In this POW we had to try to get a camel to bring bananas that he is addicted to, to a market to sell and we had to see how many we could get to the market. I had a very hard time getting the bananas to the market, because when I thought that I got a certain amount to the market I realized that I didn’t account for the camel’s eating habits. This made me very angry and I choose to take a break on the problem for the rest of the day.
My process was I would draw out a line and label all the information that was given to me. For example I put down that the distance between the two places mini camel needed to go was 15 miles. I also labeled that he only had 45 bananas at the oasis. I noted in my head that he ate one every mile and that he could only carry 15 at a time. Then I just drew it out and I got the answers 8 for the mini camel, 300 for the normal camel, I named him Larry. Here is a chart of my answers.
mini camel camel
45 bananas to start 1000 bananas to start
8 bananas to the market 300 bananas to the market
I think that this problem helped with my skills of critical thinking and evaluating my perspective and work. I also needed to persevere though this problem because there were many times that I just thought of giving up and doing a half way decent job. I knew it needed to get done so I fought through and finished the POW.
For my extension I changed the number of bananas that the camel got, I gave him 500 more. I also added robbers every five miles, who steal five bananas. Bob is a camel that has 1500 bananas in his rocket ship. He has to get some to the market to sell. He eats one every mile and can only carry 15 at a time. Every five miles he gets robbed and gives them five bananas to stay safe. How many bananas can Bob get to the market.
My process was I would draw out a line and label all the information that was given to me. For example I put down that the distance between the two places mini camel needed to go was 15 miles. I also labeled that he only had 45 bananas at the oasis. I noted in my head that he ate one every mile and that he could only carry 15 at a time. Then I just drew it out and I got the answers 8 for the mini camel, 300 for the normal camel, I named him Larry. Here is a chart of my answers.
mini camel camel
45 bananas to start 1000 bananas to start
8 bananas to the market 300 bananas to the market
I think that this problem helped with my skills of critical thinking and evaluating my perspective and work. I also needed to persevere though this problem because there were many times that I just thought of giving up and doing a half way decent job. I knew it needed to get done so I fought through and finished the POW.
For my extension I changed the number of bananas that the camel got, I gave him 500 more. I also added robbers every five miles, who steal five bananas. Bob is a camel that has 1500 bananas in his rocket ship. He has to get some to the market to sell. He eats one every mile and can only carry 15 at a time. Every five miles he gets robbed and gives them five bananas to stay safe. How many bananas can Bob get to the market.
POW #9 CUBE
In this POW I had a hard time thinking about this in my head. I could see it as soon as I drew it on the paper, but not just in my head. To figure this pow out I had to draw many cubes on my paper and put the number on the different squares. I had fun trying to find the different sides and seeing what patterns there were. I really liked the new math equations we learned and how to portray them to reality. We had to find keep making the cube bigger, doing a 5 by 5 to a 6 by six to 7 by 7 and so on, until we could find a pattern and then we could figure out how to figure out a n by n cube. I also liked how we had to change the numbers in the equation all the time, I feel like this helped us with learning how to use this type of math in more of a real environment and not just in math class.
The solution to this POW is:
CUBE 3 SIDED 2 SIDE 1 SIDE
3x3 8 12 6
4x4 8 24 24
5x5 8 36 54
NxN 8 2(n-2) 6(n-2)2
This table shows the different outcomes that you get when you have different sizes of cubes. As you can see in the table, it shows that no matter what size the cube is the three mini blocks that make up the whole, or the N blocks that make up the whole there will always be eight three sided blocks. This is because if you count all the corners on any cube no matter how big or small there is eight corners.. I also thought that the formula that I came up with to show how to figure out the different sides of N was very interesting. So for the solution you can see that to find N’s sides you have to use the formulas 2(n-2) and 6(n-2)2.
My extention for this POW is: What if your cube had one mini cube sticking out of the center on each side but each time you made the cube bigger you have to add one mini block sticking out.
I really liked this POW, I liked the fact that it made me think. I find it so fascinating that you can have a problem and once you find it out you can come up with a solution and a formula, maybe after a few problems, that can help you figure out any number or quantity in its place.
The solution to this POW is:
CUBE 3 SIDED 2 SIDE 1 SIDE
3x3 8 12 6
4x4 8 24 24
5x5 8 36 54
NxN 8 2(n-2) 6(n-2)2
This table shows the different outcomes that you get when you have different sizes of cubes. As you can see in the table, it shows that no matter what size the cube is the three mini blocks that make up the whole, or the N blocks that make up the whole there will always be eight three sided blocks. This is because if you count all the corners on any cube no matter how big or small there is eight corners.. I also thought that the formula that I came up with to show how to figure out the different sides of N was very interesting. So for the solution you can see that to find N’s sides you have to use the formulas 2(n-2) and 6(n-2)2.
My extention for this POW is: What if your cube had one mini cube sticking out of the center on each side but each time you made the cube bigger you have to add one mini block sticking out.
I really liked this POW, I liked the fact that it made me think. I find it so fascinating that you can have a problem and once you find it out you can come up with a solution and a formula, maybe after a few problems, that can help you figure out any number or quantity in its place.
