This was the problem that attracted most solutions this month. You obviously like to play with the ideas of finding out the values shapes that stand in for numbers. Do you realise that you were doing algebra type work here? Well done to all of you!! Especially to our regular contributors from Yarm Primary School, Moorfield Primary School and Tattingstone Primary School. Thank you and welcome to the 4th Grade Math Club from Seacrest Country Day School, in Naples, Florida, everybody from Key Stage 2 at Dalwood Primary School, the pupils of Worth School and Class 3/B from Mef School in Turkey also to our e-mailer p4239.

The favourite strategy seemed to be 'trial and error'; or guessing at numbers, seeing if they work and then adjusting your guess. Moorfield Primary School describe this as "trial and improve", an excellent name. They calculated the values of most shapes and were able to work as number detectives: "... we worked out that circle had to be low (value) because it was with two big numbers". Good thinking! They arrived at the same answers as Y5 pupils Bijan, John and Paul from Yarm Primary School, who said: "We worked the answer out by knowing one value and working out wards to find the values of the other shapes".

Like Tom Neill for his Bernard's Bag investigation, Carla and Luke, pupils from Year 5 at Tattingstone Primary School, drew a table to help show his thinking, while James and Matthew from Worth School, wrote equations to clearly and fully explain their solutions. They used letters to represent the various shapes:

C = Circle
S = Square
H = Hexagon
T = Triangle

To begin with we looked at the bottom two rows which were:
C+T+C+C=18
and
C+S+C+C=20

We realised that the square must be 2 more than the triangle.
Knowing this we looked down the second column from the left which was:
S+S+T+S=30

So, we realised that it must be 4S-2=30.
Then we did 30+2 divided by 4 which gave S=8, so we took away two to equal T=6.

We then looked at the second row down which was:
H+S+H+S=30
We converted this into:
2S+2H=30

We halved each side which gave:
S+H=15
Then subtracted 8 (S) and so we got
H=7

We then looked at the first column:
from the left which was:
T+H+C+C=?
this, in numbers, is:
6+7+4+4

Sibel and Yeseren of Class 3/B, Mef School in Turkey gave their solution as: ? = 21.
Because as, James and Matthew of Worth School tell us, and the students from Seacrest explained:

A triangle is worth 6
A square is worth 8
A circle is worth 4
A hexagon is worth 7

So, does ? equal 21?

Let's check:

+

+

+

= 21