Earrings

Introduction

In today's lesson you will be making earrings!

Part 1

You have lots of red and yellow beads…. How many different designs of earrings with 5 beads could you make?

• How many different 5-bead earring designs can be made with two different colours of bead?

• Check to see if your answer is correct by finding them all.  

  • You may wish to use this template (PRINT ME) to make different earrings.  

  • Alternatively do it on polypad (don't forget to take screenshots)

• What system did you use for finding them all?

• What system did you use for recording the different designs?

Part 2

• What is the rule that describes how this pattern grows, i.e. as there are more beads in the earrings, what happens to the number of different designs that you can make?

• Why does this rule work?

• Verify that your rule works by starting small.  How many designs can you make if you have 1 bead? 2? 3? 4?

• Fill in the first table.  Does this agree with your rule?

Part 3

• Let's assume we have an earring with 5 beads.  How many designs can you make if you have: 

• 3 different colours of bead?

• 4 different colours of bead?

• Hint: if you wish to start with an earring with fewer beads and see if you can spot a rule.

• Use the second (two-way) table (PRINT ME) on the right to help you summarise and present your results.

• What rule do you see.  

• Why does this rule work? 

• How many different designs can you make if there are 6 beads on the earring and you have 4 different colours of bead?

• What if there are 4 beads in 6 different colours?

• If you want more combinations, is it better to have more beads or more different colours?

• Challenge: how many different designs can you make if there are ‘b’ beads on the earring and there are ‘c’ different colours of bead?

Part 4

Thinking again about the original problem, with 5 beads and just 2 colours…

• How many of the earrings use 5 red beads?

• How many use 4 red beads and 1 yellow bead?

• How many use 3 red beads and 2 yellow beads?

• How many use 2 red beads and 3 yellow beads?

• How many use 1 red beads and 4 yellow beads?

• How many use no red beads?

Put your results in the third (two-way) table (PRINT ME). What patterns do you notice?

Do the same for other numbers of beads, still using just two colours.