Staircase Problem
Problem Statement:
Can you use 1,176 square pieces to construct a stair-like structure, increasing by one each level?
Process:
You would start this problem by using the equation x/2(x+1)=1,176. You want to get rid of any fractions in the very beginning so you multiply the whole equation by 2. After this your new equation is x(x+1)=2,352. From this you know that to get 2,352 you'll have to multiply two numbers. You also know that one of these numbers will be greater than the other by 1. From here you can use guess and check. I started with 30 and 31, which gave me 930 and that is too low. I then tried 50 and 51, which gave me 2,550. This number was too high but much closer. I decreased by a little bit until I reached 48 and 49 which gave me 1,176, the right answer. Therefore your answer is 48.
Solution:
The solution to this problem is 48 (as stated above). I know that this solution is correct because I plugged it back into the original equation, x/2(x+1)=1,176. If you replace any x's with the number 48, your equation will become 48/2(48+1)=1,176. You then simplify 48/2 to 24 and distribute. You now have 1,152+24=1,176. All you need to do is add the two numbers together and it equals 1,176 and you know that the answer.
Extension/Reflection:
Even though this problem was difficult I do consider it educationally worthwhile. I never knew how to do problems like this before and now they seem a lot easier. I learned about adding the first and last number (x+1) and dividing the last number by 2 (x/2). I liked learning how to do something new and it was challenging in an effective way.
I think that I deserve the full 25 points on this assignment because I put a lot of effort into it and tried to participate in class in order to help other kids understand as well as being available to further explain if needed. I also made sure that I fully understood what the problem was so that I got the most out of my new knowledge.
Can you use 1,176 square pieces to construct a stair-like structure, increasing by one each level?
Process:
You would start this problem by using the equation x/2(x+1)=1,176. You want to get rid of any fractions in the very beginning so you multiply the whole equation by 2. After this your new equation is x(x+1)=2,352. From this you know that to get 2,352 you'll have to multiply two numbers. You also know that one of these numbers will be greater than the other by 1. From here you can use guess and check. I started with 30 and 31, which gave me 930 and that is too low. I then tried 50 and 51, which gave me 2,550. This number was too high but much closer. I decreased by a little bit until I reached 48 and 49 which gave me 1,176, the right answer. Therefore your answer is 48.
Solution:
The solution to this problem is 48 (as stated above). I know that this solution is correct because I plugged it back into the original equation, x/2(x+1)=1,176. If you replace any x's with the number 48, your equation will become 48/2(48+1)=1,176. You then simplify 48/2 to 24 and distribute. You now have 1,152+24=1,176. All you need to do is add the two numbers together and it equals 1,176 and you know that the answer.
Extension/Reflection:
Even though this problem was difficult I do consider it educationally worthwhile. I never knew how to do problems like this before and now they seem a lot easier. I learned about adding the first and last number (x+1) and dividing the last number by 2 (x/2). I liked learning how to do something new and it was challenging in an effective way.
I think that I deserve the full 25 points on this assignment because I put a lot of effort into it and tried to participate in class in order to help other kids understand as well as being available to further explain if needed. I also made sure that I fully understood what the problem was so that I got the most out of my new knowledge.