6th Grade– CCGPS Math
LFS Unit 1: The Number System with Rational Numbers
Standards: Cluster: Apply and extend previous understandings of operations with
fractions to add, subtract, multiply and divide rational numbers.
MCC6.NS.1
Interpret and compute quotients of fractions, and solve word problems involving
division of fractions by fractions, e.g., by using visual fraction models and equations to
represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a
visual fraction model to show the quotient; use the relationship between multiplication
and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general,
(a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share
1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt?
How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?
MCC6.NS.2
Fluently divide multi-digit numbers using the standard algorithm
MCC6.NS.3
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard
algorithm for each operation.
MCC6.NS.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).
Transition Standard for 2012-2013:
MCC5.NF.6 (DOK 2)– Solve real world problems involving multiplication of fractions and
mixed numbers, e.g., by using visual fraction models or equations to represent the
problem.
Douglas County School System
6th Grade Math
Number System Fluency
7/29/2017
Page 1
K-U-D Unit 1: Number System Fluency
UNDERSTAND…
By the end of the unit, I want my students to understand…
how to extend and fluently apply the concept of part(s) of a whole to manipulate
numbers (fractions, decimals, multiples, factors, etc.) to solve real world problems.
Know
Do
Vocabulary: Evaluate; Quotient; Dividend;
Minuend; Subtrahend; Fraction; Multiple; Factor;
Factorization; Prime Number; Composite
Number; Exponent; Exponential; Distribution
Property; Decompose; Greatest Common Factor
(GCF); Least Common Multiple (LCM); Relatively
Prime; Array; Model; Sum; Difference; Algorithm
 Divide (NS.1) & multiply fractions. (NS.6) DOK1
 Fluently add, subtract, divide and multiply
multi-digit decimals. (NS.3) DOK1
 Fluently divide multi-digit numbers. (NS.2)
DOK1
 Divide whole numbers and fractions with
fractions. (NS.1) DOK1
 Interpret real world situations in expressions
and equations – by determining if
multiplication or division of whole and partial
numbers is necessary. (NF.6) DOK2
 Model visually multiplication (NF.6) and
division of fractions to represent real world
situations/word problems. (NS.1) DOK2
 Find common multiples of two whole
numbers less than or equal to 12. (NS.4) DOK1
 Find common factors of two whole numbers
less than or equal to 100. (NS.4) DOK1
 Find the greatest common factor (GCF) and
least common multiple (LCM). (NS.4) DOK1
 Factor numbers with prime factorization and
write numbers in exponential form. (NS.4)
DOK1
 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). (NS.4) DOK1
 Multiple strategies and models to solve various
problems with fractions and decimals. (NS1;
NS3)
 The standard algorithm for addition,
subtraction, multiplication and division of
multi-digit numbers and decimals. (NS3; NS4)
 The relationship between multiplication and
division. (NS1; NS4)
 Which operation(s) to apply to a word
problem and/or real world situation. (NS1)
 What dividing by a fraction means. (NS1)
Ex: ( 3 ÷





2
5
is asking
"how many 2/5are in 3?)
A number divided by a fraction has a higher
quotient than the dividend. (NS1; NS2)
The relationship between the distribution
property and factors and multiples. (NS4)
The relationship between multiples and
factors. (NS4)
The value of using properties of multiples and
factors in real world situations/word problems.
(NS1)
Divisibility rules. (NS2)
Douglas County School System
6th Grade Math
Number System Fluency
Ex: Whole numbers (36 & 8) have a common
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factor of 4. Whole numbers (9 & 2) have no
common factor. Use the distributive property to
express 36 + 8 as 4 (9 + 2).Notice: 36+8 = 44 &
4(9+2) =44.
Douglas County School System
6th Grade Math
Number System Fluency
7/29/2017
Page 3
SLM Unit 1: Number System Fluency
Key Learning
Extend and fluently apply the uses of the four basic operations (addition, subtraction, multiplication and
division) to manipulate numbers (fractions, decimals, multiples, factors, etc.) to solve real world problems.
