Filling the Pool

by Math5

As a culminating project for our geometry unit, my students engaged in the following project. This project required that they organize their problem-solving approach, collaborate with each other, and apply many of the skills and concepts developed in 5th Grade Mathematics this year. The following is the account of this work written by the students themselves.

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One day, we walked into math class and we saw a question posted on the board:

“How long does it take to fill the pool?”

At first we thought that it would be easy to find out. After all, we had a lot of practice finding volume of a rectangular prism. We all immediately left for the pool, to get our measurements. As we walked over and as we started taking our measurements, we realized that we couldn’t just take the measurements, because there was a curve at the bottom of the pool. That’s where most of our project came in. Suddenly the simple question on the board became a project that we worked on for a week and a half.  

Estimating the Volume of the Pool

We came up with four different ways to estimate the volume of the pool.

For the first estimate we made, we had to pretend that the pool was broken up into smaller rectangular prisms. So the bottom of the pool looked like a staircase. We multiplied the depth of each prism times the width of the pool times the length of each prism.

The individual prisms were:

1.3m x 14m x 2.6m= 47.32m3

1.4m x 14m x 5m= 98m3

1.5m x 14m x 3.9 = 81.9m3

1.9m x 14m x 3.8m=103.74m3

2m x 14m x 7m= 196m3

1.9m x 14m x 1m=26.6m3

When, we added up all of the volumes, we got the estimated volume, 553.56m3.

For the second estimate, we built a model of the pool out of blocks representing one cubic meter. The first layer of blocks was 23x14 cubes (the surface of water exposed) and the second layer was 18x14 cubes. When we added all the cubes up we got 574 cubes. So our third estimation for the volume is 574 cubic meters.

In the third estimate we used mean depth to figure out the volume. We found the mean depth by adding all the depths of the pool and then dividing it by the amount of depths (6). We then used the length of the pool, the width of the pool, and the mean depth of the pool, 1.7 m to find the volume of a rectangular prism. We multiplied 14•23•1.7 and got 547.4 cubic meters. So our third estimate for the volume is 574 cubic meters.  

For the fourth estimate we turned the whole pool into a trapezoidal prism. Then we flipped it 90° onto its east side. We first needed to find the area of the trapezoidal base. 3.3 meters is the sum of the lengths of two bases of the trapezoidal face of the pool (the parallel sides). These are really the east and west walls of the pool, but to make it easier to think about, we’re thinking of them as the top and bottom base of the trapezoidal prism. The height of the trapezoid is length of the pool (23 m). To find the area: (3.3 • 23) / 2 = 37.95 m2 for “Base area.” Volume is Base Area • Height of Prism: 37.95 • 14 = 531.3 m3.

Later, we figured out the mean of all of our estimated volumes, and found an approximate answer of how many cubic meters are in the pool.

Depending upon the method we used we got 4 different estimates for the volume of the pool

1. Breaking the pool into rectangular prisms based on the depths, we got 553.56m3

2. Rounding the depths, we got 574m3

3. Finding the mean depths, we got 547.4m3

4. Thinking of the pool as a trapezoidal prism, we got 531 .3m3

The 1st estimate + the 2nd estimate + the 3rd estimate + the 4th estimate / 4 (the number of estimates) =  551.565 m3 = mean average of the pool volume.

Measuring Flow Rate

Measuring how much time it takes water to fill a certain volume.

We found the time it took to fill a 1 liter graduated cylinder 5 times and averaged it. We found a mean of 9.868 seconds to fill 1 liter from the classroom sink. The way we found this rate was we had one person holding the cylinder under the running water, one person had a stopwatch, and one person watch the water level and told the timer when to click stop. We took 5 trials and the times we got were: 9.603, 10.606, 9.067, 9.816, and 10.248 seconds. Measuring was hard because the bubbles in the water threw us off. The mean was 9.868 seconds. Since 1000 liters equals one cubic meter we multiplied 9.868 by 1000 and got 9,868 seconds to fill one cubic meter. Since 10,000 seconds doesn’t mean much, we converted this to bigger time units.

9,868 seconds / 3600 = 2.741 hrs

That means it would take 2.741 hours to fill one cubic meter of water using the classroom sink.

Since we found that there were 551.565 cubic meters of water in the pool, we can multiply the volume by time to fill one cubic meter to find out how long it would take to fill the pool.

551.565 m3 • 2.741 hrs/m3 = 1511.840 hrs to fill the pool with the classroom sink.

1511.840 / 24 = 62.993 days or about 2 months!

We all know that you don’t fill a swimming pool with a classroom sink. We thought Facilities probably had a bigger pipe to fill the pool.

