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Final Exam Review: Part II (Chapters 9+) 5th Grade Regular Math First topic! Chapters 9 and 10 Data Analysis: Graphs, line plots, double bar graphs Mean, median, mode, and range Know the difference between numerical data and categorical data. 1.) What type of data is represented here? 2.) Find the Range, Mean, Mode and Median for the set of data shown on the line plot below. _X 64 X 68 X X X 70 X X X X 75 X X 80 X X 85 X X X 88 5th Grade Math Test Scores X X 90 X_ 93 1.) Numerical Data 2.) Range: Mean: Mode: Median: 29 79.42 75 80 1. Create a Stem and Leaf Graph for the following set of data. 2. Find the Range, Mean, Mode and Median. 21 21 18 22 19 33 18 30 16 18 20 STEM 1 2 3 Range: Mean: Mode: Median: 17 21.45 18 20 LEAF 6 8 8 8 9 0 1 1 2 0 3 1.) What is the total number of students who chose Soccer as their favorite sport? 2.) Did more boys or more girls participate in this survey? 3.) What is the total number of students included in this survey? 4.) What is the girls’ favorite sport? The boys’ favorite sport? 5.) How many more students preferred soccer over basketball? 1.) What is the total number of students who chose Soccer as their favorite sport? 2.) Did more boys or more girls participate in this survey? 3.) What is the total number of students included in this survey? 4.) Girls’ favorite sport? Soccer Boys’ favorite sport? 5.) How many more students preferred soccer over basketball? 9 Boys 22 Basketball 3 Types of Graphs Bar Graph Line Graph Circle Graph Line Plot Stem and Leaf Plot Double Bar Graph Double Line Graph Histogram Pictograph Next chapter…. Chapter 11 Whole Numbers: Divisibility rules, prime factorization (factor trees, prime numbers, and exponent form) Tell whether the following numbers are divisible by 2, 3, 4, 5, 6, 8, 9, 10, and 12 312 3,360 Tell whether the following numbers are divisible by 2, 3, 4, 5, 6, 8, 9, 10, and 12 312 2, 3, 4, 6, 8, 12 3,360 2, 3, 4, 5, 6, 8, 10 and 12 Tell whether the following numbers are Prime (P), Composite (C), or Neither (N). 82 109 51 136 117 313 225 Tell whether the following numbers are Prime (P), Composite (C), or Neither (N). 82 109 51 136 117 313 225 C P C C C P C Write the Prime Factorization of the number as a product of prime factors AND in exponent form. (Hint: Use Factor Trees to help you.) 108 225 Write the Prime Factorization of the number as a product of prime factors AND in exponent form. (Hint: Use Factor Trees to help you.) 108 2 x 2 x 3 x 3 x 3 2² x 3³ 225 3 x 3 x 5 x 5 3² x 5² Find the Greatest Common Factor (GCF) of the following set of numbers: 12 30 42 Find the Greatest Common Factor (GCF) of the following set of numbers: 12 30 42 6 Find the Least Common Multiple (LCM) of the following set of numbers: 12 15 20 Find the Least Common Multiple (LCM) of the following set of numbers: 12 15 20 60 Write the exponent form for the following: 2 x 2 x 3 x 3 x 3 Write the exponent form for the following: 2 x 2 x 3 x 3 x 3 2² x 3³ Write the exponent form for the following: 10,000 Write the exponent form for the following: 10,000 4 10 Write the standard numeral for the following: 3³ Write the standard numeral for the following: 3³ 27 (3 x 3 x 3) Write the standard numeral for the following: 2³ x 3² Write the standard numeral for the following: 72 2³ x 3² 2x2x2 8 x 9 3x3 Compare. Write > , < , or = 6² 4³ Compare. Write > , < , or = 6² 6 x 6 = 36 < 4³ 4 x 4 x 4 = 64 Next topic…. Chapters 12 - 15: Fractions Comparing fractions Problem Solve: Several fifth-graders have decided to join the HP track team. During yesterday’s practice, Ben ran 3/4 of a mile, Sam ran 5/8 of a mile, and Ryan ran 5/6 of a mile and Jack ran 1 ¼ miles. Order the students according to how far they ran, from shortest to longest distance (least to greatest). Who ran the farthest? Comparing fractions Answer (from least to greatest): Sam, 5/8 of a mile Ben, 3/4 of a mile Ryan, 5/6 of a mile Jack, 1 ¼ miles. Who ran the farthest? Jack Comparing fractions Problem Solve: Last weekend, Tom, Sam, Trish and Maria rode their bicycles around the park. Tom rode 5/12 miles, Sam rode 2 2 ¾ miles, Trish rode 5/6 miles and Maria rode 2 1/3 miles. Order the students according to how far they rode, from shortest to longest distance (least to greatest). Who rode the farthest? 