I’ve had the pleasure of modeling a formative assessment lesson/classroom challenge in all regular ed 6th grade classes over the past two weeks. I must say, I absolutely love how these lessons are formulated to pull out the misconceptions lurking below the surface of students’ understanding. These times were no different.
Because this task focuses on converting decimals to percentages and percentages to decimals, I kind of figure I would have to tackle the notion of the decimal point moving. I thought this would be a perfect time to make the explicit connection to place value standards from 4th and 5th grade for teachers and students. Just to be clear I’m referring to 4.NBT.1 and 5.NBT.1. As we wrapped up the lesson, in every class, students discussed how they converted the decimal to a percentage by moving the decimal point two spaces to the right and converted a percentage to a decimal by moving the decimal point two spaces to the left. I had them right where they needed to be.
Research shows students’ misconceptions aren’t alleviated by the teacher telling them their thinking is off. Having multiple opportunities where their thinking is challenged through experiences and conversations with peers is what alleviates the misconceptions. So I wrote this on the board:
We entered the values of a decimal and its percentage equivalent. I asked students the location of the decimal point for each number. Ensuring students attend to precision, I asked guiding questions to get them to articulate the decimal point was between the ones and tenths place for each number. I asked students, if the decimal point moved. Many were able to conclude the decimal did not move. We had to determine what actually moved.
Students grappled with the idea that in fact the decimal did not move but it was the digits which shifted. In one class, a student even articulated, when we multiplied by 100, the number become 100 times larger! Yes!!
Anchor charts will serve as a reminder of what is actually happening to numbers when multiplying or dividing by 100. My hope is as teachers continue the conversations about the concept, they will attend to precision and discussing the magnitude of numbers instead of stating something which is mathematically impossible.
Next stop, 8th grade classes studying scientific notation because, “Mom, the decimal point is moving again!”