Report

Created by: Miss Jessie Minor Purpose: PSSA Review for 7th Grade (Can be used as enrichment or remediation for most middle school levels) Contents: Concept explanations & practice problems. Sources: Common Core Standards from PDE website. Reinforcement: www.studyisland.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)= Number of times the event occurred Number of total trials COACH LESSON 30 2 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 3 PRACTICE EXPERIMENTAL PROBABILITY! 4 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. PRACTICE THEORETICAL PROBABILITY! Find the prime numbers– since 2, 3, and 5 are the only prime numbers in the same space… P(prime numbers)= 3/5 = 60% COACH LESSON 29 5 RATE/ UNIT PRICE/ SALES TAX! RATE: comparison of two numbers Example: 40 feet per second or 40 ft/ 1 sec UNIT PRICE: price divided by the units Example: 10 apples for $4.50 Unit price: $4.50 ÷ 10 = $0.45 per apple SALES TAX: change sales tax from a percent to a decimal, then multiply it by the dollar amount; add that amount to the total to find the total price Example 1: $1,200 at 6% sales tax = 6 ÷ 100 = 0.06 x 1,200 = 72 1200 + 72 $1272 http://www.ixl.com/math/grade-7/unit-prices COACH LESSON 4 6 PRACTICE SALES TAX! 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? 7 DISTANCE FORMULA! 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 = r 40 miles/hr = r COACH LESSON 23 8 PRACTICE THE DISTANCE FORMULA! DISTANCE = RATE X TIME WITH THIS FORMULA WE CAN FIND ANY OF THE THREE QUANTITIES, RATE, TIME, OR DISTANCE, IF AT LEAST TWO OF THE QUANTITIES ARE GIVEN. If the time and rate are given, we can find the distance: EXAMPLE: How far did Ed travel in 7 hours if he was going 60 miles per/hour? d = rt d = 60miles/hr x 7 hrs d = 420 miles Or if the distance and rate are given, we can find the time: d = rt 420miles = 60 miles/hr x t (420 miles ÷ 60 miles/hr) = 7 hours 9 PRACTICE USING THE DISTANCE FORMULA! 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 10 RATIOS & PROPORTIONS! Ratio: comparison of two numbers. Example: Johnny scored 8 baskets in 4 games. The ratio is 8 = 2 4 1 Proportion: 2 ratios separated by an equal sign . If Johnny score 8 baskets in 4 games how many baskets will he score in 12 games? 1. Set up the proportion 8 baskets = x baskets 4 games 12 games 2. Cross multiply & Divide 4x = 8 ( 12 ) 4x = 96 x = 96 4 x= 24 baskets http://www.ixl.com/math/grade-7/compare-ratios-word-problems COACH LESSON 7 11 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. EXAMPLE: 5 12 + 8 9 12 2 6 2 3 9 3 3 12: 2 2 3 9: 3 3 3 x 3 x 2 x 2 = 36 Common denominator = 36 3 x 5 = 4 x 8 = 15 + 32 = 47 36 36 36 36 36 http://www.ixl.com/math/grade-7/least-common-denominator COACH LESSON 1 12 PRACTICE FRACTIONS! 13 MULTIPLYING & DIVIDING FRACTIONS! Multiplying fractions : cross cancel and multiply straight across ¹4 X ¹5 ¹5 ²8 = 1 2 Dividing fractions : change the sign to multiply, then reciprocate the 2nd fraction 3 ÷ 5 4 8 = 3 X 8 4 5 = 24 20 REDUCE!!! http://www.ixl.com/math/grade-7/multiply-fractions http://www.ixl.com/math/grade-7/divide-mixed-numbers COACH LESSON 2 14 PRACTICE MULTIPLYING FRACTIONS! 3 X 5 4 6 1 X 49 7 13 5 X 9 4 5 15 Multiplying & Dividing Mixed Numbers! When multiplying or dividing mixed numbers, always change them to improper fractions. Example 1: Example 2: 1¾ x 1½ = 7 x 3 = 21 4 2 8 12 x 2 ½ = 12 x 5 = 60 = 30 1 2 2 http://www.ixl.com/math/grade-7/divide-mixed-numbers 16 Dividing Mixed Numbers! When dividing any form of a fraction, change the division to multiplication, then reciprocate the 2nd fraction. Example: 1¾ ÷ 1½ 7 4 ÷ 3 2 7 4 x http://www.ixl.com/math/grade-7/divide-fractions = 2 = 3 14 = 11/6 12 17 LEAST COMMON MULTIPLE! 