We wanted to know what Facilities thought of our investigatigation. We composed an email with all of our information and a question for them that said “We want to know,  How long does it take to fill the pool with the equipment that you guys fill the pool with?” They replied the next day. The email said “We have two water feeds in the pool, one is a 2 inch pipe , and one is a 1 inch.  The one inch fill line is attached to a float, so it goes on automatically when the water is low.”  That was really helpful.

All we had to do now was divide the volume by the volume per minute.  The volume of the pool is 551.565 cubic meters, as we learned earlier, and the volume per minute with the two inch pipe is 127 gallons per minute.  We were using liters, so we had to translate 127 gallons into liters, which is 480.747 liters.  We had to turn 551.565 cubic meters into liters too, which is 551,565 liters.  So, finally, we divided 551,565/480.747 which is 1,147.308 and got our answer.  But again, it is a very confusing way of reading time, so we divided it by 60, which is about 19 hours.  So it would take about 19 hours to completely fill the pool using the pool’s plumbing.

Then, of course, Michael wasn’t satisfied and tossed us another question: “What if the pool level had dropped by 2” and the refill pipe (1” diameter) had to bring the pool back to full level, how long would that take?”

Evan from Facilities informs us that there are two pipes used to fill the pool. The primary pipe is a 2 in diameter and would supply 127 gallons per minute. The second pipe, a 1 inch pipe at the top of the pool is used to automatically refill the pool when the level drops more than 2”.  

The first step was finding the volume of the missing water.  We knew that the width and length are 14 meters and 23 meters, but we needed to convert 2 inches to metric.  That happens to be 0.0508 meters, so we proceeded to do the multiplication problem: 0.0508x14x23 which equals 16.3576 m3.  So we knew the volume of the missing water.  

Next was the time to replace the missing water.  That could be figured out by dividing the amount the volume by the volume per minute.  We transferred 16.3576 cubic meters into liters which is 16357.6 liters.  Then we transferred 37 gallons into liters too, which is 140.06024 liters.  So 140.06024 liters per minute.  Finally we divided 16357.6/140.06024 which is 116.789747040274 and got our answer.  The only thing was, there are easier ways of writing time than 116 minutes, so we wrote 1 hour 56 minutes 48 seconds instead.  

We had a lot of fun doing this project and it was a huge learning experience.  It is a really fun project and hopefully we will get to do things like this in the future because it was a fun experience  to us kids.

Flower Power 2013

By Sci4

As a culminating project in Grade 4 Science, at the end of our study of plant growth and reproduction, we each designed a flower that could be pollinated by a specific pollinator. Some of us chose bees, some chose butterflies, a few picked bats, and some chose hummingbirds. We had to create a flower that would attract the chosen pollinator, be the right size and shape, and reward the pollinator to keep it coming back.

To view our projects, click the links below:

Flower Power 2013 Final Projects

• Flare
• Purple Flower of The Sun
• Friendly Flower
• Sun Trail
• Grass Lavendar
• Sunrise Flower
• Turquois Sun
• Cabbage Monster
• Blue Sea
• Starfire
• Teacu
• Bright Red
• Red Firecracker
• Dupresho
• Mixred
• Tweedy Weedy
• Shorty
• Monarch Backyard Flower
• Purplebell
• Multicolor
• Semona
• Nectarious

Operation Ice Bridge

Operation Ice Bridge - How We Got Started
by Sci5

Students recently concluded the data collection phase of their cryosphere research. They are now in the process of analyzing data and reflecting on their work. This is the first of several posts that will describe the project.


Over the past few months, we have been doing our own labs based on NASA’s Operation Ice Bridge Missions. We learned about Operation Ice Bridge through some web chats we had been doing with other NASA Airborne Research projects. Because of this we “joined” the OIB crew while they were flying over Antarctica in a DC8. Using a web tool, we could follow the flight and chat with scientists and educators during the missions.

When we were chatting with the OIB crew, we asked them about their mission. We asked them about the kinds of data they were collecting and the tools they were using. They explained that they were exploring changes in the polar ice caps. To do this, measuring the how much ice there was using a laser on the belly of the airplane. These measurements could detect very small changes in the ice. They are measuring the ice to see what the effects of global warming might be.

Click here for more information about NASA Operation Ice Bridge.

After our chat with the OIB crew, we had a class meeting brainstorming different questions and investigations about ice.

Some of our questions were:

• Why does cold air sink?
• How does ice move or change?
• Does global warming affect the ice in Antarctica?
• If not global warming, what is affecting the ice?
• At what temperatures of water and air does ice melt?
• How does ice react to different temperatures of air?
• How does ice react to different temperatures of water?
• How does ice react to different amounts of ice and water?
• Does ice react differently to relatively dry warm air vs humid warm air?
• Does the kind of ice matter? eg. small cubes, large blocks, chips, slush, etc.
• How does ice react to wind?
• How does salinity of water affect ice?

