In my head there are two things at odds:
- Practice is important in the consolidation process
- Mathematics is about thinking and reasoning… making sense of things.
So finding ways to practice a skill, while continuing to develop our ability to reason mathematically is a goal of mine. While there are lots of ways to do this (problem solving, games, open-middle …), I thought I would give an example of how we can do both do problem solving that requires thinking and reasoning and practice a new skill at the same time. So here is a problem that I give students that have recently started learning about square numbers.
A happy number is a number defined by the following process: Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number either equals 1 (where it…
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