Unit EQ
How can I effectively use the properties of numbers to understand and solve real world problems?
Concept
Concept
Concept
Fluent addition, subtraction,
multiplication and division of multidigit decimals and whole numbers.
Identification and application of
properties of numbers.
Division of whole numbers and of
fractions by fractions.
Lesson EQ’s
Lesson EQ’s
Lesson EQ’s
1. How does the answer of
multiplying a whole number by
a whole number compare with
the answer of multiplying a
whole number by a decimal?
2. How does the quotient of
dividing a decimal by a whole
number compare with the
quotient of dividing a decimal
by a decimal?
3. What strategies can I use to
become fluent in adding,
subtracting, multiplying and
dividing whole numbers and
decimals?
4. How can the divisibility rules
help me become fluent in
adding, subtracting, multiplying
and dividing whole numbers
and decimals?
1. What is the composition of
numbers?
2. What is the relationship
between factors and multiples?
3. How can I express the
composition of a number?
4. How do I decompose
numbers?
5. How can I express the
decomposition of a number?
6. When would I use factors and
multiples in everyday life?
1. How can I visually model
division by fractions?
2. How does the quotient of
dividing a whole number by a
fraction differ from dividing a
whole number by a whole
number? Why?
3. When do I need to divide by
fractions in everyday life?
4. How does the quotient from
dividing by a fraction compare
to the quotient from dividing by
a decimal?
Vocabulary
Vocabulary
Vocabulary
Quotient; Dividend; Fraction; Sum;
Difference
Multiple; Factor; Factorization;
Prime Number; Composite Number;
Exponent; Distribution Property;
Decompose; Greatest Common
Factor (GCF); Least Common
Multiple (LCM); Relatively Prime;
Factor Tree
Array; Model; Mixed Decimals;
Mixed Numbers; Improper Fraction;
Numerator; Denominator
Douglas County School System
6th Grade Math
Number System Fluency
7/29/2017
Page 4
Douglas County School System
6th Grade Math
Number System Fluency
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Domain:
Cluster:
Apply and extend previous understandings of multiplication and division to divide
Number Systems
fractions by fractions.
MCC6.NS.1
What does this standard mean?
Interpret and compute quotients of
fractions, and solve word problems
involving division of fractions by fractions,
e.g., by using visual fraction models and
equations to represent the problem. For
example, create a story context for (2/3)
÷ (3/4) and use a visual fraction model to
show the quotient; use the relationship
between multiplication and division to
explain that (2/3) ÷ (3/4) = 8/9 because
3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d)
= ad/bc.) How much chocolate will each
person get if 3 people share 1/2 lb of
chocolate equally? How many 3/4-cup
servings are in 2/3 of a cup of yogurt?
How wide is a rectangular strip of land
with length 3/4 mi and area 1/2 square
mi?
In this standard contexts and visual models can help students to understand quotients of
fractions and begin to develop the relationship between multiplication and division. Model
development can be facilitated by building from familiar scenarios with whole or friendly
number dividends or divisors. Computing quotients of fractions build upon and extends
student understandings developed in Grade 5. In 5th grade students divided whole
numbers by unit fractions. Students continue this understanding by using visual models and
equations to divide whole numbers by fractions and fractions by fractions to solve word
problems.
Mathematical Practice
Examples and Explanations
Students understand that a division problem such as 3 ÷
2
5
is asking, “how many
Standards
2
5
are in 3?” One possible
visual model would begin with three whole and divide each into fifths. There are 7 groups of two-fifths
in the three wholes. However, one-fifth remains. Since one-fifth is half of a two-fifths group, there is a
remainder of
1
2
2
5
1
2
1
2
Therefore, 3 ÷ = 7 , meaning there are 7 groups of two-fifths. Students interpret the
Douglas County School System
6th Grade Math
Number System Fluency
6.MP.1. Make sense of
problems and persevere in
solving them.
