[Type text]Revised 7-17-2014
6th Grade Mathematics Curriculum Map
2014-2015 School Year
First Semester / Second SemesterUnit 1
Number System Fluency
(5weeks) / Unit 2
Rate, Ratio and Proportional Reasoning
Using Equivalent Fractions
(4 weeks) / Unit 3
Expressions
(4 weeks) / Unit 4
One-Step Equations and Inequalities
(5 weeks) / Unit 5
Area and Volume
(4 weeks) / Unit 6
Statistics
(4 weeks) / Unit 7
Rational Explorations: Numbers and their Opposites
(3 weeks) / Unit 8
Show What We Know
(4 weeks)
Common Core Georgia Performance Standards
MCC6.NS.1
MCC6.NS.2
MCC6.NS.3
MCC6.NS.4 / MCC6.RP.1
MCC6.RP.2
MCC6.RP.3a
MCC6.RP.3b
MCC6.RP.3c
MCC6.RP.3d / MCC6.EE.1
MCC6.EE.2a
MCC6.EE.2b
MCC6.EE.2c
MCC6.EE.3
MCC6.EE.4 / MCC6.EE.5
MCC6.EE.6
MCC6.EE.7
MCC6.EE.8
MCC6.EE.9
MCC6.RP.3
MCC6.RP.3a
MCC6.RP.3b
MCC6.RP.3c
MCC6.RP.3d
(equations) / MCC6.G.1
MCC6.G.2
MCC6.G.4 / MCC6.SP.1
MCC6.SP.2
MCC6.SP.3
MCC6.SP.4
MCC6.SP.5
MCC6.SP.5a
MCC6.SP.5b
MCC6.SP.5c
MCC6.SP.5d / MCC6.NS.5
MCC6.NS.6a
MCC6.NS.6b
MCC6.NS.6c
MCC6.NS.7a
MCC6.NS.7b
MCC6.NS.7c
MCC6.NS.7d
MCC6.NS.8
MCC6.G.3 / ALL
Incorporated Standards (these are embedded in the unit but not specifically addressed)
MCC6.NS.1
MCC6.NS.2
MCC6.NS.3
MCC6.NS.4 / MCC6.NS.1
MCC6.NS.2
MCC6.NS.3
MCC6.NS.4 / MCC6.NS.1
MCC6.NS.2
MCC6.NS.3
MCC6.NS.4 / MCC6.EE.2c
MCC6.NS.1
MCC6.NS.2
MCC6.NS.3
MCC6.NS.4 / MCC6.NS.1
MCC6.NS.2
MCC6.NS.3
MCC6.NS.4
These units were written to build upon concepts from prior units, so later units contain tasks that depend upon the concepts addressed in earlier units.All units will include the Mathematical Practices and indicate skills to maintain.
NOTE: Mathematical standards are interwoven and should be addressed throughout the year in as many different units and tasks as possible in order to stress the natural connections that exist among mathematical topics.
Grades 6-8 Key: NS = The Number System, RP = Ratios and Proportional Relationships, EE = Expressions and Equations, G = Geometry, SP = Statistics and Probability.
Sixth Grade Overview
In Grade 6, instructional time should focus on four critical areas: (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking. Descriptions of the four critical areas follow:
(1) Students use reasoning about multiplication and division to solve ratio and rate problems about quantities. By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities, students connect their understanding of multiplication and division with ratios and rates. Thus students expand the scope of problems for which they can use multiplication and division to solve problems, and they connect ratios and fractions. Students solve a wide variety of problems involving ratios and rates.
(2) Students 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. Students use these operations to solve problems. Students extend their previous understandings of number and the ordering of numbers to the full system of rational numbers, which includes negative rational numbers, and in particular negative integers. They reason about the order and absolute value of rational numbers and about the location of points in all four quadrants of the coordinate plane.
