Zoo Math Days: Alligator Pool (K-10) At a glance Students will use math skills to plan a work task at the Reptile House. Grade(s) K-10 Materials Clipboard (or hard writing surface) Pencil 1 copy of student page per student or pair Simple calculator Goal(s) To practice math calculations to plan a work task Objective(s) 1. Students (K-10) will be able to determine how much time it takes the keepers to drain and refill the alligator pool. 2. Students (K-4) will be able to add and subtract to complete a pattern of numbers. 3. Students (5-10) will be able to apply the formulas for area, volume and rate. 4. Students (5-10) will be able to convert metric units. Zoo Math Days Alligator Pool, September 2009
Academic standards Ohio Mathematics Academic Content Standards (Grade: Indicators) Kentucky Core Content Mathematics Numbers, Number Sense and Operations (1: 5a.,10d.,12,15) (3: 15) (4: 3,7,9,12,13) (5: 8) (8: 6) Patterns, Function and Algebra (K: 2,3) (1: 2b.,3) (2: 2,3) (3: 1,3) (4: 5,6) (5: 3-5) (6: 1,4) (7: 1,2,4) (8: 2,3,4,6,9) (9: 1,5) Data Analysis and Probability (K: 1) (1: 4) (2: 2) (4: 1,2) Mathematical Processes (3-4: A, C & D) (5-7: B& E)(8-10: A, B, F, G & H) (8-10: A-C) Number Properties and Operations Estimation MA-(EP-1.2.1) (04-1.2.1) (06-1.2.1) (07-1.2.1) (08-1.2.1) (HS-1.2.1) Number Operations MA-(EP-1.3.2) (04-1.3.2) (05-1.3.1) (06-1.3.1) (07-1.3.1) (08-1.3.1) (HS-1.3.1) Measurement Measuring Physical Attributes MA-(EP-2.1.6) (04-2.1.6) (05-2.1.1)(05-2.1.6) (05-2.2.1) (05-2.2.3) (06-2.2.1) (07-2.2.1)(08-2.1.2) (HS-2.1.1) Systems of Measurement MA (7-2.2.1) (08-2.1.2) (HS-2.2.1) Data Analysis and Probability Data Representations MA-(EP-4.1.1) (EP-4.1.2) (EP-4.1.3) (04-4.1.1) (04-4.1.2) Geometry Shapes and Relationships MA-(08-3.1.2) ( HS-3.1.6) Algebraic Thinking Patterns, Relations and Functions MA-(EP-5.1.1) (04-5.1.1) (06-5.2.1) (07-5.2.1) (08-5.2.1) (HS-5.2.1) Indiana Mathematics Standards Number Sense (1.1.1) (2.1.1) (2.1.2) (2.1.12) (3.1.1) (5.1.2) Computation (1.2.4) (1.2.5) (5.2.1) Algebra & Functions (K.3.2) (2.3.3) (2.3.4) (6.3.1) (6.3.5) (8.3.7) Geometry (8.4.1) Measurement (K.5.2) (6.5.1) (7..5.1) (8.5.1) (8.5.2) (8.5.4) Problem Solving (1.6.5) (2.6.5) (4.7.1) (4.7.3) (5.7.1 (5.7.2) (5.7.4) (6.7.1) (6.7.3) (6.7.4) (6.7.5) (7.7.1) (7.7.4) (8.7.1) (8.7.3) (8.7.4) Algebra I & II Sequences and Series (A2.8.4) Mathematical Reasoning and Problem Solving (A1.9.1) (A2.10.2) Geometry Circles (G.6.7) Mathematical Reasoning and Problem Solving (G.8.1) (8.4.1) Integrated Mathematics II Geometry and Measurements (IM2.2.20) Zoo Math Days: Alligator Pool, September, 2009 Page 2 of 10
Background Zookeepers use math every day, not only to accomplish their work, but also to plan ahead. One reason is to figure out how long certain tasks will take so they can plan how much time to allow, and in what sequence they should do various jobs, in order to get everything done. One task the Reptile House keepers must do every week is drain the water from the central pool where the Chinese alligators and turtles live, scrub it down, and refill it, all before the building opens at 10:00 a.m. Activity Have students follow the directions on their worksheets to figure out the area of the alligator pool, the volume of water in it, and how long it takes to drain and refill it. Assessment Apply the same calculations to a task more familiar to students such as draining and refilling an aquarium or cleaning and replacing bedding in a hamster cage. This activity illustrates how math is part of a typical workday. It also gives students the opportunity to practice applying the formulas for area, volume, and rate, and to convert to metric units. Zoo Math Days: Alligator Pool, September, 2009 Page 3 of 10