6.MP.2. Reason abstractly
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solution, explaining how division by fifths can result in an answer with halves.
and quantitatively.
6.MP.3. Construct viable
arguments and critique the
reasoning of others.
Students also write contextual problems for fraction division problems. For example, the problem,
2 1
÷
3 6
can be illustrated with the following word problem:
Susan has
2
of
3
an hour left to make cards. It takes her about
1
6
of an hour to make each
card. About how many cards can she make?
This problem can be modeled using a number line.
1. Start with a number line divided into thirds.
6.MP.4. Model with
mathematics.
6.MP.7. Look for and make
use of structure.
6.MP.8. Look for and express
regularity in repeated
reasoning.
2. The problem wants to know how many sixths are in two-thirds. Divide each third in half to create
sixths.
Each circled part represents
1
6
. There are four sixths in two-thirds; therefore, Susan can make 4 cards.
Examples:

3 people share 1 pound of chocolate. How much of a pound of chocolate does each person
2
get?
Douglas County School System
6th Grade Math
Number System Fluency
7/29/2017
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Solution: Each person gets 1 lb of chocolate.
6

Manny has
1
2
yard of fabric to make book covers. Each book is made from
1
8
yard of fabric. How
many book covers can Manny make? Solution: Manny can make 4 book covers.
yd

Represent
1 2

2 3
in a problem context and draw a model to show your solution.
Context: You are making a recipe that calls for
2
3
cup of yogurt. You have
1
2
cup of yogurt from a snack
pack. How much of the recipe can you make?
Explanation of Model:
The first model shows 1 cup. The shaded squares in all three models show
2
The second model shows
The third model shows
2
3
1
2
1
2
cup and also shows
1
3
1
2
cup.
cups horizontally.
cup moved to fit in only the area shown by
2
3
of the model.
is the new referent unit (whole) .
Douglas County School System
6th Grade Math
Number System Fluency
7/29/2017
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3 out of the 4 squares in the
2
3
portion are shaded. A
1
2
cup is only
3
4
of a
2
3
cup portion, so you can
only make ¾ of the recipe.
1
2
1
2
Suggested Instructional Strategy
Use this problem: How many servings of popcorn are in 4½ cups if each person receives 3/4 cup of popcorn
The teacher provides 4½ cups of popcorn. Students use a 3/4 cup measuring cup to solve the problem. Record solutions as a group.
1. Think-Pair-Draw-Share: Put students in pairs. Have one solve the problem using a picture/diagram and the other solve using the
algorithm. Then they get together and compare.
2. Think-Pair-Share: Students solve the problem on their own, then get together and discuss how their solutions are the same and how
they are different.
3. Four Corners: Give students a problem and the quotient. Give each corner in your room a label and have students go to the corner
they think would be the correct label for the quotient.
Skill Based Task
Use representations to show that 1/4 divided by ½ is ½ that 2/3
divided by 2/5 is 5/3, that 2/3 divided by 3/4 is 8/9, and that 1½
divided by 6/4 is 1.
Problem Task



Douglas County School System
6th Grade Math
Number System Fluency
You have 5/8 pound of Skittles. You want to give your friends
1/4 lb. each. How many friends can you give Skittles to?
Explain your answer.
You have a 3/4-acre lot. You want to divide it into 3/8-acre
lots. How many lots will you have? Draw a diagram to justify
your solution.
You have a 3/4-acre lot. You want to divide it into 2 sections.
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
How many acres in each section will you have? Draw a
diagram to justify your solution.
How wide is a rectangular strip of land with length 3/4 mi.
and area 1/2 square mi.?