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 32 2 12 2 2 24: 32: 2 2 2 3 2 2 2 2 2 2 6 2 2 3 2 16 2 2 8 2 2 2 4 2 2 2 2 2 2x2x2x3x2x2 = 96 18 GREATEST COMMON FACTOR! 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. 24: 2 2 2 3 32: 2 2 2 2 2 Example: 2x2x2 = 8, so 8 is the GCF of 24 and 32. 19 PRACTICE LCM AND GCF! 20 PRACTICE LCM AND GCF! 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 21 ABSOLUTE VALUE! ABSOLUTE VALUE: the number itself without the sign; a number’s distance from zero The symbol for this is | | Example: The absolute value of |-5| is 5 The absolute value of |5| is 5 http://www.ixl.com/math/grade-7/integer-inequalities-with-absolute-values 22 PRACTICE ABSOLUTE VALUE! 23 DISTRIBUTIVE PROPERTY A(B + C) = AB + AC Solving 2 step equations: subtract 8 divide by 4 (We distributed A to B and then A to C) 4(x + 2) = 24 4x + 8 = 24 4x = 16 x= 4 •Remember when solving 2 step equations do addition and subtraction first then do multiplication and division. •This is opposite of (please excuse my dear aunt sally,) which we use on math expressions that don’t have variables. http://www.ixl.com/math/grade-7/distributive-property COACH LESSON 20 24 Associative & Commutative Property! Associative • Always has parentheses • A ( B X C) = B (C X A) • FOR MULTIPLICATION Commutative • AXB=BXA • FOR MULTIPLICATION • A+B=B+A • FOR ADDITION • A + (B + C) = B + (C + A) • FOR ADDITION http://www.mathmaster.org/video/associative-property-for-multiplication/?id=932 http://www.mathmaster.org/video/commutative-property-for-addition/?id=931 25 Stem and Leaf Plots, Box – and – Whisker Plots We use stem and leaf plots to organize scores or large groups of numbers. Example: To arrange the following numbers into a stem and leaf plot, the tens place goes in the stem column and the ones place goes in the leaf column. 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 135668 0022456689 001112335778 0112358 http://www.ixl.com/math/grade-7/interpret-stem-and-leaf-plots COACH LESSON 24 26 Stem 2 3 4 5 Leaf 135668 0022456689 001112335778 Upper quartile- 47 0112358 Lower quartile- 32 MODE—The number that occurs the most often—The mode of these scores– is 41. RANGE—The difference between the least and greatest number—is 37. MEDIAN—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—is 32. THIRD QUARTILE OR UPPER QUARTILE—The middle number of the upper half of scores—is 47. COACH LESSON 27, 25 27 Box-and-Whisker Plot! Lower extreme First quartile or lower quartile Second quartile or median Third quartile or upper quartile Upper extreme Inter quartile Range 28 PRACTICE STEM & LEAF/ BOX & WHISKERS! 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 29 PRACTICE STEM & LEAF/ BOX & WHISKERS! 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 30 Order of Operations! 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. COACH LESSON 5 31 PRACTICE ORDER OF OPERATIONS! 1.) 3 + 2(4 x 3) 2.) 12 - 15 - 3 3.) (22 + 14) – 6 4.) 64 – 8 + 8 32 PRACTICE ORDER OF OPERATIONS! http://www.mathmaster.org/video/exponent-properties-involving-products/?id=1889 1.) 2³ 2.) 3⁴ 3.) 4² = 2x2x2 = 4.) 144 = 5.) 64 = = 3x3x3x3 = = 4x4 = http://www.ixl.com/math/grade-7/exponents-with-decimal-and-fractional-bases 33 FINDING THE MISSING SIDE OF A TRIANGLE! a 50° 65° b c Finding b: Since the sum of the degrees of a triangle is 180 degrees, we subtract the sum of 65 + 50 = 115 from 180 180 - 115 = 65 …so b = 65° Finding c: If b = 65 to find c we know that a straight line is 180 degrees so if we subtract 180 – 65 = 115° …so Angle c = 115° Finding a: To find a we do the same thing. 