MIDDLE GRADES MATHEMATICS PRACTICE PACKET

Transcription

1 MIAMI-DADE COUNTY PUBLIC SCHOOLS DISTRICT SECME OLYMPIAD SECME: The Gold Standard in STEM MIDDLE GRADES MATHEMATICS PRACTICE PACKET Name:

2 Problem Scenario #1 A Million Dollars In all these tasks you should show your calculations and give your answers to the nearest whole number. 1. How many $3.50 burgers can you buy for a million, 10 6, dollars? 2. How many years does it take to earn 10 6 dollars if you are paid $30 an hour and work 35 hours a week for 50 weeks a year? Round to the nearest tenth. 3. A dollar bill weighs one gram. How many pounds do 10 6 dollar bills weigh? (10 3 grams is 1 kilogram and 1 kilogram is pounds.) 4. A dollar bill is inches thick. How many yards high is a pile of 10 6 dollar bills? Round to the nearest yard. [2]

3 Problem Scenario #2 Ice Cream You are planning to sell ice cream cones at a school sports event as a fundraiser. You expect to make and sell a total of 300 ice cream cones. You buy ice cream in 1 liter tubs. Each tub costs $2. You can fill ten cones from each tub. Each empty cone costs 5. You plan to sell each filled cone for 80. Before buying the ice cream, you survey 60 people to find out what flavors they like. Here are the results of the survey: Favorite Flavors 1. Make a list of what you will need to buy (include quantities) and each of their costs. 2. What is the total cost? 3. How much profit do you expect to make on that day? Show all your work clearly on the next page. Circle your answers. [3]

4 Work Space: [4]

5 Problem Scenario #3 Leaky Faucet Jan estimates that the faucet in her kitchen drips at a rate of 1 drop every 2 seconds. 1. Estimate how many times the faucet drips in a week. Show your calculations below. Jan estimates that approximately 575 drops fill a 100 milliliter bottle. 2. Estimate how much water her leaky faucet wastes in a year, using the conversion 365 days = 1 year. Express your answer to the nearest liter. Show your calculations below. [5]

6 Problem Scenario #4 Glasses This diagram shows three glasses (not drawn to scale). The measurements are all in centimeters. The bowl of glass 1 is cylindrical. The diameter is 5 cm and the height is 6 cm. The bowl of glass 2 is a cylinder with a hemispherical bottom. The diameter is 6 cm and the height of the cylinder is 3 cm. The bowl of glass 3 is an inverted cone. The diameter is 6 cm and the slant height is 6 cm. 1. Find the vertical height of the bowl of glass 3 to the nearest tenth. Use 3.14 for π. Show your work. cm. [6]

7 2. Calculate the volume of the bowl of each of these glasses to the nearest cubic centimeter. Use 3.14 for π. Show your work. a. Glass 1 cm 3 b. Glass 2 cm 3 c. Glass 3 cm 3 3. Find the height of the liquid in Glass 2 when it is half full. Use 3.14 for π. Round to the nearest tenth. Show your calculations below. cm. [7]

8 Additional Work Space: [8]

9 Problem Scenario #5 Fencing Rabia needs to buy fencing for her yard. The cost of 5 fence posts and 4 fence panels is $122. With the same unit prices, the cost of 21 fence posts and 20 fence panels is $570. How much does she pay if she buys 4 fence posts and 3 fence panels? Show how you figured it out. [9]

10 Problem Scenario #6 Candle Box Tom is making a little gift box to hold a candle. Draw an accurate plan for making the box using the dotted paper provided. It should be drawn so that when it is cut out it will stay in one piece. One of the sides has been drawn to start you off. Make sure that you show: the flaps needed for gluing the box together. Shade these in. the flaps needed for fastening the lid (Do not shade these in), the thumb hole, the picture of the Birthday Candle the right way up on each side, and on the lid. [10]

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12 Problem Scenario #7 25% Sale In a sale, all the prices are reduced by 25%. 1. Julie sees a jacket that cost $32 before the sale. How much does it cost during the sale? Show your calculations. $ 2. In the second week of the sale, the prices are reduced by 25% of the previous week s price. In the third week of the sale, the prices are again reduced by 25% of the previous week s price. In the fourth week of the sale, the prices are again reduced by 25% of the previous week s price. Julie says that the prices will be reduced to $0 after the four reductions because 4 x 25% = 100%. Is Julie correct? Explain why or why not. [12]

