I use this software to create the random groups. I showed them what they would receive - a bag indicating the number of items contained inside. There were large items (full size Rolo) and small items (Halloween size KitKat) and their job was to figure out the number of each. The only tool at their disposal was a kitchen scale.
I asked what information they wanted from me. They asked for the the mass of each item and (this made me very happy), the mass of an empty bag.
Given that, they got to work. Here is an example:
A couple of groups got stuck early on because they let their variables represent the masses of the items, instead of the number of items. Their system of equations broke down pretty quickly. One group was stumped for longer (they calculated a number of items greater than that indicated on the bag) and I asked others to go help them. It was really nice to see the collaboration taking place - many students looking at one whiteboard trying to find the mistake(s).
If you try this, remember that working with heavier objects gives much more successful results.
And if that wasn't enough fun for one day, we moved on to making chocolate milk.
I brought in milk, chocolate syrup, a measuring cup and glasses and actually made chocolate milk according to the information in the table.
It was evident that one was far more concentrated than the other. We filled in the last two columns of the table together. I was surprised at how much difficulty many students had coming up with the percentage of chocolate syrup. I had to say "If you got a test back and got 10 out of 110, how would you work out your mark as a percent?" to get them to make the connection. Next, I said that Jacob wanted chocolate milk with 15% syrup, but that mom took away the chocolate syrup so he had to make it using the pitchers of Noah's and Isabelle's chocolate milk.
I was really impressed that my students (collectively) found these equations. It was not straightforward - we went around the room and bounced a bunch of ideas around before landing on these. To see if they really got it, Chloë got in on the chocolate milk action:
They did great! We set up one more, not actually with the detail shown below, but well enough to say that they understood.
Here is today's homework. I hope the work we did today helps them understand mixture problems which students always find tricky.