My first POW
Alyssa Dempsie
Math 10
Ande Lloyd
Janitor POW
Monday September 19 2022
In this POW we were asked to solve how long it would take three janitors to clean the entire building individually, given a ratio of how much they cleaned in what amount of time and showing up at different times. We were told that janitor one showed up first and cleaned half the building in two hours. Then janitor two showed up and together they cleaned a quarter of the building in thirty minutes. Then janitor three showed up and all three cleaned up the last quarter of the building in ten minutes. When starting to figure out the problem I decided that if I could find the cleaning ratio for each janitor individually, then I would be able to easily solve how long they would all take assuming that each janitor cleaned at a constant rate and didn’t take any break. So I started with the first janitor if he cleaned ½ in two hours then it took him one hour to clean ¼ of the building. Then I moved to janitor two, assuming janitor one and two cleaned equal parts of the building, each janitor cleaned ⅛ of the building in thirty minutes. If doubled then the ratio is ¼ of the building in one hour. Giving janitor two the same ration and cleaning speed as janitor one. At this point, I tried to move on to janitor three, but it was more complicated and I kept getting confused or lost. Then Ande said the key was to find each janitor's hourly cleaning rates. He also hinted that to find that we would need to find how long it would take all three janitors to clean the building if they started at the same time. If janitors one two and three clean ¼ of the building in ten minutes. You can multiply them both by four to get the ratio of 4/4 in forty minutes. So it took all three janitors forty minutes to clean the whole building. Using this we set up this scale. Using this we set up an algebraic equation that showed how much each janitor cleaned in an hour. It looked like this. This shows that janitor three can clean the entire building in one hour. So after putting together all the information the final ratios said that janitor one took four hours to clean the entire building, as well as janitor two, while it only took janitor three one hour. The habit that applies most to this POW is generating ideas. This is because you had to generate ideas to come up with an initial idea on how to solve the POW. Then if that didn’t work you had to come up with another idea. Once you finally got on track you had to generate an algebraic equation to solve how much each janitor cleaned in an hour. This habit of a mathematician helped me solve this POW by coming up with ways to get past roadblocks when I got stuck. This habit helped me come to the answer on my own in a roundabout way.
Math 10
Ande Lloyd
Janitor POW
Monday September 19 2022
In this POW we were asked to solve how long it would take three janitors to clean the entire building individually, given a ratio of how much they cleaned in what amount of time and showing up at different times. We were told that janitor one showed up first and cleaned half the building in two hours. Then janitor two showed up and together they cleaned a quarter of the building in thirty minutes. Then janitor three showed up and all three cleaned up the last quarter of the building in ten minutes. When starting to figure out the problem I decided that if I could find the cleaning ratio for each janitor individually, then I would be able to easily solve how long they would all take assuming that each janitor cleaned at a constant rate and didn’t take any break. So I started with the first janitor if he cleaned ½ in two hours then it took him one hour to clean ¼ of the building. Then I moved to janitor two, assuming janitor one and two cleaned equal parts of the building, each janitor cleaned ⅛ of the building in thirty minutes. If doubled then the ratio is ¼ of the building in one hour. Giving janitor two the same ration and cleaning speed as janitor one. At this point, I tried to move on to janitor three, but it was more complicated and I kept getting confused or lost. Then Ande said the key was to find each janitor's hourly cleaning rates. He also hinted that to find that we would need to find how long it would take all three janitors to clean the building if they started at the same time. If janitors one two and three clean ¼ of the building in ten minutes. You can multiply them both by four to get the ratio of 4/4 in forty minutes. So it took all three janitors forty minutes to clean the whole building. Using this we set up this scale. Using this we set up an algebraic equation that showed how much each janitor cleaned in an hour. It looked like this. This shows that janitor three can clean the entire building in one hour. So after putting together all the information the final ratios said that janitor one took four hours to clean the entire building, as well as janitor two, while it only took janitor three one hour. The habit that applies most to this POW is generating ideas. This is because you had to generate ideas to come up with an initial idea on how to solve the POW. Then if that didn’t work you had to come up with another idea. Once you finally got on track you had to generate an algebraic equation to solve how much each janitor cleaned in an hour. This habit of a mathematician helped me solve this POW by coming up with ways to get past roadblocks when I got stuck. This habit helped me come to the answer on my own in a roundabout way.