13 3. If Julie is able to buy her jacket after the four reductions, how much will she have to pay? (Round to the nearest penny) Show your calculations. $ 4. Julie buys her jacket after the four reductions. What percentage of the original price does she save? (Round to the nearest tenth) Show your calculations. % [13]

14 Additional Work Space: [14]

15 Problem Scenario #8 A company in Australia builds and delivers cube-shaped room modules that can be put together to make a house. In the plan below, there are two bedrooms, a kitchen, and a living room composed of two cubes. The edge of each cube is 7 meters long. Note: Not drawn to scale 1. Write an expression, using exponents, that represents the total volume of the house. 2. Write an expression, using exponents, that represents the combined areas of the floors of the house. [15]

16 Additional Work Space: [16]

17 Problem Scenario #9 A photographer wants to print a photograph and two smaller copies on the same rectangular sheet of paper. The photograph is 4 inches wide and 6 inches high. Here are two ways he could do it. (Note: the diagrams are not drawn to actual size.) 1. Find the measurements of the small photographs for each arrangement. Show your calculations and explain how you figured it out. Diagram 1 Diagram 2 [17]

18 2. Find the size of the sheet of paper for each arrangement. Diagram 1 The measurements of the sheet of paper are wide and high. Diagram 2 The measurements of the sheet of paper are wide and high. [18]

19 Problem Scenario #10 A shop owner wants to prevent shoplifting. He decides to install a security camera on the ceiling of his shop. The camera can turn right round through 360 degrees. The shop owner places the camera at point P, in the corner of the shop. 1. The plan shows ten people who are standing in the shop. These are labeled A, B, C, D, E, F, G, H, I, J, K. Which people cannot be seen by the camera at P? Tell how you know and show in the picture above. [19]

20 2. The shopkeeper says that 15% of the shop is hidden from the camera. Is he correct? Explain in complete sentences and include all calculations to justify your solution in the space below. 3. Show the best place for the camera, so that it can see as much of the shop as possible. Place point Q in the picture below to show the location of the camera and shade the area that cannot be seen with the camera if it rotated 360 degrees. Explain how you know that this is the best place, using mathematics to justify your conclusion. [20]

21 Additional Work Space: [21]

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23 Non-Discrimination Policy The School Board of Miami-Dade County, Florida adheres to a policy of nondiscrimination in employment and educational programs/activities and strives affirmatively to provide equal opportunity for all as required by: Title VI of the Civil Rights Act of prohibits discrimination on the basis of race, color, religion, or national origin. Title VII of the Civil Rights Act of 1964 as amended - prohibits discrimination in employment on the basis of race, color, religion, gender, or national origin. Title IX of the Education Amendments of prohibits discrimination on the basis of gender. Age Discrimination in Employment Act of 1967 (ADEA) as amended - prohibits discrimination on the basis of age with respect to individuals who are at least 40. The Equal Pay Act of 1963 as amended - prohibits gender discrimination in payment of wages to women and men performing substantially equal work in the same establishment. Section 504 of the Rehabilitation Act of prohibits discrimination against the disabled. Americans with Disabilities Act of 1990 (ADA) - prohibits discrimination against individuals with disabilities in employment, public service, public accommodations and telecommunications. The Family and Medical Leave Act of 1993 (FMLA) - requires covered employers to provide up to 12 weeks of unpaid, job-protected leave to "eligible" employees for certain family and medical reasons. The Pregnancy Discrimination Act of prohibits discrimination in employment on the basis of pregnancy, childbirth, or related medical conditions. Florida Educational Equity Act (FEEA) - prohibits discrimination on the basis of race, gender, national origin, marital status, or handicap against a student or employee. Florida Civil Rights Act of secures for all individuals within the state freedom from discrimination because of race, color, religion, sex, national origin, age, handicap, or marital status. Title II of the Genetic Information Nondiscrimination Act of 2008 (GINA) - Prohibits discrimination against employees or applicants because of genetic information. Veterans are provided re-employment rights in accordance with P.L (Federal Law) and Section (Florida Statutes), which stipulate categorical preferences for employment. In Addition: School Board Policies 1362, 3362, 4362, and Prohibit harassment and/or discrimination against students, employees, or applicants on the basis of sex, race, color, ethnic or national origin, religion, marital status, disability, genetic information, age, political beliefs, sexual orientation, gender, gender identification, social and family background, linguistic preference, pregnancy, and any other legally prohibited basis. Retaliation for engaging in a protected activity is also prohibited. Revised: (05-12)