Models and Algorithms
TEACHER CONTENT
 Math Forum - Teacher Tutorial - http://mathforum.org/dr.math/faq/faq.divide.fractions.html
 Dividing Fractions - Teacher Tutorial - http://www.tpub.com/math1/5g.htm
STUDENT ACTIVITIES/LESSONS
 NLVM - Fraction Number Line Bars- Interactive Applet http://nlvm.usu.edu/en/nav/frames_asid_265_g_3_t_1.html?open=activities&from=category_g_3_t_1.html


Instructional
Resources/Tools
Visual Fractions - “Divide Fractions” - Interactive Applets and Game http://www.visualfractions.com/divide.htm
UEN - “Modeling Multiplication and Division of Fractions” Lesson http://www.uen.org/Lessonplan/preview.cgi?LPid=23394
Mixed Numbers and Improper Fractions
STUDENT ACTIVITIES/LESSONS
 LearnAlberta - “Improper Fractions and Mixed Numbers” Video Lesson http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=lessons&lesson=m6lessons
hell02.swf
Lessons
STUDENT ACTIVITIES/LESSONS
 Illuminations “Feeding Frenzy” - Unit Rates; Multiply/Divide Fractions http://illuminations.nctm.org/LessonDetail.aspx?id=L781
 UEN - “Sticky Note Math” Lesson - http://www.uen.org/Lessonplan/preview?LPid=15443
UEN - “Dividing Fractions” Lesson - http://www.uen.org/Lessonplan/preview?LPid=5301
Baking Cookies: http://illustrativemathematics.org/illustrations/50
Drinking Juice, Variation 2: http://illustrativemathematics.org/illustrations/412
Drinking Juice, Variation 3: http://illustrativemathematics.org/illustrations/413
How many containers are in one cup/one container: http://illustrativemathematics.org/illustrations/408
Douglas County School System
6th Grade Math
Number System Fluency
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Making Hot Cocoa, Variation 1: http://illustrativemathematics.org/illustrations/407
Making Hot Cocoa, Variation 2: http://illustrativemathematics.org/illustrations/411
Running to School, Variation 2: http://illustrativemathematics.org/illustrations/410
Traffic Jam: http://illustrativemathematics.org/illustrations/464
Video Game Credits: http://illustrativemathematics.org/illustrations/267
Literature Connections:
The Doorbell Rang by Pat Hutchins
Full House: An Invitation to Fractions by Dayle Ann Dodds.
CCGPS Internet Resources:
https://ccgps.org/6.NS.html
Douglas County School System
6th Grade Math
Number System Fluency
7/29/2017
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Domain:
Cluster:
Number Systems
Compute fluently with multi-digit numbers and find common factors and multiples.
MCC6.NS.2
What does this standard mean?
Fluently divide multi-digit numbers using
the standard algorithm.
Procedural fluency is defined by the Common Core as “skill in carrying out procedures
flexibly, accurately, efficiently and appropriately.” In the elementary grades, students were
introduced to division through concrete models and various strategies to develop an
understanding of this mathematical operation (limited to 4-digit numbers divided by 2-digit
numbers). In 6th grade, students become fluent in the use of the standard division algorithm.
This understanding is foundational for work with fractions and decimals in 7th grade.
Examples and Explanations
Students are expected to fluently and accurately divide multi-digit whole numbers. Divisors can be any
number of digits at this grade level.
As students divide they should continue to use their understanding of place value to describe what they
are doing. When using the standard algorithm, students’ language should reference place value. For
example, when dividing 32 into 8456, as they write a 2 in the quotient they should say, “there are 200 thirtytwos in 8456 ” and could write 6400 beneath the 8456 rather than only writing 64.
There are 200 thirty twos in 8456.
Mathematical Practice
Standards
6.MP.2. Reason abstractly
and quantitatively.
6.MP.7. Look for and
make use of structure.
6.MP.8. Look for and
express regularity in
repeated reasoning.
200 times 32 is 6400.
8456 minus 6400 is 2056.
