The other day I was in a class doing a demonstration on what a lesson looks like in the style of Building Thinking Classrooms.
The concept we wanted students to learn was sorting decimals. Here was the task…
At first, we asked students to simply sort the decimals from least to greatest in order to identify the largest decimal. There was no consensus about which is the largest decimal with three of the four decimals receiving votes.
Groups were given an additional minute to construct an argument to defend their answer.
Student S was called to defend his answer of 0.63.
He added zeros to make all the decimals as thousandths and reasoned 630 thousandths is the largest.
While this type of reasoning will ALWAYS work, this strategy essentially avoids having to think about decimals by turning the numbers into whole numbers (ish). Additional students added upon the thinking of Student S until we had absolute unanimity about the proper order from least to greatest.
So in our next task, we used the same decimals but asked students to place them on a number line. They were given 0.5 as a benchmark value.
While every group placed the decimals on the number line in the correct order, the decimals themselves were not remotely close to where they actually live on the line. Their placement looked something like this…
For Task 2 we gave students a set of four decimals (no context…just numbers) and told them to place those decimals on a number line from 0 to 1. Again we gave only gave 0.5 as a benchmark.
The numbers to place on the number line were: 0.19, 0.37, 0.425, and 0.258
Some groups were relatively accurate.
Other groups used tenths as additional benchmarks.
It it was clear that MANY groups need additional work with placing decimals on a number line.
While teaching this lesson, it was abundantly clear to me the difference between teaching students to get the right answer versus teaching students to understand a math concept.
Here is a video a made as a result of this experience…