West-Orange Cove ISD
6th Grade Mathematics – 2nd Six Weeks
Learning Standards:
Week 1
Oct 1 - 5
(6.1) Number, operation, and
quantitative reasoning. The student
represents and uses rational numbers in
a variety of equivalent forms. The
student is expected to:

(D) write prime factorizations
using exponents;
 (E) identify factors of a positive
integer, common factors, and the
greatest common factor of a set of
positive integers; and
Major Concepts
Key Vocabulary: exponent, base, factor, power,
composite number, prime number, prime factorization,
common factor, greatest common factor (GCF)
Math background for teachers:
 Exponential notation is a powerful way to express
repeated products of the same number. Powers of 10
express very large numbers in an efficient manner.
 When you raise numbers to powers you multiply.
 A whole number exponent is repeated multiplication
of a number of times itself.
 Prime factorization of a composite number is written
as the product of prime numbers.
 Each composite number has only one prime
factorization.
 A composite number is a whole number with more
than 2 factors.
 0 and 1 are neither prime nor composite.
 The greatest common factor (GCF) is the greatest
factor shared by all the numbers. Do not let students
confuse GCF with LCM.
Processes:
Mathematical Process Standards. The student uses mathematical processes to acquire
and demonstrate mathematical understanding. The student is expected to:
(A) apply mathematics to problems arising in everyday life, society, and the workplace;
(B) use a problem-solving model that incorporates analyzing given information,
formulating a plan or strategy, determining a solution, justifying the solution, and
evaluating the problem-solving process and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives, paper/pencil, and technology as
appropriate, and techniques, including mental math, estimation, and number sense as
appropriate, to solve problems;
(D) communicate mathematical ideas, reasoning, and their implications using multiple
representations, including symbols, diagrams, graphs, and language as appropriate;
(E) create and use representations to organize, record, and communicate mathematical
ideas;
(F) analyze mathematical relationships to connect and communicate mathematical ideas;
and
(G) display, explain, and justify mathematical ideas and arguments using precise
mathematical language in written or oral communication.
Exponents
Prime Numbers
Prime Factorization
Greatest Common Factor
Instruction
Interventions
Extensions
Resources
Prentice Hall Course 1 Textbook:
Chapter 4 – Number Theory and
2012 - 2013
Fractions
Students work in small group with the
teacher using manipulatives to determine
the GCF for sets of numbers.
4-2 Exponents – (1 day)
Basic Multiplication Facts
4-3 Prime Numbers and Prime Factorization (1
day)
A product Game
4-4 Greatest Common Factor (2 Days)
Multiplication Grid
Advanced/GT Students:
Students will problem solve using
exponential notation.
Assessments
Products/Projects
Assessment - Quiz
Product/Project
Journal Entry
Factor Trees – GCF
http://www.funtrivia.com/playquiz/quiz2715661f1
7598.html
http://nlvm.usu.edu/en/nav/frames_asid_202_g_3_
t_1.html
http://www.ixl.com/math/grade-6/greatestcommon-factor-word-problems
6.11, 6.12. 6.13 are taught every day in all concepts
Page 1
West-Orange Cove ISD
6th Grade Mathematics – 2nd Six Weeks
2012 - 2013
Write 3 x 3 x 3 x 3 using exponents
Solution: 3 x 3 x 3 x 3 = 34
Write 8 x 8 x 8 x 8 x 8 x 8 x 8 using exponents.
Solution: 8 x 8 x 8 x 8 x 8 x 8 x 8 = 8 7
The greatest common factor of two or more whole
numbers is the largest whole number that divides evenly
into each of the numbers. There are two ways to find the
greatest common factor.
The first method is to list all of the factors of each
number, then list the common factors and choose the
largest one.
Find the GCF of 36 and 54.
Example:
The factors of 36 are
1, 2, 3, 4, 6, 9, 12, 18, and 36.
The factors of 54 are
1, 2, 3, 6, 9, 18, 27, and 54.
The common factors of 36 and 54 are
1, 2, 3, 6, 9, 18
Although the numbers in bold are all common factors of
both 36 and 54, 18 is the greatest common factor.
6.11, 6.12. 6.13 are taught every day in all concepts
Page 2
West-Orange Cove ISD
6th Grade Mathematics – 2nd Six Weeks
2012 - 2013
The second method to find the greatest common factor is
to list the prime factors, then multiply the common prime
factors.
Let’s use the same numbers, 36 and 54 again to find their
greatest common factor.
