Researching Roblox +5 QUESTIONS. 1. How has the number of games on Roblox changed over the past 5 years?

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1 Researching Roblo +5 QUESTIONS In The Rise of Roblo on page 4, you determined whether questions about the gaming website Roblo were statistical or non-statistical. Use what you learned to answer five more questions about Roblo. 1. How has the number of games on Roblo changed over the past 5 years? Statistical Non-statistical 5A. Pick one of the statistical questions, and rewrite so it is non-statistical. Eplain why it s not a statistical question. 2. How many fairy wing accessories has Beeism made for Roblo avatars to wear? Statistical Non-statistical 3. During which part of the day are the most people active on Roblo: morning, afternoon, or evening? Statistical Non-statistical 4. Which of Ale Biello s games has been played the most times? Statistical Non-statistical 5B. Pick one of the non-statistical questions, and rewrite so it is statistical. Eplain why it s statistical. SEPTEMBER 3, 2018 > p. 4 The Rise of Roblo > STATISTICAL QUESTIONS

2 Measure of Center vs. Measure of Variation When you collect statistical data, you are able to describe the data by providing a measure of center. You can also describe the data by giving a measure of variation. MEASURES OF CENTER: Describe a typical or average value from a set of data MEASURES OF VARIATION: Describe how similar or dissimilar the data are from each other Mode: An ecologist finds that the most frequent height of the sunflowers in a field is 10.5 feet. Median: The middle value for the daily high temperature in the month of September was 68. Mean: A teacher hopes that his students score an average of 85 percent on their net test. Range: The range of ages of students entering a class at a local community college is 17 to 42. Interquartile Range: The heights of the players on a basketball team varies 6.5 inches from the median. Mean Absolute Deviation: A scientist finds that the lengths of sloths vary 5.5 inches from the average. YOUR TURN Determine whether the situations below describe a measure of center or a measure of variation. Then describe which type it is. 1. The most frequent score on an Earth science quiz is 86%. 2. In the U.S., families have 2.4 children on average. 3. A school wants to avoid classes having more than 1.5 years between the oldest student and the youngest student. 4. The average number of pieces of candy a child receives on Halloween is The shortest time a student takes to finish a quiz is 23 minutes while the longest is 52 minutes. 6. A clothing store wants to pay all of its cashiers about the same hourly rate % of the girls on a basketball team are taller than 65 inches. 8. The class was ordered from shortest to tallest for picture day. The student in the middle was 5 feet 2 inches tall. SEPTEMBER 3, 2018 > p. 4 The Rise of Roblo > STATISTICS

3 EXIT SLIP A SEPTEMBER 3, 2018 > p. 4 The Rise of Roblo > STATISTICAL QUESTIONS Games on Roblo fall into different categories: obstacle courses, simulation games, combat games, survival games, and competitions. Use this information to determine whether the following questions are statistical or non-statistical. 1. How many active players do simulation, combat, and survival games on Roblo each have during the evening? Statistical Non-statistical 2. How many game categories are there on Roblo? Statistical Non-statistical EXIT SLIP B SEPTEMBER 3, 2018 > p. 4 The Rise of Roblo > STATISTICAL QUESTIONS Games on Roblo fall into different categories: obstacle courses, simulation games, combat games, survival games, and competitions. Use this information to write statistical or non-statistical questions. 1. Write a statistical question about the types of games on Roblo. Eplain why it s statistical. 2. Write a non-statistical question about the types of games on Roblo. Eplain why it s not a statistical question. PERMISSION GRANTED BY SCHOLASTIC MATH TO REPRODUCE THIS PAGE FOR CLASSROOM USE ONLY BY SCHOLASTIC INC.

4 Appetizing Angles In Delicious Designs on page 6, you used lines on a cake to determine angle relationships and to find the measurements of different angles. Use what you learned to answer five more questions about angles made by intersecting lines on a frosted doughnut. C B D A +5 QUESTIONS E F G 1A. Which pairs of angles are vertical? 1B. Which pairs of angles are adjacent? 4. Angles E and G are supplementary. What is the measure of Angle G? 1C. Which pairs of angles are congruent? 2. Angle E is complementary to 56. What is the measure of Angle E? 3. What are two ways of describing the relationship between Angles C and B? SEPTEMBER 3, 2018 > p. 6 Delicious Designs > ANGLES 5. Angle C measures 34. What is the measure of an angle complementary to Angle C?

