Mathematics Pacing Guide
Time Frame: 8 Weeks – September/October Sixth Grade
Unit 1: Developing an Understanding of the Number System (Expressions & Equations)
Standards for Mathematical Practice / Literacy Standards1. Make sense of problems and persevere in solving them
5. Use appropriate tools strategically
8. Look for and express regularity in repeated reasoning / RST.6.1 Cite specific textual evidence to support analysis of science and technical texts.
RST.6.3 Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.
RST.6.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 6–8 texts and topics.
RST.6.7 Integrate quantitative or technical information expressed in words in a text with a version of that information expressed visually (e.g., in a flowchart, diagram, model, graph, or table).
Common Core / Essential Questions / Assessment / Vocabulary / Resources /
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. 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 what contexts is it important to be able to fluently add, subtract, multiply, and divide multi-digit decimal numbers?
What does it mean to fluently add, subtract, multiply, and divide multi-digit decimal numbers? / Before:
Number lines (individual and whole class)
KWL Chart
Pre-test
Brainstorming
Graphic Organizers
During:
Vocabulary Lessons (word, definition, picture, sentence)
Warm-ups (Used to review content)
Formative Assessments throughout lesson
Graphic Organizers
Class Discussion
Class Examples
Student Participation at board
Independent Practice
Real World Problems
Lesson “check points”
Partner Work
Small Group Work
KWL Chart
After:
Post-Test
Graphic Organizers
Partner Work
Small Group Work
Content Review Stations
KWL Chart
Real World Problems / Base
Decimal
Divisor
Exponent
Exponent
Factor
Greatest Common Factor (GCF)
Least Common Multiple (LCM)
Less than
Perfect square
Powers
Product
Radical sign
Square root
Sum
Whole numbers / MAISA curriculum units and resources:
http://gomaisa-public.rubiconatlas.org/Atlas/Browse/View/UnitCalendar?SourceSiteID=&CurriculumMapID=798&YearID=2013
www.brainpop.com
http://illuminations.nctm.org/
www.mathisfun.com
Fractions – multiplying & dividing
Fraction Game:
This applet allows students to individually practice working with relationships among fractions and ways of combining fractions.
Single person: http://illuminations.nctm.org/ActivityDetail.aspx?ID=18
Two-player version: http://www.nctm.org/standards/content.aspx?id=26975
This site has multiple resources for teachers and students.
http://apps.svsu.edu/mathsci-center/uploads/math/MiddleSchool.html
Compute fluently with multi-digit numbers and find common factors
and multiples
6. NS.2 Fluently divide multi-digit numbers using the standard algorithm. / Decimal
Divisor
Factors
Greatest Common Factor (GCF)
Lease Common Multiple (LCM)
Less than
Product
Whole numbers / www.brainpop.com
http://illuminations.nctm.org/
www.mathisfun.com
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. For example, express 36 + 8 as 4 (9 + 2). / What are the relationships between factors, multiples, divisors, and products?
Scaffold Questions
What are factor pairs?
How can one find the factors of numbers? The multiples of numbers?
What are some strategies for finding common factors for a set of numbers? Common multiples?
Which situations call for common factors or common multiples? For greatest common factor or least common multiple?
Apply and extend previous understandings of arithmetic to algebraic expressions.
6. EE.1 Write and evaluate numerical expressions involving whole-number exponents. / How can one use exponents to write repeated factors? / Base
Exponent
Exponent
Perfect square
Powers
Radical sign
Square root
Mathematics Pacing Guide
Time Frame: 2 Weeks - October/ November Sixth Grade
Unit 2: Understand Rational Numbers on a Number Line 6.NS.6
Standards for Mathematical Practice / Literacy Standards1. Make sense of problems and persevere in solving them
5. Use appropriate tools strategically / RST.6.1 Cite specific textual evidence to support analysis of science and technical texts.
RST.6.3 Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.
RST.6.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 6–8 texts and topics.
RST.6.7 Integrate quantitative or technical information expressed in words in a text with a version of that information expressed visually (e.g., in a flowchart, diagram, model, graph, or table).
Common Core / Essential Questions / Assessment / Vocabulary / Resources /
Apply and extend previous understandings of numbers to the system of rational numbers
6.NS.C.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
6. NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite.
b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
c. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. / How can a negative number that is further away from 0 than another negative number be greater in value?
What is the meaning of zero? / Before:
Number lines (individual and whole class)
KWL Chart
Pre-test
Brainstorming
Graphic Organizers
During:
Vocabulary Lessons (word, definition, picture, sentence)
Warm-ups (Used to review content)
Formative Assessments throughout lesson
Graphic Organizers
Class Discussion
Class Examples
Student Participation at board
Independent Practice
Real World Problems
Lesson “check points”
Partner Work
Small Group Work
KWL Chart
After:
Post-Test
Graphic Organizers
Partner Work
Small Group Work
Content Review Stations
KWL Chart
Real World Problems / Coordinate plane
Integers
Negative numbers
Opposites
Ordered pair
Origin
Quadrants
Rational number
x – axis
x – coordinate
y – axis
y – coordinate / MAISA curriculum units and resources:
http://gomaisa-public.rubiconatlas.org/Atlas/
Browse/View/UnitCalendar?SourceSiteID=
&CurriculumMapID=798&YearID=2013
http://illuminations.nctm.org/
http://apps.svsu.edu/mathsci-center/uploads/math/MiddleSchool.html
This site has many resources for teachers.
