## Geometry Reflection's:

Reflections

Teddy Rodd

12/10/2015

40 points: Describe one topic you feel you have mastered this semester. Describe the activities that helped you learn this activity (show 1-2 pieces of evidence). How do you know you have mastered this skill (show 1-2 pieces of evidence)? You should reference 3-4 pieces of evidence for this answer. Your evidence should be annotated and described, not just pasted on your DP.

A topic I feel I have mastered this semester has been Pythagoras theorem which is a method in which to find the sides of a right angled triangle. And then from finding the sides of the triangle you can find other things like the area, perimeter, and the volume. All shapes are made up of triangles, so whenever you need to know the size of a shape just draw triangles inside the shape. Most of solving a math problem is knowing how to set it up in the easiest way to solve the problem.

10 points: How have the Explorations (and group discussions of Explorations) changed your experience as a math student this year? In what ways have they made math class more challenging, and in what ways have the Explorations and discussions helped you learn?

The explorations have been very helpful this year for understanding the topics we have been studying. It takes the math and puts it into more real life problems like distances from one place to another or finding costs and values of certain items. The reason why this is so helpful is because when you get taught this new kind of math in a more memorable way it will stick in your head much longer. You can think to yourself about the time you did a problem about finding the distance of biking home from school. And once you remember that you will probably remember how you found it, so you will always be able to do that kind of math.

Choose one of the two questions below (10 points):

30 points: Which Habit of a Mathematician do you feel you have the most mastery over? Explain what this skill is and what it means to you. Explain how you have demonstrated this skill, the activities that helped you develop this skill, and how you have grown in that problem-solving skill this semester. You should reference 2-3 pieces of evidence for this answer. Your evidence should be annotated and described, not just pasted on your DP.

The habit of a mathematician I have used the most this year has been generating Ideas and reflecting on all of the work that I do. When we get an assignment or project I am very quick to start working on it, and thinking of new ideas. Once I get my work done I do a good job on reflecting on how I got there and how I know I am right. The place where these two skills are seen the most is in our weekly POWS, usually seen in the process and the justification.

10 points: For which Habits) do you feel you have the most room to stretch? What do you think held you back from improving in this skill this semester?

One habit of a mathematician that I struggle with the most is recognizing and resolving errors in my work. It is really hard when I get really existed on a problem and think that I got the answer right only to find out I was wrong. Once this happens it is really hard to start over and try to find the answer again. The work were this is seen the most if the explorations they are like many POWS and take a lot of thought to solve.

Teddy Rodd

12/10/2015

40 points: Describe one topic you feel you have mastered this semester. Describe the activities that helped you learn this activity (show 1-2 pieces of evidence). How do you know you have mastered this skill (show 1-2 pieces of evidence)? You should reference 3-4 pieces of evidence for this answer. Your evidence should be annotated and described, not just pasted on your DP.

A topic I feel I have mastered this semester has been Pythagoras theorem which is a method in which to find the sides of a right angled triangle. And then from finding the sides of the triangle you can find other things like the area, perimeter, and the volume. All shapes are made up of triangles, so whenever you need to know the size of a shape just draw triangles inside the shape. Most of solving a math problem is knowing how to set it up in the easiest way to solve the problem.

10 points: How have the Explorations (and group discussions of Explorations) changed your experience as a math student this year? In what ways have they made math class more challenging, and in what ways have the Explorations and discussions helped you learn?

The explorations have been very helpful this year for understanding the topics we have been studying. It takes the math and puts it into more real life problems like distances from one place to another or finding costs and values of certain items. The reason why this is so helpful is because when you get taught this new kind of math in a more memorable way it will stick in your head much longer. You can think to yourself about the time you did a problem about finding the distance of biking home from school. And once you remember that you will probably remember how you found it, so you will always be able to do that kind of math.

Choose one of the two questions below (10 points):

**Describe a moment when you had a breakthrough in understanding a challenging concept. What nurtured your breakthrough? How did this empower you in moving forward? What did you learn from that experience?**

30 points: Which Habit of a Mathematician do you feel you have the most mastery over? Explain what this skill is and what it means to you. Explain how you have demonstrated this skill, the activities that helped you develop this skill, and how you have grown in that problem-solving skill this semester. You should reference 2-3 pieces of evidence for this answer. Your evidence should be annotated and described, not just pasted on your DP.