The scale we set up
40 minutes =4/4 or 100%
50 minutes = 5/4 or 125%
60 minutes = 6/4 or 150%
50 minutes = 5/4 or 125%
60 minutes = 6/4 or 150%
The algebraic equation
J1 + J2 + J3 = 6/4 or 150%
J1 = 1/4 or 25%
J2 = 1/4 or 25%
25 + 25 +J3 = 150
50 - 50 + J3 = 150 - 150
J3 = 100%
J1 = 1/4 or 25%
J2 = 1/4 or 25%
25 + 25 +J3 = 150
50 - 50 + J3 = 150 - 150
J3 = 100%
Energy Project Museum
Overview
To start off this unit we went to a hydroelectric dam, and step-down transformer. The next day we went to the Farmington school of energy, to see a different perspective and how other people thought. We spent the next few weeks we spent time understanding the process of energy generation, transformation, how efficient different forms are, and the math behind energy efficiency. Next we went out into the community and did different things, that applied what we had learned. My group taught fifth and fourth graders why things are magnetic. Then we created projects based on topics we chose and showcased them at All School Exhibition.
The Project
Water Wheel and Poster
Words From Poster
Definition -
Hydro power is a term used to describe the collection or development of electricity through water’s gravitational and kinetic force.
What is it? -
Hydroelectric plants are usually placed in dams where they can be most efficient. It all starts with a gate that controls a consistent flow of water through a penstock. A penstock is a tube that leads from the dams reservoir into the section filled with turbines. This flow of water begins spinning turbines that are connected to generators. These generators contain an electro magnet and coils of copper. When the water pushes against the turbine the resistance allows the turbine to spin the electromagnet inside of the generator developing electricity this process is referred to as mechanical energy. The energy is transferred into a transformer where it is then kept or sent out.
Merits -
Hydroelectricity would allow each state to use their own energy rather than relying on international fuel sources. It would create jobs in rural areas and boost local economies. In the United States alone, Hydroelectricity will create around 66,500 stable jobs. Hydroelectricity will provide flood control, irrigation support, clean drinking water, and renewable energy. Hydropower plants will be able to have quick reactions to changes in demand. It has affordable construction and maintenance. Hydropower collaborates well with other renewable energy. Such as the pumped storage, which involves shifting water between to pools, allowing for less construction, pairs well with wind and solar energy during high demand. Hydropower education programs can be found nationwide for anyone interested in getting a job with this business.
Demerits -
Dams from hydroelectricity can cause flood risk, obstruct fish migration paths, disrupt river ecosystems, and displace people. A study published in the journal water says that by 2050 one in five dams will be in high flood risk areas rather than 1 in 25 dams which is the current rate. Also, 61% of all global hydropower dams will be in basins with very high or extreme risk for droughts, floods, or both. Dams block fish from swimming upstream which is crucial to their survival. Swimming upstream is a part of a fish’s reproductive cycle. If they can’t swim upstream they can’t reproduce. Hydroelectric dams block the annual flow of nutrients and sediments, this causes water quality concerns for the health of humans and animals. About 80 million people worldwide have been displaced by dam projects. Many of these people end up impoverished and marginalized. These are long lasting effects.
Evolution -
In 1882 the first power plant started operation in Appleton, Wisconsin. The first hydroelectric plant opened in San Bernardino, California 1887. In 1907 hydroelectricity was 15% of electrical generation in the United States. In 1920 it accounted for 25%, by 1980 hydropower capacity tripled compared with 1920. During the great depression in 1931, construction of the Hoover dam began employing nearly 20,000 people. By 1937 the Hoover Dam began generation. 1941 - 1945 the Bureau of Reclaims produced enough electricity to make 69,000 airplanes and 5,000 ships and tanks. Now there is a vast improvement in hydropower potential, through new technologies including pumped storage, modernization of existing plants, adding generation to existing non-powered dams, marine and hydrokinetic projects.
Why Switch? -
Green energy is needed now more than ever. With climate change on the rise, it is becoming more and more clear that humanity needs to switch to renewable energy sources. The way that we currently obtain the majority of our energy in the United states is by mining mountains for coal and breaking up the earth to drill for oil. This is highly damaging to the environment. Hydroelectricity is less damaging, while there is risk of increasing floods, there are teams of people who do risk assessments. Making it less likely to have a high flood risk. The same thing goes for fish migration, as well as the development of tunnels so as to allow them to swim upstream and continue their reproductive cycle. As for the displacement of people, the positives for the environment would be this way. Hydroelectricity would highly improve pollution and create an overall healthier world.
Hydro power is a term used to describe the collection or development of electricity through water’s gravitational and kinetic force.
What is it? -
Hydroelectric plants are usually placed in dams where they can be most efficient. It all starts with a gate that controls a consistent flow of water through a penstock. A penstock is a tube that leads from the dams reservoir into the section filled with turbines. This flow of water begins spinning turbines that are connected to generators. These generators contain an electro magnet and coils of copper. When the water pushes against the turbine the resistance allows the turbine to spin the electromagnet inside of the generator developing electricity this process is referred to as mechanical energy. The energy is transferred into a transformer where it is then kept or sent out.
