Problems About Patterns:
Step 1:
State problem in own words:
Question: You have 1176 identical square pieces. Can you use all the pieces to construct a stair-like structure?
Restated Question: Is it possible to construct stairs increasing by one each row by using all 1176 identical pieces?
Step 2:
-Describe what you did in attempting to solve the problem
-Include things that didn't work or seemed like a waste of time
Well what was a waste of time for me for a while was when I was trying to add up each stair row individually, that took forever and I would mess up a lot. What finally led me in the right direction was finding a pattern, our teacher showed us a trick to add up all the numbers quicker and I saw a pattern in that. The pattern and equation that I saw was X * x/2 + x/2, X being the last row at the bottom of the stairs. So their was a lot of guess and check, but it so much faster than everything else I tried, and I got much better at it the more I did it.
Step 3:
-State solution
-How did you know the solution was complete or correct?
I got the answer of 48 steps at the bottom, decreasing by one every row going up. I knew the answer was correct because the question asked to find a stair-like structure that could add up to 1176, and my answer fit those requirements.
Step 4: Extension/Reflection
-Did you consider it educationally worthwhile?
-What did you learn from it?
-Did you enjoy working on it?
-Was it too hard or too easy?
Educationally I found it challenging because it took me a while and I felt proud of myself when I understood the problem. It was worth my time because I actually learned something when I tried and failed, and then learned from my mistake. I learned how to analyze a problem and make an equation that I could easily plug things into to find my answers. I enjoyed finding the right answers and being proud of myself. It was not too hard or too easy, it was very challenging at first, but then I got the hang of it and I felt really smart solving each problem.
Grade I give myself:
I would give myself 15/15 because I exceeded the expectations when I answered all the questions, and when I found the equation to solve all the problems.
State problem in own words:
Question: You have 1176 identical square pieces. Can you use all the pieces to construct a stair-like structure?
Restated Question: Is it possible to construct stairs increasing by one each row by using all 1176 identical pieces?
Step 2:
-Describe what you did in attempting to solve the problem
-Include things that didn't work or seemed like a waste of time
Well what was a waste of time for me for a while was when I was trying to add up each stair row individually, that took forever and I would mess up a lot. What finally led me in the right direction was finding a pattern, our teacher showed us a trick to add up all the numbers quicker and I saw a pattern in that. The pattern and equation that I saw was X * x/2 + x/2, X being the last row at the bottom of the stairs. So their was a lot of guess and check, but it so much faster than everything else I tried, and I got much better at it the more I did it.
Step 3:
-State solution
-How did you know the solution was complete or correct?
I got the answer of 48 steps at the bottom, decreasing by one every row going up. I knew the answer was correct because the question asked to find a stair-like structure that could add up to 1176, and my answer fit those requirements.
Step 4: Extension/Reflection
-Did you consider it educationally worthwhile?
-What did you learn from it?
-Did you enjoy working on it?
-Was it too hard or too easy?
Educationally I found it challenging because it took me a while and I felt proud of myself when I understood the problem. It was worth my time because I actually learned something when I tried and failed, and then learned from my mistake. I learned how to analyze a problem and make an equation that I could easily plug things into to find my answers. I enjoyed finding the right answers and being proud of myself. It was not too hard or too easy, it was very challenging at first, but then I got the hang of it and I felt really smart solving each problem.
Grade I give myself:
I would give myself 15/15 because I exceeded the expectations when I answered all the questions, and when I found the equation to solve all the problems.