RIC-0563 Developing algebraic thinking

SHAPES
Teachers notes
Introduction
Shapes begins with a small triangle using only six tiles and ends with Box
Sum, a two-dimensional representation of a cube using eight tiles. The
equations become progressively more difficult to solve simultaneously;
however, several patterns do appear.
Looking at
the Algebra
Triangle 6
In Triangle 6, the algebra is straightforward. Each of the three digits a,
c and e has to be used in two equations as shown below.
a + b + c = c + d + e = e + f + a
a + b = d + e, c + d = f + a
a To create the smallest sum 6, we use 0, 1 and 2 at the
b f vertices; for the largest sum 21 we use 7, 8 and 9.
c d e
Notice the clockwise order of the digits in the
examples.
2
3
5
9
4 3
8 7
8 7
5 4
0 5 1
1 9 2
1 9 2
7 6 8
Triangle 9
For Triangle 9, the three digits in the vertices are again important in
finding a solution.
a
b i
c h
d e f g
a + b + c + d = d + e + f + g = g + h + i + a
a + b + c = e + f + g, d + e + f = a + i + h
Notice the clockwise (or anticlockwise) order of consecutive
digits in the following solutions.
8
1 0
3 5
7 4 2 6
5
8 7
0 2
4 9 1 3
3
4 7
8 6
2 5 9 1
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