the paw-shake problem billy is a dog trainer. he loves to train dogs to do lots of tricks! ? his...
TRANSCRIPT
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 ?