180 – 50 = 130 …so a = 130° http://www.ixl.com/math/grade-7/find-measures-of-complementary-supplementary-verticaland-adjacent-angles 34 PRACTICE FINDING THE MEASURE OF <A IN THE TRIANGLE ABC BELOW! A 30 C B m<A + 90 + 30 = 180 m<A = 35 A square has 4 angles which each measure 90 degrees. D A 45 45 C 45 45 B 36 Pythagorean Theorem To find the missing hypotenuse of a right triangle, we us the formula… c² C² C² C² Height = 6 in Base = 8 inches C = = = = A² + B² 6²in + 8²in 36 in² + 64 in² 100 sq in = in² = 10 in² http://www.mathmaster.org/video/pythagorean-theorem/?id=1922 37 AREA OF A TRIANGLE! A = base x height 2 Area = base x height 2 A = 10in x 8 in 2 A = 80 in² 2 Height= 8 in Base= 10 in A = 40 in² Definition of height is a line from the opposite vertex perpendicular to the base. COACH LESSON 12 http://www.ixl.com/math/grade-7/area-of-triangles-and-trapezoids 38 PRACTICE FINDING THE AREA OF A TRIANGLE! AREA = ½ (BASE X HEIGHT) A = ½ bh Height= 2 ft Area = ½ bh A = ½ (4ft)(2ft) A = ½ 8ft A =4 ft² Base= 4 ft 39 FINDING THE AREA OF A PARALLELOGRAM! h b 40 AREA OF A RECTANGLE & A SQUARE! Area of a RECTANGLE = Length x Width Area of a SQUARE = Side x Side Example: 2ft 4ft 2ft 2ft http://www.ixl.com/math/grade-7/area-of-rectangles-and-parallelograms 41 PRACTICE FINDING PERIMETER! PERIMETER IS THE OUTER DISTANCE AROUND A FIGURE. 9 FT 3FT P = a+ b + c + … P = 9FT + 9FT + 3FT + 3FT P = ____ FT 42 FINDING PERIMETER AND AREA OF COMPOUND FIGURES! To find the area of a compound figure, we simply have to find the area of both figures, then add them together. 6FT AREA = LENGTH X WIDTH A = 2FT X 6FT A = 12FT² 2FT 3FT 7FT AREA = LENGTH X WIDTH A = 3FT X 5FT A = 15 FT² TOTAL AREA = 12FT² + 15FT² = 27FT² 43 CONGRUENT ANGLES & CONGRUENT SIDES! Congruent angles and sides mean that they have the same measure. Use symbols to show this! http://www.ixl.com/math/grade-7/identify-complementary-supplementary-vertical-andadjacent-angles 44 Complementary angles : angles whose sum equals 90 degrees Supplementary angles: angles whose sum equals 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 equal sides Line of symmetry: when a line can cut a figure in two symmetrical sides COACH LESSON 17 45 Parallel lines: lines that never touch--- symbol Perpendicular lines: lines that intersect---symbol Skew lines: lines in different planes that never intersect Plane: a flat, 2-Dimensional surface, formed by many points A point (0-Dimension); A line (1-D); A plane (2-D); A solid (3-D) Vertical angles: angles that share a point and are equal Adjacent angles: are angles that are 180 degrees and share a side COACH LESSON 18 46 RECOGNIZING ADJACENT ANGLES! ADJACENT ANGLES: ANGLES THAT SHARE A COMMON SIDE. In the figure below: ANGLES 3 AND 4 ARE ADJACENT ANGLES. ANGLES 2 AND 3 ARE ALSO ADJACENT ANGLES. What are some other adjacent angles? 2 3 1 4 http://www.ixl.com/math/grade-7/identify-complementarysupplementary-vertical-and-adjacent-angles 47 REVIEW: CLASSIFY LINES! Intersecting lines: occupy the same plane AND meet at only one point Perpendicular lines: two lines intersect and form right angles (90°) The symbol is: Parallel lines: extend forever in both directions in the same plane and never intersect The symbol is: Skew lines: a pair of lines that are not parallel but never intersect AND occupy two different planes 48 REVIEW: CLASSIFY LINES! Supplementary angles: sum is 180 degrees Complementary angles: sum is 90 degrees Straight angle: equal to 180 degrees http://www.ixl.com/math/grade-7/identify-complementarysupplementary-vertical-and-adjacent-angles 49 PRACTICE GEOMETRY! What is the total number of lines of symmetry that can be drawn on the trapezoid below? Circle One: A .) 4 B .) 3 C .) 2 D .) 