# Number Sense Brings Happiness

Today, my objective was to teach students how to convert a fraction to a decimal or an equivalent percent. In prior years, the lessons I found were all very procedural-based. However, this year, I decided to open the lesson with a Number Talk instead. It was a simple opener. I warned students I was about to post a familiar fraction on the board and their job was to determine the equivalent decimal and/or percent. There was a catch, they could not use an algorithm or the reasoning of, “I just knew that one.”

When everyone understood the directions, I posted ¾. Their job was to put their thumbs up when they knew the equivalent decimal and additionally, had an explanation that would satisfy the requirements. At first, a few students struggled with explaining their answer without just “knowing” some form of ¾, but eventually, students rose to the task. I also shared examples of other student responses (from previous conversations I had with students) to make sure everyone could truly understand the number sense objective.

Next, I showed them the next fraction  ⅞. With the first round completed, the students were able to offer incredible explanations that touted number sense. At this point, I segwayed into the term “terminating decimal” and showed them the algorithm of the numerator divided by the denominator, inserting a decimal, etc. Now they had a choice as to how to solve the next problems, but I did not point out this fact. I simply posted another fraction and had them find its decimal equivalence. With each new fraction presented, students gravitated towards showing and thinking about the numbers and their connectedness over the algorithm. There were a few times where the algorithm was actually easier, and they noticed this too. Their energy was as extraordinary as their flexible thinking.

This was one of those days, a day where a lesson invigorated the class and their teacher. This was a day where I know that students left class thinking about numbers, procedures and the actual relationship between the two. This was a good day to be a math teacher.