Merits -
Hydroelectricity would allow each state to use their own energy rather than relying on international fuel sources. It would create jobs in rural areas and boost local economies. In the United States alone, Hydroelectricity will create around 66,500 stable jobs. Hydroelectricity will provide flood control, irrigation support, clean drinking water, and renewable energy. Hydropower plants will be able to have quick reactions to changes in demand. It has affordable construction and maintenance. Hydropower collaborates well with other renewable energy. Such as the pumped storage, which involves shifting water between to pools, allowing for less construction, pairs well with wind and solar energy during high demand. Hydropower education programs can be found nationwide for anyone interested in getting a job with this business.
Demerits -
Dams from hydroelectricity can cause flood risk, obstruct fish migration paths, disrupt river ecosystems, and displace people. A study published in the journal water says that by 2050 one in five dams will be in high flood risk areas rather than 1 in 25 dams which is the current rate. Also, 61% of all global hydropower dams will be in basins with very high or extreme risk for droughts, floods, or both. Dams block fish from swimming upstream which is crucial to their survival. Swimming upstream is a part of a fish’s reproductive cycle. If they can’t swim upstream they can’t reproduce. Hydroelectric dams block the annual flow of nutrients and sediments, this causes water quality concerns for the health of humans and animals. About 80 million people worldwide have been displaced by dam projects. Many of these people end up impoverished and marginalized. These are long lasting effects.
Evolution -
In 1882 the first power plant started operation in Appleton, Wisconsin. The first hydroelectric plant opened in San Bernardino, California 1887. In 1907 hydroelectricity was 15% of electrical generation in the United States. In 1920 it accounted for 25%, by 1980 hydropower capacity tripled compared with 1920. During the great depression in 1931, construction of the Hoover dam began employing nearly 20,000 people. By 1937 the Hoover Dam began generation. 1941 - 1945 the Bureau of Reclaims produced enough electricity to make 69,000 airplanes and 5,000 ships and tanks. Now there is a vast improvement in hydropower potential, through new technologies including pumped storage, modernization of existing plants, adding generation to existing non-powered dams, marine and hydrokinetic projects.
Why Switch? -
Green energy is needed now more than ever. With climate change on the rise, it is becoming more and more clear that humanity needs to switch to renewable energy sources. The way that we currently obtain the majority of our energy in the United states is by mining mountains for coal and breaking up the earth to drill for oil. This is highly damaging to the environment. Hydroelectricity is less damaging, while there is risk of increasing floods, there are teams of people who do risk assessments. Making it less likely to have a high flood risk. The same thing goes for fish migration, as well as the development of tunnels so as to allow them to swim upstream and continue their reproductive cycle. As for the displacement of people, the positives for the environment would be this way. Hydroelectricity would highly improve pollution and create an overall healthier world.
Reflection
Alyssa Dempsie
Ande
Energy Project Reflection
Tuesday May 16 2023
One takeaway I have from the energy project in math is the Ohm’s law triangle. This can be seen in my confidence in my ability to solve problems involving the triangle. If I were to have a problem in which I need this triangle, I feel very confident in my ability to solve it using the triangle. This proves I took this away due to the fact that I rarely remember things I am taught after a unit. Much less am I able to solve a problem using what I’ve been taught after. Just as I am confident in my ability to use the Ohms law triangle, I am confident in my participation with my Energy Museum group.
During the Energy Museum, I built a water wheel and helped my partner with our poster. We came up with the idea of lighting a light bulb with a water wheel. I said I could figure that out, so I started researching designs and asking my partner’s opinion throughout the decision process. When I finally settled on a design, I got to work making a materials list. Then I asked my partner what I could help with. They said I could write some paragraphs for our poster. So I worked on that. Then the next day, when one of the materials I requested became unavailable, I found a different material that could be used. On the last day, I finished the water wheel early and helped my partner with the poster. I feel as though I participated just the right amount in this project.
Ande
Energy Project Reflection
Tuesday May 16 2023
One takeaway I have from the energy project in math is the Ohm’s law triangle. This can be seen in my confidence in my ability to solve problems involving the triangle. If I were to have a problem in which I need this triangle, I feel very confident in my ability to solve it using the triangle. This proves I took this away due to the fact that I rarely remember things I am taught after a unit. Much less am I able to solve a problem using what I’ve been taught after. Just as I am confident in my ability to use the Ohms law triangle, I am confident in my participation with my Energy Museum group.
During the Energy Museum, I built a water wheel and helped my partner with our poster. We came up with the idea of lighting a light bulb with a water wheel. I said I could figure that out, so I started researching designs and asking my partner’s opinion throughout the decision process. When I finally settled on a design, I got to work making a materials list. Then I asked my partner what I could help with. They said I could write some paragraphs for our poster. So I worked on that. Then the next day, when one of the materials I requested became unavailable, I found a different material that could be used. On the last day, I finished the water wheel early and helped my partner with the poster. I feel as though I participated just the right amount in this project.