5 Transversals to Parallel Lines A transversal is a line that intersects two or more other lines. When the transversal intersects parallel lines, it creates pairs of congruent angles (angles that have the same measure). VOCABULARY CORRESPONDING ANGLES: Angles that are in the same position on two parallel lines in relation to the transversal transversal YOUR TURN Determine whether each of the following statements is true or false based on the information given below. If false, eplain why or give an eample that disproves the statement. D parallel lines C D B C D B A A E F ALTERNATE INTERIOR ANGLES: Angles that lie between the two parallel lines on opposite sides of the transversal transversal parallel lines ALTERNATE EXTERIOR ANGLES: Angles that lie outside the two parallel lines on opposite sides of the transversal transversal parallel lines E G F H F H E G 1. Lines D and F are parallel. TRUE FALSE 2. Angles 1 and 3 are corresponding angles. TRUE FALSE 3. Line F is a transversal. TRUE FALSE 4. The value of angle 7 is 53. TRUE FALSE 5. Angles 1 and 5 are corresponding angles. TRUE FALSE 6. Angles 4 and 8 are alternate interior angles. TRUE FALSE 7. Angle 6 is congruent to angle 4. TRUE FALSE 8. Angles 7 and 1 are alternate eterior angles. TRUE FALSE SEPTEMBER 3, 2018 > p. 6 Delicious Designs > ANGLE RELATIONSHIPS

6 EXIT SLIP A SEPTEMBER 3, 2018 > p. 6 Delicious Designs > ANGLES 1. If two angles are vertical, then they must be. A complimentary B congruent C supplementary 2. Angles are adjacent when they. A share a verte and a side B form a right angle C sum to 180 degrees Draw at least 3 intersecting lines in the space to the right. 1A. Label 2 adjacent angles Q and R. 1B. Label 2 vertical angles S and T. 2. Draw another line to create 2 complementary angles. Label these angles U and V. SEPTEMBER 3, 2018 > p. 6 Delicious Designs > ANGLES EXIT SLIP B

7 Racing Rates +5 QUESTIONS In Searching for Sloths on page 8, you found unit rates to compare the speeds of sloths and other creatures in the rainforest. Use what you learned to answer five more questions about the rates of speed of other animals. 1A. At top speed, it would take a tiger shark 3 hours to swim 93 miles. What is its speed in miles per hour? 3. The western pygmy possum skitters 2,640 feet in 10 minutes. What is its speed in miles per hour? 1B. A shortfin mako shark can swim miles in 5 hours at its top speed. Which shark swims at a faster unit rate, the tiger shark or the shortfin mako shark, and by how much? 2. An African elephant can travel up to 118,800 feet in 1 hour. What s its top speed in miles per hour? (Hint: There are 5,280 feet in a mile.) 4. Hummingbirds may be small, but they re speedy! At their top speed, they can zip along at 1,518 feet in 30 seconds. What is their speed in miles per hour? 5. A lion s top speed is 39.7 miles per hour. How many feet could it cover in 1 minute? SEPTEMBER 3, 2018 > p. 8 Searching for Sloths > UNIT RATE

8 Graphing Relationships You can use points on a graph to eplain a proportional relationship. For each unit moved along the -ais, you move a number of units along the y-ais. A unit rate can be described by the points (0, 0) and (1, r), where r represents the unit rate. EXAMPLE: An Amazon river dolphin s swimming speed in miles per hour can be described by the graph below. What is the dolphin s unit rate of speed? Step 1: Identify and label the points as ordered pairs on the graph. y 50 AMAZON RIVER DOLPHIN S SPEED (4,48) Step 2: List the ordered pairs in a table of values. (hours) y (miles) miles (1,12) (2,24) (3,36) (0,0) hours YOUR TURN Use the graphs to complete each table and find the unit rate. y COST OF ORANGES cost (dollars) weight (pounds) Step 3: Determine the relationship between the - and y-values. You increase by 1 unit along the -ais and increase by 12 units along the y-ais (hours) y (miles) Step 4: Determine the unit rate. The graph and table show us that the relationship between the - and y-values are proportional. For the point (1, r), r = 12. So the unit rate of the dolphin s speed is 12 miles per hour. y UNIT RATE: Continue on the net page SEPTEMBER 3, 2018 > p. 8 Searching for Sloths > UNIT RATE

