Math
Toothpick Squares Open-Ended Problem Reflection
Problem Statement
In the Toothpick Squares Open-Ended problem, we are trying to find how many toothpicks are in the 100th pattern. In the first square pattern there is four toothpicks, the second square pattern has twelve toothpicks, and the third square pattern has twenty-four toothpicks. It is helpful to create a table with X representing the number of squares and Y representing the number of toothpicks used to create the square. Your task is to find out how many toothpicks are in the 100th pattern.
Process Description
My first step after reading the problem was to count how many toothpicks were in each set. I then tested to see if the number of toothpicks were a linear or a quadratic function. To help organize the givens in the problem I created a table with X representing the number of squares and with Y representing the number of toothpicks used to create the square. The difference between the first numbers were eight and the second difference between the first and second number was twelve, so this pattern is neither linear or quadratic. Then, I came up with the equation N=3x+1 to find how many toothpicks were in the top row. This equation is originally from f(n)=__n+/-__ which we have been studying over the last few weeks of class. I plugged in the numbers into the top row (N=3x=1) and got 31 toothpicks. Then I came up with the equation N=2x+1 to find how many toothpicks were in the bottom row. After plugging in the numbers for all 10 rows and got 21 toothpicks per row. Then to find the total number of toothpicks in the 100th square pattern I added 31 from the top row and 189 (21 times 9 rows) to get 220 total toothpicks.
Solution
After finishing this problem, I found that if you have a square that is 10 by 10, then you will have 100 small squares making up the pattern. The total number of toothpicks would then be 220. This is the sum of all rows together (189+31). I think that this is the complete answer and I checked my math with a calculator and my peers to double check my work.
Self Assessment & Reflection
While doing this problem I revisited a few important things that include taking my math really slow and making sure I fully understand each step and going back and checking my answers with peers. If I were to give myself a grade on this assignment, I would give myself a 10 out of 10 because I answered all of the reflection topics with a lot of detail and explained my work step by step. Also on the worksheet I showed all of my work and made sure to label everything needed. On the syllabus I would say that the mathematical practices and expectations number 3: Make sense of problems and persevere in solving them relates to this problem because I had to go back and redo my work and reread the question to fully understand the task that we were given.
Problem Statement
In the Toothpick Squares Open-Ended problem, we are trying to find how many toothpicks are in the 100th pattern. In the first square pattern there is four toothpicks, the second square pattern has twelve toothpicks, and the third square pattern has twenty-four toothpicks. It is helpful to create a table with X representing the number of squares and Y representing the number of toothpicks used to create the square. Your task is to find out how many toothpicks are in the 100th pattern.
Process Description
My first step after reading the problem was to count how many toothpicks were in each set. I then tested to see if the number of toothpicks were a linear or a quadratic function. To help organize the givens in the problem I created a table with X representing the number of squares and with Y representing the number of toothpicks used to create the square. The difference between the first numbers were eight and the second difference between the first and second number was twelve, so this pattern is neither linear or quadratic. Then, I came up with the equation N=3x+1 to find how many toothpicks were in the top row. This equation is originally from f(n)=__n+/-__ which we have been studying over the last few weeks of class. I plugged in the numbers into the top row (N=3x=1) and got 31 toothpicks. Then I came up with the equation N=2x+1 to find how many toothpicks were in the bottom row. After plugging in the numbers for all 10 rows and got 21 toothpicks per row. Then to find the total number of toothpicks in the 100th square pattern I added 31 from the top row and 189 (21 times 9 rows) to get 220 total toothpicks.
Solution
After finishing this problem, I found that if you have a square that is 10 by 10, then you will have 100 small squares making up the pattern. The total number of toothpicks would then be 220. This is the sum of all rows together (189+31). I think that this is the complete answer and I checked my math with a calculator and my peers to double check my work.
Self Assessment & Reflection
While doing this problem I revisited a few important things that include taking my math really slow and making sure I fully understand each step and going back and checking my answers with peers. If I were to give myself a grade on this assignment, I would give myself a 10 out of 10 because I answered all of the reflection topics with a lot of detail and explained my work step by step. Also on the worksheet I showed all of my work and made sure to label everything needed. On the syllabus I would say that the mathematical practices and expectations number 3: Make sense of problems and persevere in solving them relates to this problem because I had to go back and redo my work and reread the question to fully understand the task that we were given.