2 Comparing fractions Problem Solve: Maria rode Tom rode Sam rode Trish rode 2 2 2 2 1/3 miles 5/12 miles ¾ miles 5/6 miles Who rode the farthest? Trish Addition and Subtraction of Fractions & Mixed Numbers Plot each fraction on the number line. ½ 1¼ ⅞ 1⅝ ___________________________ 0 1 2 Plot each fraction on the number line. ½ 1¼ ⅞ 1⅝ ½ ⅞ 1¼ 1⅝ ___________________________ 0 1 2 Estimate the sum or difference. 2 5 + 6 7 Estimate the sum or difference. 2 5 + 6 7 ½ + 1 = 1½ Estimate the sum or difference. 8⅝ - 3½ Estimate the sum or difference. 8⅝ - 3½ 8½ - 3½ = 5 Find the actual sum or difference. 3 7 + 9 14 Find the actual sum or difference. 3 7 + 1 9 14 1/14 Find the actual sum or difference. 8 ¼ - 2 ⅞ Find the actual sum or difference. 8 ¼ - 2 ⅞ 5⅜ Find the actual sum or difference. ¼ + 2 ⅞ + 1 ½= Find the actual sum or difference. ¼ + 2 ⅞ + 1 ½= 4⅝ For word problem practice, review textbook pages 355, 378 and 379. Multiplication & Division of Fractions Find the product or quotient. ¾ x ⅝ Find the product or quotient. ¾ x 15 32 ⅝ Find the product or quotient. 5 x ¼ Find the product or quotient. 5 x ¼ 5 = 1¼ 4 Find the product or quotient. 2¾ x 3½ Find the product or quotient. 2¾ x 9⅝ 3½ Find the product or quotient. 7 8 ÷ 1 4 Find the product or quotient. 7 8 ÷ 1 4 7 = 3½ 2 Find the product or quotient. 6 ÷ ¾ Find the product or quotient. 6 ÷ 8 ¾ Find the product or quotient. 7½ ÷ 1¼ Find the product or quotient. 7½ ÷ 6 1¼ Vera bought 5¼ pounds of wood chips for her guinea pig’s cage. She will use 2/3 of the wood chips. How many pounds of wood chips will Vera use? Vera bought 5¼ pounds of wood chips for her guinea pig’s cage. She will use 2/3 of the wood chips. How many pounds of wood chips will Vera use? 5¼ x 2/3 = 3½ Next topic… Chapter 16: Fractions, Decimals, Percents Ratios, rates, unit rates, maps & scales, solving proportions Complete the chart. Write all fractions in simplest form. Fractions Decimals Percents .22 7% ⅛ Complete the chart. Write all fractions in simplest form. Fractions 22 = 11 100 50 7 100 Decimals Percents .22 22% .07 7% ⅛ .125 12.5% Write the decimal, fraction (in simplest form) and percent that represent the shaded part. Write the decimal, fraction (in simplest form) and percent that represent the shaded part. .55 55 = 11 100 20 55% Use the picture to write the ratios. Tell whether the ratio compares part to part, part to whole, or whole to part. All shapes to triangles. Rectangles to ovals. Ovals to all shapes. Use the picture to write the ratios. Tell whether the ratio compares part to part, part to whole, or whole to part. All shapes to triangles. 18 : 9 whole to part Rectangles to ovals. 3:6 part to part Ovals to all shapes. 6 : 18 part to whole Which of the following shows two equivalent ratios? a. 7 : 9 and 14 : 16 b. 7 : 9 and 14 : 18 Which of the following shows two equivalent ratios? b. 7 : 9 and 14 : 18 7 = 14 9 18 Write two equivalent ratios for each of the following. a. 12 : 15 b. 1 3 Write two equivalent ratios for each of the following. a. 12 : 15 b. 24 : 30 4:5 1 2 3 3 6 9 *Note: There is more than 1 right answer. Tell whether the ratios form a proportion. Write yes or no. 4 10 and 26 24 65 6 and 27 9 Tell whether the ratios form a proportion. Write yes or no. 4 and 10 Yes 26 24 65 6 and 27 9 No Solve the following proportions using Cross Products. Show your work!! 8 36 = x 9 54 x = 12 20 Solve the following proportions using Cross Products. Show your work!! 8 = 36 x 9 54 x = 12 20 36x = 8(54) 12x = 9(20) 36x = 432 12x = 180 36 36 x = 12 12 12 x = 15 Find the % of the number. 75% of 120 Find the % of the number. 75% of 120 .75 x 120 = 90 Find the % of the number. 30% of 50 Find the % of the number. 30% of 50 .30 x 50 = 15 Find the % of the number. 6% of 300 Find the % of the number. 