24 MIAMI-DADE COUNTY PUBLIC SCHOOLS DISTRICT SECME OLYMPIAD SECME: The Gold Standard in STEM MIDDLE GRADES MATHEMATICS PRACTICE PACKET ANSWER KEY

25 THE SCHOOL BOARD OF MIAMI-DADE COUNTY, FLORIDA Dr. Lawrence S. Feldman, Chair Dr. Marta Pérez, Vice Chair Dr. Dorothy Bendross-Mindingall Ms. Susie V. Castillo Dr. Steve Gallon III Ms. Perla Tabares Hantman Dr. Martin Karp Ms. Lubby Navarro Ms. Mari Tere Rojas Mr. Sebastian Lorenzo Student Advisor Mr. Alberto M. Carvalho Superintendent of Schools Ms. Maria L. Izquierdo Chief Academic Officer Office of Academics and Transformation Ms. Lisette Alves Assistant Superintendent Division of Academics Mr. Cristian Carranza Administrative Director Division of Academics Department of Mathematics and Science Ms. Michelle R. White Executive Director Department of Mathematics and Science

26 ANSWER KEY Please have SECME students complete the problems over the next two months in preparation for the SECME Math Challenge. Students should fully understand the critical thinking involved in solving these types of problems ,714 burgers or 19 years 3. 2,205 pounds yards Problem Scenario #1: A Million Dollars Problem Scenario #2: Ice Cream 1. One point for each answer below for a total of 10 points 15 tubs of Vanilla ice cream Cost of Vanilla ice cream: $30 8 tubs of Strawberry ice cream (cannot buy 7.5 tubs) Cost of Strawberry ice cream: $16 5 tubs of Chocolate Chip ice cream (cannot buy 4.5 tubs) Cost of Chocolate Chip ice cream: $10 3 tubs of Mint ice cream Cost of Mint ice cream: $6 300 Ice Cream Cones Cost of Ice Cream Cones: $15 2. $ $163 profit ,400 drips 2. 2,742 liters Problem Scenario #3: Leaky Faucet Problem Scenario #4: Glasses cm 2. One point for each answer below for a total of 3 points a. 118 cm 3 b. 141 cm 3 c. 49 cm cm

27 Problem Scenario #5 Fencing Rabia needs to buy fencing for her yard. The cost of 5 fence posts and 4 fence panels is $122. With the same unit prices, the cost of 21 fence posts and 20 fence panels is $570. How much does she pay if she buys 4 fence posts and 3 fence panels? $94 Show how you figured it out. Students may solve this in various ways, possibly including solution of the simultaneous equations 5x + 4y = 122 and 21x + 20y = 570 to give x = 10 and y = 18. Students may also show alternate methods, such as the guess and check method, in which they arrive at the correct solution.

28 Problem Scenario #6 Candle Box Tom is making a little gift box to hold a candle. Draw an accurate plan for making the box using the dotted paper provided. It should be drawn so that when it is cut out it will stay in one piece. One of the sides has been drawn to start you off. Make sure that you show: the flaps needed for gluing the box together. Shade these in. the flaps needed for fastening the lid (Do not shade these in), the thumb hole, the picture of the Birthday Candle the right way up on each side, and on the lid.

29 Candle Box Correctly positions: The base hexagon The rectangles The candles The lid hexagon The flaps and thumb hole Points Section points 10 Total: 10

30 Problem Scenario #7 25% Sale In a sale, all the prices are reduced by 25%. 1. Julie sees a jacket that cost $32 before the sale. How much does it cost during the sale? Show your calculations. 24 $ Shows correct work such as: 32 4 = 8 and 32 8 = 24 or (32) = 24 or 32(0.75) = In the second week of the sale, the prices are reduced by 25% of the previous week s price. In the third week of the sale, the prices are again reduced by 25% of the previous week s price. In the fourth week of the sale, the prices are again reduced by 25% of the previous week s price. Julie says that the prices will be reduced to $0 after the four reductions because 4 x 25% = 100%. No Is Julie correct? Explain why or why not. Gives a correct explanation such as: Each reduction is 25% of the previous week s price, and as the price goes down each week, the 25% will be smaller amount each week.

