37817

The first section of the task was set as a paired exercise where students looked at trying to find solutions to TWO+TWO=FOUR. Checking as students found the answers I was able to see any that worked and any that didn’t. I was also able to chat to them about the methods they were using. During our discussion afterwards we looked at some misconceptions and ideas for solving the problem. One girl’s first thought was that W and O must be less than 5 and T must be greater than 5. I picked out the positive point from this that there must be a number in the thousands column in the answer which was where the thought stemmed from. By asking other girls to see where the flaw in the logic was we moved on to looking at a number that was a solution to the problem where the W wasn’t less than 5. 582+582=1264. The main error that students made was finding what they thought was a solution, such as 540+540=1080 where the o’s in two and four work but the r in this answer is the same as the o so doesn’t follow the criteria for the problem. To find a solution students’ used a combination of trial and error with their knowledge of place value. Some students worked systematically once they found a solution. For example once you have 734+734=1468 we can look at 744+744 and 724+724. These don’t work because of duplication of numbers in the answer but looking at 714+714=1428 this does work.
Other solutions that the girls found were as follows:
1. 534+534=1068
2. 632+632=1264
3. 928+928=1856
4. 673+673=1346
5. 846+846=1692
6. 765+765=1530
7. 836+836=1672
Student then asked whether decimals were possible. If they were then systematically you could, for example, have 53.4+53.4=106.8 and 5.34+5.34=10.68.
Once we had discussed tactics for finding solutions students were given 8 minutes to find as many solutions as possible to ONE+ONE=TWO. Once the time was up the pair with the highest number of solutions gave their answers and the rest of the class checked them and then gave any other answers that they had. The following are the solutions that they found:
1. 417+417=834
2. 216+216=432
3. 432+432=864
4. 231+231=462
5. 291+291=582
6. 271+271=542
7. 427+427=854
8. 236+236=472
9. 281+281=562
10. 452+452=904
11. 467+467=934
We didn’t get to trying to show that we had all the possible solutions.