The idea for today's lesson was for student's to explore the relationship between the least common multiple (lcm) and the greatest common divisor (gcd) for two values a and b. Before diving into this investigation the next portfolio problem was assigned. This assignment asks students to write-up the solution to one of the three Chinese Remainder Theorem problems we worked on in class and to explain the mathematical relationships that are present.
The next piece of the lesson was for students to pick their own pairs of values and see if they could establish any connections between the pair of numbers and the gcd and lcm of the pair. From the discussion I had with my substitute, it appears that only a handful of students actually worked on this task.
Worse, when discussing their results and presenting arguments that supported their results students presented the arguments of:
- You have to take it on faith
- It is magic
Students were to explore the relationship of lcm and gcd for a set of three integers. It appears that the only person in the classroom who explored this idea was the substitute.
As it is Friday, I will be speaking to the class on Monday about their behavior and work ethic. I intend on putting a stop to the intellectual laziness that has presented itself recently.
Visit the class summary for a student's perspective and to view the lesson slides.
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