Math POW 1
Problem Statement
You have to figure out how many eggs there are.
The answer you come up with has to be divisible by 7.
The last digit has to be 1.
If you round it down to the nearest 10th, It has to be divisible by 2,3,4,5, and 6.
Process
I went through all the multiples of 7 and got into the hundreds. I discovered patterns, like the only solutions I got that worked for the rule ended in 1, and they weren’t frequent.
It took about 5-6 minutes to refine my thinking process on how to make sure the solution I found was correct. I used a lot of ‘process of elimination’.
I only found this out right after I presented, but theres a pattern: a correct solution would only occur every 420 numbers.
The difference between 721 and 301 is 420.
Add 420 to 721 and you get 1,141 and that fits the rule
Solution
I found alot of solutions including 301, 721, and 1,141.
If you take 301, round it to the nearest 10th, you get 300. If you divide 300 by 2,3,4,5, and 6, it’ll fit the rule.
I used the process of elimination to find 301 and 721, I found all the multiple of 7 and tested the ones that ended in the number 1.
Evaluation
I enjoyed working on the problem. It was challenging at first but once you’ve understood it, and figured it all out, it’s satisfying.
Yes, I think it was educationally worthwhile. I forgot most of the things that they taught me in middle school because of summer vacation and whatnot. It was a good mental refresher.
And if everything above isn't satisfying proof that I did the "work"
You have to figure out how many eggs there are.
The answer you come up with has to be divisible by 7.
The last digit has to be 1.
If you round it down to the nearest 10th, It has to be divisible by 2,3,4,5, and 6.
Process
I went through all the multiples of 7 and got into the hundreds. I discovered patterns, like the only solutions I got that worked for the rule ended in 1, and they weren’t frequent.
It took about 5-6 minutes to refine my thinking process on how to make sure the solution I found was correct. I used a lot of ‘process of elimination’.
I only found this out right after I presented, but theres a pattern: a correct solution would only occur every 420 numbers.
The difference between 721 and 301 is 420.
Add 420 to 721 and you get 1,141 and that fits the rule
Solution
I found alot of solutions including 301, 721, and 1,141.
If you take 301, round it to the nearest 10th, you get 300. If you divide 300 by 2,3,4,5, and 6, it’ll fit the rule.
I used the process of elimination to find 301 and 721, I found all the multiple of 7 and tested the ones that ended in the number 1.
Evaluation
I enjoyed working on the problem. It was challenging at first but once you’ve understood it, and figured it all out, it’s satisfying.
Yes, I think it was educationally worthwhile. I forgot most of the things that they taught me in middle school because of summer vacation and whatnot. It was a good mental refresher.
And if everything above isn't satisfying proof that I did the "work"
Math POW 3
Problem Statement
As an alternative to the overland route taken by East-coast Americans during the mass migration to the west, some people sought passage by sea. This route, though longer, had proven to have some advantages over the more common wagon train transportation. There were also some disadvantages, but that’s not important.
A ship leaves the harbor of New York and heads for San Francisco. At the same time a similar ship leaves the port of San Francisco and sails for New York. The route has to take the ships all the way down south around South American continent to reach the other coast.
Each month a similar ship leaves the same ports at New York and San Francisco. The New York ships are a month apart, as are the San Franciscan ships.
If a ship leaves the port of New York in January, how many ships from San Francisco does it meet in the 6 month journey?
Process
I began the problem on a whiteboard in Jocelyn’s class. I drew a map of the North and South American continents. I then pin-pointed on the map the locations of New York city on the East Coast, and San Francisco on the West. I drew, as best I could, the sea-route the ships would take that connected the two cities.
Then I did some thinking. If it takes 6 months to complete the entire journey, then at the end of 3 months your ship would have to at about 50% completion of the journey. So I made a half-way marker on the sea-route I drew earlier and titled it “3 months”. I did this 4 more times, dividing the route into the months it would take and corresponding that with your location on the route. There were 5 points I marked in total, not counting your final destination which would be reached on month 6.
I put my finger on the New York marker. And another finger from my opposite hand on the San Francisco marker. And I moved both to their next marker in their journey. I tried to use my fingers as “ships” but that was just too time consuming, frustrating, and confusing.
So I thought of a solution. I tore the limbs of my dino chicken nuggets that I was eating, and each limb would be a ship. I had 12 limbs in total, since six ships would leave each harbor one month after the other. I then found my solution.
Solution
My solution was four ships. If you leave on a ship in January, and head for San Francisco, you will meet four ships from San Francisco that are heading to New York. The solution was very easy to find after I ripped my dino nuggets into pieces and used each piece to represent a ship. It was a waste of time trying to use my fingers because there was a lot of things to factor in and I don’t have an unlimited number of fingers that can stretch across my paper.
Evaluation
I thought that this problem made for a great POW. It gave me a lot of room to explore ideas and consider factors for the solution of the problem. The solution was made clear after a fair amount of effort and time, and it wasn’t impossible to find the solution in the end.
POW 7
Problem Statement
In this problem, theres a large group of ducks. Theres two types of ducks, a regular adult duck and a duckling. Each type has their own weight. When we combine two adult ducks with two ducklings, we get 14 kg. When we add another adult and duckling, we get 19 kg. How much do both types of duck weigh.
Process
First, I drew a visual representation of what the problem is telling me about the duck groups:
b b b s s (b s)
b= Big Ducks
s= Small Ducks
() = Ducks added later
Solution
So I took a few steps back, and tried the only other solution I had. I gave the big duck the number 4 and the small duck the number 1. I went through the numbers again and I came up with 19, the correct answer. I knew this was the correct answer because it was the only other possible combination of numbers you could assign the “Ducks Added Later” and still fit the rule.
Sir Arthur Conan Doyle once said, “Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth.”
Evaluation
I feel like this was a fairly easy problem. It didn’t prove to be time consuming, in fact I solved it within a number of minutes when I devoted my full attention to it. Overall, I liked the problem. Though it is simple, it made me think. I think this was a very successful problem. I believe in all mathematics, as long as you are able to think for yourself and find your own truth, then you are correct.
In this problem, theres a large group of ducks. Theres two types of ducks, a regular adult duck and a duckling. Each type has their own weight. When we combine two adult ducks with two ducklings, we get 14 kg. When we add another adult and duckling, we get 19 kg. How much do both types of duck weigh.
Process
First, I drew a visual representation of what the problem is telling me about the duck groups:
b b b s s (b s)
b= Big Ducks
s= Small Ducks
() = Ducks added later
Solution
So I took a few steps back, and tried the only other solution I had. I gave the big duck the number 4 and the small duck the number 1. I went through the numbers again and I came up with 19, the correct answer. I knew this was the correct answer because it was the only other possible combination of numbers you could assign the “Ducks Added Later” and still fit the rule.
Sir Arthur Conan Doyle once said, “Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth.”
Evaluation
I feel like this was a fairly easy problem. It didn’t prove to be time consuming, in fact I solved it within a number of minutes when I devoted my full attention to it. Overall, I liked the problem. Though it is simple, it made me think. I think this was a very successful problem. I believe in all mathematics, as long as you are able to think for yourself and find your own truth, then you are correct.