As we all know, the past day has been incredibly cold. Typically in the mornings, our class waits outside while the rest of the school begins its day. During this time we observe what is going on in nature. It's an opportunity for informal science exploration and discussion. Today, everyone independently came inside because we all sensed it was far too cold to look at ice crystal formations. The question of just how cold led to a nice integer conversation.
One fourth student in charge of the weather got very excited that it had been 18 degrees outside. A sixth grader disagreed, saying that it had been -18 degrees. My mentor teacher drew up a thermometer in Fahrenheit to discuss the difference between negatives and positives on a number scale. The class could easily say that a warm 70 degree day would be 37 degrees above freezing, but the fourth graders had a lot of difficulty calculating how many degrees below freezing the temperature was last night. My MT let the class know that it was -4 degrees at the moment. It took the fourth graders a little bit of mental sweat to understand that -4 degrees meant 37 degrees below freezing. But after my MT pulled out an integer line, they understood and began to calculate other "below freezing" temperatures.
I have seen these students use thermometers easily, but I think integers still trouble the fourth graders. Negatives were always difficult for me as a kid, and I could relate to a particular student who exclaimed, "how can four be above and below zero?!" I have a feeling we are going to pay a lot more attention to our thermometers this week so that we can move more easily between negatives and positives.
This is a great example / artifact that includes a lot of different types of knowledge and a lot of big ideas (both mathematic and scientific). Most important in your analysis here is for you to ask what this reveals about how students think about the big ideas? First, what is the big idea of this "task"? Second, what does it reveal about students' current mathematical thinking?
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