Student Page Grades K-4 You are a zookeeper for the Reptile House. One job you have to do every week is drain the water out of the alligator pool, scrub it down, and then fill the pool back up with clean water. You need to figure out how long this will take. Solve the following problems to figure it out: 1) There are about 6,000 liters of water in the pool. It takes about 1 minute to drain 600 liters of water. Finish the pattern in the numbers to estimate how long it would take to drain all the water from the pool. 1,200 2,400 3,600 4,800 6,000 2 4 6 2) The spout that fills the pool is much slower than the drain. In 1 minute, only about 100 liters of water runs into the pool. Finish the next pattern of numbers to estimate how long it would take to fill the pool with 6,000 liters of water. 500 1,000 1,500 2,000 2,500 Continue in the next table Draw a box around the time for 6,000 liters. 3) How long does it take to drain and refill the pool? Fill in the numbers and circle the correct math operation in the equation and then solve it: + or - = Zoo Math Days: Alligator Pool, September, 2009 Page 4 of 10
Student Page Grades 4-7 Zookeepers use math every day, not only to accomplish their work, but also to plan ahead. One way they use math is to figure out how long certain tasks will take so they can plan how much time to allow, and in what sequence they should do various jobs, so that everything gets done. One task the Reptile House keepers must do every week is drain the water from the central pool where the alligators and turtles live, scrub it down, and refill it, all before the building opens at 10:00 a.m. Use the information and hints provided to figure out how much time you would need to allow if you were a keeper in the Reptile House. Hints: Make a plan. What do you need to know to solve this problem? Make a list below, and then put the list in order to make a series of steps for solving this problem. For Your Information: 1) The area of the bottom of the pool is 172,021 cm 2. 2) The water in the pool is 38 cm deep. 3) The water drains at about 630 liters per minute. This is called the flow rate of the drain pipe. 4) The water fills at about 109 liters per minute. This is the flow rate of the spout. 5) It takes the keepers 15 minutes to scrub down the drained pool. Remember: 100 centimeters (cm) = 1 meter (m) 1 cm 3 = 1 milliliter (ml) 1,000 ml = 1 liter (L) Volume = area of the bottom X height (or depth) of the water Rate = Volume [That's why it's expressed as liters per minute (L/min)] = Volume Rate Zoo Math Days: Alligator Pool, September, 2009 Page 5 of 10
Student Page Grades 8-10 Zookeepers use math every day, not only to accomplish their work, but also to plan ahead. One way they use math is to figure out how long certain tasks will take so they can plan how much time to allow, and in what sequence they should do various jobs, so that everything gets done. 2) Notice that the pool is just about circular. (It is actually a 16-sided shape, but for this purpose it will be good enough to pretend it's a circle. This is a form of estimation). The distance from the center of the pool to the edge is approximately 234 cm. One task the Reptile House keepers must do every week is drain the water from the central pool where the alligators and turtles live, scrub it down, and refill it, all before the building opens at 10:00 a.m. Use the information and hints provided to figure out how much time you would need to allow if you were a keeper in the Reptile House. Solve: 1) Make a plan. What do you need to know to solve this problem? Make a list below. Using the information below, figure out how much water is in the pool: (Round to the nearest whole number) a) Area = πr 2 b) Volume = Area X depth c) Circumference = 2πr d) The pool gets filled to approximately 38 cm deep. Record your calculations and the total volume of the water in the pool: Zoo Math Days: Alligator Pool, September, 2009 Page 6 of 10