Douglas County School System
6th Grade Math
Number System Fluency
7/29/2017
Page 12
There are 60 thirty twos in 2056.
60 times 32 is 1920.
2056 minus 1920 is 136.
There are 4 thirty twos in 136.
4 times 32 is 128.
The remainder is 8. There is not a full thirty two
in 8; there is only part of a thirty two in 8.
This can also be written as
8
32
or 1 . There is ¼
4
of a thirty two in 8.
8456 = 264 * 32 + 8
Douglas County School System
6th Grade Math
Number System Fluency
7/29/2017
Page 13
Suggested Instructional Strategy
1. Think Aloud: Do the problem with a partner while explaining and telling what you are thinking and doing.
2. Have students identify in a problem set when they would use mental math and when they would use the standard algorithm.
3. Connect students’ existing strategies for division with the standard algorithm.
4. As a starter activity, use division problems that can reasonably be solved by using mental math (e.g., 105/25), estimation (e.g.,
150 ÷ 12, 227 ÷ 30), and reasoning (e.g., when I think of 105 divided by 25, I think of 4 sets of 25 with 5 left over, the 5 left over is
5/25 which is 1/5, so the answer is 4 1/5). Model for the students your thinking as you work through the problem. (Note: This
strategy would not apply to complex division problems for which the algorithm is most appropriate [e.g., 4567 ÷ 192]).
Skill Based Task
248 divided by 18.
Instructional
Resources/Tools
Problem Task
I spent $504 on 28 tickets for a rock concert. How much did I
spend on each ticket?
Elementary & Middle School Mathematics (VanDeWalle, 7th Ed.)
 TEACHER CONTENT
o Division of Whole Numbers: p. 232-237
 STUDENT ACTIVITIES
o Division of Whole Numbers: p. 232-237 Figures 12.23-12.27 & problems in bold print
Elementary & Middle School Mathematics (VanDeWalle, 6th Ed.)
 TEACHER CONTENT
o Division of Whole Numbers: p. 236-241
 STUDENT ACTIVITIES
o Division of Whole Numbers: p. 236-241 Figures 13.24-13.28 & problems in bold print
Internet:
Division of Whole Numbers
TEACHER CONTENT
 LearnAlberta - “Division of Whole Numbers” - Video Tutorial –
http://www.learnalberta.ca/content/me5l/html/math5.html?goLesson=9
Douglas County School System
6th Grade Math
Number System Fluency
7/29/2017
Page 14
STUDENT ACTIVITIES/LESSONS
 BBC - Division Strategy Practice http://www.bbc.co.uk/skillswise/numbers/wholenumbers/division/written/game.shtml
 Division by a 2-Digit Number - Algorithm Applet - http://www.doubledivision.org/
http://nlvm.usu.edu/en/nav/frames_asid_197_g_2_t_1.html?open=activities&from=search.html?qt=division
Literature Connection: The Phantom Tollbooth by Norton Juster
CCGPS Internet Resources:
https://ccgps.org/6.NS_41B6.html
Douglas County School System
6th Grade Math
Number System Fluency
7/29/2017
Page 15
Domain:
Cluster:
Number Systems
Compute fluently with multi-digit numbers and find common factors and multiples.
MCC6.NS.3
What does this standard mean?
Fluently add, subtract,
multiply, and divide multidigit decimals using the
standard algorithm for each
operation.
Procedural fluency is defined by the Common Core as “skill in carrying out procedures flexibly,
accurately, efficiently and appropriately.” In 4th and 5th grades, students added and subtracted
decimals. Multiplication and division of decimals was introduced in 5th grade (decimals to the
hundredth place). At the elementary level, these operations were based on concrete models or
drawings and strategies based on place value, properties of operations, and/or the relationship
between addition and subtraction. In 6th grade, students become fluent in the use of the standard
algorithms of each of these operations.
Examples and Explanations
The use of estimation strategies supports student understanding of operating on
decimals.