Mathematics Pacing Guide
Time Frame: 4 Weeks – November/December Sixth Grade
Unit 3: Understand Multiplication and Division of Fractions (The Number System - 6.NS.1)
Standards for Mathematical Practice / Literacy Standards1. Make sense of problems and persevere in solving them
5. Use appropriate tools strategically / RST.6.1 Cite specific textual evidence to support analysis of science and technical texts.
RST.6.3 Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.
RST.6.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 6–8 texts and topics.
RST.6.7 Integrate quantitative or technical information expressed in words in a text with a version of that information expressed visually (e.g., in a flowchart, diagram, model, graph, or table).
WHST.6.2 Write informative/explanatory texts, including the narration of historical events, scientific procedures/ experiments, or technical processes.
d. Use precise language and domain-specific vocabulary to inform about or explain the topic.
f. Provide a concluding statement or section that follows from and supports the information or explanation presented.
SL.6.2. Interpret information presented in diverse media and formats (e.g., visually, quantitatively, orally) and explain how it contributes to a topic, text, or issue under study.
SL.6.4. Present claims and findings, sequencing ideas logically and using pertinent descriptions, facts, and details to accentuate main ideas or themes; use appropriate eye contact, adequate volume, and clear pronunciation.
SL.6.5. Include multimedia components (e.g., graphics, images, music, sound) and visual displays in presentations to clarify information.
Common Core / Essential Questions / Assessment / Vocabulary / Resources /
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. 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? / How can you use the relationship between division and multiplication to divide fractions by fractions?
How does modeling help us understand the relationship between multiplication and division of fractions?
How is dividing by fractions different from dividing by a whole number? / Fraction project – presentation
Before:
KWL Chart
Pre-test
Brainstorming
Graphic Organizers
During:
Vocabulary Lessons (word, definition, picture, sentence)
Warm-ups
Formative Assessments throughout lesson
Graphic Organizers
Class Discussion
Class Examples
Student Participation at board
Independent Practice
Real World Problems
Lesson “check points”
Partner Work
Small Group Work
KWL Chart
After:
Post-Test
Graphic Organizers
Partner Work
Small Group Work
Content Review Stations
KWL Chart
Real World Problems / Denominator
Divide
Fraction
Improper fraction
Lease Common Multiple
Least Common Denominator
Mixed number
Multiply
Numerator
Quotient
Reciprocal
Whole number / MAISA curriculum units and resources:
http://gomaisa-public.rubiconatlas.org/
Atlas/Browse/View/UnitCalendar?
SourceSiteID=&CurriculumMapID=
798&YearID=2013
www.visualfractions.com
www.mrnussbaum.com
www.brainpop.com
http://illuminations.nctm.org/
www.mathisfun.com
Mathematics Pacing Guide
Time Frame: 3 Weeks – January Sixth Grade
Unit 4: Develop an Understanding of Rational Numbers (The Number System 6.NS.6, 6.NS.5, 6.NS.7)
(Expressions & Equations 6.EE.6)
Standards for Mathematical Practice / Literacy Standards1. Make sense of problems and persevere in solving them
5. Use appropriate tools strategically / RST.6.1 Cite specific textual evidence to support analysis of science and technical texts.
RST.6.3 Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.
RST.6.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 6–8 texts and topics.
RST.6.7 Integrate quantitative or technical information expressed in words in a text with a version of that information expressed visually (e.g., in a flowchart, diagram, model, graph, or table).
Common Core / Essential Questions / Assessment / Vocabulary / Resources /
Apply and extend previous understandings of numbers to the system of rational numbers
6. NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, debits/credits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
6. NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
6. NS.7 Understand ordering and absolute value of rational numbers.
a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.
b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3 o C > –7 o C to express the fact that –3 o C is warmer than –7 o C.
c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars.
d. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represent a debt greater than 30 dollars. / How can a negative number that is further away from 0 than another negative number be greater in value?
What is the meaning of zero?
How can you compare two positive or negative numbers in real-world situations by using a number line? / Before:
KWL Chart
Pre-test
Brainstorming
Graphic Organizers
During:
Vocabulary Lessons (word, definition, picture, sentence)
Warm-ups (Used to review content)
Formative Assessments throughout lesson
Graphic Organizers
Class Discussion
Class Examples
Student Participation at board
Independent Practice
Real World Problems
Lesson “check points”
Partner Work
Small Group Work
KWL Chart
After:
Post-Test
Graphic Organizers
Partner Work
Small Group Work
Content Review Stations
KWL Chart
Real World Problems / Absolute value
Axes
Coordinate plane
Coordinates
Horizontal number line
Integer
Linear equation
Negative number
Opposites
Ordered Pair
Origin
Positive number
Quadrants
Rational number
Reflection across the axis
Vertical number line
x – axis
x – coordinate
y – axis
y – coordinate / MAISA curriculum units and resources:
http://gomaisa-public.rubiconatlas.org/Atlas/
Browse/View/UnitCalendar?SourceSiteID=
&CurriculumMapID=798&YearID=2013
www.brainpop.com
http://illuminations.nctm.org/
www.mathisfun.com
Reason about and solve one-variable equations and inequalities
6. EE.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. / Addition
Algebraic Expression
Coefficient
Division
Exponents
Expression
Like terms
Multiplication
Numerical Expression
Subtraction
Term
Variable
Mathematics Pacing Guide