Day 1:
1. Let n = 6. Pick 5 whole numbers and see what the remainder is when you divide them by 6.
2. What are all the possible remainders when dividing by 6?
3. What do you notice about the remainders if you pick values in order to divide by 6? i.e. Find
6,7,8,… divided by 6 and keep going until you notice a pattern.
4. What are the possible remainders when dividing by n?
5. Pick a value for n (other than 6) then design and print a clock face with all of its remainders
evenly spaced.
Day 2:
1. Last class we learned that the remainders keep repeating and that all possible remainders go
from 0 to one less than the number. We can use the clock model to find the remainder when any
number is divided by n. For my example when n = 6, if I want to know the remainder when 10 is
divided by 6 I go around the clock 10 times (starting at 0). The number we end up on is 4. Use
your clock to find the remainder when each of these values is divided by n:
a. 10
b. 15
c. 17
d. 22
2. Another way to write the remainder is using the word “mod.” We could say 10 ≡ 4 (mod 6)
because 10 divided by 6 left a remainder of 4. The “≡” symbol means congruent. Re-write your
answers to question 1 in this new notation.
3. In the 𝑎 ≡ 𝑏 (mod 𝑛) form we want b to be the smallest possible positive remainder. For
example, we said 10 ≡ 4 (mod 6). We can also say that 16 ≡ 10 (mod 6) since 16 and 10 both
have a remainder of 4 when divided by 6, but it is preferred to say 16 ≡ 4 (mod 6). Solve for x
in the following:
a. 28 ≡ 𝑥 (mod 8)
b. 𝑥 ≡ 3 (mod 7)
c. 5 ≡ 2 (mod 𝑥 )