RIC-0563 Developing algebraic thinking

PENTOMINO PUZZLES
Teachers notes
Group 3
The last group also contains three pentominoes.
b
c
d
a
d
e
a
e
b
c
d
a
b
e
c
The algebra involves three equations, which are the same for each
pentomino.
a + b = b + c + d = d + e.
With a + b = b + c + d, then a = c + d.
Similarly, with d + e = b + c + d, then e = b + c.
There are two possible arrangements of tiles for the greatest sum.
Since a is a single digit, the greatest possible sum for c + d is 9.
This gives c = 1 and d = 8, with e = 7 and b = 6, or c = 2 and d = 7,
with e = 9 and b = 6.
The greatest sum is 15.
The least possible sum for c + d is 3, with a = 3, c = 2, and d = 1.
This arrangement gives b = 4 and e = 6, with the least possible sum being 7.
Here are some other solutions:
7
1
4
6
4
8
5
8 5
4
2
7
5
9
3
Questions for
discussion
Why can’t the remaining four pentominoes be used for pentomino
puzzles? Observe that in the first three pentominoes shown below, digits
would need to be repeated. The fourth pentomino would have only one
line of digits.
R.I.C. Publications ® www.ricgroup.com.au DEVELOPING ALGEBRAIC THINKING 95
ISBN 978-1-74126-088-5