This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
This activity investigates how you might make squares and pentominoes from Polydron.
If you had 36 cubes, what different cuboids could you make?
We had a very impressive number of responses
to this tricky problem. Thank you everyone who sent in their
solutions. There were a couple of different ways of looking at the
problem and because you explained your solutions so clearly, we can
see that both are equally good.
I counted how many times the 5 was in the units of the minutes
(eg 01:25) each hour (6 times) then multiplied it by 24 (144).
Then I counted how many times the 5 appeared in the tens of
minutes (eg 12:50) in 24 hours (24).
Finally I counted how many times it appears in the hours section
(eg 05:00) (2).
I added it all up and got 170. The answer is the same for the 12
hour clock, because there's just two 5 o'clocks instead of 05:00
Those of you who agreed with this
Laurie from Rhodes Avenue, George (who didn't
tell us where he goes to school), Miriam from Archbishop Temple
High School, Edward from WMMS, Xavier from Thomas Deacon Academy,
Elliot (who didn't tell us where he goes to school), Alex and Grant
from St Benedict', Mike (who didn't tell us where he goes to
school) and Shasvat from GIIS. Well done.
Another solution came in from Jonathan from
St. Andrews Primary (Devon). This is quite a different solution to
Cassandra's because Jonathan looked at the problem in a different
way. When Jonathan worked out his total, he counted the 5's that
would be on the clock if he looked at it every minute. So, for
example, at 05:53 there are two, then at 05:54 there are two, and
at 05:55 there are three and so on. Here is his explanation:
My answer is 504. This is how I worked it out. I worked out that
5 appears 16 times in 22 hours (05, 15, 25, 35, 45, 50, 52, 53, 54,
55, 56, 57, 58, 59), but I had to add 60 more 5s when the hour was
5 or 15 to make 76.
I multiplied 16 x 22 to make 352, added 2 x 76 (152) to make my
Here is the sum to show what I did: (16 x22) + (76 x2) =
Yes I think it is the same with a twelve hour clock, it just has
2 5s instead of 15.
Michael from Henry Park Primary School in
Singapore, Laura and Matthew from Radstock School, Amy from
Talycopa Primary, Emily, Tishtrya, Michelle and Fionnuala from
Ursuline High School, Oliver from Aycliffe, Calum, Fergus and Nancy
from St Anne's Primary, Class 5AH from Aston Fields, Khalid, Piotr
and Antranig from Dubai International Academy, Julieta from The
Grange School, Jozie and Molly from Cumnor Primary, Jacob from St
Edburg's, Caitlin, Molly and Oliver from Great Torrington Junior
School, Katie, Theona and Abigail from St Joseph's RC High School,
Christopher and Zoe from Randlay Primary School, Isabella from
Parkland Junior School, KS2 Class from Ysgol Aberdyfi, Jessica,
Isobel, Emma, Lily, Alice, Lotty, Helena, Molly, Martha, Isabella,
Lucy, Matilda and Nathalie from St Ives, The Extenstion Maths Group
at St Nicolas C of E Junior School and Alex from Waddinton Redwood
Primary School all sent in good solutions which agree with
Finally, a special mention to the Junior
Class at Ysgol Bryncrug who sent in this Word document which
explained their thinking very, very clearly. They also thought the
solution was 504 and in the document, they talk us through how they
solved the problem. Thank you!