Example:
 First, students estimate the sum and then find the exact sum of 14.4 and 8.75.
An estimate of the sum might be 14 + 9 or 23. Students may also state if their
estimate is low or high. They would expect their answer to be greater than 23.
They can use their estimates to self-correct.
Mathematical Practice Standards
6.MP.2. Reason abstractly and quantitatively.
6.MP.7. Look for and make use of structure.
6.MP.8. Look for and express regularity in
repeated reasoning.
Answers of 10.19 or 101.9 indicate that students are not considering the
concept of place value when adding (adding tenths to tenths or hundredths
to hundredths) whereas answers like 22.125 or 22.79 indicate that students are
having difficulty understanding how the four-tenths and seventy-five
hundredths fit together to make one whole and 25 hundredths.
Students use the understanding they developed in 5th grade related to the patterns
involved when multiplying and dividing by powers of ten to develop fluency with
operations with multi-digit decimals.
Douglas County School System
6th Grade Math
Number System Fluency
7/29/2017
Page 16
Suggested Instructional Strategy
Have students look at student work that contains a common misconception and look at errors and discuss how to correct the error.
Skill Based Task
Skill-based Task:
Problem Task
The school had a bake sale and raised $75.55. If each cookie cost $0.05, how
many cookies were sold? Explain how you got your answer.
1. 242.134 + 308.02
2. 38.9 – 14.334
3. 11.82 x 2.81
4. 341.8 ÷ 1.2
Instructional
Resources/Tools
Elementary & Middle School Mathematics (VanDeWalle, 7th Ed.)
 TEACHER CONTENT
o Computation with Decimals: p. 342-345
 STUDENT ACTIVITIES
o Computation with Decimals: p. 342-345 Activity 17.11-17.13 & problems in bold print
Elementary & Middle School Mathematics (VanDeWalle, 6th Ed.)
 TEACHER CONTENT
o Computation with Decimals: p. 346-350
 STUDENT ACTIVITIES
o Computation with Decimals: p. 346-350 Activity 18.12-18.14 & problems in bold print
Internet:
Addition/Subtraction of Decimals
STUDENT ACTIVITIES/LESSONS
 NLVM - Base Block Decimals http://nlvm.usu.edu/en/nav/frames_asid_264_g_3_t_1.html?from=category_g_3_t_1.html
 NLVM - Circle 3 - Adding Decimals - Puzzle http://nlvm.usu.edu/en/nav/frames_asid_187_g_3_t_1.html?open=instructions&from=category_g_3_t_1.html
 LearnAlberta - “Solving Problems with Decimals” Video Lesson http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=lessons&lesson=m6lessonshell05.
swf
 LearnAlberta - “Addition and Subtraction of Decimals” Video Lesson http://www.learnalberta.ca/content/me5l/html/math5.html?goLesson=7
Douglas County School System
6th Grade Math
Number System Fluency
7/29/2017
Page 17

Math Play - Jeopardy - Computation Game - http://www.math-play.com/Decimals-Jeopardy/decimalsjeopardy.html
Multiplication/Division of Decimals
TEACHER CONTENT
 LearnAlberta - Multiplication and Division of Decimals - Video Tutorial http://www.learnalberta.ca/content/me5l/html/math5.html?goLesson=10
CCGPS Internet Resources:
https://ccgps.org/6.NS_8KH5.html
Douglas County School System
6th Grade Math
Number System Fluency
7/29/2017
Page 18
Domain:
Cluster:
Number Systems
Compute fluently with multi-digit numbers and find common factors and multiples.
MCC6.NS.4
What does this standard mean?
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).
Students will find the greatest common factor of two whole numbers less than or equal to 100.
Students also understand that the greatest common factor of two prime numbers will be 1
Examples and Explanations
Mathematical Practice Standards
Students will find the greatest common factor of two whole numbers less than or equal to 100.
