Unit Plan Components
Big Goal
Standards
Big Ideas
Unpacked Standards
Scaffolded Learning
Resources
Appropriate Length of
Time
Aligned Assessment
Comments
This unit plan identifies a big goal for the overall unit assessment, as well as goals for each
daily formative assessment. The big goal is written for all students, not a set percentage.
Math content standards have been identified from the Common Core State Standards.
Additionally, corresponding Mathematical Practices have been selected for this unit. The
Mathematical Practices logically connect to the unit’s content standards. Remediation
standards have been identified from the fifth grade Common Core State Standards and
mastery of them will support mastery of the first grade standards. Enrichment standards
have not been identified because there are no corresponding standards in seventh grade.
However, with the CCSS enrichment should be deepening student understanding of the
grade level standards.
The big ideas for this unit have been identified and written in with the unit’s Big Goal.
The CCSS have been unpacked into daily objectives. Each daily objective is written with a
measurable verb and can be completed in a single lesson.
The daily objectives build on one another in a logical sequence.
Resources have been identified for the overall unit, as well as for individual objectives.
The unit is designed for 13 days. There are 11 daily objectives, plus one buffer day and one
day for the assessment. The buffer day is included to circumvent potential schedule
changes.
Each daily objective has one corresponding assessment item. Because all daily objectives
build to a single standard, there is not a need for multiple assessment items per objective.
6th Grade Mathematics: Prime Factorization, Greatest Common Factor, and
Least Common Multiple Unit Plan
Prime Factorization, Greatest Common Factor and Least Common Multiple
Number
Common Core Standard
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole
6.NS.4
Mathematical
numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1- 100 with a
common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4(9 + 2)
In grade 6, students construct arguments using verbal or written explanations accompanied by expressions, equations,
Practices
6.MP.3
Construct
viable
arguments and
critique the
reasoning of
others
Notes and
Resources
inequalities, models, and graphs, tables, and other data displays (i.e. box plots, dot plots, histograms, etc.). They further refine
their mathematical communication skills through mathematical discussions in which they critically evaluate their own thinking
and the thinking of other students. They pose questions like “How did you get that?”, “Why is that true?” “Does that always
work?” They explain their thinking to others and respond to others’ thinking.
There are resources located for individual objectives throughout the unit plan. The resources included in this section apply to
multiple objectives. They should be used to help develop the teacher’s content knowledge and to consider how topics could
be introduced to students.
Khan Academy - Greatest Common Factor and Least Common Multiple (including word problems)
Inside Mathematics provides resources and videos that illustrate what a classroom focused on discussion and explanation
could look like.
Unit Goal
Remediation
Standards
All students will score at least an 80% on the End of Unit Assessment.
All students will score at least an 80% on daily formative assessments (e.g. observational notes, exit tickets, etc.)
By the end of this unit students will be able to work with factors through 12 and multiples through 100, both in straight math
and word problems. Additionally, students will develop the skill of explaining their mathematical reasoning (mathematical
practices) as they apply the content.
5.NBT.5. Fluently multiply multi-digit whole numbers using the standard algorithm.
5.NBT.6. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies
based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and
explain the calculation by using equations, rectangular arrays, and/or area models.
Enrichment
Standards
There are no additional standards to push toward “enrichment”, however enrichment should be created through these
standards and could include, more challenging word problems, larger numbers, or working with more than 2 numbers.
Unit Timing
This unit has been designed for 13 days. There are 11 daily objectives, plus one buffer day and a day for the assessment.
Each objective is intended to be taught in a single day. Objectives are listed in the order they should be taught.
Mathematical
Practices
Objective
Notes
Assessment Item
Answer
MP.3
SWBAT explain their
reasoning when
determining if a
number is prime or
composite.
An explanation of prime and
composite numbers, and how to
identify them are included at
Khan Academy - Prime and
Composite Numbers
This is a remedial objective,
found in the 5th grade Common
Core State Standards.
However, because it is a
foundational skill for later
objectives, it is included in this
unit plan. Teachers should use
their judgment when analyzing
diagnostic assessment data to
determine the best setting for
teaching this objective (whole
class, small group, etc.).
Determine if the numbers
below are prime or
composite. Then, justify
your decision.
I know that 32 is a composite
number because it has more than 2
factors. Factors of 32 include: 1, 32,
2, 16, 4, and 8.
32
I know that 2 is prime because it only
has two factors, 1 and itself.
2
NOTE: Student must answer both
parts of the question correctly to
receive credit.
Common Misconception:
Students often think that all odd
numbers are prime and all even
numbers are composite. To
circumvent this misconception,
teachers should provide clear
definitions and examples early
in the lesson.
NOTE: 1 is neither prime nor
composite.
MP.3
SWBAT explain their
thinking when
finding the greatest
common factor of
two whole numbers
less than 100 using
factors lists.