For some of the questions we asked the OIB crew about them in later chats. For others, we actually designed some experiments to try and figure things out.

We will describe each experiment in later posts...

Airplane Math 2

by Math 4
Our flight planning continues...

We were planning a mission to go from Wallops Space Flight Center to Boston, to NYC, to Philadelphia, to Baltimore, to Washington, DC and back to Wallops.

We are testing air quality and circling each of these cities once. 

We will be flying NASA's P-3B Orion. 

NASA P-3B Orion in flight
Discover-AQ

To find out if our mission was possible we had to do some math. YAY!!! (standing O for math)

When flying between cities we are flying 450 mph. When circling to collect data we are flying 250 mph. Each circle for collecting data is 125 miles. There are five circles. 

First we added up all the spaces between each city.

417 mi + 191 mi + 81 mi + 89 mi + 36 mi + 121 mi = 935 miles

We need to figure out how much fuel this will take.

To do this, we need to know how much time it will take to fly 935 miles. We need to divide 935 by 450. That equals 2 hrs with a remainder of 35 miles. We then had to figure out how long it will take to fly 35 miles. It will take an extra 5 minutes to fly the remaining 35 miles. Total cruise time is 2 hrs 5 min.

Now we need to know how much fuel for data collection. Each circle is 125 miles and there are five of them. 125 x 5 = 625 miles. It will take 2 hrs 30 minutes. (625 / 250 = 2 and 1/2)

[insert work here]

Total mission time: 

2 hr 5 min (cruise) + 2 hr 30 min (data) + 3 hrs (safety margin) = 7 hrs 35 min

This would take 32,502 lbs of fuel.

YAY!!! We can fly the mission with almost 30,000 lbs of fuel to spare!

Emily and Sally asked us if we were going to do more than one spiral at each city. Now we need to see if we can do that.  

Airplane Math

by Math 4
4th Grade Math is practicing their multiplication and division skills. We decided to make some problems that NASA Mission Planners might need to work out.

NASA Airborne Research has a variety of airplanes that they use for Earth Science research. These planes are like flying laboratories and observation posts. The chart below gives some information about some of the aircraft used in missions we’ve been following this year. We are using this data to create interesting multiplication and division problems.

*	*	*
Global Hawk UAV	DC-8	P-3 Orion
12,000 lbs of fuel	160,000 lbs of fuel	60,000 lbs of fuel
30 hours flight duration	12 hours flight duration	14 hours flight duration
Take-off Weight: 25,600 lbs	Take-off Weight: 340,000 lbs	Take-off Weight: 135,000 lbs
1900 lb payload	30,000 lb payload	14,700 lb payload
397 mph	518 mph	460 mph
12,658 mile flight range	6214 mile flight range	4373 mile flight range
65,000 ft max altitude	41,000 ft max altitude	32,000 ft max altitude
Humans: 0 (UAV)	Humans: 50	Humans: 24
Missions: HS3, ATTREX	Missions: OIB	Missions: Discover-AQ
Flights: 9	Flights: 23	Flights: 10
*	*	*

Our first problem: How much fuel does each plane use in one hour of flight?

Operation Ice Bridge

by Sci 5
Inspired by NASA Operation Ice Bridge, 5th Grade Science students have been designing original research, collecting and analyzing data. They will continue to share their research through this blog throughout the winter.

Our Operation Ice Bridge work continues...

Our testing rig: Vernier LabQuest with temperature and light intensity probes.

We are trying to learn about global warming and how it affects the polar ice caps. We are testing the albedo of different ground covers, including sand, snow, woodchips, grass, pavement, water, soil and ice. Albedo is the light that is reflected off of a surface. We are measuring albedo because we noticed that the air temperatures were different over different ground cover. We are trying to find out if the reason there are different temperatures is because there are different amounts of light reflected from surfaces. If there is a lot of reflected light, it might cause it to get warmer. If the snow and ice have such a high albedo, maybe that warms the air and adds to the melting of the polar ice. Because of global warming, the greenhouse gasses make it harder for the reflected heat to escape. The warm air gets trapped and melts the polar ice. We know from other work that cold air sinks. Could high albedo cause less melting? We are also wondering how the industrial countries in the Northern Hemisphere are affecting things. Are there more sources of greenhouse gasses in the Northern Hemisphere than in the Southern Hemisphere? Is there a difference in how the Arctic is being affected compared to the Antarctic?

Does albedo change the air temperature?
Does albedo change the melting rates of snow and ice?
Does albedo change as snow/ice melts?
Do different surface and air temperatures affect the albedo of snow/ice?

Maybe sand has such a high albedo because it is made of tiny crystals like snow and ice are... maybe snow (sparkly crushed up ice) works the same way... maybe it gets hot like sand does with the sun’s light...

