RIC-0563 Developing algebraic thinking
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EXCITING EXPONENTS<br />
Teachers notes<br />
Introduction<br />
Looking at the<br />
algebra<br />
Exciting<br />
exponents 1<br />
A common topic in the algebra curriculum is that of exponents. Later,<br />
as work with the distance formula begins, students observe sums of<br />
squares as the radicand (the number beneath the radical). Proficiency<br />
with number theory concepts, for example squaring or cubing a number,<br />
often makes work much quicker. Estimation strategies also aid in making<br />
decisions.<br />
In Exciting exponents 1, basic rules of exponents with whole numbers<br />
are covered, along with simple number theory ideas.<br />
• Any positive whole number raised to the zero power is 1.<br />
• 1 raised to any whole number power is 1.<br />
• 5 raised to any positive whole number power always has a 5 in the<br />
ones place.<br />
Using these three ideas and some estimation strategies, the 10 tiles<br />
can be placed to satisfy the five equations. There are two distinct<br />
solutions.<br />
0<br />
7 = 1<br />
9<br />
1 = 1<br />
or<br />
0<br />
9 = 1<br />
7<br />
1 = 1<br />
3<br />
2 = 8<br />
2<br />
5 = 2 5<br />
6<br />
2 = 6 4<br />
Exciting<br />
exponents 2<br />
Exciting exponents 2<br />
continues with the ideas above, but also focuses<br />
on the relative magnitude of numbers raised to various powers.<br />
3<br />
5 = 1 2 5<br />
4<br />
2 = 1 6<br />
0<br />
7 = 1<br />
3<br />
8 = 512<br />
2<br />
1 7 = 28 9<br />
68 DEVELOPING ALGEBRAIC THINKING www.ricgroup.com.au R.I.C. Publications ®<br />
ISBN 978-1-74126-088-5
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