Maths Likes

Math5 asked mathematicians on Twitter, "What do you like about math(s)?" We got some great responses. You can see the responses by clicking this link: https://storify.com/mwilkinson3/maths-likes?utm_content=storify-pingback&utm_medium=sfy.co-twitter&utm_campaign=&utm_source=t.co&awesm=sfy.co_bzd6

Soil Nutrient Lab

Soil Nutrient Lab

Our work in Michael’s 4th Grade Science class this year started with looking at the needs of living things. We came up with all kinds of things we thought we needed, but narrowed down to the basic needs of living things: food, water, air, habitat. We’ve been told that the plants bring the nutrients into the ecosystem by absorbing them from the soil. We wanted to see if we could find those nutrients ourselves. We learned that there are three main nutrients for life: nitrogen, potassium, and phosphorous. So we decided to test for these in the garden. Shouldn’t there be plenty of nutrients there since we were growing things to eat?

Collecting Soil Samples

We collected soil samples from the garden beds, the pond, the area outside the garden beds under the woodchips, and in the runoff from the playground by the bridge. We tested each of these soils for the three nutrients and found that while there was sufficient phosphorous and potassium in the soil, there was very little nitrogen. When we went back to the garden, we could see the effect on the squash plants. Their leaves were yellow-green with yellow and brown spots and the edges of the leaves were dry brown. These were signs of not enough nitrogen.

These leaves don't look healthy.

How can we grow healthy plants to eat in a garden without enough nitrogen? We wanted to find a way to improve the soil, so we brainstormed some solutions. We thought adding compost or fertilizer might help. We also remembered that there are some plants that help put nitrogen into the soil. We remembered from our “Three-Sisters” study last year (corn-beans-squash) that one of the things the beans did was help with nitrogen, we thought planting beans might help. We also wanted to try alfalfa. So we took some small pots and prepared the soil five different ways: control soil with no change, soil mixed with osmocote pellets, soil mixed with compost, soil planted with beans, soil planted with alfalfa. We put these under constant light and water and will test the soil nitrogen levels in a few weeks.

In the meantime, we learned that bacteria helped convert nitrogen from the air into nitrogen that plant roots could absorb. Maybe there wasn’t enough bacteria in the soil from the garden. Upperschool Science Teacher (and class parent) Howie Waldman came to class to help us grow some bacteria from the soil and compost. It only took a day for there to be a lot of growth. Howie is going to help us to try to make microscope slides of the bacteria next, so we can see individual cells.

We also noticed a lot of living things in the compost - macroinvertibrate decomposers. We found nematodes, earthworms, pseudoscorpions, weevils, isopods, and others we haven’t yet identified.

We’re learning a lot about soil, how it works and how it helps us to be healthy. Like the song says, dirt really did make our lunch. We can’t live without healthy soil.

DATA UPDATE 10/21/14

After one month, we tested our soil treatments for nitrogen levels with Rapitest kits:

Soil Treatment	Nitrogen Level after 1 month
Control	Depleted (N0)
Osmocote	Surplus (N4+)
Compost	Surplus (N4+)
Beans	Deficient (N1)
Alfalfa	Deficient (N1)

Conclusions

We can improve the nitrogen in the soil using compost and Osmocote. It only takes a little of these to raise the nitrogen in the soil. Planting beans and alfalfa changed the nitrogen a little bit, we need a lot more bean and alfalfa or more time to bring the nitrogen up enough. So, if we want healthy garden soil, we need to add a little compost to the soil.

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?