Technology Integration Workshop
2016
Unit Title: Numbers and Operations - Factors and Divisors
Grade Level: 6th Grade
Subject Area: Math
Duration/Length/Number of class periods: 5 class periods, 50 minutes each
Description:
Students will develop a better understanding of whole numbers and will learn about factors, divisors, prime and composite numbers.
Students will use that knowledge to find the prime factorization for whole numbers. Prime factorization will be used in following
lessons to find LCM, GCF and finding equivalent numbers (fractions, decimals, percents).
Established Goals (National, State, Local):
Focused Instruction
1.1 I can demonstrate prime factorization using exponents. (6.1.1.5, 6.1.1.7)
STANDARD 6.1.1
Read, write, represent and compare positive rational numbers expressed as fractions, decimals, percents and ratios; write positive
integers as products of factors; use these representations in real-world and mathematical situations.
BENCHMARK: 6.1.1.5 Factors & Prime Factors
Factor whole numbers; express a whole number as a product of prime factors with exponents.
BENCHMARK: 6.1.1.7 Positive Rational Numbers: Equivalent Representations
Convert between equivalent representations of positive rational numbers.
What Enduring Understandings are desired?
Students will be comfortable with using different representations of equivalent numbers (fractions, decimals, percents). Students can
understand relationships among factors, multiples, divisors, products and quotients. Students will be able to express whole numbers
as the product of prime factors, including the use of exponential notation and understand that each whole number has a unique prime
factorization.
What Essential Questions will be considered?
What are connections between factors and divisors?
What are different ways to represent equivalent numbers?
What will we use prime factorization for?
Students will know / be able to:
Students will determine factors and divisors of given numbers.
Students will identify prime numbers.
Students will create a prime factorization of a given number using an organized process. (tree diagram)
Students can use exponents to express repeated multiplication.
Description
Units must include at least one
of each formative, summative,
introductory activity and
learning activity. Check the
appropriate box; one per row.
Day 1
What do these numbers have in common - Do Now
Show students sets of numbers (2,3,5,7,11,13 or 2,4,8,16,32,64 or
5,10,15,20,25,30,35 as examples). Have students come up with different
commonalities between the set of numbers. Popsicle stick with students their
ideas.
Introduce Factors
Factors - Whole numbers that multiply with another whole number to make a
whole number.
Example - 3 x 4 = 12 and 2 x 6 = 12.
Factor Game
1st couple rounds - Mr. Kennedy vs. the Class
Player 1 picks a number and gets those points. Player 2 picks all of the factors
of Player 1’s number and gets those points. Player 2 picks a new number
(scores points) and Player 1 scores points for all of the factors of Player 2’s
number. Players will lose a turn if they pick a number that has run out of factors
or didn’t have any in the first place (what do we call those numbers?)
Factor Game
Have students play factor game with partners (using paper copies).
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4b.
Factor Game Paper
What is the cheatcode for this game? Popcorn ideas from students.
Show table for all the numbers in factor game. Popsicle stick students, they can
pick number and write down all of the factors. Fill in their score vs. opponents
score. What numbers are the best to pick? Which numbers are the worst to
pick?
Factor Game Table
Day 2
Factors of favorite numbers (students should pick 3, if they don’t have any, have
them use lucky number generator - Pick 3)
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X
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Review Factors and introduce Divisors vocab terms.
Divisors - Dividing a whole number by another whole number that will make a
whole number.
Example - 12 / 3 = 4 and 12 / 4 = 4. What is the connection between factors and
divisors?
X
Factor Game
1st round - Mr. Kennedy vs. the Class
Factor Game
Product Game
Just like connect four! Place piece by moving 1 number marker. So if I want to
cover up 20, and 1 marker is on a 4, I need to move the other marker to what?
(5, because 20 / 4 =5 or 4 x 5 = 20).
Product Game
Mr. Kennedy vs. the Class.
x
Have students play product game with partners (using paper copies, paper
clips).
Product Game Paper
X
Group Discussion
Is there anything interesting about our game boards? (Any numbers we couldn’t
make?)
What numbers did we notice have multiple factors?
If 1 of the numbers is 5, how many products can we make on the game board?
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4b.
Exit Slip
List the factors of the given numbers (2-3 examples)
List the multiples (or products if 1 number is) - (2-3 examples)
Day 3
Plickers Warm Up
5 questions to check that students can identify the factors and divisors of whole
numbers. After each example, review what all the factors are for the given
number or what divisor(s) can make the whole number.
x
X
Elbow Partners
Give each group of students 2-3 numbers (3-36, a small and a big for each
group)
Show class examples for 1,2,37,42. Cut out rectangles or squares from grid
paper to make the numbers. Come up with every example that makes a
rectangle or square (think of the factors!).
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Student from each group will show on document camera the different examples
for each number in order. (take pictures or draw on board the examples,
showing them in order as students go).
When finished, check each number with class. Are the any numbers that have
more factors than shown? What do we notice about certain numbers (some will
have squares, these are perfect squares!, some will only have 1 rectangle, what
will we call these - prime?
X
Prime Number Table
Visualization shows which numbers are prime and which numbers are composite
(whole numbers that have factor pairs other than 1 and itself).
Homework - In your own words
Using frayer model diagrams, students will pick 3 of the following vocab words:
Whole Numbers, Factors, Divisors, Prime Number, Composite Number - Show
example for Perfect Square
Homework - Whole Number Vocab
Day 4
x
6a.
Homework check in - Elbow Partners.
Show examples from homework, get feedback from partner. Does definition
make sense? What other examples could you have? If section isn’t filled in,
what help can partner give? Does your partner have a great diagram to show
the class?
Show student examples with document camera (1 for each vocab term).
x
Kahoot Quiz - Types of Whole Numbers
Kahoot - Whole Numbers
X
X
X
Prime Factorization Instruction (on the board, students take notes in notebooks) Constructing Prime Factorization Trees
Examples for Factor Trees
X
Practice on your own (computer)
Students can make their own factor trees (refer to notes or elbow partner when
needed)
Factor Trees Practice
6a.
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Homework
Students create factor trees for 3 examples.
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6a.
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Day 5
Homework check in -elbow partners check that bottom row of tree is all prime
numbers.
Why are prime numbers important? “They are the building blocks for all whole
numbers. And there is only one way to find the prime factorization for any whole
number!” (Can show this on the board)
Is there a shorter way to write prime factorizations? (We can group the same
prime numbers together and use exponents to show how many times they are
multiplied) (Can show this on the board, will be more practice with this in next
unit)
Week in review:
Prime Factorization practice
Students that finish practice early can review vocab terms, exit slips and
homework in notebooks.
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6a.
Assessment on 4 Learning Targets
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Materials, tools and resources
Day 1: Make flipchart for Do Now and examples, Factor Game online at Illuminations, Factor Game and Factor Table Paper copies,
paper clips
Day 2: Make flipchart for Do Now and examples/vocab terms, Factor Game and Product Game at Illuminations, Product Game paper
copies, Exit Slip
Day 3: Plicker cards, mobile app, and quiz made. Grid paper and scissors, document camera, Prime Numbers table on Wikipedia,
Homework-Frayer Model
Day 4: Flip chart for prime factorization trees instruction, document camera, student computers with link to Kahoot.it and Prime Factor
trees on mathplayground.com, Homework-Factor Trees
Day 5: Make flipchart for homework check in and review time, student computers with link to Prime Factorization practice on IXL,
Assessment handout
Unit Plan Author (name, school and optional email address or hyperlink to teacher’s web page)
Nathan Kennedy
Olson Middle School - Minneapolis Public Schools
[email protected]
Additional credit given to