Tug of War

was a popular problem this month. I think it was because of Sniffles! It attracted many responses and, most importantly, many different ideas about how the problem could be solved. Although there were many different strategies, they had something in common. See if you can discover what it is.

Cale, who is in class 4 Blue at The British School in Tokyo, starts us off:
Just say the P.E. teachers each rate 10 in strength on a scale from 0-10. That is 40 altogether.
The grandparents each rate 8 in strength on a scale 0-10. That is also 40 altogether.

Sniffles tied with people who have the following values, 10+8+8.
So, therefore, Sniffles rates 26.

In the third heat:
P.E. teachers rate 40 altogether.
Sniffles rates 26. Three grandparents rate 8+8+8 so they rate 24.
So, Sniffles plus the grandparents rate 24+26 = 50

This is how Marion explains her thinking:

Justin assigns a number to each person to help him solve the problem:

How is this different from the way that Georgia devises to help her decide on the winners?

Hmmm... people and dogs who are fractions. This was a good and effective strategy. It was also used by Duncan and James of Y4, Hutton Rudby CP School, NorthYorkshire. Tom, however, does not use common fractions but decimal fractions - and just as effectively as Georgia. Here is a part of the work that shows Tom's solution, Can you see the connection between Georgia's and Tom's work?

As this is a little difficult to read, let's also look at this explanation from Zain, Richard, Craig and Jamie from Glenmead Primary in Birmingham, who called each grandparent's strength 'g'.
This meant that each P.E. teacher had a strength of 1.25g (4xP.E. = 5g).
Sniffles was equal to one P.E. teacher plus two grandparents so Sniffles had a strength of 3.25g (1x1.25g + 2x1g).
The final tug of war was Sniffles (3.25g) and three grandparents (3 x 1g) verses four P.E. teachers (4 x 1.25g).
This resulted in 6.25g verses 5g - result Sniffles and the Grandparents won.

David, a year 4 pupil, also wrote equations to show his thinking. Can you see the ways in which his work is the same as well as the differences with the solution above?
These 'tuggers' were also given letters so you knew who was who:

Teachers = T
Grandparents = G
Sniffles = S

What we know:
From the first heat we know that
4T=5G
From the second heat we know that
S=T+2G
The last heat was
3G+S may or may not equal 4T

This is how David went on to find a solution:
Turn S and G into T

That means,

G=4/5T
S=T+2(4T/5) or T+8T/5
3G+S then becomes 3(4/5T)+(T+8T/5)
which (if you remove the brackets) becomes
12T/5+T+8T/5
12T/5+5T/5+8T/5=25T/5
25T/5=5T
So ... 3G+S=5T

And 5T is bigger than 4T

Can you work out in David's work which team 5T represents and which is 4T?

As the pupils from Room 14, and Luke, Ryan and James wrote:

Although, maybe it wasn't Sniffles who drew you to solving the problem, maybe it was those teachers who thought they were so strong. Andrew and Jj from Y4 at Hutton Rudby C.P. School in North Yorkshire seem to think along these lines.
The people who win are the dog Sniffles and the three grandparents. Because Sniffles nearly beat 1 PE teacher and 2 grandparents, and 5 grandparents had a draw with 4 PE teachers. The teachers will have a row because they won't admit they have the same strength.
Maybe!!