I teach this lesson on a rainy day. I start by asking them the question, "How much rain do you think we'll receive today?" I remind them to use prior knowledge and to think independently, then write their estimate in their science notebook. As I live in Tucson, I gave them the additional hint of asking them to keep their guesses under one inch. As you will see, their response to this was very informative.
After I'd listed all of their estimates (projected onto the wall with a document camera) I asked them to think silently about the question below. I set a timer in Class Dojo.
I tell them that there is something we need to do before we can put these guesses in order from least to greatest. I state that while we could put them in order the way they are written, but it would be difficult and inefficient. What step do we need to take so that it is easier to put these values in order?
After two minutes, I asked for volunteers. They struggled with this. I had them turn and talk. Finally, one child was able to articulate that they were fairly certain that some of the guesses were larger than an inch. I asked them what led them to that conclusion. They said they knew that 1 centimeter was smaller than an inch, and were pretty sure that two or even three might be smaller than an inch, but that 9 centimeters, and definitely 11 centimeter and larger, was larger than an inch. Many of them then looked puzzled, and expressed their confusion over why they didn’t know how to change centimeters to inches the way they know that millimeters fit into a centimeter, for example. I reminded them that we use two different measurement systems and that converting between them takes several steps. Before they learn to do that, my job is to ensure that they understand each system. Still, the problem remained that they felt that certainly some of their guesses were greater than 1 inch, thus ignoring the hint I gave them.
So we then got out the ruler and looked at an inch and a centimeter. I demonstrated how to block off just one inch and they saw that one inch equals more than two but less than three centimeters. Then I showed them how to look it up on Google and we saw that, of course, 1 inch = 2.54 centimeters. We rounded that to 2 ½ centimeters.
Interestingly, out of all the students, only this child retained the idea that we were working with inches, as stated in the original question.
The rest of them became fixated on centimeters based on the belief that centimeters are smaller than inches, and that is where most of them ran into a roadblock. You can see that only 3 of the 20 students present during this lesson stayed with inches.
The actual rainfall on the day I taught this lesson was 0.11 inches. (The range was 0.08 - 0.30). This rain log map is a great source for obtaining specific precipitation data.
I convert their centimeter guesses to inches and round to the closest quarter inch. Rounding to the closet 0.25 is not an appropriate skill to teach them. They need to continue on focus on rounding to the closet ten, hundred and thousand! Then we work together to order their estimates (to the closet quarter inch, a third grade standard) and find the median (middle), mode (most common) and the mean (average). I take them through the exercise of finding the average because this is a gifted class and many of them need enrichment but I am careful to explain it just as thoroughly as I would to any third grade class. Some of my students need enrichment in math, but I want to make sure that the process is also clear to the students who are on-level or struggling in math.