RIC-0563 Developing algebraic thinking

SHAPES
Teachers notes
Pentagon
The equations for Pentagon can be solved so that the remaining equations
each have a sum of two digits on both sides of the equal sign.
j
a + b + c = c + d + e = e + f + g = g + h + i = i + j + a
b
j
a + b = d + e, c + d = f + g, e + f = h + i
c
i
d
h
g + h = j + a b + c = i + j
e f g
9
0
0
1
9
8
7
6
2
3
4
2
5
7
5
3
8
4
6
1
Box Sum
The final problem in this section is Box Sum. It has appeared in many
different puzzle books, usually with no mathematical background
information. Since the sum of each face of the cube must be the same,
there are six algebraic expressions that are equal. Subtracting like
terms from various equations provides several relationships among
the digits.
b
f
a
e
g
c
d
h
a + b + c + d = a + b + f + e = a + d + h + e =
d + h + g + c = b + c + g + f = e + f + g + h
c + d = f + e, b + f = d + h, a + e = c + g
b + c = e + h, a + b = g + h, a + d + f + g
All six of the equations show that the sum of the two
digits on one edge of the cube is the same as the sum
of the two digits on the edge diagonally across on the
opposite face.
8 5
8 7
4 8
3 2
6
1
7
4
2 3
6
To start, select an edge and two digits. Now, select two other digits that
give the same sum. With these initial selections, the remaining tiles
become easier to place.
4
9
1
1 6
9
5
3
2
86 DEVELOPING ALGEBRAIC THINKING www.ricgroup.com.au R.I.C. Publications ®
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