6th Grade Mathematics
UNIT 1: FRACTIONS AND DECIMALS
Fractions and Decimals/ 4 Weeks
Students will learn to apply and extend their previous understanding of multiplication and division
to divide fractions by fractions. Students will use the meaning of fractions, the meanings of
multiplication and division and the relationship between multiplication and division to understand
and explain why the procedures for dividing fractions make sense. They will also compute multidigit numbers with and without decimals fluently. Students use these operations to solve real-life
problems.
1
6th Grade Mathematics
Key Ideas:
 Operations on decimals and whole
numbers are based upon place value
relationships.
 The relationship of the location of the
digits and the value of the digits is part of
understanding multi-digit operations.
 Fluently divide multi-digit numbers using
standard algorithms
 Multiplication and division are inverse
operations.
 Division can be represented using
multiple formats
 Fluently add, subtract, multiply and divide
multi-digit decimals using standard
algorithms
 Models can be used to show
multiplication and division of fractions
Guiding/Focus Questions:
 How do we divide multi-digit numbers
 How do we add, subtract, divide and multiply
multi-digit decimals?
 How do we convert improper fractions and
mixed numbers?
 How do we simplify fractions?
 How do we multiply fractions and mixed
numbers?
 How do we divide fractions?
 How can we use models to divide fractions?
NYS Common Core Standards for Mathematics
[Resource: https://www.engageny.org/resource/grade-6-mathematics]
Focus Standards:
Apply and extend previous understandings of multiplication and division to divide fractions by
fractions.
6.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.
Compute fluently with multi-digit numbers and find common factors and multiples.
6.NS.2 Fluently divide multi-digit numbers using the standard algorithm.
6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard
algorithm for each operation.
6.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.
Foundational Standards(Prerequisites):
Gain familiarity with factors and multiples.
4.OA.4 Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number
is a multiple of each of its factors. Determine whether a given whole number in the range 1– 100 is
a multiple of a given one-digit number. Determine whether a given whole number in the range 1–
100 is prime or composite.
Understand the place value system.
5.NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by
powers of 10, and explain patterns in the placement of the decimal point when a decimal is
multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
2
6th Grade Mathematics
Perform operations with multi-digit whole numbers and with decimals to hundredths.
5.NBT.6 Find whole-number quotients of whole numbers with up to four-digit dividends and twodigit 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.
5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or
drawings and strategies based on place value, properties of operations, and/or the relationship
between addition and subtraction; relate the strategy to a written method and explain the
reasoning used.
Use equivalent fractions as a strategy to add and subtract fractions.
5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by
replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum
or difference of fractions with like denominators.
Apply and extend previous understandings of multiplication and division to multiply and divide
fractions.
5.NF.4Apply and extend previous understandings of multiplication to multiply a fraction or whole
number by a fraction.
5.NF.7Apply and extend previous understandings of division to divide unit fractions by whole
numbers and whole numbers by fractions.
Focus Standards for Mathematical Practice:
MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively. Students make sense of quantities and their
relationships in problems. They understand “how many” as it pertains to the divisor in a quotient
of fractions problem. They understand and use connections between divisibility and the greatest
common factor to apply the distributive property. Students rely on estimation and properties of
operations to justify the reason for their answers when manipulating decimal numbers and their
operations. Students reason abstractly when applying place value and fraction sense when
determining the placement of a decimal point.
MP.6 Attend to Precision. Students use precise language and place value when adding,
subtracting, multiplying, and dividing by multi-digit decimal numbers. Students read decimal
numbers using place value.
MP.7 Look for and make use of structure. Students find patterns and connections when
multiplying and dividing multi-digit decimals. Students recognize that when expressing the sum of
two whole numbers using the distributive property, there is a number which represents the
greatest common factor of those numbers and both are multiples. When dividing fractions,
students recognize and make use of a related multiplication problem or create a number line and
use skip counting to determine the number of times the divisor is added to obtain the dividend.
Students use the familiar structure of long division to find the greatest common factor in another
way.
MP.8 Look for and express regularity in repeated reasoning. Students determine reasonable
answers to problems involving operations with decimals. Estimation skills and compatible numbers
are used. Students discover, relate, and apply strategies when problem-solving.
3
6th Grade Mathematics
Content/Skills
 Basic operations
 Fractions
 Decimals
 Problem solving strategies
 Fluently divide multi-digit numbers using standard algorithms
 Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithms
 Changing mixed numbers and improper fractions
 Simplifying fractions
 Multiply fractions and mixed numbers
 Divide a fraction by a fraction
 Identify steps to solve problems including identifying relevant and irrelevant information
Vocabulary/ Key Terms
 Prime Number
 Composite Number
 Factors
 Greatest Common Factor
 Multiples
 Least Common Multiple
 Dividend
 Divisor
 Reciprocal
 Multiplicative Inverses
 Algorithm
 Distributive Property
 Estimate
For ELLs, have them create a mini-glossary; instruct them to list each term, its meaning, and an
illustration for each. When students have finished their glossaries, have them share them with the
class. Allow them to use the glossaries as they work the exercises in the lesson and remind them to
use them when they do their homework.
4
6th Grade Mathematics
ASSESSMENT EVIDENCE
Initial Assessment: Unit Readiness Test
Formative Assessments:
 Quizzes
 Exit Slips
 Checks for Understanding
 Short and Extended-Response questions used throughout the unit.
 Mathematical Reflections
 Formative Assessments Tasks
 Performance Task 1 (Multi-digit operations including division)
 Performance Task 2(Decimal operations)
 Performance Task 3 (Division of fractions)
Summative Assessments:Unit Test
TEACHING PLAN
Teaching and Learning Activities:
I.
Administer the Unit Readiness Test (to assess knowledge of fractions)
II.
Use the content/skills as learning goals for each lesson
Lesson 1: Review basic fraction operations
Lesson 2: Dividing fractions by whole numbers
Lesson3: Dividing fractions by fractions
Lesson 4: Solving word problems involving the division of fractions by fractions
Lesson 5: Dividing multi-digit numbers
Lesson 6: Decimal operations
III.
Assess students on the unit.
 Final Performance Assessment
 Unit Test
Resources Needed:
 Connected Math Project 3 (CMP3): Prime Time; Let’s Be Rational
 NYS Common Core Math Module: 2
 https://www.engageny.org/resource/grade-6-mathematics-module-2
 Impact Mathematics Course 1
 Math Handbook
 MathXL (Pearson’s online homework, tutorial, and assessment system)
 Glencoe New York State Review Series
 Ready New York CCLS (6th Grade)
 http://www.livebinders.com/play/play?id=953710#anchor
 http://www.algebrahelp.com/
5
6th Grade Mathematics

https://grade6commoncoremath.wikispaces.hcpss.org
6
6th Grade Mathematics
CALENDAR
Time
Spent
1 Week
Standards
6.NS.2
Topics To
Cover
 Dividing
Whole
Numbers
2 Weeks 6.NS.1
6.NS.4
 Review of
Fractions
 Dividing
Fractions
1 Week
 Decimal
Operations
6.NS.3
Resources Needed











Connected Math Project 3 (CMP3): Prime Time; Let’s Be
Rational
NYS Common Core Math Module: 2
https://www.engageny.org/resource/grade-6mathematics-module-2
Impact Mathematics Course 1
Math Handbook
MathXL (Pearson’s online homework, tutorial, and
assessment system)
Glencoe New York State Review Series
Ready New York CCLS (6th Grade)
http://www.livebinders.com/play/play?id=953710#anchor
http://www.algebrahelp.com/
https://grade6commoncoremath.wikispaces.hcpss.org
7