This Wednesday’s lesson was a bit chaotic and unfortunately I do not have any pictures from it. The girls were both hyper and cranky, and it was hard to keep their attention for more than five consecutive minutes; after that they would start either jumping around or demanding games (which we did play a fair amount of). Nonetheless, I did attempt a few things and hopefully they absorbed something out of what I said. I am often amazed by how Katie remembers ideas from discussions where I thought that she was not really paying attention or understanding much.
The lesson began with a discussion of the homework. One of the problems involved counting outfits again: Dora had 3 different colored shirts and 4 pairs of shorts; how many outfits did she have? I specified the colors and gave them a paper with many (more than 12) uncolored Doras for them to color. They both correctly came up with 12. When Katie was coloring hers (prior to the lesson) I first told her to color as many as she could come up with. After 8 fairly random ones, she got bored and said that she was done. I then had her check for each shirt, in turn, whether she combined it with every pair of shorts. This led to her finding the remaining 4.
During the lesson, I drew a 3 by 4 grid, with shirts drawn above the columns and shorts along the rows. I filled in a few squares of the grid and tried to explain that if I filled in all of them then I would get all of the outfits. I couldn’t tell whether they understood the reason because they took turns saying things like, “but you didn’t fill in the square with a red shirt and blue shorts yet,” and “can you please fill in the one with the yellow shirt and yellow shorts.” I also had the thought of having them compute 3 times 4 in a different way and pointing out that it’s also 12, but at this point my five minutes were up and it no longer mattered what I said.
After the lesson I decided that it was a good thing that I didn’t get a chance to connect the outfits problem to multiplication. My guess is that they would not have been impressed. Perhaps the best thing to do is to have them do the ‘grid type’ problems separately from the multiplication problems and wait until they make the connection on their own. It will probably be a lot more meaningful that way.
This raises a more general question for the teachers (in a broad sense) out there: how do you decide when to point out connections to students and when to wait until they figure them out on their own? Ideally they would be left to make as many on their own as possible, but I am sure that this is not always realistic. Also, it feels like you would want to sometimes nudge them in order to move forward with certain concepts.
The other topic that I attempted during the lesson was classifying quadrilaterals. We started discussing the definitions of rectangles, squares, rhombuses, etc. The girls both knew what a right angle is, and that squares and rectangles have four right angles, which was a good start. My attempts to go any further were, however, unsuccessful. I want to come back to the topic next time, discussing whether squares are rectangles and rhombuses, and playing with axes of symmetry for all these figures.