Kayla Cindric

Claim of Growth: In 10th grade Geometry I grew in the ability to take what I learned in class and previous math classes the tools, formulas, and equations to help solve problems in tests and projects.

 

Class and Instructional Unit: In 10th grade geometry, we were learning in the Lessons 5-6 how to use inverse sine, inverse tangent, and inverse cosine to find an angle in a triangle. We also learned when to use these “tools”. The purpose of learning these geometry tools is to be able to develop our knowledge of how they are used and to use them in our daily lives and solve many problems that these tools need to be used.

Specific Learning Endeavors: First, we were learning about what inverse sine, inverse tangent, and inverse cosine were and when they are used (Which is to find the angles and not the side lengths). I had to take this knowledge of how to use these terms in order to understand them better and to solve problems. Since we had already learned about sine, tangent, and cosine and how to use them, we knew the appropriate equation to help solve the missing component of the triangle.

Purpose, Process, and Products: We learned that the difference between the inverse and just the “non-inverse” trigonometry tools is that one is finding the missing side and the other is finding a certain angle. We practice using situations and problems in our textbooks to practice using these trigonometry tools until we got the hang of it. We finally took quizzes and tests to put our knowledge of how to use them to the test.

Geometry, itself, is very challenging for me. Math, in general, is not my most skilled subject. The most challenging part of learning these tools are using them. It was difficult to remember SOH-CAH-TOA (sine-opposite over hypotenuse, cosine-adjacent over hypotenuse, and tangent-opposite over adjacent.) I did not understand what tool I needed to use to find the angle or the side length. I would use the inverse of tan, but would put the hypotenuse over adjacent. I finally asked for help from my intervention specialist to help me remember how to use the tools correctly and she taught me SOH-CAH-TOA to remember, it helped a little bit until I would write SOA-COA-TOA. I practice a lot on certain problems to get me to memorize and finally I was able to remember the tools and how to use them.

 

 

Artifact: My artifact would be some of my key problem (problem below) because they involve using the inverse geometry to solve the angle(s) that we learned how to use in class. It shows that I did very well on them and now know how to use them. (Problem below)

 

In this artifact you see that I used the inverse tan to find an angle in a right triangle. And used that angle and the 90° to find the third angle. You can see how I got the answer for the angles. Before this unit, I would not even know how to even begin this question, but now, since I know how to do this and I can start it and finish it.

 

 

 

 

 

 

 

 

 

 

 

 

 

Since we already know the measurements of angle C and B(90°) all we have to add the two together and subtract that by 180 and you get 52.125°. We were able to find all sides and angles of this triangles using our toolkit.

 How Artifact Exhibits Growth: This artifacts shows growth because I had to take what I learned in this unit in Geometry class, truly understand it in order to solve this question and get it correct. In Algebra in 9th grade we learned how to use tan, but not sine or cosine, so I did not know how to start or solve this problem. But by the end of this unit, I learned and understood how to use tan, cosine, and sine. I was able to see a huge growth from even the beginning of the year and not knowing these things to now and knowing them.

 

 

Learning Endeavor/Artifact: Another Endeavor that also show this growth is creating my Genetic Counseling Report. In 10th grade Geometry and Biology, we completed a project in which we were given a patient with a disease (See Biology portfolio for more information on Biology portion). For the Geometry portion, we found the probabilities (how likely something is to occur/the outcomes’ likelihood) of two people’s genotypes and the what the possible genotypes of their future child (If they had the disease, did not have the disease, or was a carrier)

This artifact shows that we created a genetic counseling report by answering this question: “My spouse and I were like to have a child. What is the possibility of our child having the disease or not?” And then took what we know about each parent’s family history. For the husband, we knew that his sister and niece both has Cystic Fibrosis which means his parents must be carriers (Cc), so we created a Punnett square (A square divided into four sections that tell what the possible genotypes are) from his parent’s genotypes. We eliminated the husband having Cystic Fibrosis because he does not have the symptoms. We, then, came up with the probability of him being a carrier P(Maria’s husband is Cc)=2/3=0.6667 and not having the disease at all P(Maria’s husband is CC)=1/3=0.33. We, then, moved on to the wife. She knew nothing about her family history since she was adopted. So, we had to take the general population of Caucasians who had Cystic Fibrosis which was 1/3,300 and subtracted and calculated from that number and made a Punnett square. Since the wife did not have the symptoms, we eliminated the possibility of her having Cystic Fibrosis. We, then, we left with the possibilities of her being a carrier P(Maria is Cc)=0.034218  and not having the disease P(Maria is CC)=0.965782. Next, we created a tree diagram which started with the possible genotypes of the wife. From each of those branched were two more branches which were the husband’s genotype. From those two branches were four branches that were the possible genotypes of their child.

 

P(Child does not carry CF mutation)=0.655389.

P(Child has CF)=0.0057                   

P(Child does not have CF but is a carrier)=0.339011

 

In the end, we found out the possible genotypes for the wife, the husband, and their child.

 

The biggest challenge was that my group and I did not understand and did not know where to start or how to start finding the probabilities. It was challenging to find the possible genotypes when you don’t know the family history of one of the parents and therefore did not know if they were a carrier of the disease or just did not have the disease at all. It was a very difficult process to find that person’s possible genotypes. I overcame this challenge asking my peers for help. I soon found out that in order to find the person’s genotype, I had to use the general population of Caucasians who had the disease to calculate the possibilities of them not having the disease. One artifact is my genetic counseling report because it shows step by step process my group and I had to calculate through to find the possible genotypes of the parents’ and future child’s genotypes. It shows the Punnett squares and tree diagrams that at the beginning I did not know how to do, but at the end I did.

 

Artifacts Exhibit Growth: I am able to solve two peoples’ genotypes and their future child’s possible genotypes just by knowing their ethnicity and knowing the general population of that ethnic group having that disease. I don’t even have to know the genotypes of the parents’ parents. I also am better at making tree diagrams and creating a correct one. Before, I did not know how to start one or what I needed to include, but after I finished this project, I know what to include and how to start one now.