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# Four approaches to adding up all integers from 1 to 203.

We’re looking at #4 here, guys: “Use a non-calculator shortcut to add up all the integers from 1 to 203.”

Are these differences significant? Which is most appropriate to introduce to students first? Do you introduce multiple techniques explicitly to your classes? What does this student work indicate about the way this class was taught?

Or, talk about whatever you like.

## 2 replies on “Four approaches to adding up all integers from 1 to 203.”

[…] Update: For pictures of student work on this, see the next day’s post. […]

I like it!

The “there are 101.5 pairs” is pretty nice, but explaining what .5 pairs is and why we can still multiply by 104 is a bit of extra work.

The leftover number in the middle is definitely great. That’s just one step away from noticing that the middle number is also equal to the average of the first and last, so we can use (average) * (how many) to get (first+last)/2 * n as a general formula.

The insertion of a 0 in front is super-clever and is great for this situation but not as nice when you’re summing some other arithmetic sequence whose 0th term wouldn’t be 0.