I asked some students today to add the numbers from 1 through 100. After fielding some questions and making sure the students knew we were adding 1 + 2 + 3 + … + 99 + 100, they were off!
A few tried the obvious… 1 + 2 + 3..the long way. Luckily I had only given them about 1/8 of a page to work on!
The way I tried to show was using some skills we learned back in elementary school…looking for groups of numbers that add up nicely. For example, add the list: 2 + 7 + 4 + 3 + 6 + 8. Did you get 30? I did…but I did some rearranging (2 + 8) + (3 + 7) + (4 + 6) and said 10 + 10 + 10 is 30. I used that, along with an abbreviated list of numbers, to get the sum:
By adding groups of 100, I was able to get 4900! Then there’s the extra 100 sitting on top, which brings us to 5000. The missing 50 brings us right up to 5050.
A student, though, took a different approach. Same idea, different way of looking at it. I was impressed!
I presented a modified version…he wrote out a bunch more work. I presented only the pattern that he figured out from looking at it.