6.MP.7. Look for and make use of
For example, the greatest common factor of 40 and 16 can be found by
structure.
1) listing the factors of 40 (1, 2, 4, 5, 8, 10, 20, 40) and 16 (1, 2, 4, 8, 16), then taking the
greatest common factor (8). Eight (8) is also the largest number such that the other
factors are relatively prime (two numbers with no common factors other than one).
For example, 8 would be multiplied by 5 to get 40; 8 would be multiplied by 2 to get 16.
Since the 5 and 2 are relatively prime, then 8 is the greatest common factor. If
students think 4 is the greatest, then show that 4 would be multiplied by 10 to get 40,
while 16 would be 4 times 4. Since the 10 and 4 are not relatively prime (have 2 in
common), the 4 cannot be the greatest common factor.
2) listing the prime factors of 40 (2 • 2 • 2 • 5) and 16 (2 • 2 • 2 • 2) and then multiplying
the common factors
(2 • 2 • 2 = 8).
Students also understand that the greatest common factor of two prime numbers will be 1.
Douglas County School System
6th Grade Math
Number System Fluency
7/29/2017
Page 19
Students use the greatest common factor and the distributive property to find the sum of two
whole numbers. For example, 36 + 8 can be expressed as 4 (9 + 2) = 4 (11). Students find the
least common multiple of two whole numbers less than or equal to twelve.
For example, the least common multiple of 6 and 8 can be found by
1) listing the multiples of 6 (6, 12, 18, 24, 30, …) and 8 (8, 26, 24, 32, 40…), then taking the
least in common from the list (24); or
2) using the prime factorization.
Step 1: find the prime factors of 6 and 8.
6=2•3
8=2•2•2
Step 2: Find the common factors between 6 and 8. In this example, the common
factor is 2
Step 3: Multiply the common factors and any extra factors: 2 • 2 • 2 • 3 or 24 (one of the 2s is
in common; the other 2 and the 3 are the extra factors.
Suggested Instructional Strategy
Solve for LCM and/or GCF using factor towers, Venn diagrams, and factor trees.
Use a model to show that 4(9 + 2) is four groups of 9 and four groups of 2.
Skill Based Task
Find the greatest common factor of 24 and 60.
Find the least common multiple of 6 and 10.
Use the distributive property to show 15 + 75.
Instructional
Hot dogs come in packs of 8. Buns come in packs of 12. How many
packs of hot dogs and bags of buns would you have to buy to have an
equal number of hot dogs and buns?
You need to make gift bags for a party with the same number of
balloons and candy in each bag. One package of candy has 24
pieces. One package of balloons has 20 balloons. You need to use all
the candy and all the balloons. What is the greatest number of gift bags
that you can make containing an equal number of items?
Elementary & Middle School Mathematics (VanDeWalle, 7th Ed.)
 TEACHER CONTENT
o Properties of Multiplication and Division: p. 160-161
Douglas County School System
6th Grade Math
Number System Fluency
Problem Task
7/29/2017
Page 20
Resources/Tools
Elementary & Middle School Mathematics (VanDeWalle, 7th Ed.)
 TEACHER CONTENT
o Properties of Multiplication and Division: p. 157-158
Web:
Greatest Common Factor and Least Common Multiple
TEACHER CONTENT
 Amby - Teacher Tutorial - http://amby.com/educate/math/
STUDENT ACTIVITIES/LESSONS
 Illuminations - “The Venn Factor” Lesson - http://illuminations.nctm.org/LessonDetail.aspx?id=L859
 Illuminations - “Factor Findings” Lesson - http://illuminations.nctm.org/LessonDetail.aspx?id=L872
 Illuminations - “Factor Trail Game” Lesson - http://illuminations.nctm.org/LessonDetail.aspx?id=L719
 NLVM - Factor Tree - Interactive Applet - http://nlvm.usu.edu/en/nav/frames_asid_202_g_2_t_1.html?from
 LearnAlberta Spy Guys - “Factors, Multiples, and Prime Factorization” Video Lesson http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=lessons&lesson=m6lessons
hell07.swf
 IXL - GCF and LCM Word Problems - Assessment - http://www.ixl.com/math/grade-6/greatest-commonfactor-word-problems
Greatest Common Factor Lesson
http://www.math.com/school/subject1/lessons/S1U3L2GL.html
This lesson is a resource for teachers or for students after participating in lessons exploring GCF.

