Construct a Concept - Sample Lesson Plan
Concept: Prime numbers
Grade level: 4th - 5th
NCTM Standards Addressed: Problem-solving, Communication, Reasoning, Connections, Number Theory,
Multiple Representations
IN State Standards Addressed: Grade 5, Number Sense 5.1.6 Understand that numbers break down in
different ways and that these numbers are called composite numbers, 5.1.7 Know that some numbers do not have any
factors except 1 and themselves and that such numbers are called prime numbers.
I. Sorting and categorizing (can be considered a warm-up activity)
Group students for the days lesson (pairs, 3’s or 4’s). Present students with a list of numbers containing
both prime and composite numbers. Refer to task sheet with the following numbers: 5 7 12 18 23 30 36 37
Give students 3-5 minutes to decide how to sort the numbers into 2 groups and come up with a rule for
organizing the numbers that way. (Note: incorporate special needs student & partners into groups)
II. Reflecting and Explaining
Ask for volunteers to share their two groups and their rules for each group with the class.
Anticipated or possible responses:
5 7 23 37 --> odd numbers
12 18 30 36 --> even numbers
12 18 30 36 --> multiples of 6
5 7 23 27 --> not multiples of 6
5 7 12 18 --> lower half
23 30 36 37 --> upper half
5 7 23 37 --> prime numbers
12 18 30 36 --> not prime (composite)
As each group presents their solution to the task, ask the class if the numbers could be divided by those
rules. If possible - praise them for finding an effective way to divide the set of numbers. If there is more than one
response to the task, then add the following numbers (2,3,6,9,11,13,24,39) and ask them to go back to the original
task and see if their rule is still a workable solution or if they had to change their rule.
Odd and even number groups still works.
Multiples of 6 or non-multiples of 6 groups still works.
Prime and non-prime (composite) groups still works.
If the class still has more than one way to divide the groups, it is time to present your version of how the
numbers should be divided (but don’t tell your rule).
Examples
2 3 5 7 11 13 23 37
Non-examples
6 9 12 18 24 30 36 39
Now ask the students to check their rules and decide if their rule still works. If their rule doesn’t work - ask
them to see if they can come up with a rule that does work. Give them all time to check their rules or come up with
new ones.
Sellers, 2003
III. Generalizing and Articulating
Offer a number on the overhead (say 52) and ask students if that number goes in the example group or the
non-example group. When they respond, ask them to tell the class exactly why they think they would put “52” in the
examples (or non-examples) group. Ask if others agree or disagree with the placement of the “52”. At this point you
are trying to get the students to give you a verbal definition of “prime” numbers and also a verbal explanation of why
the other numbers are not prime.
If students don’t know the word “prime”, but are articulating the rule for prime numbers you can ask if they
have heard of the word prime, and if so, why does that word seem to fit the examples.
Get several students to articulate the definition of prime and non-prime(composite) numbers. If they
describe the rule by saying that prime numbers are only divisible by one and the number itself; ask them what they
mean by divisible? If they mention factors (numbers with only 2 factors), ask them what they mean by factors? Be
sure to get students to verbalize their own definitions and be sure that most of the class agrees with the correct
definition of prime numbers and/or composite numbers (numbers with 3 or more factors).
IV. Verifying and Refining (any part can be used as evaluation if students write down
something that is visibly measurable as proof they understand the concept)
This is where you can choose to do one of a number of things:
(1) Provide the class with more examples or non-examples and ask them to tell you
whether the number you give is prime or not and why?
(2) Ask students to suggest other prime numbers and tell why they are prime.
(3) Ask students to suggest other non-prime (composite) numbers and tell why
they are not prime, but are composite.
(4) Help students to make “connections” to geometry by asking them to make
visual representations of prime or composite numbers.
a) Use graph paper or color tiles
b) Tell students they will try to represent the number they are given in a rectangular fashion and
to try representing the number in as many rectangular formations as possible.
c) Assign prime numbers to half of the class.
d) Assign composite numbers to the other half of the class.
e) Example: with 7 the only rectangle is a 1x7 or a 7x1 rectangle.
f) Example: with 12 the possible rectangles are 1x12, 12x1, 2x6, 6x2, 3x4, or 4x3
g) Have students share their representations with color tiles on the overhead or on their graph
paper.
h) Once again ask students to explain what they notice about the rectangular representations for
prime numbers and those for composite numbers.
i)They should recognize that the rectangle dimensions represent the factors of the numbers they
represent.
(5) Assign several larger numbers as homework and ask students to investigate them and come with proof that they
are either prime or composite. Ask them to find other ways to check for prime numbers. (to be used as assessment)
V. Resources: Teaching Middle and Secondary Mathematics by James Cangelosi, (1996)
VI. Where will this lesson lead - possible extensions or lessons to follow:
1) factors, factor trees
2) prime factorization
3) greatest common devisor
4) least common multiple
Sellers, 2003
Task: Sort the following numbers into 2 sets and be able to explain the rationale
behind your thinking.
2
5
7
12
18
23
30
36
37
Set #1
________________________
Set #2
_______________________
Rule for membership in set #1
Rule for membership in set #2
________________________
________________________
Set #1
________________________
Set #2
________________________
Rule for membership in set #1
Rule for membership in set #2
________________________
________________________
Set #1
________________________
Set #2
_________________________
Rule for membership in set #1
Rule for membership in set #2
________________________
_________________________
Set #1
________________________
Set #2
_________________________
Rule for membership in set #1
Rule for membership in set #2
________________________
_________________________
Sellers, 2003
Find my rule!
Look at the following lists of numbers and see if you can find my rule for deciding
which group the numbers belong to. Think of other numbers that might fit either
group as a way of demonstrating your understanding.
Examples
Non-examples
2 3 5 7 11 13 23 37
9 12 15 18 24 27 30 36 39
Rule for Examples
Rule for Non-examples
More Examples
More Non-examples
Concept(s): _______________________
____________________________
Characteristics:
Sellers, 2003