 2 Series 3 2 1 0 Category 1 Category 2 Category 3 Category 4 Lesson 31