Tuesday, May 1, 2012

Calendar Pattern: Fractions & Music

Each month we do a calendar pattern from Bridges in Mathematics. After doing patterns for several years, the proficiency level is high; we've seen and worked through a lot of complex problems. So this month I proposed a new challenge: make a calendar that includes 2-3 patterns. After reading about Teaching Fractions Through Music, I suggested that the pattern include music, looking at fractions in notes and/or rests.

The student-generated calendar included the following (easy) pattern(s):
  • rest, rest, note, note
  • color: red, blue, green
In order to create the more difficult pattern of fractional note/rest values, a chart was used showing rests with values of 1/1 to 1/32 and notes with values of 1/1 to 1/32.

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.
Big grins. We continued to check our work against the visual model. It helped everyone...including me. Fractions cause me huge math anxiety. (It takes every brave bone in me to post this!)  I was only taught fraction rules. Each time I teach fractions, I feel like I'm trying to undo what was done to me. It's thrilling to see the visual models increase kids' understanding.

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