The purpose of this problem is to use the digits 1, 2, 3, and 4, to create arithmetic expressions to find different numerical values. I had to find every possible way to find the values of every number from the number 1 to the number 25. We were allowed to use the numbers 1, 2, 3, 4 in any way we wanted as long as it was in an arithmetic expression and was in the order of operations, for example: (1+2)*3+4.
I first wrote out all the numbers, 1 through 25, in a column on my paper. By doing this, I could easily organize my equations by placing them next to the number they equal. I started off my using the equations (1*2*3*4), which equals 24, and (1+2+3+4), which equals 10. This allowed me to continue looking for different equations by changing the signs. I also used the equations I found first to find other numbers by adding 1 or subtracting 1. I wasn’t able to find any patterns, but I was able to conjecture and test by creating random equations and seeing if that fits with any of the numbers. When I got stuck, I would ask my peers to help me out by having them coach me through the problem.
I first wrote out all the numbers, 1 through 25, in a column on my paper. By doing this, I could easily organize my equations by placing them next to the number they equal. I started off my using the equations (1*2*3*4), which equals 24, and (1+2+3+4), which equals 10. This allowed me to continue looking for different equations by changing the signs. I also used the equations I found first to find other numbers by adding 1 or subtracting 1. I wasn’t able to find any patterns, but I was able to conjecture and test by creating random equations and seeing if that fits with any of the numbers. When I got stuck, I would ask my peers to help me out by having them coach me through the problem.
1. (4/2+1)/3
3. (2x4+1)/3 5. (4x3)/2-1, (2x4)/1-3 7. (4x3)/2+1 9. (2x3)+4-1, (3x1)+2+4, (2x1)+3+4, 2/1+3+4 11. (4x3)-2+1, (2x3)+4+1, (4x2)+(3x1), ((4x22)+3)/1, (4/1)x2+3 13. 4x3-1+2 15. 3x4+2+1 17. (2+4)x3-1 19. (2+3)x4-1, (2+4)x3+1 21. (2x4-1)x3 23. 2x3x4-1 25. 4x3x2+1 |
2. 4-3-1+2, 1-4+3+2, 3-4+1+2
4. 4/2+3-1 6. (4x2)+1-3 8. 2+3+4-1 10. 1+2+3+4, (4x2)+3-1 12. (4x2)+3+1 14. 1x2x4+2, (3+4)x2x1, (3+4)x2/1 16. (4+3)+1x2 18. (2+4)x3x1, (2+4)x3/1 20. (2+3)x4x1, (2+3)x4/1 22. (3x4-1)x2 24. 1x2x3x4, 2x3x4/1, (1+2+3)x4 |
Variations of the Problem:
Instead of using the numbers 1, 2, 3, 4, students would use the numbers 5, 6, 7, and 8 to create as many problems as they can for the numbers -16 through 26. Students can use addition, subtraction, division and multiplication, but it does not have to be in the order of operations.
Instead, use numbers 2, 4, 6 and 8 to create as many problems as possible for the numbers 1 through 20. Some numbers may not be possible, and if there isn’t they must look for the pattern.
Evaluation:
I think I successfully completed this problem because I figured out an equation for each number, 1 through 25. Whenever I got stuck, I would ask for help, however that was only on a few numbers. The rest of the numbers were easy enough for me to complete them successfully with maybe a few other equations. Overall, I think I did well on this problem and I hope I continue to do well on all my work.
Instead of using the numbers 1, 2, 3, 4, students would use the numbers 5, 6, 7, and 8 to create as many problems as they can for the numbers -16 through 26. Students can use addition, subtraction, division and multiplication, but it does not have to be in the order of operations.
Instead, use numbers 2, 4, 6 and 8 to create as many problems as possible for the numbers 1 through 20. Some numbers may not be possible, and if there isn’t they must look for the pattern.
Evaluation:
I think I successfully completed this problem because I figured out an equation for each number, 1 through 25. Whenever I got stuck, I would ask for help, however that was only on a few numbers. The rest of the numbers were easy enough for me to complete them successfully with maybe a few other equations. Overall, I think I did well on this problem and I hope I continue to do well on all my work.