The habit of a mathematician I have used the most this year has been generating Ideas and reflecting on all of the work that I do. When we get an assignment or project I am very quick to start working on it, and thinking of new ideas. Once I get my work done I do a good job on reflecting on how I got there and how I know I am right. The place where these two skills are seen the most is in our weekly POWS, usually seen in the process and the justification.

10 points: For which Habits) do you feel you have the most room to stretch? What do you think held you back from improving in this skill this semester?

One habit of a mathematician that I struggle with the most is recognizing and resolving errors in my work. It is really hard when I get really existed on a problem and think that I got the answer right only to find out I was wrong. Once this happens it is really hard to start over and try to find the answer again. The work were this is seen the most if the explorations they are like many POWS and take a lot of thought to solve.

## POWS 10th grade:

Problem of the Week 1

POW Writeup due 9/15

Teddy Rodd

Understanding:

In this Pow there is a person named Delilah who wants to fill in her rectangular garden beds with flowers. The size of the beds is shown in the picture below. She wants to put one flower in every square foot of space. Daisies cost one dollar. Begonias cost one dollar and fifty cents. Cannas cost two dollars. Roses cost two dollars and fifty cents each. Cattleya Orchids cost three dollars. What is the lowest amount of money to pay for the flowers in her garden in dollars.

Process:

The first step that I took in solving the Pow was adding up all the numbers along the sides so that I could accurately find the area of the boxes inside the box. The proportion of the box once everything was added up was a width of eleven and a height of six. To save money I knew that I had to buy more of the cheap plants and less of the expensive ones. So I put the most expensive plants in the smallest section of the garden, and the least expensive in larger sections. The way I determined the size of all the boxes was I multiplied the base times the height. The box in the middle I had discovered that it was a two by two box. To find out how much it would cost to populate all of the section with each of the specific kinds of plants I got the area and multiplied it by the cost of the plants. After I got the cost it would take to file each of the individual beds I added those costs together to get the total cost.

Solution:

The least amount of money it would take for Delilah to fill her garden beds is one hundred and eight dollars.

Daisies cost: 21$

Begonias cost: 30$

Cannas cost: 30$

Roses cost: 15$

Cattleya Orchids cost: 12$

Total cost of everything: 108$

Justification:

Compared to The Pows the I did last year this is one of my new favorites, although I think that the Pows in the future should be a little more difficult because I solved this one really fast. If there is any way to make the garden without spending more than one hundred and eight dollars the answer still eludes me. Therefore I must conclude that my answer is correct, I have gone over it many times over and over again and I do not see any flaws in my math.

POW Writeup due 9/15

Teddy Rodd

Understanding:

In this Pow there is a person named Delilah who wants to fill in her rectangular garden beds with flowers. The size of the beds is shown in the picture below. She wants to put one flower in every square foot of space. Daisies cost one dollar. Begonias cost one dollar and fifty cents. Cannas cost two dollars. Roses cost two dollars and fifty cents each. Cattleya Orchids cost three dollars. What is the lowest amount of money to pay for the flowers in her garden in dollars.

Process:

The first step that I took in solving the Pow was adding up all the numbers along the sides so that I could accurately find the area of the boxes inside the box. The proportion of the box once everything was added up was a width of eleven and a height of six. To save money I knew that I had to buy more of the cheap plants and less of the expensive ones. So I put the most expensive plants in the smallest section of the garden, and the least expensive in larger sections. The way I determined the size of all the boxes was I multiplied the base times the height. The box in the middle I had discovered that it was a two by two box. To find out how much it would cost to populate all of the section with each of the specific kinds of plants I got the area and multiplied it by the cost of the plants. After I got the cost it would take to file each of the individual beds I added those costs together to get the total cost.

Solution:

The least amount of money it would take for Delilah to fill her garden beds is one hundred and eight dollars.

