Mathematics Instructional Design
Lesson Planning Template
Class: 6th Grade
Lesson: CMP3 Inv 3 Prob3.1
Date: 2016-2017
Important Mathematics to Develop
Factorization (factor/s), Prime factorization, prime numbers, nonprime numbers, classifying the Number “1”
Fundamental Theorem of Arithmetic- each whole number can be written as a product of primes in one way and only one
way.
Focus Question: How can you find the prime factorization of a number?
Standards for Mathematical Practice and Content
6.EE.A.2a Write expressions that record operations with numbers and with letters standing for numbers.
Note: The development of in this lesson/ Unit is primarily with numerical expressions is further developed with expressions
containing variables in Variables and Patterns.
6.EE.A.2b Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view
one or more parts of an expression as a single entity.
Note: the words term and coefficient are developed in Variables and Patterns.
6.NS.B.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of
two whole 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).
Note: the development of the Distributive Property with variables is contained in Variables and Patterns.
SMP.3 Construct viable arguments and critique the reasoning of others.
SMP.8 Look for and express regularity in repeated reasoning.
Learning Intention
We are learning that all whole numbers (greater than 1) can be represented as a product of factors.
Success Criteria
We will be successful when we can:
 decompose a number into its factors.
 demonstrate the factorization of a number into its prime factors.
 articulate the strategies used in the factorization of a number into its prime factors.
Mathematical Task and needed material
Additional notes
Labsheet 3.1A The Product Puzzle (one per student)
Labsheet 3.1B List of Factor Strings (accessibility)
Students can work in pairs and then share their work with
other pairs.
6/2016
5-10 minutes Notes/Reflection
Launch
Connecting to Prior Knowledge (TE pg.135 ): Discuss and Connect to the idea of creating
factor pairs for a number and move the thinking to creating a longer string of factors.
Demonstrate using a factor tree and show factor string.
Eg. Factor pairs: 24 = 4 x 6, 2 x 12, or 3 x 8. Ask students if they can think of three factors for
24 that do not include the number 1. Is there a different string of three numbers that will
give you a product of 24?
Longer strings 24 = 4 x 2 x 3, 2 x 2 x 6, 3 x 4 x 2
Let’s look at 360. What numbers can you multiply to get a product of 360?
How could we organize our solution? Show factor tree after students suggestions
Launch Video to illustrate the concept of factor strings.
Factor tree and factor string
Focus on the factors and not
the order of the factors.
4 x 2 x 3 vs 3 x 4 x 2 (same
factors)
Consider using video for visual
learners.
Presenting the Challenge: Pass out Present the Product PuzzleState the Problem as searching for strings that are the factorization of 840.
Explore
20- 30 minutes
Whole group
Questions for students to consider as they work on the Product Puzzle, “How do you know
when you have found the longest possible string?”
Small group/ Individual
Have students record the strings they find on the Labsheets 3.1A. and 3.1B
As you (teacher) circulate push students to find strings longer than those they may have.
You may have students record their findings on the board or on a large poster, listing the
strings they have found.
Summarize
10-15 minutes
Whole group
Ask students to look closely/ carefully at the strings on the board.
Discuss any revisions, strings that could be added.
Relate strings with two factors and those with three.
Ask students to provide explanation for how a string with three factors relate to a string
with four factors.
How could we use a string with five factors to get a string with six factors? Six to seven?....
Longest string of factors made up of prime numbers is called the prime factorization of the
number.
*How can you find the prime factorization of a number?
*How could students apply this process of prime factorization to their lives?
Apply
*Consider what are the main
ideas you want students to
leave with?
Assign problems from ACE
(Application, Connections
Extensions) relative to
Problem 3.1 (pgs. 54-60)
Assign questions from
Mathematical Reflections(pg.
61)
5-10 minutes
Mr. Rawlings has 60 cookies. He wants to give each of his 16 grandchildren the same
number of cookies. What is the greatest number of whole cookies he can give each child?
After he gives his grandchildren their cookies, how many will he have left?
Use the following questions to assess students understanding at the end of the lesson.
 What evidence do I have that students understand the Focus Question?
o Where did my students get stuck?
o What strategies did they use?
o What breakthroughs did my students have today?
6/2016
Students may work in pairs.
Create a large poster for
students to record their
strings.
Look for problems/tasks that
are more than just additional
practice but an application of
the skill taught.