Again, I can take credit for none of this. On Dan Meyer's page I found this exercise to explore the volume of an octagonal prism.
I showed the first clip and simply asked the students "what is the first question to come to mind?" Almost unanimously they asked "how long to fill?" One or two jokers asked what this had to do with anything, I replied that they needed patience.
I asked the students what they needed to know in order to answer the question of how long it will take. If they said something vague like the dimensions of the container, I forced them to tell me which dimensions were necessary. One student without provocation on the third day of class stated that the apothem was necessary, and even gave the formula for volume as 4*apothem*side length* volume. I was so proud.
From there I showed the video that filled the tank, and then asked them to extrapolate the information. I followed up with the sequel of how long to empty. Overall a very good opener.
I used this with a group of trigonometry students and all told it took about 25 minutes.
I showed the first clip and simply asked the students "what is the first question to come to mind?" Almost unanimously they asked "how long to fill?" One or two jokers asked what this had to do with anything, I replied that they needed patience.
I asked the students what they needed to know in order to answer the question of how long it will take. If they said something vague like the dimensions of the container, I forced them to tell me which dimensions were necessary. One student without provocation on the third day of class stated that the apothem was necessary, and even gave the formula for volume as 4*apothem*side length* volume. I was so proud.
From there I showed the video that filled the tank, and then asked them to extrapolate the information. I followed up with the sequel of how long to empty. Overall a very good opener.
I used this with a group of trigonometry students and all told it took about 25 minutes.