This was a popular problem. 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. 

  <p><strong style="font-weight: 400;">Cale</strong> , who is at
  The British School in Tokyo, starts us off:<br />
  <em>Just say the P.E. teachers each rate 10 in strength on a
  scale from 0-10. That is 40 altogether.<br />
  The grandparents each rate 8 in strength on a scale 0-10. That is
  also 40 altogether.</em></p>

  <p><em>Sniffles tied with people who have the following values,
  10+8+8.<br />
  So, therefore, Sniffles rates 26.</em></p>

  <p><em>In the <strong style="font-weight: 400;">third
  heat</strong> :<br />
  P.E. teachers rate 40 altogether.<br />
  Sniffles rates 26. Three grandparents rate 8+8+8 so they rate
  24.<br />
  So, Sniffles plus the grandparents rate 24+26 = 50</em></p>

  <p>This is how <strong style="font-weight: 400;">Marion</strong>
  explains her thinking:<br />
  <img alt="Marion's solution." src=
  "/content/01/06/penta1/fig1.jpg" /></p>

  <p><strong style="font-weight: 400;">Justin</strong> assigns a
  number to each person to help him solve the problem:<br />
  <img alt="Justin's solution." src=
  "/content/01/06/penta1/fig2.jpg" /></p>

  <p>How is this different from the way that <strong style=
  "font-weight: 400;">Georgia</strong> devises to help her decide
  on the winners?<br />
  <img alt="Georgia's solution." src=
  "/content/01/06/penta1/fig3.jpg" /></p>

  <p><strong style="font-weight: 400;">Hmmm...</strong> people and
  dogs who are fractions. This was a good and effective strategy.
  It was also used by <strong style="font-weight: 400;">Duncan and
  James</strong> of Hutton Rudby CP School, NorthYorkshire.
  <strong style="font-weight: 400;">Tom</strong> , 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?<br />
  <img alt="Duncan and James' solution." src=
  "/content/01/06/penta1/fig4.jpg" /></p>

  <p>As this is a little difficult to read, let's also look at this
  explanation from <strong style="font-weight: 400;">Zain, Richard,
  Craig and Jamie</strong> from Glenmead Primary in Birmingham, who
  called each grandparent's strength 'g'.<br />
  <em>This meant that each P.E. teacher had a strength of 1.25g
  (4xP.E. = 5g).<br />
  Sniffles was equal to one P.E. teacher plus two grandparents so
  Sniffles had a strength of 3.25g (1x1.25g + 2x1g).<br />
  The final tug of war was Sniffles (3.25g) and three grandparents
  (3 x 1g) verses four P.E. teachers (4 x 1.25g).<br />
  This resulted in 6.25g verses 5g - result Sniffles and the
  Grandparents won.</em></p>

  <p><strong style="font-weight: 400;">David</strong> 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?<br />
  These <strong style="font-weight: 400;">'tuggers'</strong> were
  also given letters so you knew who was who:<br />
  <br />
  <em>Teachers = T<br />
  Grandparents = G<br />
  Sniffles = S</em></p>

  <p><strong>What we know:</strong><br />
  <em>From the first heat we know that<br />
  4T=5G<br />
  From the second heat we know that<br />
  S=T+2G<br />
  The last heat was<br />
  3G+S may <strong style="font-weight: 400;">or</strong> may not
  equal 4T</em></p>

  <p>This is how David went on to find a solution:<br />
  <em>Turn S and G into T</em></p>

  <p><em>That means,</em></p>

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

  <p><em>And 5T is bigger than 4T</em></p>

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

  <p>As the pupils from <strong style="font-weight: 400;">Room
  14</strong> , and <strong style="font-weight: 400;">Luke,
  Ryan</strong> and <strong style=
  "font-weight: 400;">James</strong> wrote:</p><strong style=
  "font-weight: 400;">the 3 Grandparents + Sniffles beat the 4
  Teachers!</strong> <br />

  <p>Although, maybe it wasn't Sniffles who drew you to solving the
  problem, maybe it was those teachers who thought they were so
  strong. <strong style="font-weight: 400;">Andrew and Jj</strong>
  from Hutton Rudby C.P. School in North Yorkshire seem to think
  along these lines.<br />
  <em style="font-weight: 400;">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.</em><br />
  Maybe!!</p><br />