My year 11 students are nearing exam time and the last item on our course is an introduction to logarithms. They had just learned the laws of logs and so we finished the lesson with this activity. I put some pink papers around the classroom, each with a requirement.
Each group of students had to use their sticky notes to add one or more expressions to each pink poster. I was quite impressed by their responses and it was clear they had understood our lesson objectives.
After learning about indices recently, I asked my year 10s to respond to this question for homework: Among the natural numbers, are there more square numbers or cube numbers?
I want to teach them over the course of two years to express their mathematical thinking in words. I asked for a paragraph for homework. Some students wrote me a single sentence, others a few sentences. Some included examples.
The next lesson this led to a really interesting discussion about the size of an infinite set. How many items in the set of square numbers? Could you count all the cube numbers? If there is a cap on the size of the number, then there are certainly more squares than cubes. But when you let the numbers go to infinity, it’s a different story altogether.
I hope to do more activities like this with them this year. They should be able to express and justify their opinions.