RIC-0563 Developing algebraic thinking
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PLUS AND TIMES<br />
Teachers notes<br />
Plus 9<br />
Plus 9 also has numerous solutions. The algebra is very similar to what<br />
is described for Plus 5. Look at the diagram below.<br />
f<br />
g<br />
b c a d e<br />
h<br />
i<br />
In this problem, we have the equation b + c + a + d + e = f = g + a + h + i.<br />
This simplifies to (b + c) + (d + e) = (f + g) + (h + i).<br />
Once again, the number in the centre can be any digit 0 to 9. Using<br />
parentheses shows that we need four pairs that have the same sum.<br />
Lots of possibilities exist; however, an additional method to solve the<br />
problem is to create two Plus 5s as shown below.<br />
1<br />
9<br />
2 0 3<br />
8 7 6<br />
4<br />
5<br />
Now, move a vertical pair from one plus to the other and a horizontal<br />
pair from one plus to the other. The problem is solved.<br />
1<br />
9<br />
2 0 3<br />
8 7 6<br />
4<br />
5<br />
R.I.C. Publications ® www.ricgroup.com.au DEVELOPING ALGEBRAIC THINKING 77<br />
ISBN 978-1-74126-088-5
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