What a morning we had! We took our math lesson outside, in the cool breeze, to make a number line from 0-100. Although students have experience with number lines, it was interesting to watch them struggle to fill in missing numbers on the line. Counting by 10"s I laid down hoops to show "decades". Students followed and counted by 10's. Students were then paired to fill in the numbers that were missing in between each decade. I immediately noticed that students did not know how to evenly spread out the missing numbers so that the "5's" increments were in the middle of the 10's. Many students began making tick marks, but did not spread them out evenly between each 10. Once we corrected this, I asked students to stand on various points of the number line and we worked as a class to determine which "decade" the student was closer to.
Students have learned, for years, that if a number is between 0-4 they round down and 5 or more they round up. The problem is that they could not explain why they did this. By standing on the number line, they were able to see which "decade" they were closer to. When we reached the middle, such as 55, students had to decide would they round down to 50 or up to 60. Following the old way of learning it, they said 60, but when I questioned why, they could not explain it to me. We then decided that if we were on a road trip and got half way through our trip and figured out we forgot something, would we go all the way back or continue on to the next point? We would continue on, rather than driving all the way back. If we were closer to the 50 mark, like 52 or 53, it would be a short trip back, but once we made it to 55 or higher, it would be smarter to move on to 60.
Tomorrow, we carry on the learning using 0-99 charts to see if students can determine word problems that ask students to round/estimate.