Process:
In this POW I had to draw different scales with different outcomes. I was doing his to get a visual of what I was doing. I had to put a different amount of bags of coins on the scale to see which had the less coins, then you can figure out which bag has the less amount of coins. To start I put four bags on each side to equal the eight bags total. Then I would be able to see which side weighs less. Then you take the four bags on the one side that weighs less and split that into two bags each that go on either side. After this you can see which side rises and falls, then you will just take the two that are left and you will split that so that you can see which one will weigh less. And you will keep doing this process to find the answer.
Solution:
The answer to the problem is yes you can do this weighing and seeing who is taking the gold. You have to first you will pick three bags and put it on one side of the scale, then put three on the other side of the scale. You will have two left over. If the scale with three on each side is even you will just have to put the two that were left over on the scale and see which weighs less. If the the scale with three is uneven you will know that it the one that weighs less in in there you can take two bags and put one on each side of the scale. If the scale is even you will know that the uneven one is the one you left out. If it isn’t even you will know which out of the two is the one that has less. I figured this out by drawing out scales and seeing visually what would happen. Then I just kept trying different patterns and different numbers of bags on each side to see what would make it work and if you could even do one that was smaller than using the scale three times.
Extention:
What if there were 16 bags instead of eight. Could you find a way of making it less than four times using the scale? And then after that 32 bags, could you make it less than five times? Did you find a pattern?
Evaluation:
I think that this POW was pretty easy to complete and find the solution, but harder to explain than most of the POW’s in the past. It was hard for me to show you what was going on in my head. I think that in the past pows there has been math that once you got the answer you could understand the math that goes along with it, but in this one it was harder to tell you what I did. In this one I just used my head and guessed what I thought would work and then draw it out to see how it would work visually. Then I could tell if it would work in less than three tries or if I needed to change the “formula.” I really liked this pow and thought that it was a lot of fun to mess around with the numbers that were floating around in my head. I am also one of those people that can picture things in my head very well and I do a lot of mental math and a lot of things mentally in general. So in this pow I could use that to my advantage.
POW #7 ALICE STUCK IN TIME
Process
My process throughout this pow was I would start with the real time (12) next to the time in wonderland (12) then I would put the real time (1) and next to it I would put wonderland’s time, but with the time difference (1:30), if it were a thirty minute gain. so it ended up looking like this:
12 12
1 1 30
2 3
3 4 30
4 6
5 7 30
6 9
7 10 30
8 12
9 1 30
10 3
11 4 30
12 6 and so on and so forth...
Then you find out that it takes 24 hours to get back to real time. I found out in class that if you multiply twelve by the number of times the hour appears on a clock you will get your answer, for example:
30 minute gain = 24hrs
60 minute gain = 12 hours
10 = 72
7 = 102.857
3 = 240
5 = 144
20 = 36
This shows you that if you divide the number you are looking for (x) by 60 (which is a full hour/minute) then you will multiply that by twelve. In conclusion this pow was pretty easy just a lot of writing and lots of thinking, but overall it was pretty easy. I liked this POW and thought that it was relatively easy. I think that I learned that sometimes things are easier than they look and that if you step back and look at things outside of the box you might see a pattern and be able to figure out how to solve the problem easier and more efficient.
Extention
What if you had a 15 hour clock instead of a 12 hour clock to deal with.
Evaluation
I really liked this process and I really liked that it was one of the easier pows. I liked that I could just add an hour or half an hour, or whatever X was, to the time and keep doing this process until I got the answer. I also learned that sometimes things are easier than they look and that if you step back and look at things outside of the box you might see a pattern and be able to figure out how to solve the problem easier and more efficient. I really enjoyed working on this POW and I really liked finding the answer.
My process throughout this pow was I would start with the real time (12) next to the time in wonderland (12) then I would put the real time (1) and next to it I would put wonderland’s time, but with the time difference (1:30), if it were a thirty minute gain. so it ended up looking like this:
12 12
1 1 30
2 3
3 4 30
4 6
5 7 30
6 9
7 10 30
8 12
9 1 30
10 3
11 4 30
12 6 and so on and so forth...
Then you find out that it takes 24 hours to get back to real time. I found out in class that if you multiply twelve by the number of times the hour appears on a clock you will get your answer, for example:
30 minute gain = 24hrs
60 minute gain = 12 hours
10 = 72
7 = 102.857
3 = 240
5 = 144
20 = 36
This shows you that if you divide the number you are looking for (x) by 60 (which is a full hour/minute) then you will multiply that by twelve. In conclusion this pow was pretty easy just a lot of writing and lots of thinking, but overall it was pretty easy. I liked this POW and thought that it was relatively easy. I think that I learned that sometimes things are easier than they look and that if you step back and look at things outside of the box you might see a pattern and be able to figure out how to solve the problem easier and more efficient.
Extention
What if you had a 15 hour clock instead of a 12 hour clock to deal with.
Evaluation
I really liked this process and I really liked that it was one of the easier pows. I liked that I could just add an hour or half an hour, or whatever X was, to the time and keep doing this process until I got the answer. I also learned that sometimes things are easier than they look and that if you step back and look at things outside of the box you might see a pattern and be able to figure out how to solve the problem easier and more efficient. I really enjoyed working on this POW and I really liked finding the answer.