Worksheet · Modular arithmetic
Times tables on a circle
Name: Date:
Before the film: predict
Ten dots on a circle are numbered 0 to 9. Each dot n is joined to dot 2n, counting past 9 back to 0. Which dot does 7 join?
Starter
With 10 dots and times 2, list where every dot 0 to 9 goes.
Draw the ten lines. Which dots get two lines arriving?
Core
With 200 dots and times 2, where do dots 150 and 199 go?
With 200 dots, which dots go to themselves under times 2? Under times 3?
How many cusps do times 2, times 3 and times 4 give?
Challenge
With 200 dots, show that times 101 sends every even dot to itself and every odd dot to the opposite side.
With 200 dots, what does times 201 draw, and why?