Problems

Materials:

  • paper, pencil, crayons or pencil crayons

Isaiah and Jasmine were making necklaces for their friends.
They decided to make the necklaces very mathematical.
Each necklace was to have eight beads, four of one colour and four of another.
And each had to be symmetrical so the first four beads would look the same as the last four beads, like this.

Necklace with 8 beads, red rectangle bead, yellow circle bead, yellow circle bead, red rectangle bead, red rectangle bead, yellow circle bead, yellow circle bead, red rectangle bead

How many different necklaces could they make?
Can you find them all?

How will you keep track of the necklaces?
How do you know there aren’t any others?

Possible Extensions

What if they had 9 beads, five of one colour and four of another?
What if they had 10 beads, five of each?
Design your own symmetrical necklace using two colours.

Adapted from nrichmaths.org