Example:
The prime factorization of 36 is
2x2x3x3
The prime factorization of 54 is
2x3x3x3
Notice that the prime factorizations of 36 and 54 both
have one 2 and two 3s in common. So, we simply
multiply these common prime factors to find the greatest
common factor. Like this…
2 x 3 x 3 = 18
Both methods for finding the greatest common factor
work!
Basic Multiplication Facts:
 Students should already know basic multiplication
facts; however, it is crucial to emphasize the
memorization of these facts throughout the entire
year
6.11, 6.12. 6.13 are taught every day in all concepts
Page 3
West-Orange Cove ISD
6th Grade Mathematics – 2nd Six Weeks
2012 - 2013
Processes:
Week 2 & 3
Oct 8 – 12
Oct 15 - 19
Learning Standards:
6.1B Generate equivalent forms of rational
numbers including whole numbers, fractions, and
decimals. Readiness Standard
6.2A Model addition and subtraction situations
involving fractions with objects, pictures, words
and numbers. Supporting Standard
6.2B Use addition and subtraction to solve
problems involving fractions and decimals.
Readiness Standard
6.2D Estimate and round to approximate
reasonable results and to solve problems where
exact answers are not required. Supporting
Major Concepts
Fractions
o
o
o
o
o
Equivalent fractions
Simplifying fractions
Improper fractions
Mixed numbers
Comparing and ordering
fractions
Least Common Multiple (LCM)
Fractions and decimals
Standard
Instructional
The next two weeks are focused on fractions and connecting
fractions to decimals and the least common multiple (LCM).
Key Vocabulary: fraction, denominator, numerator, simplify,
simplest form, improper fraction, equivalent fraction, proper fraction,
mixed number, multiple, common multiple, least common multiple
(LCM), least common denominator (LCD), terminating decimal,
repeating decimal
Math background for the teacher:
 Three categories of models exist for working with fractions –o
area, length, and set or quantity.
 Equivalent fractions are two ways of describing the same amount
by using different-sized fractional parts.
 A fraction does not say anything about the size of the whole or
the size of the parts.
 A fraction tells only about the relationship between the part and
the whole.

6.11, 6.12. 6.13 are taught every day in all concepts
Resources
Prentice Hall Course 1 Textbook:
Literature: The Man Who Counted: A
Collection of Mathematical Adventures
Chapter 4 – Number Theory and
Fractions
Lab 4-5a Modeling Fractions and 4-5
Equivalent Fractions (2 days)
Lab 4-6a Improper Fractions (2 days)
4-6b Fraction Measurements (1 day)
4-7 Least Common Multiple (1 day)
4-8 Comparing and Ordering Fractions
(1 day)
4-9 Fractions and decimals (2 days)
Mathematical Process Standards. The student uses mathematical processes to acquire
and demonstrate mathematical understanding. The student is expected to:
(A) apply mathematics to problems arising in everyday life, society, and the
workplace;
(B) use a problem-solving model that incorporates analyzing given information,
formulating a plan or strategy, determining a solution, justifying the solution, and
evaluating the problem-solving process and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives, paper/pencil, and technology as
appropriate, and techniques, including mental math, estimation, and number sense as
appropriate, to solve problems;
(D) communicate mathematical ideas, reasoning, and their implications using multiple
representations, including symbols, diagrams, graphs, and language as appropriate;
(E) create and use representations to organize, record, and communicate mathematical
ideas;
(F) analyze mathematical relationships to connect and communicate mathematical
ideas; and
(G) display, explain, and justify mathematical ideas and arguments using precise
mathematical language in written or oral communication.
Interventions
Extensions
Assessment
Formal assessment
The students will work with the teacher
in small groups to explore fractions using
manipulatives and multiplication
strategies to find the LCM and LCLD.
Advanced/GT Students:
Students will convert between fractions,
decimals, whole numbers, and percent.
Students will practice problem solving
and converting answers to decimals,
fractions, and percents.
Product/Project
Students will write a
letter to the editor
explaining the concepts
of LCM, LCD, and
GCF.
Fraction circles
Fraction Sticks
Pattern blocks
Red/Yellow Counters
Page 4
West-Orange Cove ISD
6th Grade Mathematics – 2nd Six Weeks
Activity: Who is Winning? The students are playing red light-green
light. Who is winning? The fractions tell how much of the distance
they have already moved. Mary ¾, Harry ½, Larry 5/6, Juan 5/8,
Miguel 5/9, Kim 2/3. Students will place the names on the number
line to show where they are between the start and finish.
Activity: Use the class (# of students for the whole) write fractions
for boys/girls, wearing white, wearing blue, long hair, etc.
Activity: Four students are sharing 10 brownies so that each one will
get the same amount. How much can each child have?
