1. The Paw-shake Problem Billy is a Dog Trainer. He loves to train dogs to do lots of tricks! ? His favourite is to teach them how to shake hands.

2. The Paw-shake Problem One day, Billy thought to himself… “If I could teach all the dogs to shake hands with each other… …how many paw-shakes would there be ?”

3. The Handshake Mystery Let’s start with 2 dogs 1 paw-shake How many paw-shakes will there be ? ?

4. The Handshake Mystery How about… 3 dogs How many paw-shakes will there be ? 3 paw-shakes ?

5. 1 paw-shake Rocky shook Dexter’s paw How did Billy get the answer of… 3 paw-shakes ? That means… 3 paw-shakes 2 paw-shakes Rocky shook Theo’s paw Dexter shook Theo’s paw Each dogs shakes paws 2 times! Remember…

6. Let’s start making a table… How many paw-shakes have we counted so far ? 3 handshake ? Number of paw-shakes Number of Dogs 2 1 3 3 Let’s continue the table… How many paw-shakes would there be if there were 4 dogs ? 4 ?

7. ? Number of paw-shakes Number of Dogs 2 Work out your answer on a piece of paper with your table group. Have a go! 1 33 4 ? 10

8. Group 6Group 5Group 4Group 3Group 2Group 1 What answer did your group come up with? How did your group come up with that answer? Use the dogs below to show your working out. 1 2 3 4 5 6

9. ? Let’s look at the problem another way. 1 2 3 4 5 6 Theo can’t shake his own paw.

10. ? … and another way. 1 2 3 6 Theo can’t shake his own paw.

11. The Handshake Mystery 4 dogs How many paw-shakes would there be ? 6 paw-shakes ?

12. 10 ? Number of paw-shakes Number of Dogs 21 33 4 6 Can you see a pattern forming? ? 5 ? 1 2 3 4 0 10 What if… 5 dogs shook paws?

13. Can you see a pattern in this table? 10 Number of paw-shakes Number of Dogs 21 33 4 6 5 Let’s add the number of dogs with the number of paw-shakes! 3 6 Work out the pattern with your group 10

14. Work out The next part of the table with your group. Number of paw-shakes Number of Dogs 21 3 3 4 6 1 0 Create a number sequence. What if… 6 dogs shook paws?! 5 10 6 ?