Sifting For Primes Plus
Lesson Plan – Teacher Guide
Teacher: Ramona Gillen
Date(s):
Subject area / course / grade level: Math Grade 6
Materials:
100 Chart for each student
Pencil
Colored pencils
TEKS/SEs:
5.3(D), 5.5(B)
6.1(D), 6.1(E), 6.1(F)
Lesson objective(s):
Students will identify the prime numbers between 1 and 100. Students will also find multiples of 2, 3, 5, and 7.
Instructional strategies:
Students will use a process known as the Sieve of Eratosthenes to name the prime numbers between 1 and 100.
The process is named for a Greek mathematician who is known for his work with prime numbers. At the same
time students will create a coded system for the numbers 1-100 to identify common factors and common
multiples of certain prime numbers.
See attached teacher guide for instructions.
Differentiation strategies to meet diverse learner needs:
Evaluation of student learning:
1
Sifting For Primes Plus
Lesson Plan – Teacher Guide
Supplies: (per student)
100 chart
4 different colored pencils
Instructions:
This activity is normally done as a whole class activity with the teacher modeling. Students should have
already developed definitions for prime (a natural number with exactly two factors) and composite (a natural
number with more than two factors). They should also understand that the number one is neither prime nor
composite since it has only one factor. I usually begin by having students write these definitions on the back of
their 100 chart.
The first step is to create a code at the top of the 100 chart. A star on number one (neither prime nor
composite), a circle around prime numbers, and an “X” on composite numbers. In addition, students will use
the four different colored pencils to shade the four corners of the code box. One colored corner to denote
multiples of two, one corner in a different corner to denote multiples of three, one for multiples of five and one
for multiples of seven. See the attached model which demonstrates this coding.
The teacher will guide the students in the activity. “What shall we put on the number one? How many factors
does it have?” Since it is neither prime nor composite a star should be put on the number one. “What about the
number two? Is it prime or composite? How do you know?” Since two is a prime number it should be circled.
Since two is a prime number, any multiple of two will be composite because they will have more than two
factors. So all the even numbers will have an “X” on them.
The students will then start the color coding. They will use the colored pencil they have chosen for multiples of
two and shade the appropriate corner of each even number on the chart. Make certain that they shade only the
corner since many of these numbers will also have 3, 5, and 7 as factors.
After all the multiples of two have been coded ask the class about the next number, which is 3. “Is three prime
or composite? How do you know?” Since three has only two factors it should be circled as a prime. Just as all
multiples of 2 were composite, all the multiples of 3 are composite. So each multiple of 3 should be marked
with an “X”. The students will notice that some of the multiples of 3 have already been marked as composite
because they are also multiples of 2. The students should then use the colored pencil they have chosen for the
multiples of three and shade the appropriate corner of each multiple of three on the chart. Those that are even
numbers will already have a corner shaded for a multiple of two so they will shade a different corner with the
color chosen for three. Students will begin to notice patterns in the multiples of three and for the numbers that
are multiples of both two and three.
The class is now ready to consider the next number that is not marked with an “X”. Is five prime or composite?
Since it has only two factors it is prime and should be circled. All multiples of five can now be marked with an
“X” if they have not already been marked. Students will notice that the multiples of five lie in two rows and are
easy to identify. They should use the colored pencil they have chosen for multiples of five to shade the
appropriate corner for each multiple of five on the chart. Again, some of these numbers may have already been
shaded in other corners to denote multiples of two and three.
Since six has already been marked with an “X” as composite the class must now consider the number seven.
Since it has only two factors it is prime and should be circled. Students can count by sevens to mark and “X”
on all the multiples of seven that have not already been marked. They use the colored pencil they have chosen
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Sifting For Primes Plus
Lesson Plan – Teacher Guide
for multiples of seven to shade the appropriate corner of all the multiples of seven. As before, some of these
multiples will have other corners shaded as multiples of two, three, or five.
We will not be shading multiples of the rest of the primes on the charts since we ran out of corners to mark. At
this point the remaining unmarked numbers are prime. Students will notice that when then mark out the
multiples of these numbers they already have an “X”. They can finish circling the primes and should be able to
count 25 circled numbers when they are finished.
Students can observe patterns in the multiples. They can also observe that if a number is a multiple of both two
and three, then it is also a multiple of six. If a number is a multiple of both two and seven, then it is also a
multiple of fourteen. This chart should be kept as a resource for students. It is useful in assignments such as
prime factorization, common factors, greatest common factors, common multiples, least common multiple,
simplifying fractions, etc.
3
Name:
Code
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
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81
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84
85
86
87
88
89
90
91
92
93
94
95
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100
Name:
2
Code
Neither Prime nor Composite
3
Prime
5
7
Composite
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
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21
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100