The student-generated calendar included the following (easy) pattern(s):
- rest, rest, note, note
- color: red, blue, green
The pattern on the calendar used two rests going down the value chart starting at 1/1, followed by two notes going up the value chart starting at 1/32.
As we went through the month, we analyzed what had to happen from day to day in order to change the value of the rest or note. In doing so, we explored a lot about fractions. To make it easier, we looked at a visual model using tile.
The first change was easy. From Day 1 to day 2, the value went from 1/1 to 1/2; to achieve that change, you simply divide by 2. Other days were harder. From Day 13 to Day 14, for example, the value went from 1/32 to 1/16. At first I heard, "divide it by 2!" But when we looked at the visual model, we could see that 1/32 divided by 2 would not result in 1/16. But multiplying by 2 would.
As we went, a couple generalizations emerged:
- when you divide a fraction the denominator gets bigger but the number gets smaller.
- when you multiply a fraction the denominator gets smaller but the number gets bigger.