Thursday, November 14, 2013

Exploring Factors

Today in math, we looked at factors. To do this, we used coloured tiles to make rectangles. I showed the students how a rectangle that was two blocks wide and ten blocks long could represent the equation 2 X 10 = 20 in the same way an array would. I then rotated the rectangle to show that the same rectangle also represented 10 X 2 = 20.

My intention was to allow the students to work with partners to create their own rectangles using the tiles, and to make the connection to multiplication facts. We set a few simple parameters first, both to keep the task from becoming too simple and to prevent us from running out of tiles. We decided that the smallest any side could be was two tiles, and that the largest any side could be was twelve tiles. We also decided that it was important to right each multiplication fact two ways so that we didn't end up making the same rectangles over again by mistake.

The students set right to work making their rectangles, and enjoyed the idea of using large quantities of tiles. I noticed right away that many groups would make a rectangle, draw it, write the facts, and then promptly destroy it and start again. I encouraged them to think of a way that they could change their existing rectangles by making the sides larger or smaller in order to change the facts represented. This both saved time and allowed students to gain a deeper appreciation of the relationship between these numbers. For example, without doing this, a student might not realize that the rectangle representing 12 X 3 is not that different from the one representing 4 X 10.

Our next step will be to explore the factors of the products that we created. None of the groups today created rectangles with the same products, so it will be fun to experiment with this. I plan to have each group look at the rectangles they created and try to find different way to make the same product. For example, if a group built a 6 X 4 rectangle, they will need to build 1 X 24, 2 X 12, and 3 X 8 rectangles as well. This will also be a good activity to look back on while studying surface area later this year!

No comments:

Post a Comment