6% of 300 .06 x 300 = 18 What is the unit rate ? Show your work!! a. Earn $56 for an 8 hour day b. Score 120 points in 15 games What is the unit rate ? Show your work!! a. $$ hours b. points games $56 = x 8 1 x = $7 per hour 120 = x 15 1 x = 8 points per game If the map scale is 1 in. = 15 miles, what is the map distance if the actual distance is 60 miles? If the map scale is 1 in. = 15 miles, what is the map distance if the actual distance is 60 miles? Inch Miles 1 = x 15 60 15x = 1(60) 15x = 60 15 15 x = 4 inches It takes Kenny 25 minutes to inflate the tires of 50 bicycles. How long will it take him to inflate the tires of 120 bicycles? It takes Kenny 25 minutes to inflate the tires of 50 bicycles. How long will it take him to inflate the tires of 120 bicycles? minutes bicycles 25 = x 50 120 50x = 25 (120) 50x = 3,000 50 50 x = 60 minutes How many pizzas do you need for a party of 135 people if at the last party, 90 people ate 52 pizzas? How many pizzas do you need for a party of 135 people if at the last party, 90 people ate 52 pizzas? pizzas people 52 = x 90 135 90x = 52 (135) 90x = 7,020 90 90 x = 78 pizzas Next chapter…. Chapter 22: Measurement Customary measurement of length, mass and volume Metric measurement of length, mass and volume Customary Measurements A system of measurement used in the United States used to describe how long, how heavy, or how big something is Examples: inches, feet, yards, miles Customary Measurement of length 12 inches = 1 foot 3 feet = 1 yard 36 inches = 1 yard 5,280 feet = 1 mile Customary Measurements of weight/mass 16 ounces (0z) = 1 pound (lb) 2000 pounds (lbs) = 1 ton (T) Customary Measurement of Capacity/ Volume Capacity/volume: how much a container can hold 8 fl oz = 1 cup 2 cups = 1 pint 2 pints = 1 quart 2 quarts = 1/2 gallon 4 quarts = 1 gallon Metric Measurements A system of measurement used in most other countries to measure how long, how heavy, or how big something is Metric Measurements of Length 10 millimeters (mm) = 1 centimeter (cm) 100 centimeters = 1 meter (m) 1,000 meters = 1 kilometer (km) Metric Measurements of Weight/Mass 1,000 milligrams (mg) = 1 gram (g) 1,000 grams = 1 kilogram (kg) Metric Measurements of Capacity/ Volume The milliliter (mL) is a metric unit used to measure the capacities of small containers. Example= a dropper The liter (L) is equal to 1,000 mL, so it is used to measure the capacities of larger containers. Example= a bottle of soda Remember… King Henry’s Daffy Uncle Drinks Choc Milk *This can help you with conversions……… Next chapter… Chapter 23: Geometry Quadrilaterals, Plotting coordinates on a grid Perimeter and Area Volume of rectangular prisms Quadrilaterals Quadrilaterals are any four-sided shapes. They must have straight lines and be two-dimensional. Examples: squares, rectangles, rhombuses, parallelograms, trapezoids, kites More about quadrilaterals The Square The square has four equal sides. All angles of a square equal 90 degrees. The Rectangle The Rectangle has four right angles and two sets of parallel lines. Not all sides are equal to each other. The Rhombus A rhombus is a four-sided shape where all sides have equal length. Also opposite sides are parallel and opposite angles are equal. A rhombus is sometimes called a diamond. The Parallelogram A parallelogram has opposite sides parallel and equal in length. Also opposite angles are equal. Plotting Coordinates Plotting Coordinates (continued) (x,y) Find the point on the x-axis first (horizontal / left to right) Then find the point on the y-axis and graph (vertical / up and down) Finding the Perimeter To find the perimeter of most two-dimensional shapes, just add up the sides Area Area is the measurement of a shape’s surface. Remember that units are squared for area!! Finding the Area of a Square To find the area of a square, multiply the length times the width A= (l)(w) A=2x2 A = 4 cm² Finding the area of rectangles To find the area of a rectangle, just multiply the length and the width. A= (l)(w) Volume Volume is the amount of space that a substance or object occupies, or that is enclosed within a container Remember that the units of volume are cubed (example: inches^3) because it measures the capacity of a 3-dimensional figure! Finding the Volume of Rectangular Prisms To find the volume of a rectangular prism, multiply the length by the width and by the height of the figure V = (l)(w)(h) V=6x3x4 V = 72 cm³ Practice, Practice, Practice!