1 Which figure below correctly shows all the possible lines of symmetry for a square? Circle One: A.) Figure 1 B.) Figure 2 C.) Figure 3 D.) Figure 4 http://www.ixl.com/math/grade-7/symmetry 50 Finding Volume of a Quadrilateral! [Volume= units³ or cubed units] 4 ft 3 ft V = 5ft x 3ft x 4ft = 60ft³ http://www.ixl.com/math/grade-7/volume 5 ft 51 Identifying similar figures! Two figures are similar if they have exactly the same shape, but may or may not have the same size. The symbol is ≈ X For example: ∆ ABC ≈ ∆ XYZ A Which angle is similar to angle B? Angle: _______ B C Y Z 52 Chord: line that cuts the circle and does not go through the center of the circle Diameter: distance across the center of the circle (double radius) Radius: the distance half way across the circle ( ½ diameter) Segment: the area of a circle in which a chord creates Sector: a pie-shaped part of a circle made by two radii Circumference: distance around the outside of the circle Arc: a connected section of the circumference of a circle COACH LESSON 15 53 Central angles: angles in the center of the circle formed by two radii Inscribed angles: angles on the inside of the circle formed by two chords COACH LESSON 15 54 PRACTICE FINDING THE CIRCUMFERENCE OF A CIRCLE! A B C D 4 8 16 32 *USE ∏= 3.14 HINT: Circumference= 2∏r OR ∏· D 55 PRACTICE FINDING THE AREA OF A CIRCLE! If the diameter of a car tire is 50 cm, what is the area of that circle? A B C D 50.14 cm² 314 cm² 7,850 cm² 1,000 cm² *USE ∏= 3.14 HINT: Area = ∏ x r² 56 MORE PRACTICE! 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 B C D chord radius diameter central angle 57 Adding Negative Numbers! Rules: Negative + Negative = Negative -4 + -3 = -7 Positive + Positive = Positive 4+3=7 Negative + Positive = ? (Keep the sign of the larger integer & subtract) -4 + 3 = -1 http://www.ixl.com/math/grade-7/add-and-subtract-integers 58 Multiplying & Dividing Negative Numbers! Rules: Negative x Negative = Positive Negative ÷ Negative = Positive -4 x -2 = 8 -4 ÷ -2 = 2 Positive + Positive = Positive Positive ÷ Positive = Positive 4x2=8 Negative x Positive = Negative -4 x 2 = -8 4÷2=2 Negative ÷ Positive = Negative -4 ÷ 2 = -2 http://www.ixl.com/math/grade-7/integer-multiplication-and-division-rules 59 Comparing & Ordering Integers! NEGATIVE POSITIVE Negative integers further to the left of zero have less value. Positive integers further to the right of zero have greater value. Example: -3 IS GREATER THAN -6 COACH LESSON 3 60 Inequalities! Use the following symbols for inequality number sentences: < less than -4 < 2 ≤ less than or equal to 3≤4 > 6>3 greater than ≥ greater than or equal to -5 ≥ -6 http://www.ixl.com/math/grade-7/solve-one-step-linear-inequalities 61 Solving One-Step Equations! To solve for a variable in an equation, the variable must be alone on one side of the equals sign. Use a model or an inverse operation to solve a one step equation. Example: 3x = 24 Step 1: Divide by 3 on both sides of the equation 3x = 24 3 3 x = 8 COACH LESSON 21 http://www.ixl.com/math/grade-7/solve-two-step-linear-equations 62 Modeling Mathematical Situations! We can translate math sentences to numbers and symbols only Examples: Translate: “five more than” (5 + a quantity) Translate: “three times a number” (3 x n, or 3n) When you combine both: “five more than three times a number” 5 + 3n or 3n +5 COACH LESSON 22 63 Functions! Functions: inserting a value in for x to find y or f(x) Example: f(x) = 2x + 4 Then f(x) = 2 (2) + 4 f( x) = 4 + 4 f(x) = 8 So y=8 If x = 2 Also, a function is when we put a value in and get an answer out. http://www.ixl.com/math/grade-7/evaluate-a-function COACH LESSON 20 64 Scientific Notation! Scientific notation -- 4.057 x 10⁶ 4.057 x 10⁶ (This means to move the decimal six places to the right.) becomes 4,057,000 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 equals 1. 