This problem was a very creative and useful way of harnessing the use of consecutive sums, (Consecutive sums are sums added up by consecutive numbers 1,2,3 etc.) This problem was called the "1-2-3-4 Puzzle" and made us think back to when we did consecutive sums and allowed us to use the skills necessary for solving the problem. The problem asked us to use the numbers 1,2,3, and 4 and use any mathematical operations in order to get the numbers 1-25. We were able to use any mathematical operation, which meant that we could divide, add, use exponents, square roots, etc. We could also mix up the order of the numbers which meant they didn't have to be consecutive and could also juxtapose numbers, meaning that we could combine 1 and 2, to make 12 etc.
The process I went through was definitely interesting because surprisingly the problem was not too hard. I usually have more trouble with math in terms of frustration and stress, but I actually felt confident in my answers and process. I first, wrote down all of the answers that were given in the description of the problem (1,3,6) and looked over the mathematical operations that were used in the higher numbers that we weren't supposed to find, in order to review any strategies I could use for the smaller numbers. I began to re-use mathematical operations in order to find most of the numbers at a random pace because I wouldn't be looking for a specific number but I would still be receiving answers that I needed. For example the answer 9 had an operation of 1x2+3+4 and that inspired the operation of 24, which was 1+2+3x4. Another example would be, the operation of 11 (3x2+4+1) which inspired the operation of 19 (12+3+4). Both examples used the tool of using almost the same equation but with a minor tweak which greatly helped me understand how numbers reacted with mathematical operations. Once I had 5 numbers I needed to solve, I saw that all the numbers were in the middle (14,15,16,17,18). I thought that the order was peculiar because that they were all consecutive and I began to experiment with different mathematical operations I used in the past problems. I finally experimented enough to find a mathematical operation for the number 14 and used 14, to get 16. This time consuming process helped me find 15, which helped me find 17 and then 18. This process was the same process I used on my examples I shared above and greatly helps to accurately find a number range I could shoot for.
Answers (IN ORDER)
2+1x3-4=1 1+2+3-4=2 23-4-1=3 32-4-1=4 23-4+1=5 3+( sqrt 4x2+1) =6 4x3/2+1=7 2+3+4-1=8 1x2+3+4=9 1+2+3+4=10 3x2+4+1=11
32+4-1=12 14-3+2=13 21-3-4=14 3x4+2+1=15 12x4/3=16 4+1x3+2=17 42+3-1=18 12+3+4=19 1x2+3x4=20 24-3x1=21 24-3+2x1=22
24-3+2x1=23 1+2+3x4=24 1+2x3x3=25
If I were to extend this problem, I would definitely say that there should be a challenge option in terms of more numbers or a hint to an equation if there was one. Other than that I thought that this problem was a good shift from consecutive sums.
Habits I definitely improved on were experiment through conjectures and be confident, patient and persistent. I believe I have improved on experimenting through conjectures because the entire problem required to conjecture and test by inputting values and mathematical operations in order to find different answers. I also improved on being confident by starting the problem on time (avoiding procrastination) and improved on being patient by seeking the answers throughout without leaving the work area. I also improved on being persistent by working hard and trying my best to work through the problem on my own.
Answers (IN ORDER)
2+1x3-4=1 1+2+3-4=2 23-4-1=3 32-4-1=4 23-4+1=5 3+( sqrt 4x2+1) =6 4x3/2+1=7 2+3+4-1=8 1x2+3+4=9 1+2+3+4=10 3x2+4+1=11
32+4-1=12 14-3+2=13 21-3-4=14 3x4+2+1=15 12x4/3=16 4+1x3+2=17 42+3-1=18 12+3+4=19 1x2+3x4=20 24-3x1=21 24-3+2x1=22
24-3+2x1=23 1+2+3x4=24 1+2x3x3=25
If I were to extend this problem, I would definitely say that there should be a challenge option in terms of more numbers or a hint to an equation if there was one. Other than that I thought that this problem was a good shift from consecutive sums.
Habits I definitely improved on were experiment through conjectures and be confident, patient and persistent. I believe I have improved on experimenting through conjectures because the entire problem required to conjecture and test by inputting values and mathematical operations in order to find different answers. I also improved on being confident by starting the problem on time (avoiding procrastination) and improved on being patient by seeking the answers throughout without leaving the work area. I also improved on being persistent by working hard and trying my best to work through the problem on my own.