It went something like this:
"Wow, its sure raining out there!" The students immediately reacted to this with stories about how wet they got or how it was actually a perfect day to stay at home and nurse their cold (which many of them had today).
"I wonder how much water is actually coming down..." I say as we watch the dreariness. "I think you should calculate it. Find a whiteboard and figure out in your groups if the rain that falls in 1 hour in 1 square kilometre will be enough to fill a milk tank!"
I mentioned the milk tank because in students in Math 10 need to know how to calculate the volume of a cylinder. They also need to convert between different units of measurement, so at some point I 'happen' to mention to each group that 1 cubic cm is exactly 1mL.
Most students felt a little overwhelmed at the problem initially, because they had nothing to work with. Besides the 'square km' I did not have any numbers for them. They stare a little blankly at the rain drops gushing out of the sky thinking, How can we ever count those all?
How much DOES it rain in an hour? If you put a cup outside, will it overflow? Probably not. Ok. So less than 4 inches. Most groups chose a number between 5 mm and 1.5 cm.
It is astonishing. 10 mm of rain over a square kilometre gives about 10 Million Litres of Water! What happens to all this water?
Different groups came up with a variety of interesting points:
-It would take about 120 milk trucks to carry the water that falls in an hour.
-It would take about 16,000 hours to fill (or drain) a milk tank through a small hole at a rate of 3mL/hr.
-If it rained milk, 3 families in one group could be supplied enough milk in 1 hour for more than 3000 years. This lead to the calculation that all of their families (from the 18 students present today) would have enough milk for more than 200 years.
My students usually work on whiteboards... be it standing at vertical whiteboards or sitting around small portable whiteboards. This for several reasons.
- It is easier for students to 'think together' when they can all write and see the workspace.
- Students put 'pen-to-paper' much quicker when the surface they work on is non-permanent.
- Knowledge permeates through the class quickly when students are standing and can see each other's work. (As I was going around and suggesting it might be useful to know that 1 mL = 1cubic cm, I was surprised to see that information made it around the classroom before I did. The group shown below had that written on their board before I could feed them that 'tip'.)
- I can quickly assess students progress and understanding from anywhere in the room.
I often take a quick snapshot of their whiteboards so I can analyze them. Students usually do not receive a formal mark for this work, but it gives me a good idea what concepts need to be covered and what still needs some work.
Taking a quick look at the whiteboards shown I gather some interesting information.
- The group above is clearly able to work in both imperial and metric units and make necessary conversions from one to the other. This is a course requirement, so I have evidence that they 'get' that learning target.
- The group below understands volumes, rates, and conversions but their understanding of units of measurements in 1D vs 2D vs 3D needs some work. They are the only group that condensed a large number into an exponent.
As I clean up the room at the end of the day, my sister walks into the room. She looks at some of the remnants of calculations left on the boards. "You know," she says, "there's this really great problem I love to do with my students. Have them figure out how much water falls in 1 day in 1 square kilometre! I did that in my math class today." I grinned. It simply was the perfect day for the rainy day problem.
(Note: Thanks to D.O. for sharing the Rainy Day Problem with us a few years ago in a Pro-D session! I, for one, have used many variations of it since.)
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