9 y JESS S JOB WAGE 2. UNIT RATE: y pay (dollars) time (hours) MONDAY S RAINFALL ACCUMULATION y amount (inches) time (hours) BILLY S SAVINGS ACCOUNT OVER 6 MONTHS y 3. UNIT RATE: y 4. UNIT RATE: amount (dollars) 1, y month SEPTEMBER 3, 2018 > p. 8 Searching for Sloths > UNIT RATE

10 EXIT SLIP A SEPTEMBER 3, 2018 > p. 8 Searching for Sloths > UNIT RATE 1A. It would take a tiger 5 hours to travel 171 miles at its top speed. What s that speed in miles per hour? 1B. At top speed, a desert warthog can travel 900,240 feet in 5 hours. What s its speed in miles per hour? (Hint: 1 mile = 5,280 feet) 1C. Which animal s unit rate is faster and by how much? SEPTEMBER 3, 2018 > p. 8 Searching for Sloths > UNIT RATE 1A. Swimming at its top speed, a blue whale would take 1 hour to travel 121,440 feet. What s that speed in miles per hour? (Hint: There are 5,280 feet in a mile.) 1B. A yellowfin tuna can zip through 61,248 feet of water in just 15 minutes. What s its top speed in miles per hour? 1C. Describe the relationship between the top speed of the blue whale and that of the yellowfin tuna. EXIT SLIP B

11 High-flying Formulas +5 QUESTIONS In Learning the Ropes on page 14, you used a formula to solve for different values related to slacklining. Use what you learned and the diagram below to answer five more questions about this eciting activity. F = B L 4 S (feet) (pounds) (feet) 1. A slackliner weighs 240 pounds. He sets up a 40-foot line with 1.5 feet of sag. What is the tension force of his slackline in pounds-force? 4. A slackliner weighs 80 pounds and her line has 6 inches of sag. If her line has 800 pounds-force of tension, how long is her line? 2. A 30-foot line is set up for a slackliner who weighs 110 pounds. If the line has 0.6 feet of sag, what s its tension force? 3. Last year, three French slackliners set the world record for the longest highline. The highline towered 1,115 feet in the air and measured 5,453 feet in length! How much would this record-setting line sag if the tension force is 900 pounds-force and the person on the line is 175 pounds, rounded to the nearest tenth? 5A. A new slackliner weighs 115 pounds. He sets up his slackline with 0.5 feet of sag and a length of 16 feet. What is the tension force of his slackline? 5B. Beginners typically start with a slackline that has between 700 and 900 pounds-force of tension. Does the new slackliner s tension force fall within this range? If not, how could he adjust his line to be in this range? SEPTEMBER 3, 2018 > p. 14 Learning the Ropes > FORMULAS

12 Writing Equations An equation can be used to relate two quantities. To write an equation, you must identify an independent variable (an unknown whose value changes on its own and causes changes in other variables) and a dependent variable (an unknown whose value changes in response to changes in the independent variable). EXAMPLE: A teacher was born on January 1, What is her age during any given year? Step 1: Identify the variables. INDEPENDENT VARIABLE: Current year The current year is stable and changes regularly. It is not influenced by any other factors. DEPENDENT VARIABLE: Teacher s age The teacher s age changes based on what the current year is. Step 2: Identify meaningful variables to represent the unknowns. Current year = y Teacher s age = a Step 3: Identify the relationship between the current year and the teacher s age. In 1984, the teacher was 1. In 1985, the teacher was 2. In 1986, the teacher was 3. The teacher s age is always 1,983 less than the year. Step 4: Write an equation to show the relationship between the two variables. Usually, the dependent variable is isolated on the left of the equation. So a = y 1,983 YOUR TURN Identify the independent variable and the dependent variable for each situation below. Then write an equation to represent the problem. 1. On a class field trip, there needs to be 1 chaperone for every 5 students. How many chaperones must there be for any number of students? Independent variable: Dependent variable: Equation: 2. A baseball inning lasts about 19 minutes. About how long will a baseball game be for any number of innings? Independent variable: Dependent variable: Equation: 3. A pan of brownies gets split among a group of friends. What fraction of the pan of brownies will each friend get for any number of friends that share the brownies equally? Independent variable: Dependent variable: Equation: 4. A family orders a number of pizzas to be delivered. Each pizza costs $ There is a flat delivery charge of $8.00. How much will the family pay for their dinner for any number of pizzas? Independent variable: Dependent variable: Equation: 5. A company sells bracelets. Each bracelet costs $18. The company pays a flat operational fee of $150. Also, the materials and labor for each bracelet cost $4.50. What is the company s profit for any number of bracelets sold? Independent variable: Dependent variable: Equation: SEPTEMBER 3, 2018 > p. 14 Learning the Ropes > WORKING WITH VARIABLES

