Thinkers
Being a critical thinker is one of the most important characteristics of an IB student. The piece of work that I chose to represent this characteristic is a math investigation based on quadratic equations and investigating patterns “Crosses” in the unit “Off the Straight and Narrow”. The target of this investigation is to investigate the rules of what happens to the value of numbers within the cross placed on a one to one-hundred grid. Hence, this assessment is marked against Criterion B: Investigating Patterns.
I chose a math investigation to represent myself as a thinker as I was able to learn from previous mistakes and improve my skills in this investigation. I think that this piece of work reflected that I am a thinker as I investigated the relationship within each change. By doing so, I had to look at each change to think carefully and recognize the relations between each change. I also had to consider different possibilities of algebraic equations that represented the change. As I had come to a clear and correct solution, it shows that I have been a critical thinker within this assessment. I am a thinker as I thought diligently about how I can clearly present and justify my results to the marker. Within this assessment, I showed good organization and application skills as I clearly presented my results in tables and diagrams. Again being organized shows that I have clearly thought of the best way to present my work clearly.
In this math investigation, I began by investigating what happens to the total value of the three specific equations, given the varied numbers in the cross, depending on where it is placed. Next, I placed my results for three different experiments into a clear table, listing out the middle number, as well as the total sum of the three equations for each test.This has helped me to predict the quadratic equations that represented the pattern displayed in the results. Furthermore, I justified my predictions by explaining why my method works, and justified my equations with other numbers and the term x. I repeated the steps above for a different sized cross to identify a general rule for crosses of all sizes. As I wrote a small explanation for each shape, hence, I did not write a conclusion for this investigation. This investigation clearly shows every stage my thinking process that has resulted in my final conclusion.
I feel that this piece of work was done well as I now have a better understanding of the structure of math investigations. I demonstrated good thinking, organization and application skills within this assessment. I think that this assessment still lacked a further justification of the equation with different sized crosses due to the lack of time. If I have a chance to do this investigation again, I would manage my time better. Another aspect that I will improve in further investigations is to select numbers in sequence during different tests to better identify a pattern instead of selecting random numbers.
I chose a math investigation to represent myself as a thinker as I was able to learn from previous mistakes and improve my skills in this investigation. I think that this piece of work reflected that I am a thinker as I investigated the relationship within each change. By doing so, I had to look at each change to think carefully and recognize the relations between each change. I also had to consider different possibilities of algebraic equations that represented the change. As I had come to a clear and correct solution, it shows that I have been a critical thinker within this assessment. I am a thinker as I thought diligently about how I can clearly present and justify my results to the marker. Within this assessment, I showed good organization and application skills as I clearly presented my results in tables and diagrams. Again being organized shows that I have clearly thought of the best way to present my work clearly.
In this math investigation, I began by investigating what happens to the total value of the three specific equations, given the varied numbers in the cross, depending on where it is placed. Next, I placed my results for three different experiments into a clear table, listing out the middle number, as well as the total sum of the three equations for each test.This has helped me to predict the quadratic equations that represented the pattern displayed in the results. Furthermore, I justified my predictions by explaining why my method works, and justified my equations with other numbers and the term x. I repeated the steps above for a different sized cross to identify a general rule for crosses of all sizes. As I wrote a small explanation for each shape, hence, I did not write a conclusion for this investigation. This investigation clearly shows every stage my thinking process that has resulted in my final conclusion.
I feel that this piece of work was done well as I now have a better understanding of the structure of math investigations. I demonstrated good thinking, organization and application skills within this assessment. I think that this assessment still lacked a further justification of the equation with different sized crosses due to the lack of time. If I have a chance to do this investigation again, I would manage my time better. Another aspect that I will improve in further investigations is to select numbers in sequence during different tests to better identify a pattern instead of selecting random numbers.
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