I recently ran Julie's version of Capture Recapture with Goldfish activity with my Algebra 1 classes today. It was a huge hit!

This is a middle school topic, but proportional reasoning is so important it needs to be repeated every year in basic high school courses. Driving past the topics is not supposed to be the point! In

*HPL*terms, I thought of this as an "activate prior knowledge" task that we tried to fit firmly into place with an engaging transfer task.

Julie's recommendation about showing the video is spot on: you absolutely MUST show the video. I broke it down as follows:

- the first 1:30 to
(but without revealing the math or the solution)*reveal the problem and the general idea*

Only after we had done our own work to rediscover the mathematics did I show the next 33 seconds of the video:

- the next 33 seconds to
*reveal the mathematics needed to estimate*

Once we had done that, then I did the final big reveal:

- the next 13 seconds to
*reveal the exact number of balls in the tank*

Once they had seen all of this, it was time for a transfer task.

I had students work in groups, recording their four trials on their data worksheets, taking an average of their estimates for each trial, and finally counting out their exact number of goldfish and writing a summary statement about how close (or far off) they had been. When they were done, they sent a representative to the whiteboard to add their group's data and best estimates to our table of whole-class results.

When we had everybody's data and estimates added to the table on the whiteboard, we discussed how accurate this method seemed and came up with other situations in which this method would be useful.

The hardest thing in Algebra 1 in my opinion is getting students to

**skills and concepts as being discrete topics that you can mentally "put away" after the chapter test and to**

*stop seeing**start seeing*skills and concepts as new tools you want to "keep close at hand" in your mental tool belt.

So connecting proportional reasoning to tangible (and often edible) results in the real world is at least as important as the content of the lesson itself. This goes beyond merely "spiraling" back; it requires

*integrating*into mathematical thinking and problem-solving from each moment forward.

I would love to see a real world application day after this. Watch cars on the streets and predict traffic for the day. Poll the class and predict how many pets in the school. Lunch poll your class and compare to cafeteria statistics.

ReplyDeleteGreat lesson, thanks to you and Julie!

I'm doing this lesson with my Algebra 1 students on Monday. Thanks so much for the clear ideas and the link to Julie's post. I can't wait to try it with the launch video :-)

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