31 3. If Julie is able to buy her jacket after the four reductions, how much will she have to pay? (Round to the nearest penny) Show your calculations. Shows correct work such as: 32 x or 24 x or 24 (24 x 0.25) = (10 x 0.25) = (13.5 x 0.25) = $ $ $ 4. Julie buys her jacket after the four reductions. What percentage of the original price does she save? (Round to the nearest tenth) Show your calculations Shows correct work such as: = / 32 x 100 = % 68.3% or / 32 x 100 = % 100% % = % 68.3% 68.3 %

32 Problem Scenario #8 A company in Australia builds and delivers cube-shaped room modules that can be put together to make a house. In the plan below, there are two bedrooms, a kitchen, and a living room composed of two cubes. The edge of each cube is 7 meters long. 1. Write an expression, using exponents, that represents the total volume of the house. 5(7 3 ) OR Write an expression, using exponents, that represents the combined areas of the floors of the house. 5(7 2 ) OR

33 Problem Scenario #9

34 Security Camera 1. Draws a straight line from the security camera (P) to the opposite side of the room as shown. May describe the sight line. This line shows that F and H cannot be seen by the camera at P. Minus 1 for extras. P Rubric Points 1 2 Section points A B Entrance C D E F G H J K 2. Correctly, shows/explains the area that cannot be seen by the camera. Three of the twenty squares cannot be seen 3/20 = 15% Q P A B Entrance C D E F G 1 H J K Q can be placed one square left or right of the centre. The area of two of the twenty squares cannot be seen if the camera is placed at Q (or to the side of Q), the centre of the side. 2/20 = 10% Partial credit Correctly shows the area that cannot be seen but no calculation. 1 2 (1) 4 Total points 10

35 Non-Discrimination Policy The School Board of Miami-Dade County, Florida adheres to a policy of nondiscrimination in employment and educational programs/activities and strives affirmatively to provide equal opportunity for all as required by: Title VI of the Civil Rights Act of prohibits discrimination on the basis of race, color, religion, or national origin. Title VII of the Civil Rights Act of 1964 as amended - prohibits discrimination in employment on the basis of race, color, religion, gender, or national origin. Title IX of the Education Amendments of prohibits discrimination on the basis of gender. Age Discrimination in Employment Act of 1967 (ADEA) as amended - prohibits discrimination on the basis of age with respect to individuals who are at least 40. The Equal Pay Act of 1963 as amended - prohibits gender discrimination in payment of wages to women and men performing substantially equal work in the same establishment. Section 504 of the Rehabilitation Act of prohibits discrimination against the disabled. Americans with Disabilities Act of 1990 (ADA) - prohibits discrimination against individuals with disabilities in employment, public service, public accommodations and telecommunications. The Family and Medical Leave Act of 1993 (FMLA) - requires covered employers to provide up to 12 weeks of unpaid, job-protected leave to "eligible" employees for certain family and medical reasons. The Pregnancy Discrimination Act of prohibits discrimination in employment on the basis of pregnancy, childbirth, or related medical conditions. Florida Educational Equity Act (FEEA) - prohibits discrimination on the basis of race, gender, national origin, marital status, or handicap against a student or employee. Florida Civil Rights Act of secures for all individuals within the state freedom from discrimination because of race, color, religion, sex, national origin, age, handicap, or marital status. Title II of the Genetic Information Nondiscrimination Act of 2008 (GINA) - Prohibits discrimination against employees or applicants because of genetic information. Veterans are provided re-employment rights in accordance with P.L (Federal Law) and Section (Florida Statutes), which stipulate categorical preferences for employment. In Addition: School Board Policies 1362, 3362, 4362, and Prohibit harassment and/or discrimination against students, employees, or applicants on the basis of sex, race, color, ethnic or national origin, religion, marital status, disability, genetic information, age, political beliefs, sexual orientation, gender, gender identification, social and family background, linguistic preference, pregnancy, and any other legally prohibited basis. Retaliation for engaging in a protected activity is also prohibited. Revised: (05-12)