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.

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Presentation transcript:

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.

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 ?”

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

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

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…

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

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

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

? Let’s look at the problem another way Theo can’t shake his own paw.

? … and another way Theo can’t shake his own paw.

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

10 ? Number of paw-shakes Number of Dogs Can you see a pattern forming? ? 5 ? What if… 5 dogs shook paws?

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

Work out The next part of the table with your group. Number of paw-shakes Number of Dogs Create a number sequence. What if… 6 dogs shook paws?! ?