10th grade math
Problem statement
For the past two weeks, the majority if not all of class time was spent working on desmos. Throughout those two weeks we learned about TRANSFORMING parabolas. Moving them up and down and right and making them skinnier and making them wider... All of that good stuff.
Basketball problem
On our first day of desmos, we transformed parabolas through points to determine whether some dude who was shooting a basketball would make the ball inside the basket. We had no knowledge on parabolas and the problem didn't require any evaluation on any equations.
Polygraph one
The goal of this problem was to partner up with another person via computer and guess what parabola the person chose on the computer. Using the vocabulary that I learned in the previous activity, I had to guide the other person to choose the parabola that I chose.
Polygraph two
On the third day we learned how to sketch a parabola and gained an even better understanding of the vocabulary. We had to use those two skills to follow the instructions given and draw a proper parabola.
match my parabola
In this activity we had to create the parabola so it would touch all of the dots. This was a interesting activity because had to figure out what the equation was. In the beginning it was kind of difficult but once you did a couple of them it got easier.
marble slide
So what we worked on in this was that we had to great the parabola in a certain shape so when you dropped the ball it would touch all the stars.
what i learned
What did I learn during this time when we worked on this, well good question. Of course I learned plenty things but below this I will be stating the top three things that I felt I really helped me during this course.
3. How to a parabola equation from y=a( x + h )^2 -8 knowing that a determines width
- The vocabulary, I learned all these new terms that would help me explain the parabola better, especially when it came to having to find out what parabola your partner had chosen in the polygraph one activity. Examples of these terms would be
- Concave up (When it looks like a smiley face)
- Concave down (When it looks like a sad face)
- Vertex(The turning point)
- X Intercept(When it touches the x axis twice)
- Line of symmetry ( When it's symmetric across the y axis)
3. How to a parabola equation from y=a( x + h )^2 -8 knowing that a determines width
- A=Width and if a>0 its bigger and if a<0 it's slimmer.
- H=left to right so if it's h>0 it's to the left and if it's h<0 it's to the right
- K= height or you can say up and down
- If a>0, the parabola is concave up. If 0<a<1, then the parabola gets wider
peer critique
Ernesto
I was very thurough with my reasoning and explained my ideas very clearly. I needed to fix a couple of things in the "What I learned" section. There were errors such as incorrect annotation and mistakes that involved the content.
Jacob
I showed my work with evidence and the viewers are able to understand what points I'm trying to show them. I can get across ideas and interpretations with the audience grasping the concepts with little to no difficulty.
Probability
Problem Statement
Would you gamble your extra credit point for a chance at $20? That was basically our teachers way of starting the unit, we got to play the lottery; picking 5 numbers between 1-47 and a mega number between 1-27. The first 5 I had chosen were 14, 43, 5, 32, and 17. The mega number I chose was 22! We also had to make a guess of what we thought the odds were of winning the lottery. At the end of the unit we actually calculated the probability of winning; which I will display soon after.
Process and Solution
When we started the unit we got asked the question of what we thought the odds of winning the lottery were. I responded with 1 in 1.5 million; which was way off.
Conbinations & Probability
The number 4,969,962,360 is the total number of possible combinations there are, and the 120 above is the chances of winning. When my group and I first started trying to calculate the sample space/number of total outcomes we added all the denominators together, after looking back at our notes from a worksheet we had done previously during the unit (Mr. B's Closet) we realized you actually multiply both the numerator and denominator. After doing this we got the probability of winning the lottery which is 120/4,969,962,360 which is equal to 1/41,416,353. My original guess was 1/1,500,000; I was 39,916,353 numbers off, good job Ivanna!
Expected Value
This is an image of the work my group and I did to figure out the expected value for spending 1 on a lottery ticket. First you plug in the payout multiplied by the probability of winning, after that you add it to the amount of money you will spend multiplied by the probability of losing. I learned how to do this from a worksheet called expected value.
Problem Evaluation
I really like the way this class is structured, in the sense that we get a problem and then learn all the necessary skills to solve it at the end of the unit. I personally thought that this was a short problem, and that we could've been more challenged after all the work in the unit.
