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Created by: Miss Jessie Minor Purpose: PSSA Review for 7th Grade (Can be used as enrichment or remediation for most

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

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Created by: Miss Jessie Minor Purpose: PSSA Review for 7th Grade (Can be used as enrichment or remediation for most

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  1. 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

  2. EXPERIMENTAL PROBABILITY! Number of times the event occurred Number of total trials IN ORDER TO CALCULATE EXPERIMENTAL PROBABILITY OF AN EVENT USE THE FOLLOWING DEFINITION: P(Event)= COACH LESSON 30

  3. 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

  4. PRACTICE EXPERIMENTAL PROBABILITY!

  5. 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

  6. 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

  7. 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?

  8. 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

  9. 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

  10. PRACTICE USING THE DISTANCE FORMULA! Michael enters a 120-mile bicycle race. He bikes 24 miles an hour. What is Michael'sfinishing time, in hours, for the race? A    2B    5C    0.2D     0.5

  11. 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

  12. 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 + 8 12 9 12 9 2 6 3 3 12: 2 2 3 3 x 3 x 2 x 2 = 36 2 3 9: 3 3 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

  13. PRACTICE FRACTIONS!

  14. MULTIPLYING & DIVIDING FRACTIONS! Multiplying fractions : cross cancel and multiply straight across ¹ 4 X ¹ 5 = 1 ¹ 5 ² 8 2 Dividing fractions : change the sign to multiply, then reciprocate the 2nd fraction 3 ÷ 5 4 8 = 3 X 8 = 24REDUCE!!! 4 5 20 http://www.ixl.com/math/grade-7/multiply-fractions http://www.ixl.com/math/grade-7/divide-mixed-numbers COACH LESSON 2

  15. PRACTICE MULTIPLYING FRACTIONS! 1 X 7 3 X 5 6 5 X 4 9 5 49 13

  16. Multiplying & Dividing Mixed Numbers! When multiplying or dividing mixed numbers, always change them to improper fractions. Example 1: 1 ¾ x 1 ½ = 7 x 3 = 21 4 2 8 Example 2: 12 x 2 ½ = 12 x 5 = 60 = 30 1 2 2 http://www.ixl.com/math/grade-7/divide-mixed-numbers

  17. Dividing Mixed Numbers! When dividing any form of a fraction, change the division to multiplication, then reciprocate the 2nd fraction. Example: 1 ¾ ÷ 1 ½ = 7 ÷ 3 4 2 7 x 2 = 14 = 11/6 4 312 http://www.ixl.com/math/grade-7/divide-fractions

  18. 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 16 2 2 6 2 2 8 2 2 2 3 2 2 2 4 2 2 2 2 2 24: 32: 22 22 22 32 2 2x2x2x3x2x2 = 96

  19. 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: 32: Example: 2x2x2 = 8, so 8 is the GCF of 24 and 32. 22 22 22 32 2

  20. PRACTICE LCM AND GCF!

  21. PRACTICE LCM AND GCF! What is the greatest common factor (GCF) of 108 and 420 ?A     6B     9C     12D     18 What is the least common multiple (LCM) of 8, 12, and 18 ?A      24B      36C      48D      72

  22. 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

  23. PRACTICE ABSOLUTE VALUE!

  24. DISTRIBUTIVE PROPERTY A(B + C) = AB + AC (We distributed A to B and then A to C) • Solving 2 step equations: 4(x + 2) = 24 • 4x + 8 = 24 • subtract 8 4x = 16 • divide by 4 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

  25. Associative & Commutative Property! Associative Commutative A X B = B X A FOR MULTIPLICATION A + B = B + A FOR ADDITION • 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/video/associative-property-for-multiplication/?id=932 http://www.mathmaster.org/video/commutative-property-for-addition/?id=931

  26. 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 1 3 5 6 6 8 0 0 2 2 4 5 6 6 8 9 0 0 1 1 1 2 3 3 5 7 7 8 0 1 1 2 3 5 8 http://www.ixl.com/math/grade-7/interpret-stem-and-leaf-plots COACH LESSON 24

  27. Stem 2 3 4 5 Leaf 1 3 5 6 6 8 0 0 2 2 4 5 6 6 8 9 0 0 1 1 1 2 3 3 5 7 7 8 0 1 1 2 3 5 8 Upper quartile- 47 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

  28. Box-and-Whisker Plot! First quartile or lower quartile Upper extreme Second quartile or median Third quartile or upper quartile Lower extreme Inter quartile Range

  29. 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

  30. 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 Range: Mode: Median:

  31. Order of Operations! 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

  32. PRACTICE ORDER OF OPERATIONS! 1.) 3 + 2(4 x 3) 2.) 12 - 15 - 3 3.) (22 + 14) – 6 4.) 64 – 8 + 8

  33. PRACTICE ORDER OF OPERATIONS! http://www.mathmaster.org/video/exponent-properties-involving-products/?id=1889 1.) 2³ = 2x2x2 = 4.) 144 = 3x3x3x3 = 2.) 3⁴ = 5.) 64 = = 4x4 = 3.) 4² http://www.ixl.com/math/grade-7/exponents-with-decimal-and-fractional-bases

  34. FINDING THE MISSING SIDE OF A TRIANGLE! 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° a 50° 65° b c http://www.ixl.com/math/grade-7/find-measures-of-complementary-supplementary-vertical-and-adjacent-angles

  35. PRACTICE FINDING THE MEASURE OF <A IN THE TRIANGLE ABC BELOW! A 30 B C m<A + 90 + 30 = 180 m<A =

  36. A square has 4 angles which each measure 90 degrees. D A 45 45 45 45 C B

  37. Pythagorean Theorem To find the missing hypotenuse of a right triangle, we us the formula… A² + B² = C² c² = A² + B² C² = 6²in + 8²in C² = 36 in² + 64 in² Hypotenuse Height = 6 in C² = 100 sq in = in² C = 10 in² Base = 8 inches http://www.mathmaster.org/video/pythagorean-theorem/?id=1922

  38. AREA OF A TRIANGLE! A = base x height 2 Area = base x height 2 A = 10in x 8 in 2 A = 80 in² 2 A = 40 in² Height= 8 in Base= 10 in 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

  39. PRACTICE FINDING THE AREA OF A TRIANGLE! AREA = ½ (BASE X HEIGHT) A = ½ bh Area = ½ bh A = ½ (4ft)(2ft) A = ½ 8ft A =4 ft² Height= 2 ft Base= 4 ft

  40. FINDING THE AREA OF A PARALLELOGRAM! h b Area = b x h

  41. AREA OF A RECTANGLE & A SQUARE! Area of a RECTANGLE = Length x Width Area of a SQUARE = Side x Side Example: 2ft 2ft 4ft 2ft A = l x w A = s x s A = 4ft x 2ft A = 8ft² A = 2ft x 2ft A = 4ft² http://www.ixl.com/math/grade-7/area-of-rectangles-and-parallelograms

  42. 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

  43. 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 AREA = LENGTH X WIDTH A = 3FT X 5FT A = 15 FT² 2FT 7FT 3FT TOTAL AREA = 12FT² + 15FT² = 27FT²

  44. 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-and-adjacent-angles

  45. 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

  46. 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

  47. 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-complementary-supplementary-vertical-and-adjacent-angles

  48. 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

  49. 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-complementary-supplementary-vertical-and-adjacent-angles

  50. PRACTICE GEOMETRY! What is the total number of lines of symmetry that can be drawnon 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

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