Daisies cost: 21$

Begonias cost: 30$

Cannas cost: 30$

Roses cost: 15$

Cattleya Orchids cost: 12$

Total cost of everything: 108$

Justification:

Compared to The Pows the I did last year this is one of my new favorites, although I think that the Pows in the future should be a little more difficult because I solved this one really fast. If there is any way to make the garden without spending more than one hundred and eight dollars the answer still eludes me. Therefore I must conclude that my answer is correct, I have gone over it many times over and over again and I do not see any flaws in my math.

Problem of the Week 3

Due Friday, October 2

A large tent is being set up for a fair. Two poles, QU and RT, are placed perpendicular to the ground and 12 m apart. Pole QU is 4 m in length and pole RT is 7.5 m in length. A tarp is placed over the poles and secured to the ground at P, 3 m from the base of pole QU, and S, 4 m from the base of pole RT. Determine P Q + QR + RS, the length of the tarp.

Understanding: Find the length of the tarp. QU and RT are parallel to each other and perpendicular to the ground. RT is is 7.5 meters long, QU is 4 meters in length. PU is 3 meters in length, TS is 4 meters in length. Use PQ, QR,RS to find the total length of tarp.

Process: I started by finding the length of PQ, and RS. I found them by using the pythagorean theorem A squared plus B squared equals C squared. Then if QU is 4 meters then the upper part of RT is 3.5 meters long. So then I do pythagoreans theorem again with 12 and 3.5 this time which gives me 12.5 meters for QR. Once dose I added PQ, QR, RS together to get the answer.

Solution: The answer is the tarp is a total of 26 meters long.

Justification: This one took a while for me to solve this has been the hardest problem that we have done so far. In this problem you had to make triangles inside of the shape so you could find the answer. I know that I am correct because I followed all the rules of math, I did not use the wrong equations.

Due Friday, October 2

A large tent is being set up for a fair. Two poles, QU and RT, are placed perpendicular to the ground and 12 m apart. Pole QU is 4 m in length and pole RT is 7.5 m in length. A tarp is placed over the poles and secured to the ground at P, 3 m from the base of pole QU, and S, 4 m from the base of pole RT. Determine P Q + QR + RS, the length of the tarp.

Understanding: Find the length of the tarp. QU and RT are parallel to each other and perpendicular to the ground. RT is is 7.5 meters long, QU is 4 meters in length. PU is 3 meters in length, TS is 4 meters in length. Use PQ, QR,RS to find the total length of tarp.

Process: I started by finding the length of PQ, and RS. I found them by using the pythagorean theorem A squared plus B squared equals C squared. Then if QU is 4 meters then the upper part of RT is 3.5 meters long. So then I do pythagoreans theorem again with 12 and 3.5 this time which gives me 12.5 meters for QR. Once dose I added PQ, QR, RS together to get the answer.

Solution: The answer is the tarp is a total of 26 meters long.

Justification: This one took a while for me to solve this has been the hardest problem that we have done so far. In this problem you had to make triangles inside of the shape so you could find the answer. I know that I am correct because I followed all the rules of math, I did not use the wrong equations.

**Economical**King:

Process: In this POW the king wanted to find out who of his “trusted” treasure guardians stoll the kings eight bags of gold. So to find out who took his gold he weighed each of the bags of gold to see which one was lighter.

Solution: The method that I used to see who the thief was I put six bags on the pan scale out of the eight bags. If the two side stay even that means that the two bags that were not weighed at all are the ones. Then you weigh those two and whichever one goes up is the lighter bag of gold. Next if one side goes up that means that one of those three are the culprits. Then you put two of those three on the scale and if they stay even it means that the one on the ground is the lighter, but if one side goes up that means that one is the lighter one.

Extension: The kings farmer noticed that the weight of the shipment of wheat have been slowly decreasing to figure out who was to blame he visited each of the kings twelve warehouses and had them measure the hay in each one on a bathroom scale. Who committed this most terrible crime towards the kingdom?

Evaluation: Out of all the POWS that we have done so far I solved this one the fastest. For about twenty minutes I was staring at the page with zero idea of how I could weigh all eight of them in less the three tries. But the moment that I considered I could just way the six all the puzzle pieces popped into place. This POW did not teach me any new content but It definitely made my mind stretch in a lot of new ways. This POW does not need any changing it is already a very interesting and enjoyable problem. This one I thought was a little bit too easy, I solved it in less than half the time it usually takes me.