Thursday, September 30, 2010
Place Value Structures, Class #4
Today was our last class on place value structures using material from Bridges. For the last three weeks we've been considering place value in base five, looking at units (1), strips (5), mats (25), and stripmats (125). Today I asked students to imagine what the pieces might look like if we were working in base four. They began by building the pieces with tile. They debated over whether the mat should have 16 pieces or 24 pieces. (I think that a few jumped from the logic that if base 5 had 25 pieces, then base 4 should have 24 pieces.) We looked at the base five chart we'd made. Students recalled that with base five, each place value was x5, so decided that with base four, each would be x4 with a total of 16 for a mat. No easy task.
They cut a unit, strip and mat from graph paper. I then asked them to cut out a strip mat. When they couldn't agree on the area, I asked them to build mats with tile. Ah-ha! Then they remembered how to follow the place value pattern and had no trouble building a stripmat of 64.
base ten pieces and asked them to create a strip mat. With shining eyes and wide grins they asked me for TEN MATS and told me that a strip mat would have 1000 units. They built a strip mat and then proceeded to tell me what the next piece would look like and that it would have 10,000 units. "And then 100,000 and then 1,000,000...!!!!!!!!!!!!!" They helped me to complete a venn diagram comparing base five and base ten.
Sir Cumference and All the King's Tens and talked about place value in base ten. I also read The 329th Friend and asked them to build 329 (and a few additional numbers) with the base ten pieces.
It isn't unusual for teachers to ask, "Why do we teach other bases to children?" It's elementary, my dear! When we teach other bases, we give children an opportunity to develop conceptual understanding of place value. That deep understanding transfers to work in "our base," base ten. The lightbulbs in my classroom were going off so fast today that the electric meter must have been smokin'! Base ten place value means something new and exciting.
It's elementary. :)
You've been a wonderful class! Can't wait to see you again!