RIC-0563 Developing algebraic thinking

SHAPES
Teachers notes
Triangle 10
Triangle 10 can be considered an extension of Triangle 9, where the
middle digit f is 0. Other solutions do exist, however, where f is not 0.
a
b j
c i
d e f g h
a + b + c + d = d + e + f + g + h = h + i + j + a
a + b + c = e + f + g + h, d + e + g = a + j + i
In the solutions below, again notice the clockwise (or
anticlockwise) order of consecutive digits.
6
1 7
8 3
5 9 0 2 4
3
4 7
8 6
2 9 0 5 1
9
1 3
5 4
8 6 0 2 7
Here are solutions where f ≠ 0.
8
7 4
2 6
1 3 5 9 0
3
4 7
8 6
2 9 0 5 1
9
1 3
5 4
8 6 0 2 7
Rectangle
Rectangle is one of the most difficult number tile puzzles in the book. The
equations are easily determined; however, finding the proper location
of digits is not easily accomplished.
a
b
c
d
j
e
i
h
g
f
a + b + c + d = d + e + f = f + g + h + i = i + j + a
a + b + c = e + f, d + e = g + h + i, f + g + h = j + a
8
4
5
9
6
1
9
2
8
2
3
0
8
0
3
6
0
2
3
4
1
1
7
9
5
7
4
5
7
6
R.I.C. Publications ® www.ricgroup.com.au DEVELOPING ALGEBRAIC THINKING 85
ISBN 978-1-74126-088-5