Self Evaluation
I don't know that I did all that good in this unit so if we were grading on correction I would probably get a B, but if we grading upon completion and effort then I deserve an A. I worked very well with my group and asked questions when I was confused. I had made one of my goals last semester to work hard and not get off task, This semester I did complete that goal. On the other hand I had also made a goal to meet with Mr. Carter once a week for tutoring which I didn't, that was beacause I felt I had a good grasp on what we were learning.
Edits
• Add more to self evaluation
• Add something about groupwork
• Format for less confusion
• Take off smiley face
Height of the flagpole
Problem StatementFind the height of the HTHCV flagpole. Why? Mr. Tim wants a new flag, but there are regulations on the size of the flag you can have based on the flagpoles height.Process & SolutionMy initial guess for the flagpoles height was between 29-34 ft. That was after we went outside and looked at it. I compared the height of the flag pole to my height to see how many of me it would take to make the flagpole. Throughout learning similarity we learned about different methods to estimate the height of the flagpole. We used the shadow method, mirror method, and clinometer method. By definition similarity is when the only difference between the 2 shapes is size. That means the corresponding angles must be the same, and the corresponding sides must be proportional.
Average Height x
--------------- = -----------------
Average Shadow Flag Pole Shadow
Once we had the proportion set up we were able to plug in the numbers, and cross multiply to get the estimated height of the flag pole.
66 x 65x 22,506
--- = ---- 65x = 66 x 341 ----- = ------- x=356 in.
65 341 65 65
Mirror MethodIn the mirror method you also use the angle angle theorem to prove similarity between the triangles. The two triangles meet at one point, where the mirror reflects. The angle coming off the mirror id the same on both sides. The other angle we use for the angle angle theorem is the right angle on both triangles. In order to find the height of the flagpole we had to find our height (P), our distance from the mirror (X), and the distance from the mirror to the flagpole (M), in order to find the height of the flagpole (H). The proportion we had set up was
P M 62 M
-- = --- Then we plugged ----- = ----
X H in the numbers 31 207
Then we proceeded to cross multiplying and got the height of the flagpole as M=34.5 ft.Clinometer MethodIn the clinometer method we used an isosceles triangle because by definition they have 2 equal angles meaning they have 2 equal sides. Therefore by knowing the length of one of the lines making up the right angle we would be able to estimate the height of the flag pole. We used the clinometer to make one of the angles 45 and the 90 degree angle made by the flagpole. We then added the distance from the base to your feet and your feet to your eyes. 341+60= 401 in. which is 33 ft. Because an isosceles triangle has 2 equal sides we made an assumption that the flag pole is about 33 ft, tall.Final EstimationMy final estimation because from all the data we collected is 30 ft. That is a very close estimation based on the mean of all the a groups estimates.Problem EvaluationSelf Evaluation
I enjoyed this problem very much. It wasn't the hardest but I enjoyed how many different methods we tried to find the height. I enjoyed learning all the topics, and felt that my group really pushed my thinking. The explaining of the methods and the problem itself gave me a new way of looking at math. Right below we can see my math group and I.If I were to grade myself on this similarity unit I would give me an A. This is because I felt that my thinking was pushed and I did work hard with my group not only to get the right answer but to understand. The evidence I have chosen to showcase is my powerschool; this shows that I do get my work done on time, and work with my group. I got an A on my unit test because I do feel that I understand the topic all around.
Edits- Add a picture of the flagpole
- Explain how your test score reflects the learning you did
- Spelling and grammatical errors
- Picture of your grades
Probability
Problem Statement
Would you gamble your extra credit point for a chance at $20? That was basically our teachers way of starting the unit, we got to play the lottery; picking 5 numbers between 1-47 and a mega number between 1-27. The first 5 I had chosen were 14, 43, 5, 32, and 17. The mega number I chose was 22! We also had to make a guess of what we thought the odds were of winning the lottery. At the end of the unit we actually calculated the probability of winning; which I will display soon after.
Process and Solution
When we started the unit we got asked the question of what we thought the odds of winning the lottery were. I responded with 1 in 1.5 million; which was way off.
Conbinations & Probability
The number 4,969,962,360 is the total number of possible combinations there are, and the 120 above is the chances of winning. When my group and I first started trying to calculate the sample space/number of total outcomes we added all the denominators together, after looking back at our notes from a worksheet we had done previously during the unit (Mr. B's Closet) we realized you actually multiply both the numerator and denominator. After doing this we got the probability of winning the lottery which is 120/4,969,962,360 which is equal to 1/41,416,353. My original guess was 1/1,500,000; I was 39,916,353 numbers off, good job Ivanna!