13 EXIT SLIP A SEPTEMBER 3, 2018 > p. 14 Learning the Ropes > FORMULAS A slackline has a length of 20 feet and 0.9 feet of sag. The slackliner weighs 198 pounds. F = B L 4 S 1A. What is the value of each of the variables B, S, and L? (feet) (pounds) 1B. Replace the variables in the equation to find the slackline s tension force. (feet) 1. A beginner is practicing on a 15-foot slackline and weighs 90 pounds. Her line has a tension of 780 pounds-force. How much sag does her line have, rounded to the nearest hundredth? 2. A beginner s slackline should have at least 700 pounds-force and at most 900 pounds-force of tension. What is the range in possible slackline lengths for a beginner who weighs 80 pounds and keeps the sag of the slackline to 0.75 feet? SEPTEMBER 3, 2018 > p. 14 Learning the Ropes > FORMULAS (feet) EXIT SLIP B B L 4 S F = (feet) (pounds)

14 DAY 1 Which of the following numbers is smaller and by how much: four hundred two ten thousandths or forty-two thousandths? Write your answer in word form. Problem of the Day Try one of these quick eercises each day as a fast, fun way to start your math lesson! DAY 2 The most money ever paid for a comic book was dollars, for Action Comics #1, the first appearance of Superman. What is that price in standard form? DAY 3 Draw an acute isosceles triangle. DAY 4 In 2014, the average middle school student spent about $360 on clothing, shoes and accessories. One-third of the total was spent on shoes. What was spent on shoes? DAY 5 Decorative lines on a cake make an angle that measures 37 degrees. This angle is: A obtuse C perpendicular B acute D supplementary DAY 6 How many faces does a square pyramid have? A 3 C 5 B 4 D 6 DAY 7 Jeremiah earned $64.00 for every 5-hour shift he worked as a lifeguard this summer. What is Jeremiah s rate per hour? DAY 8 A newborn calf weighs 67 pounds, and its mother weighs 941 pounds. Write an equation and solve to find how much more the cow weighs than the calf, using the variable w. DAY 9 Grace wants to know how many games on Roblo have been played more than 100 million times. Is her question statistical or non-statistical? Eplain. DAY 10 The length of the Nile River in Africa is about 6,853 kilometers. How many miles long is that, rounded to the nearest whole number? (Hint: 1 kilometer = miles) DAY 11 What is the greatest common factor of the following numbers? 24, 90, 78 DAY 12 Solve the equation for tension on a slackline where B = 145 pounds, L = 25 feet, and S = 1.1 feet. Round your answer to the nearest whole number. F = B L 4 S DAY 13 The entire sith grade was surveyed on their favorite season. Which graph would best display the results of the data? Why? DAY 14 Use the digits 1 to 9, at most one time each, to fill in the boes to make two different pairs of fractions that have a product of 2 3. = 2 3 DAY 15 The following data set represents the number of minutes a student read each day over the course of one week: 15, 36, 7, 65, 29, 13, 38. What is the mean? DAY 16 What is the value of this epression when p = 9? 3p 2 8 DAY 17 The U.S. Constitution was signed on September 17, Find two factors, not including 1, that show how many years have passed since the signing. DAY 18 Evan can run 2 miles in 19 minutes. Josie can run 4 miles in 35 minutes. Who can run a mile the fastest and by how many minutes? DAY 19 Which epression below has a value greater than 7? A C B D DAY 20 Nico and three friends had lunch at their favorite burger spot. Their total bill was $29.00, and they wanted to leave an 18% tip. How much money did they leave in total? Permission granted by Scholastic MATH to reproduce this page for classroom use only by Scholastic Inc. All Rights Reserved. SEPTEMBER 3, 2018