Activity: Use manipulatives to represent equivalent fractions. 12/5
and 2 2/5, 1/3 and 3/9, 1/3 and 6/18.
Activity: Students will name a fraction that is close to 1. Next name
another fraction that is even closer to l than the first. After they name
the second fraction closer to l they must explain why they believe the
fraction is closer to one than the previous fraction. Continue for
several fractions in the same manner. Next do the same activity using
½ as the target.
2012 - 2013
http://express.smarttech.com/?url=htt
p://exchangedownloads.smarttech.co
m/public/content/9c/9ca457d5-a38e4bc2-8b9fa0afa75e70c6/%232%20FractionsPart
1.notebook#
http://express.smarttech.com/?url=htt
p://exchangedownloads.smarttech.co
m/public/content/5d/5d0f2aab-2fff498c-889ca98bfad16b8f/Expressions%20and%2
0Variables.notebook#
http://express.smarttech.com/?url=htt
p://exchangedownloads.smarttech.co
m/public/content/85/854f063e-6b7f42e2-a79a25139ec1268e/Fractions_Decimals_Pe
rcents.notebook#
Basic Multiplication Facts:
Students should already know basic multiplication facts; however, it
is crucial to emphasize the memorization of these facts throughout the
entire year
6.11, 6.12. 6.13 are taught every day in all concepts
Page 5
West-Orange Cove ISD
Week 4
Oct 22 – 26
6th Grade Mathematics – 2nd Six Weeks
Learning Standards:
6.1B Generate equivalent forms of rational numbers including
whole numbers, fractions, and decimals. Readiness Standard
6.2A Model addition and subtraction situations involving
fractions with objects, pictures, words and numbers.
Supporting Standard
6.2B Use addition and subtraction to solve problems
involving fractions and decimals. Readiness Standard
6.2D Estimate and round to approximate reasonable results
and to solve problems where exact answers are not required.
Supporting Standard
6.8 Select and use appropriate units to solve problems
involving time. Supporting Standard
Major Concepts
Adding and subtracting fractions with like
denominators
Adding and subtracting fractions w/unlike
denominators
Instruction
Resources
Key Vocabulary: fraction, numerator, denominator, benchmark,
mixed number, equation
Prentice Hall Course 1 Textbook
Math background for the teacher:
 The meanings of each operation on fractions are the same as the
meanings for the operations on whole numbers
 In addition and subtraction of fractions, the numerator tells the
number of parts and the denominator the type of part. It is the
parts that are added or subtracted.
 Students should use invented strategies for solving addition and
subtraction of fractions prior to teaching traditional algorithms.
 In order to add or subtract fractions you must have like or common
denominators.
 Students may find using a number line a useful tool in solving
addition and subtraction of fractions
 Students may solve equations using a number line without first
finding a common denominator
6.11, 6.12. 6.13 are taught every day in all concepts
2012 - 2013
Processes:
Mathematical Process Standards. The student uses mathematical
processes to acquire and demonstrate mathematical understanding. The
student is expected to:
(A) apply mathematics to problems arising in everyday life, society, and
the workplace;
(B) use a problem-solving model that incorporates analyzing given
information, formulating a plan or strategy, determining a solution,
justifying the solution, and evaluating the problem-solving process and
the reasonableness of the solution;
(C) select tools, including real objects, manipulatives, paper/pencil, and
technology as appropriate, and techniques, including mental math,
estimation, and number sense as appropriate, to solve problems;
(D) communicate mathematical ideas, reasoning, and their implications
using multiple representations, including symbols, diagrams, graphs, and
language as appropriate;
(E) create and use representations to organize, record, and communicate
mathematical ideas;
(F) analyze mathematical relationships to connect and communicate
mathematical ideas; and
(G) display, explain, and justify mathematical ideas and arguments using
precise mathematical language in written or oral communication.
Interventions
Extensions
Literature: The Man Who Made Parks
Chapter 5: Adding and Subtracting Fractions
5-l & 5-2 Estimating Sums and Differences with
like denominators and 5-2a Lab (1 day)
5-3 Modeling Unlike Denominators (1 day)
Students will work in
a small group with the
teacher using
manipulative to add
and subtract fractions
that do not have a
common denominator.
Basic Multiplication
Facts
5-4 – 5-5 Mixed Numbers (1 day)
5 – 6 and Solving fraction equations (1 day)
Fraction Games
http://www.ixl.com/math/grade-7/add-and-subtractfractions
Advanced/GT
Students:
Students will problem
solve using division to
Assessment
Assessments:
Formal adding and
subtracting fractions
with common and
unlike denominators
Products/Project
Students will write and
reflect a journal entry
on the process of adding
and subtracting
fractions with unlike
denominators
Page 6
West-Orange Cove ISD
6th Grade Mathematics – 2nd Six Weeks
Activity: Students will solve then share their strategies (at this point
you have not taught traditional algorithms).
