One of the commenters gave a great suggestion: > I would use bar models to show how the whole changes. First, draw one bar (table) with 3 students inside; labe

One of the commenters gave a great suggestion: > I would use bar models to show how the whole changes. First, draw one bar (table) with 3 students inside; label the bar one whole, star one student and label that student as one third of that whole. Do the same thing beside the first bar model, again showing the bar as one whole, starring one student and labelling that student as one third. Then, push the two bar models together (I’d use a Smart Board) to show a new whole: the two bars together with 6 students in the one bar is labeled as the new whole. Point out that this is a NEW whole, with a different # of pieces. Now they would see the 2 starred students in the one new bar made up of 6 total students, so the “old” 1/3 student becomes the “new” 1/6 student once the whole changes. This is like a name change, once the size of the whole changes. You can also show them that by cutting each “student” in half, you would get an equivalent fraction of 1/3 = 2/6 of the first one whole bar. So 1/3 = 2/6, not two 1/3’s = 2/6. http://www.marilynburnsmathblog.com/can-1-3-1-3-2-6-it-seemed-so/#comment-27347 http://www.marilynburnsmathblog.com/can-1-3-1-3-2-6-it-seeme...