This is an account of a lesson I taught today, with 19 children aged 8 to 11. The aims of the lesson were:
(1) Looking at, and describing.
(2) Working with other people.
This is part of a unit of work aimed at developing childrens' understanding of place value. This is one of a series of lessons in which we will explore various bases using Cuisenaire rods.
The children worked in pairs of their choosing, and one three. I started by presenting this video. We watched it twice, and then I asked them to describe what they had seen, continue the pattern (using rods of their own), and describe anything they noticed. Here are their responses:
- The language of "swapping", "trading in" and "exchanging" reds for a green.
- "...because 1 green is equivalent to 3 reds", and "three reds was the same size as a green so it turned into a green".
- Predictions of the pattern in reds and greens.
- "There are no threes in the pattern".
One child who was not particularly engaged last week seemed to enjoy using the rods to mimic my actions on the video almost exactly, and became increasingly engaged in this lesson.
I invited children to share any descriptions with the whole class, and a number were willing to do so, and gave extraordinarily clear descriptions. It was also interesting that all of the other children seemed to be listening.
- "The reds go 21Ø3, 21Ø3, 21Ø3..."
- The use of the word "reset" to describe exchanging a green for three reds.
- "He went backwards as soon as he got to 4|0 he did 3|3 which indicates the fact that he was going back..."
- "4 greens 0 reds... is actually 3 greens 3 reds..."
- "The numbers in the green column stay the same until the change [of green for reds]"
- "Browns are worth 4 reds", and "This time four reds are one brown instead of 3 reds making 1 green".
- "The cycle repeats itself over again multiple times".
- Lots of descriptions of the patterns in browns and reds, such as "browns go 1111, 2222" and reds go "1230 1230".
Perhaps we will follow this with some addition and subtraction in various bases (perhaps moving into binary, and/or extending to base 5), and then some times tables (perhaps in base 6), depending on how the children get on with it. Finally we might do some work in base 9, 10 and 11.
At some point I think it would be fun to do some work on logic gates, and maybe some programming.