Explain how you would find
the greatest common factor
of 36 and 72 using factor
lists.
I know that factors are the numbers I
multiply together to get a product.
36: 1, 2, 3, 4, 6, 9, 12, 18, and 36
72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36,
72
Now I have to find the largest factor
that they have in common. I see that
it’s 36.
GCF = 36
MP.3
MP.3
MP.3
MP.3
SWBAT explain their
thinking when
finding the prime
factorization of a
number less than
100.
SWBAT explain their
thinking when
finding the greatest
common factor of
two whole numbers
less than 100 using
prime factorization.
SWBAT explain their
thinking when
rewriting addition
sentences using the
distributive property
and greatest
common factors.
SWBAT explain their
thinking when
finding the least
common multiple of
two whole numbers
less than or equal to
12 using multiple
lists.
There is not an explicit lesson
on using exponents when
writing the prime factorization of
a number. Teachers should
analyze the diagnostic
assessment data to determine
student proficiency and
understanding of using
exponents. A mini lesson on
exponents may need to be
included prior to this lesson.
Explain how you would find
the prime factorization of 36.
Possible explanation is included on
the assessment attachment.
Answer
36 = 3 x 3 x 2 x 2 or
32 x 22
Explain how you would find
the greatest common factor
of 50 and 48 using prime
factorization.
Possible explanation included on
the assessment attachment
Explain how you would
rewrite 84 + 28 by using the
distributive property.
To rewrite an addition expression I
need to find the GCF. Using factor
lists I know that 7 is the GCF of 84
and 28. I put the GCF on the outside
of the parenthesis and its other
factor inside:
7 (12+4)
I know that multiples are the
To use multiple lists I have to list the
multiples of 8 and 9.
8: 8, 16, 24, 32,40, 48, 56, 64, 72,
80, 88, 96
9: 9, 18, 27, 36, 45, 54, 63, 72, 81,
90, 99, 108
Next I need to find the smallest
multiple that is in both lists. I see
that number is 72.
LCM = 72
Explain how you would use
multiple lists to find the least
common multiple of 8 and 9.
Answer
The greatest common factor is 2.
MP.3
MP.3
MP.3
SWBAT explain their
thinking when using
prime factorization
to find the least
common multiple of
two numbers that
are less than or
equal to 12..
SWBAT explain their
thinking when
solving word
problems involving
greatest common
factor.
SWBAT explain their
thinking when
solving word
problems involving
least common
multiple.
Students should explain how
they knew it was a great
common factor problem in their
explanation.
Although not explicit in the
objective, in their explanation
students should explain how
they knew it was a least
common multiple problem.
Explain how you would use
prime factorization to find
the least common multiple
of 12 and 10.
Possible explanation included on the
assessment attachment
Thayer bought 48 cupcakes
and bought 32 pieces of
pizza for his sister’s birthday
party. Each guest will
receive the same number of
cupcakes and pizza. What
is the maximum number of
guests that can attend the
party? How many cupcakes
will each guest receive?
How many pieces of pizza
will each guest receive?
Explain your thinking as you
solve this problem.
Train A passes the
Haddonfield Station every
10 minutes. Train B passes
the station every 8 minutes.
In how many minutes will
they pass the station at the
same time? Explain your
thinking as you solve this
problem.
NOTE: Students could choose to
solve using factor lists or prime
factorization. Teachers should use
their judgment and the explanations
provided in previous GCF problems
when determining student mastery.
Answer
The least common multiple is 60.
Sixteen guests can attend the party
(GCF)
Each guest will receive 2 pieces of
pizza and 3 cupcakes.
NOTE: Students could choose to
solve using multiple lists or prime
factorization. Teachers should use
their judgment and the explanations
in previous LCM problems when
determining student mastery.
The trains will pass the station at the
same time in 40 minutes.
Score Level
4
3
2
1
0
Mathematical Knowledge and Explanation
 The answer is correct and all steps necessary to solve are shown.
 If necessary, the answer is labeled (typically for word problems)
 The written or oral explanation includes details about what they did and why they did it with
specific correct vocabulary
 If specified by the question, includes a picture or model with a clear explanation of all components
 The answer is correct and all steps necessary to solve are shown
 If necessary, the answer is labeled (typically for word problems)
 The written or oral explanation includes details about what they did, but may be less specific with
why they did it
 If specified by the question, includes a picture or provides a model with a mostly clear explanation
of all components
 The answer is correct, but the explanation provided is incorrect or minimal
 The answer is incorrect, but the explanation provided demonstrates understanding of most of the concept
 If the assessment item requires a picture or model, but it is not included, students score a 2 (even with a
correct answer and explanation)
 Both the answer and the explanation are incorrect
 The answer is incorrect and an explanation is not provided