Thinking and Re-thinking about Fractions
Last month, I was passing through the hallway one of our high schools, when I overheard a teacher delivering a lesson. He was discussing equations of some sort, where a fraction was multiplied by a variable. In this particular case, he was asking about 2/3 x 6. He checked the class for understanding: "Do we all know how to multiply a fraction by a whole number?" Think about that for a second. What is your go-to method for solving 2/3 x 6? Thinking about fractions Prior to this year, if someone asked how to multiply a fraction by a whole number, I would have given them the “algorithmic“ method of doing so: create a fraction out of the whole number by placing a numerator of six over a denominator of one. Then multiply my 6/1 fraction by 2/3: multiplying the numerators together and then multiplying the denominators together. This would give me 12/3, which could then be reduced to 4. Rethinking about fractions For the first tim...