RIC-0563 Developing algebraic thinking
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PRIMES AND COMPOSITES<br />
Teachers notes<br />
Introduction<br />
Looking at<br />
the algebra<br />
Lots of primes,<br />
lots of composites<br />
The number tile activities in this section are designed to provide<br />
emphasis on primes and composites by having students create a variety<br />
of each—one, two, three, or four digits in length. Number theory ideas<br />
and problem-solving strategies are an integral part of the activities.<br />
Work with prime numbers and composite numbers serves as a basis<br />
for later work with factoring. As students progress through the activities,<br />
several key points need to be brought to their attention.<br />
• 1 is neither prime nor composite.<br />
• The only even prime number is the one-digit number 2; all other<br />
prime numbers are odd.<br />
• Prime numbers, other than 2, must have an odd digit in the ones<br />
place.<br />
• The only prime number with the digit 5 in the ones place is the<br />
number 5; all other numbers with a 5 in the ones place are multiples<br />
of 5.<br />
• Multiplace prime numbers, therefore, have 1, 3, 7 or 9 in the ones<br />
place.<br />
• Just because the ones digit is odd does not guarantee that the number<br />
is prime. Divisibility tests play an important role in determining the<br />
primeness of the number.<br />
• A number is even when the ones digit is 0, 2, 4, 6, or 8 and therefore<br />
not prime (other than 2).<br />
Beginning this section is Lots of primes, lots of composites. Eight<br />
number tiles are used to create four 2-digit prime numbers, followed<br />
by creation of four composite 2-digit numbers. Here are some possible<br />
solutions:<br />
Lots of primes<br />
Lots of composites<br />
29 83 90 18<br />
41 61 63 39<br />
53 59 75 65<br />
67 47 92 74<br />
Primes and In Primes and composites, students are first required to use all 10<br />
composites number tiles to create three 2-digit prime numbers and two 2-digit<br />
composite numbers. Secondly, they are required to create two 2-digit<br />
prime numbers and three 2-digit composite numbers. Both tasks have<br />
numerous solutions and focus on the points listed above. Here are some<br />
possible solutions:<br />
23 60 90 71<br />
47 80 65 23<br />
59 84<br />
36 DEVELOPING ALGEBRAIC THINKING www.ricgroup.com.au R.I.C. Publications ®<br />
ISBN 978-1-74126-088-5
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