Today's warm-up was a counting circle. We started at 27x - 52 and added -2x + 5. Some students were intimidated at first, but quickly realized that they needed to deal with like terms separately.
The picture you see is of Vector from Despicable Me. One of my Calculus & Vectors students drew it, framed it and wants it to stay permanently on the whiteboard!
I started today's activity by standing, holding a stack of Styrofoam cups and asked my students what questions came to mind. It did not take long before someone asked "How many cups would it take to reach your height?". Boom! I displayed their random groups for today and explained their task to them. Each group got 10 cups and had to determine how many cups it would take to reach my height. They picked up the handout and started measuring.
Someone asked how tall I am - I said they could measure me. Two groups did, but were not very accurate, as it turns out. Most students were not being at all precise with their measurements. They said the lip was about 1 cm and 10 cups were 20 cm tall and thought that was good enough. It took some prompting to get them to be more accurate and reason through whether the rate of change made sense (some had RoC of 1 then 1.6, then 1.2...). They all eventually got to an equation, but then all but one group whose equation was correct put my height in for the number of cups! I asked them to talk about what each variable represented, but they did not see any issues with their work. Here are their results:
The closest group was 5 cups off - in previous years they were much closer. We talked about how they should have been using their equation to calculate the number of cups versus what they had actually calculated. We also discussed the sources of error.
To close out the class I showed them a short stack of red cups that look something like this
and asked if they would need more or fewer of these cups to reach my height.They reasoned through this really well and even showed that with only 7 cups, the Styrofoam cup stack would already be taller.