RIC-0563 Developing algebraic thinking
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PLUS AND TIMES<br />
Teachers notes<br />
Times<br />
In Times, numerous solutions also exist. If we label the 5 digits as before,<br />
then we have the equation b x a x c = d x a x e.<br />
b<br />
d<br />
a<br />
e<br />
c<br />
Simplifying, we obtain the equation b x c = d x e if a ≠ 0<br />
The algebra shows that we need to find two pairs of number tiles that<br />
have the same product. The number tile a can be any digit 1 to 9. If a,<br />
however, is 0, it does not matter whether or not the products are the<br />
same since the final product will still be 0.<br />
The greatest possible product of 216 occurs when a = 9, and the product<br />
of each pair is 24 = 3 x 8 = 4 x 6.<br />
Can all the digits 0 to 9 be used for b, c, d, and e?<br />
No! Certainly 0 is out, since the product would be 0. Since there are no<br />
multiples of 5 and 7, these two tiles cannot be used either. All three,<br />
however, will work as values for a.<br />
78 DEVELOPING ALGEBRAIC THINKING www.ricgroup.com.au R.I.C. Publications ®<br />
ISBN 978-1-74126-088-5
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