Create Presentation
Download Presentation

Download

Download Presentation

Created by: Miss Jessie Minor Use: PSSA Review For 7th Grade Sources: Common Core Standards from PDE website .

91 Views
Download Presentation

Download Presentation
## Created by: Miss Jessie Minor Use: PSSA Review For 7th Grade Sources: Common Core Standards from PDE website .

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**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'sfinishing time, in hours, for the race? A 2B 5C 0.2D 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 • MILES = 7 HOURS • 60MILES/HR**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 9 2 6 3 3 2 2 2 3 3 x 3 x 2 x 2 = 36 2 2 3 3 3 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 X 5 = 1 8 2 Dividing fractions : change the sign to multiply and reciprocate the 2nd fraction 3 ÷ 5 4 8 = X 8 = 24 4 5 20 • http://www.ixl.com/math/grade-7/multiply-fractions http://www.ixl.com/math/grade-7/divide-mixed-numbers LESSON 2**X 5**6 X 7 49 13 X 4 9 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 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 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**6B 9C 12D 18 What is the least common multiple (LCM) of 8, 12, and 18 ?A 24B 36C 48D 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 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**Stem and leaf plots-Box 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 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**Stem**2 3 4 5 Leaf 1 3 5 6 68 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 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 Range: Mode: Median:**Box-and –whisker plot**First quartile or lower quartile Third quartile or upper quartile Upper extreme Second quartile or median Lower extreme 60 50 40 30 20 Inter quartile range**ABSOLUTE VALUE = the number itself without the sign.**The symbol for this is----- The absolute value of Is 5 -5 Is 5 The absolute value of 5 http://www.ixl.com/math/grade-7/integer-inequalities-with-absolute-values**ORDER OF OPERATIONS**Please, Excuse, My, Dear, Aunt, Sally 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**http://www.mathmaster.org/video/exponent-properties-involving-products/?id=1889 2³ = 2x2x2 144 3x3x3x3 3⁴ = 64 = 4x4 4² 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 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. a 50° 65° b c http://www.ixl.com/math/grade-7/find-measures-of-complementary-supplementary-vertical-and-adjacent-angles**Pythagorean Theorem**To find the missing hypotenuse of a right triangle, we use the formula c² = A² + B² c² = A² + B² C² = 6²in + 8²in C² = 36 sq in + 64 sq in Hypotenuse Height = 6 in C² = 100 sq in = sq in C = 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 Area = ½ bh A = ½ (4ft)(2ft) A = ½ 8ft A =4 ft² 2 ft height 4 ft base**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 2ft 4ft 2ft A = l x w A = 4 ft x 2ft A = 8ft² 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 AREA = LENGTH X WIDTH A = 3FT X 6FT A = 18FT² AREA = LENGTH X WIDTH A = 4FT X 4FT A = 16 FT² 3FT 7FT 2FT**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-vertical-and-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-and-adjacent-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**y Quadrant ll Quadrant I 6 5 4 3 2 1 Point of Origin [0, 0] axis 1 2 3 4 5 6 x -6 -5 -4 -3 -2 -1 0 -1 -2 -3 -4 -5 -6 Quadrant lll Quadrant lV Ordered pair: 2 is x value and 6 is y value [2, 6] LESSON 16**What is the total number of lines of symmetry that can be**drawnon the trapezoid below? A 4B 3C 2D 1 Which figure below correctly shows all the possible lines of symmetry for a square? A Figure 1B Figure 2C Figure 3D 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 2 Area = ∏ x r Circumference= 2∏r Circumference = distance around the outside of the circle 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-vertical-and-adjacent-angles