Learning by doing

I had the opportunity to teach two of the same class yesterday, back to back.  The subjects were adding and subtracting integers and introducing coordinate graphing.  During the first block period, I addressed questions from the homework, and gave the students questions from the book to do on their own.  The point was to recognize that there are many ways to say the same equation: 12 - 12 is the same as 12 + -12 and -12  - -12 and -12 + 12 all equal zero, but -12 + -12 is -24 and not the same thing.  The students had many questions throughout the period, and we ended up only doing 3 of the 6 activities we had planned for the period.  I did introduce coordinate graphing, attempting to model by drawing a graph free-hand on the white board; however, when I went around the room to see what kids were drawing, I saw several that did not have negative numbers on their axes, and I had forgotten to stress that the axes cross at (0,0). 

During the second period, I managed to stay on time better by not having as many students come to the board to answer the questions, but just having them answer from their seats.  I also decided to model the graphing under the doc cam, where I used a ruler and had the same graph paper the students had.  I stressed that the axes cross at the origin, located at (0,0) and that each axis is just a number line, with both positive and negative numbers.  We had significantly more time at the end of the period to introduce the graphing homework, and were able to check in with students individually to see if they understood the concepts before the period ended.  The second time around was so much better!