Distributive Property
STUDENT ACTIVITIES/LESSONS
 Study Stack - Matching Game - http://www.studystack.com/matching-1870
 Illuminations - “Distributing and Factoring Using Area” Lesson http://illuminations.nctm.org/LessonDetail.aspx?id=L744
CCGPS Internet Resources:
https://ccgps.org/6.NS_B3VJ.html
Douglas County School System
6th Grade Math
Number System Fluency
7/29/2017
Page 21
More Resources – Misconceptions – Take Note
Resources:
Lesson Websites:
Visually model word problems with fractions - www.thinkingblocks.com *Great with the SmartBoard!
Factors & Multiples: http://www.math.com/school/subject1/lessons/S1U3L1GL.html
Greatest Common Factor: http://www.math.com/school/subject1/lessons/S1U3L2GL.html
Factoring: http://www.purplemath.com/modules/factnumb.htm
Divisibility Rules: http://mathforum.org/dr.math/faq/faq.divisibility.html
Game Websites:
Higher order fraction addition: http://fen.com/studentactivities/MathSplat/mathsplat.htm
Factor & Multiple Jeopardy: http://www.math-play.com/Factors-and-Multiples-Jeopardy/Factors-and-MultiplesJeopardy.html *Up to four teams – keeps score for you!
Factors/Divisibility Rules: http://www.aaamath.com/g57f-findafactor.html
Prime Factorization/Multiples/Factors Jeopardy: http://www.quia.com/cb/8436.html
Least Common Multiple: http://www.aaamath.com/g57i-lcm.html
Add/Subtract/Multiply/Divide Fractions: http://www.funbrain.com/fractop/index.html
Literature:
My Full Moon is Square by Elinor J. Pinczes
The Doorbell Rang by Pat Hutchins
Spaghetti and Meatballs for All by Marilyn Burns
Dad’s Diet by Barbara Comer
One Riddle, One Answer by Laura Thompson
“Beasts of Burden” in the Man Who Counted: A Collection of Mathematical Adventures by Malba Tahan
Douglas County School System
6th Grade Math
Number System Fluency
7/29/2017
Page 22
Misconceptions/Suggestions:
Dividing a number by a fraction does not produce a smaller quotient than the dividend. Instead, dividing a number by a
fraction produces a quotient larger than the dividend. Why? Dividing by a fraction is solving how many parts are in the
whole.
When dividing decimals, students tend to focus on the algorithm and not consider the actual values of the numbers. Start
division of decimals with estimation.
Take Note:
A strong focus is on fluency and on real world application this year! Please visit the corestandards.org Mathematics
standards page 4 to read more about how we must shift the students’ way of thinking and their approach to mathematics.
Addition, subtraction and multiplication of fractions and mixed numbers have been moved from this unit! Division by
fraction is the primary focus.
Students should already know, but you may have to review:
Decimal place values to the 10thousandths place;
The standard algorithm for addition, subtraction, multiplication and division;
How to use estimation to predict and assess whether a solution is reasonable;
How to add, subtract and multiply fractions and mixed numbers;
A simplified fraction regardless of the value of the numerator and/or the denominator is always between 0 & 1. (Later this
year, they will learn the value of a fraction is also between 0 & -1);
Fractions are just a representation of division.
Just as multiplication is repeated addition, division is repeated subtraction.
Douglas County School System
6th Grade Math
Number System Fluency
7/29/2017
Page 23