This activity investigates how you might make squares and pentominoes from Polydron.
If you had 36 cubes, what different cuboids could you make?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Abi of Moorfield Junior
School found the following combinations of three biscuits from the
$12$ different varieties, this was the same as that sent in by
Sarah and Helen from
Glenmead Primary in Birmingham. They show their answers as
a list, but first they
explain the strategy they used to help them with so many
First, we started with alphabetically, ABC, DEF, GHI and
Then we did the first letter of the first three biscuits
Next we took the second letters (BEH) of each plate of
Finally, we sorted out the ones left over.
The possible plates of biscuit varieties that the girls came up
Prateeksha , from
Riccarton Primary School, shows a slightly different strategy. It
is a list like Emma and
Abi's but can you see how the information has been organised in
this list? The organisation is what shows Prateeksha's
Is this list the same as Terry and Daren's from Alma Primary School in
Joanna from W.C.P.School
in Manchester sent in a
list of their 'plates' and used letters to represent the
biscuit varieties, as did James from Girton Glebe Primary School
near Cambridge. Although the order of their answers was different,
the combinations were the same.
Hannah, Amy, Jenny
and Emma , also from
Moorfields School, seem to have a completely different way of
figuring out their solution. But have they?
Can you see what they have done?
But how do you keep track of all that information? This is what
Alex from Brecknock
I started with abc, then def, ghi, jkl and then mixed them
I made a list of all the biscuits as they were used, after that I
crossed out a letter every time I used one of that type.
Hmm, it looks like 'a and f' in the centre line are not matched
with other biscuits. Why do you think that is?
Oskar , a fellow
pupil from Brecknock Primary, started with A(lmond finger) and I
moved 1 A forward 1 place and another A forward 2 places. I did the
same with the next plate then the next plate and so on. The
solution ended up like this:
Nathan , also from
Brecknock explains; first I wrote a table .
I started with kbc then I made sure that I used each biscuit
I continued with the rest of the biscuits. When I had used all the
biscuits I had to mix the biscuits about. This was my answer:
kbc, def, ahf, jk, dbe, bgc, jhb, fki, aij, iel, lgd, gca.
The students of Ms Brown's
class also organized their information in a table , but in different way then
Oskar. Did they arrive at a different answer the other pupils
They begin by explaining their notation. They used a combination
of letters (for the variety of biscuit) and numbers (to show if it
was the first, second or third biscuit selected).
A lmond Fingers = A1 (biscuit 1), A2 (biscuit 2),
A3 (Biscuit 3).
B ourbon = B1, B2, B3.
C hocolate Chip = C1, C2, C3.
D igestive = D1, D2, D3.
E aster Biscuits = E1, E2, E3.
F ig Rolls = F1, F2, F3.
G ingernuts = G1, G2, G3.
H oneynut cookies = H1, H2, H3.
I ced Wafers = I1, I2, I3.
J ammy Dodgers = J1, J2, J3.
K iwi Cookies = K1, K2, K3.
L emon puffs = L1, L2, L3.
Working it out:
Altogether there are $36$ Biscuits.
$12$ types of biscuits and $12$ plates.
So, what did they do with the information? They used a
spreadsheet and built a table like this. One of the pupils
Put A-B-C together, D-E-F together, G-H-I together and J-K-L
Now there are $2$ of each biscuit left.