Cherry Factor Trees
Author: Laura B.
State: Georgia
Grade Span: 3-5
Subject: Mathematics
Assignment Type: Individual
Recommended Time Frame: One 60-90 minute class period
Summary of Project
Students create factor trees that mimic the shape of ordinary prime factorizations but look like spring cherry
blossom trees.
Materials and Resources Needed
Whole class
Per Group
1 gallon baggie containing the following for each student: A brown “trunk”
with a composite number written on it,
2 large brown rectangles for the first
two factors, 4 medium brown rectangles for the next level of factors, and at
least 8 small brown rectangles for the
prime factor level, quarter-size pink
circles for the prime factors, and at
least 25 pink and green one square
inch tissue paper squares for decorating the trees with buds and leaves)
Per Student
Black Construction Paper
Glue
Pencils
Black Markers
Key Vocabulary

Composite

Factorization

Factor

Prime

Product
Engaging Questions:
1. How do you break a product down to its prime factorization?
2. How can you use the prime factorization of a product to simplify fractions or find common denominators?
3. Will the prime factorization be affected by the two initial factors you choose?
Implementing the Activity
Start by discussing prime and composite numbers. Ask for a composite number and demonstrate how to
make a Factor Tree on the board, dividing the composite number into two suggested factors, then continuing
to “boil” it down until only prime factors are left. Invite students to do the same, but starting with different initial
factors (ex. Using 6x8 for 48 instead of 12x4). Students will discover that prime factors will remain the same
regardless of initial break down.
Step-By-Step Procedures:
1. Each student selects a composite number from the baggie, as difficult as he or she chooses.
Students may also flip the trunk over and create a factor tree for any composite number they wish.
2. They will glue the trunk to the black construction paper, leaving the top of the trunk loose.
3. They will then determine two factors of that composite number and write one on each of two large
branches from the bag, and glue them under the top of the trunk, creating two large sections for the
tree.
4. Next, they will determine factors for their new branch numbers, and continue until they get to a prime
factor. Prime factors are written on pink circles to show that they are prime factors.
5. Trees are complete when each branch ends in a pink circle/prime factor.
6. To decorate the trees, students take tissue squares and wrap them around the top of a pencil, then
dip the tip into white glue and attach them anywhere to their trees, without blocking the numbers.
End Result
Students will create prime factorizations of their composite number and notice which numbers are prime and
which ones must continue to be “broken down” into their prime factors. Students who complete this activity
find it much easier to recognize prime numbers and have less trouble with fractions as a result.
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Rubric
Math Problem Solving — Cherry Factor Trees
Teacher Name: _________________________________
Student Name: _________________________________
CATEGORY
4
3
2
1
Mathematical
Concepts
Explanation shows
complete
understanding of
the mathematical
concept of
factoring.
Explanation shows
substantial
understanding of
the mathematical
concept of
factoring.
Explanation shows
some
understanding of
the mathematical
concept of
factoring.
Explanation shows
very limited
understanding of
the underlying
concept of
factoring.
Mathematical
Errors
90-100% of the
steps have no
mathematical
errors.
Almost all (85-89%)
of the steps have
no mathematical
errors.
Most (75-84%) of
the steps have no
mathematical
errors.
More than 75% of
the steps have
mathematical
errors.
Neatness and
Organization
The work is
presented in a
neat, clear,
organized fashion
that is easy to read.
The work is
presented in a neat
and organized
fashion that is
usually easy to
read.
The work is
presented in an
organized fashion
but may be hard to
read at times.
The work appears
sloppy and
unorganized. It is
hard to know what
information goes
together.
Strategy/
Procedures
Typically, uses an
efficient and
effective strategy to
find the factors.
Typically, uses an
effective strategy to
find the factors.
Sometimes uses
an effective
strategy to find the
factors, but does
not do it
consistently.
Rarely uses an
effective strategy
to find the factors.
Checking
The work has been
checked by two
classmates and all
appropriate
corrections made.
The work has been
checked by one
classmate and all
appropriate
corrections made.
Work has been
checked by one
classmate but
some corrections
were not made.
Work was not
checked by
classmate OR no
corrections were
made based on
feedback.
Explanation
Oral explanation is
detailed and clear.
Oral explanation is
clear.
Oral explanation is
a little difficult to
understand, but
includes critical
components.
Oral explanation is
difficult to
understand and is
missing several
components OR
was not included.
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For Differentiated Instruction
Struggling learners: Teacher can give simpler composite numbers (12, 20, etc.) as needed.
Advanced learners: Any student may choose his or her own composite number to be satisfactorily challenged.
(ex.112, 225, 96)
Additional Notes
EIP students often have trouble knowing when they have reached the end of a branch (prime number). One
option is to have a bag of ready-made pink circles with the prime numbers already on them; they need to
continue factoring their numbers until they can use a pink circle.
Design first, glue last. Once it’s glued down, it’s hard to fix them!
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