Where do you like to do math?

by Math4

Where do you most enjoy working on mathematics? What kind of a space helps you think? When you're stuck on a problem, where do you go? What do you do to get un-stuck?

We asked this question of Marcus du Sautoy via twitter and here is his response:

Read the comments below to see our thoughts, AND please share your thoughts with us.

Operation Ice Bridge

by Sci5

We have been working on Operation Ice Bridge aka OIB. After following the NASA Airborne Sciences OIB missions over Antarctica,  we decided we would follow in NASA’S footsteps and do our own ice bridge study. We started by going outside and taking the icy and slushy snow temperatures we also took the temperatures of the soil, wood chips, grass and pond water. We also did an inside sort of control trial with regular freezer ice. 

We are are looking at what the conditions are like over ice. What happens when it's sunny or windy? What changes how ice melts?

We took temperatures of the air near the surface of the ground and at 1, 2, and 3 foot heights. We use a PVC pipe with holes through it to hold our temperature probes. We are also measuring the soil temperature. We've been looking at the data and trying to find patterns. One thing we noticed is that it's different over different kinds of ground cover. We are wondering if that has anything to do with how much light is reflected from the surface. We are planning to measure the reflected light and see if there are temperature differences with that.

Using LabQuest and Vernier Temperature Probes

While doing IceBridge work we learned many things. We have talked about how global warming has maybe done some things with the polar ice caps. We are trying to find ways to test this out. We learned a lot of side things also, like snow is so reflective from the sun because it has a lot of something called albedo. We learned that global warming is caused because our atmosphere is thickening. When the light and heat from the sun hit the ground/snow/Antarctica it bounces right back up and since the atmosphere has thickened, it gets trapped and stays. The role the humans have in this is WE are making the atmosphere thicker.

Our First Data

We have come up with some good hypotheses. We have done some good control tests and outside tests. Next we should go on to testing our hypotheses in the classroom. We should also do more outside trials and look more deeply for patterns. 

Follow our mission and share your comments.

It's A Heartbeat Away

by Math4
(Teacher's note: this group is practicing the multiplication algorithm, multiplying multi-digit factors and working with multi-step applications of the algorithm.)

We came into the room on Monday morning and our teacher had this up on the board:

We then all started asking questions and sharing ideas about what might make our hearts beat faster or slower.

• how many times does it beat in a minute?
• how do we know how fast it beats?
• it matters if you're exercising or still
• depends on what you're doing
• might matter what you're eating
• running beats fast
• depends how long you live
• health condition might affect
• months have different numbers of days
• leap years...
• does gravity matter?
• does mass/weight matter?
• does our heart slow down while sleeping?
• does fatigue or dehydration affect?
• does age matter?
• rate is always changing... need an estimate
• does height matter?
• get resting, then exercising, get an average... rate between the two
• everyone will have a different answer
• does respiration rate matter?

We wanted to figure out how many times our heart would beat in a minute while we were sitting down. We thought this might be a lower number of beats because when you’re exercising your heart beats faster. We called this our resting pulse. We used this to calculate how many times our heart would beat in an hour and then in a day. Then we tried jogging around to get our exercise rate.
This got us interested in how gravity might affect pulse rates and what the differences might be for someone on the International Space Station. We tweeted some questions to space to get some more information. 

We learned that Suni Williams has the record for female EVA time (50hrs 40min). We wondered how many times her heart beat during those EVAs. Our school nurse came and talked to us about how our hearts work, how it beats, why it beats and some of the different things that make it beat faster or slower. We learned that when you are excited, your heart beats faster. Since Suni was out it space, she was probably pretty excited and maybe nervous or even a bit scared, so her pulse rate might be like our exercise pulses. 

When we measured our own pulses, we found that everyone had different rates. We decided to “average” our data and use the pulse that was in the middle of the class data. Our teacher told us that is called the median. Our median resting pulse rate was 76 beats per minute and our median exercise rate was 106 beats per minute. We used the median exercise rate to find out that Suni’s heart beat about 322,240 times during all of her EVA time!

We also got curious about pulses of other animals. We asked ISS National Lab what the Medaka fish pulse was. We decided to give the Medaka fish 85 days mission, the same length as CMDR Hadfield’s mission. The Medaka have a pulse of 116 beats per minute. That means their heart would beat 14,198,400 times during that mission!

Read more about the Medaka fish on ISS.

We also figured out that our hearts would beat about 39,945,600 times in 2013!

This was a lot of fun. It was a great learning experience. It was cool to learn about how many times our heart beats. It was fun learning about what could affect your heart. 

Try these experiments out in your classroom and see what you find. Write us in the comments section and let us know what  you learn.