Expected Value
This is an image of the work my group and I did to figure out the expected value for spending 1 on a lottery ticket. First you plug in the payout multiplied by the probability of winning, after that you add it to the amount of money you will spend multiplied by the probability of losing. I learned how to do this from a worksheet called expected value.
Problem Evaluation
I really like the way this class is structured, in the sense that we get a problem and then learn all the necessary skills to solve it at the end of the unit. I personally thought that this was a short problem, and that we could've been more challenged after all the work in the unit.
Self Evaluation
I don't know that I did all that good in this unit so if we were grading on correction I would probably get a B, but if we grading upon completion and effort then I deserve an A. I worked very well with my group and asked questions when I was confused. I had made one of my goals last semester to work hard and not get off task, This semester I did complete that goal. On the other hand I had also made a goal to meet with Mr. Carter once a week for tutoring which I didn't, that was beacause I felt I had a good grasp on what we were learning.
Edits
• Add more to self evaluation
• Add something about groupwork
• Format for less confusion
• Take off smiley face
Height of the flagpole
Problem StatementFind the height of the HTHCV flagpole. Why? Mr. Tim wants a new flag, but there are regulations on the size of the flag you can have based on the flagpoles height.Process & SolutionMy initial guess for the flagpoles height was between 29-34 ft. That was after we went outside and looked at it. I compared the height of the flag pole to my height to see how many of me it would take to make the flagpole. Throughout learning similarity we learned about different methods to estimate the height of the flagpole. We used the shadow method, mirror method, and clinometer method. By definition similarity is when the only difference between the 2 shapes is size. That means the corresponding angles must be the same, and the corresponding sides must be proportional.
- My Initial Guess Before Taking Measurements: 29-34 ft.
- Estimation Using The Shadow Method: 29 ft.
- Estimation Using The Mirror Method: 35 ft.
- Estimation Using The Clinometer Method: 33 ft.
Average Height x
--------------- = -----------------
Average Shadow Flag Pole Shadow
Once we had the proportion set up we were able to plug in the numbers, and cross multiply to get the estimated height of the flag pole.
66 x 65x 22,506
--- = ---- 65x = 66 x 341 ----- = ------- x=356 in.
65 341 65 65
Mirror MethodIn the mirror method you also use the angle angle theorem to prove similarity between the triangles. The two triangles meet at one point, where the mirror reflects. The angle coming off the mirror id the same on both sides. The other angle we use for the angle angle theorem is the right angle on both triangles. In order to find the height of the flagpole we had to find our height (P), our distance from the mirror (X), and the distance from the mirror to the flagpole (M), in order to find the height of the flagpole (H). The proportion we had set up was
P M 62 M
-- = --- Then we plugged ----- = ----
X H in the numbers 31 207
Then we proceeded to cross multiplying and got the height of the flagpole as M=34.5 ft.Clinometer MethodIn the clinometer method we used an isosceles triangle because by definition they have 2 equal angles meaning they have 2 equal sides. Therefore by knowing the length of one of the lines making up the right angle we would be able to estimate the height of the flag pole. We used the clinometer to make one of the angles 45 and the 90 degree angle made by the flagpole. We then added the distance from the base to your feet and your feet to your eyes. 341+60= 401 in. which is 33 ft. Because an isosceles triangle has 2 equal sides we made an assumption that the flag pole is about 33 ft, tall.Final EstimationMy final estimation because from all the data we collected is 30 ft. That is a very close estimation based on the mean of all the a groups estimates.Problem EvaluationSelf Evaluation
I enjoyed this problem very much. It wasn't the hardest but I enjoyed how many different methods we tried to find the height. I enjoyed learning all the topics, and felt that my group really pushed my thinking. The explaining of the methods and the problem itself gave me a new way of looking at math. Right below we can see my math group and I.If I were to grade myself on this similarity unit I would give me an A. This is because I felt that my thinking was pushed and I did work hard with my group not only to get the right answer but to understand. The evidence I have chosen to showcase is my powerschool; this shows that I do get my work done on time, and work with my group. I got an A on my unit test because I do feel that I understand the topic all around.
Edits- Add a picture of the flagpole
- Explain how your test score reflects the learning you did
- Spelling and grammatical errors
- Picture of your grades