10 ⁰ = 1 Any number raised to the 1st power equals that number. 8¹ = 8 65 METRIC SYSTEM & CONVERSTION! DekaKilo- Meter Liter Gram Deci- Hecto- Centi- Milli- START where your at and move the decimal to where you want to go. Example 1: 4 kilometers = 4000 meters Example 2: 36 millimeters = 3.6 centimeters http://www.ixl.com/math/grade-7/evaluate-a-function COACH LESSON 11 66 PRACTICE UNIT CONVERSIONS! 67 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. 68 PRACTICE WEIGHT UNIT CONVERSIONS! The flower box in front of the main city library weighs 124 ounces. What does the flower box weigh in pounds? 69 PRACTICE MORE UNIT CONVERSIONS! 70 Unit Multipliers: 1. Always list the conversion. 2. Identify the correct multiplier. 3. Set up the multiplication problem with units being opposite (top & bottom) 4. Multiply & Simplify For example: Change 240 feet to yards a) First list the conversions: 3 feet OR 1 yard 1 yard 3 feet b) Since we want yards multiply by 1 yard 3 feet c) So 240 feet x 1 yard 1 3 feet d) Then 240 feet = 80 yards COACH LESSON 9 71 Ratios & Proportions: A ratio is a comparison between two numbers. Two ratios separated by an equals sign is called a proportion. To solve a proportion, we cross multiply and divide. Example: 4 = 2 5 = x 4x = 10 4 4 x = 10 4 x=2½ http://www.ixl.com/math/grade-7/understanding-ratios COACH LESSON 7 72 Rational & Irrational Numbers An Irrational Number is a real number that cannot be written as a simple fraction. A Rational Number can be written as a simple fraction. Irrational means not Rational. Example: 7 is rational, because it can be written as the ratio 7/1 Example 0.333... (3 repeating) is also rational, because it can be written as the ratio 1/3 73 Practice Irrational Numbers! Which of these is an irrational number? 74 Rational Numbers on a Number Line! Fraction Decimal Percent Place number over its place value and reduce Divide by 100 Multiply by 100 75 = 3 100 4 0.75 0.75 x 100 = 75% 125 = 1 1000 8 0.125 0.125 x 100 = 12.5% 150 = 3 = 1 ½ 100 2 1.50 1.50 x 100 = 150% COACH LESSON 4 75 Points on a Coordinate Grid! Quadrant II Quadrant I Quadrant III Quadrant IV Point of Origin [0, 0] Ordered pair: [3, 2] 3 is x value and 2 is y value COACH LESSON 16 76 Scaling! A scale 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. Example: An architect’s floor plan for a museum exhibit 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 Use cross 0.5 = 3.75 products to 2 p solve the proportion 0.5 x p = 2 x 3.75 0.5 p = 7.5 p = 15 COACH LESSON 14 http://www.mathmaster.org/video/scale-and-indirect-measurement/?id=1858 77 SOLVING 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) Notice the pattern: 7,14,21,28 2) Write the different operations that you can perform on 7 to get 14. a) 7 + 7 = 14 b) 7 x 2 = 14 3) Check these operations with the next term in the pattern. c) 14 + 7 = 21 d) 14 x 2 = 28 4) Find the next term in the pattern to determine how many bottles Erin will have on Friday. 5) 28 + 7 = 35 COACH LESSON 19 78 Estimation! Estimating involves finding compatible numbers that will make the numbers easier to operate. There are 52 weeks in a year. Leo’s salary is $51,950. Estimate how much money Leo makes in one week. $51,950 is about $52,000. Divide the compatible numbers. $52,000 divided 52 = $1,000 COACH LESSON 10 79 Histogram is a bar graph without the spaces between the bars. 4 3 2 1 0 a b c Bar graphs have spaces to show differences in data. 4 3 2 1 0 a b http://www.ixl.com/math/grade-7/interpret-histograms c COACH LESSON 26 80 Double and Triple Bar & 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 COACH LESSON 25 81 Making Predictions! We can use trends or patterns seen 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 COACH LESSON 31 82