Inquiries-Week 9: Mod Multiplication

Thanks to Sam Graf for introducing me to this and suggesting some toys. IntroductionMultiplication tables can be fun. Line up your numbers, multiply, and find patterns. Like with 5x5, we can fill it out and highlight symmetry, divisibility, squares, and so much more. In this inquiry, we're going to play with a different version of these tables. Starting with SixTake that 5x5 multiplication table and divide each number by 6, and write down the remainder. Another way to say this is mod 6.1-5 multiplication table like above, but with mod 6 applied.What do you notice? What patterns emerge in the table? What numbers produce zeros?What numbers don't produce zeros?Make a table for the numbers that don't produce zeros, and apply mod 6 as before. This is called a Cayley tableMultiplication with 1 and 5 mod 6 producing all 1's and 5'sFor each number in the table, look at its powers mod 6 and note any observations: Here is 5:ActivityNow, let's take what we did with six and repeat it with other…