The Paw-shakeProblem

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-shakeProblem

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?”

Let’s start with

2 dogs

1 paw-shake

How many paw-shakes will

there be?

?

How about…

3 dogsHow many

paw-shakes will there be?

3 paw-shakes?

1paw-shake

Rocky shook Dexter’s paw

How did Billy get the answer

of…

3 paw-shakes

?

That means…

3paw-shakes

2paw-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?

Number ofpaw-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 ?

Number ofpaw-shakes

Number of Dogs

2Work out your answer on a

piece of paper with your

table group.

Havea go!

1

3 3

4 ?

1 0

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.

12 34 56

Let’s look at theproblem

another way.

1

2

3

4

5

6

Theo can’tshake hisown paw.

… and another

way.

1

2

3Theo can’tshake hisown paw.

4 dogsHow many

paw-shakes would there be?

6 paw-shakes?

10

Number ofpaw-shakes

Number of Dogs

2 1

3 3

4 6

Can you see a pattern forming?

?

5 ?

1

2

3

4

0

10

What if…

5 dogs shook paws?

Can you see a pattern in this

table?

10

Number ofpaw-shakes

Number of Dogs

2 1

3 3

4 6

5

Let’s add thenumber of dogs with

the number of paw-shakes!

3

6Work out

the pattern with your group

10

Work out The next part of the

table with your group.

Number ofpaw-shakes

Number of Dogs

2 1

3 3

4 6

1 0

Create a number

sequence.

What if…

6 dogs shookpaws?!

5 10

6 ?