Right now my classes are working on the 7th grade common core ratios and proportions domain. Specifically we are exploring 7.RP.3 multi step ratio and percent problems. I've introduced several different models- ratio tables, proportions, equations, and a visual method using a 100 square grid of graph paper. Students are welcome to use any strategy when solving problems...most seem to be gravitating towards the ratio table as it gives them a little more structure when trying to interpret the problem.
Yesterday I wanted students to practice solving ratio/percent problems in a variety of contexts. We used individual dry erase boards (actually Communicators- clear plastic sleeves- I like these better as I can slide graph paper or a blank ratio table in them). I had my problems on a PowerPoint, and the process was to put a new problem up, walk around and question assumptions/strategies, and share the answer.
Here is where the "subtle differentiation" came in. I wanted to challenge students who were able to answer the question, but still be able to work with students who made a mistake or had a misconception. This year I've been making a conscious effort to focus on SMP 3- critiquing reasoning of others, so for each problem I created a "common misconception" response. I asked students who had the correct solution to try and determine what had gone wrong. I've used a similar strategy using actual student work but wasn't sure I would have enough time to identify one during every problem. I also used a variety of strategies in my misconceptions, so even though a student solved it with a ratio table, they had to analyze an error I made writing an equation to represent the situation.
It led to some interesting discussion and I was able to work with a few more students on the original problem. Concept assessment Monday, so we'll see!