Mark bought 4 ¼ lb of candy for his mom. The candy looked
so good that he ate 7/8 of a pound of it. How much did he
give to his mom?
2012 - 2013
determine the unit
rates and ratio.
Students will use
recipes and sales ads
in problem solving.
Jack and Jill ordered two medium pizzas, one cheese and one
pepperoni. Jack ate 5/6 of a pizza and Jill at ½ of a pizza.
How much pizza did they eat together?

Basic Multiplication Facts:
Students should already know basic multiplication facts; however, it is crucial
to emphasize the memorization of these facts throughout the entire year
6.11, 6.12. 6.13 are taught every day in all concepts
Page 7
West-Orange Cove ISD
Week 5
Oct 29 – Nov 2
6th Grade Mathematics – 2nd Six Weeks
Learning Standards:
6.1B Generate equivalent forms of rational numbers including
whole numbers, fractions, and decimals. Readiness Standard
6.2D Estimate and round to approximate reasonable results
and to solve problems where exact answers are not required.
Supporting Standard
6.8 Select and use appropriate units to solve problems
involving time. Supporting Standard
Instruction
.
Key Vocabulary: fraction, numerator, denominator, benchmark, mixed
number, equation
Math background for teacher:
 For multiplication by a fraction, repeated addition and area models
support development of the algorithm for multiplication of fractions.
 For division by a fraction, the two ways of thinking about the operation
– partition and measurement will lead to two different though process
for division and both are important.
 Students’ first experiences with multiplication should involve finding
fractions of whole numbers. For example how much is 1/5 of 45? Or if
the whole is 24 what is 3/8s of the whole?
 Developing the algorithms:
o Common denominator algorithm – this relies on the
measurement or repeated subtraction concept of division. First
Major Concepts
Multiplying and dividing
fractions
Resources
Prentice Hall Course 1
Textbook
6-1 & 6-2 Multiplying
Fractions
6-3 & 6-4 Dividing
Fractions
6-5 Solving fraction
Equations
http://www.brainpop.com/
math/numbersandoperatio
ns/multiplyinganddividing
fractions/preview.weml
2012 - 2013
Processes:
Mathematical Process Standards. The student uses mathematical processes to acquire
and demonstrate mathematical understanding. The student is expected to:
(A) apply mathematics to problems arising in everyday life, society, and the workplace;
(B) use a problem-solving model that incorporates analyzing given information,
formulating a plan or strategy, determining a solution, justifying the solution, and
evaluating the problem-solving process and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives, paper/pencil, and technology as
appropriate, and techniques, including mental math, estimation, and number sense as
appropriate, to solve problems;
(D) communicate mathematical ideas, reasoning, and their implications using multiple
representations, including symbols, diagrams, graphs, and language as appropriate;
(E) create and use representations to organize, record, and communicate mathematical
ideas;
(F) analyze mathematical relationships to connect and communicate mathematical ideas;
and
(G) display, explain, and justify mathematical ideas and arguments using precise
mathematical language in written or oral communication.
Interventions
Extensions
Students will work in small groups with
the teacher using manipulatives and grid
paper to develop algorithms for
multiplying and dividing fractions.
Basic Multiplication Facts
Advanced/GT Students:
Students will solve advanced equations
using the order of operations. Students
will problem solve and write equations to
solve the problems.
Assessment
Assessments:
formal understanding
and ability to apply
knowledge
Products/project
Students will illustrate
solutions to the
following:
¾x5½
1 1/8 of 40
get common denominators and then divide numerators.
Example, 5/3/ ¼ = 20/12 / 3/12 = 20 /3 = 30/3 = 6 2/3
o
Invert and multiply algorithm – Invert the divisor and multiply.
6.11, 6.12. 6.13 are taught every day in all concepts
Page 8
West-Orange Cove ISD
6th Grade Mathematics – 2nd Six Weeks
2012 - 2013
Students must understand the math behind this
concept/strategy (multiply by the denominator and divide by
the numerator)
Activity: Students will illustrate the following fractions of whole
numbers:
 There are 15 cars in Steven’s car collection. 2/3 of the cars are
red. How many red cars does Steven have?
 The walk from school to the library takes 15 minutes. If we had
already walked 2/3 of the way how many minutes had we walked?
 ¼x5=?
 4x½=?
6.11, 6.12. 6.13 are taught every day in all concepts
Page 9