On Tuesday, December 15th, I led the students in a number talk on fractions. Diane and asked me to design a fractions number talk since her students had been working on fractions during their math workshop. I thought of using the easier operation of adding fractions but setting the challenge in the problem with unlike denominators. The denominators I chose could lead to a large common denominator or a smaller one if the students reduced the fractions first.
As our Number Talk progressed, the students shared responses and strategies that Diane and I both anticipated. Many students were able to see the relationship and equivalencies between fractions. Toward the end of the Number Talk, Diane and I were both incredible impressed by the flexible thinking from one of her fifth graders. Instead of trying to find common denominators with 8 and 10, the student thought of a way to make the denominator (8) of the first fraction (6/8) into the value of 10 in order to match the denominator of the second fraction (6/10). As a result he multiplied 8 by 1.25 in order to have common denominators of 10. What was interesting was he also multiplied the numerator by 1.25 to make it an equivalent fraction and got 7.5 as the numerator. That led to a wonderful conversation of whether you can have decimal numbers in a fraction. What do you think?