This is a wonderful addition puzzle that somebody showed me: apparently, it was invented in 1916 by the German mathematician Issai Schur and it looks like this: suppose you were to put a set of numbers into two partitions so that no two numbers added up to a third number in that partition? How high could you get, if you started with 1?
In this case, you have 2 "cauldrons" and you put 1 in the first cauldron, 2 in the second, 3 in the first, but you have to put 4 in the second, because 1 + 3 = 4. Sounds good! So you have 1 and 3 in cauldron 1, and 2 and 4 in cauldron 2. Where should you put 5? It can go in either one, so..... the problem sounds very simple, and you and you're student will be outraged by what happens when you get to 9......
What's great about this problem is that it is very easy to differentiate: just add another cauldron (this activity has puzzle sheets for 2 - 5 cauldrons; you can cut them out and make a 6 + cauldron puzzle if you like.)
A great activity to practice basic addition facts, problem solving strategies AND a challenge problem for ALL your students!
I included a poster about the creator of the problem, Issai Schur, as well as answer sheet, number tiles to cut out, and an excellent set of teaching tips on strategies for teaching and checking work. My kids loved this; so will yours!