3) Use the information below to calculate how long it takes to drain, clean, and refill the pool. Round off to whole numbers. a) The pool drains at about 630 liters per minute. b) The pool fills at about 109 liters per minute. c) It takes the keepers 15 minutes to scrub down the drained pool. Record your calculations and your final answer: Remember: 100 centimeters (cm) = 1 meter (m) 1 cm 3 = 1 milliliter (ml) 1,000 ml = 1 liter (L) Hint: Rate = Volume [That's why it's expressed as liters per minute (L/min)] = Volume Rate Zoo Math Days: Alligator Pool, September, 2009 Page 7 of 10
1) Answer Page Grades K-4 1,200 2,400 3,600 4,800 6,000 2 4 6 8 10 2) 500 1,000 1,500 2,000 2,500 3,000 5 10 15 20 25 30 3,500 4,000 4,500 5,000 5,500 6,000 35 40 45 50 55 60 3) 10 + 60 = 70; It takes a total of 70 minutes to drain and refill the pool. Zoo Math Days: Alligator Pool, September, 2009 Page 8 of 10
Answer Page Grades 4-7 Step 1) Find the volume of water in the pool: Since Area X Depth = Volume, then 172,021 cm 2 X 38 cm = 6,536,798 cm 3. Convert the answer to liters: Since 1 cm3 = 1 ml and 1,000ml = 1 L, then 6,536,798 cm 3 = 6,536,798 ml = 6,536.798 L (move the decimal) = 6,537 L (round up). Step 4) Add the times together to figure out how long this job will take. 10 minutes to drain + 15 minutes to scrub + 1 hour to fill = 1 hour and 25 minutes to complete the job. Step 2) Use volume and flow rate to figure out long it takes the pool to drain: Since Volume Rate =, then 6,537 L 630 L/min. = 10 minutes. Step 3) Use volume and flow rate to figure out long it takes the pool to fill: Since Volume Rate =, then 6,537 L 109 L/min. = 59.9 minutes, or about one hour. Zoo Math Days: Alligator Pool, September, 2009 Page 9 of 10
Answer Page Grades 8-10 Step 1) Find the area of the bottom of the pool: The distance from the center of the pool to the edge is given as 234 cm. Students have to recognize that this is the radius (r). Since Area = πr 2, then π X (234) 2 = 172,021 cm 2 Step 2) Find the volume of water in the pool: Since Area X Depth = Volume, then 172,021 cm 2 X 38 cm = 6,536,798 cm 3. Convert the answer to liters: Since 1 cm3 = 1 ml and 1,000ml = 1 L, then 6,536,798 cm 3 = 6,536,798 ml = 6,536.798 L (move the decimal) = 6,537 L (round up). Step 3) Use volume and flow rates to figure out how long it takes the pool to drain: Rearrange the equation, Rate = Volume, to solve for time, = Volume Rate. To help students figure this out, use easy numbers as examples: What if the pipe drained 2 L per minute, and you had 4 L of water? It would drain 2 liters in the first minute, and 2 in the second minute. What if it drained 2 L per minute, and you had 6 L of water? It would drain 2 liters in the first minute, 2 in the second minute, 2 in the third minute. So what's the pattern for figuring this out? You're dividing the amount of water into chunks of 2 liters each: volume divided by flow rate. So, 6,537 L 630 L/min = 10 minutes. Step 4) Use volume and flow rate to figure out long it takes the pool to fill: Since Volume Rate =, then 6,537 L 109 L/min = 59.9 minutes, or about an hour. Step 5) Add the times together to figure out how long this job will take and when they should start: 10 minutes to drain + 15 minutes to scrub + 1 hour to fill = 1 hour and 25 minutes to complete the job. If the building opens at 10:00 a.m., the keepers must start draining the pool no later than 8:35 a.m. Actually, they probably start a little earlier to allow time to get the animals back in the pool before the building opens. Zoo Math Days: Alligator Pool, September, 2009 Page 2 of 10