(3) Students understand the use of variables in mathematical expressions. They write expressions and equations that correspond to given situations, evaluate expressions, and use expressions and formulas to solve problems. Students understand that expressions in different forms can be equivalent, and they use the properties of operations to rewrite expressions in equivalent forms. Students know that the solutions of an equation are the values of the variables that make the equation true. Students use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one‐step equations. Students construct and analyze tables, such as tables of quantities that are in equivalent ratios, and they use equations (such as 3???) to describe relationships between quantities.
(4) Building on and reinforcing their understanding of number, students begin to develop their ability to think statistically. Students recognize that a data distribution may not have a definite center and that different ways to measure center yield different values. The median measures center in the sense that it is roughly the middle value. The mean measures center in the sense that it is the value that each data point would take on if the total of the data values were redistributed equally, and also in the sense that it is a balance point. Students recognize that a measure of variability (interquartile range or mean absolute deviation) can also be useful for summarizing data because two very different sets of data can have the same mean and median yet be distinguished by their variability. Students learn to describe andsummarize numerical data sets, identifying clusters, peaks, gaps, and symmetry, considering the context in which the data were collected.
Students in Grade 6 also build on their work with area in elementary school by reasoning about relationships among shapes to determine area, surface area, and volume. They find areas of right triangles, other triangles, and special quadrilaterals by decomposing these shapes, rearranging or removing pieces, and relating the shapes to rectangles. Using these methods, students discuss, develop, and justify formulas for areas of triangles and parallelograms. Students find areas of polygons and surface areas of prisms and pyramids by decomposing them into pieces whose area they can determine. Theyreason about right rectangular prisms with fractional side lengths to extend formulas for the volume of aright rectangular prism to fractional side lengths. They prepare for work on scale drawings andconstructions in Grade 7 by drawing polygons in the coordinate plane.
Standards for Mathematical Practice
The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).
HENRY COUNTY SCHOOLS
2014-2015Curriculum Map (Yearly Overview)
First Semester
Course: 6th Grade MathematicsGrade Level: 6
DATES /UNIT
/CONTENT STANDARDS
/ ESSENTIAL QUESTIONS /ENDURING UNDERSTANDINGS
The students will… /ASSESSMENTS
AUGUST/ SEPTEMBER
Aug 4 –Sept 5
Labor Day: 9/1
PL: 9/2 / Unit 1
Number System Fluency / MCC6.NS.1
MCC6.NS.2
MCC6.NS.3
MCC6.NS.4 / “How can factors and multiples help us? How do we use and work with fractions?” / • Find the GCF of 2 whole numbers 100
• Find the LCM of 2 whole numbers 12
• Use the distributive property to express a sum of 2 whole numbers 1-100 with a common factor as a multiple of a sum of 2 whole numbers with no common factor.
• Interpret and compute quotients of fractions
• Solve word problems involving division of fractions by fractions using visual fraction models and equations to represent the problem.
• Fluently divide multi-digit numbers using the standard algorithm
• Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. / * Ga OAS System
* NAEP Questions
* Performance and
Culminating Tasks
*Common Unit Tests
* Formative Assess.
SEPTEMBER/
OCTOBER
Sept 8 –
Oct 3
Fall Break:10/6-10 / Unit 2
Rate, Ratio and Proportional Reasoning
Using Equivalent Fractions / MCC6.RP.1
MCC6.RP.2
MCC6.RP.3a
MCC6.RP.3b
MCC6.RP.3c
MCC6.RP.3d / “How does ratio demonstrate the relationship between two quantities? How does ratio and proportion help to solve real world problems?” / • gain a deeper understanding of proportional reasoning through instruction and practice
• will develop and use multiplicative thinking
• develop a sense of proportional reasoning
• develop the understanding that ratio is a comparison of two numbers or quantities
• find percents using the same processes for solving rates and proportions
• solve real-life problems involving measurement units that need to be converted / * Ga OAS System
* NAEP Questions
* Performance and
Culminating Tasks
*Common Unit Tests
* Formative Assess.
OCTOBER/
NOVEMBER
Oct 13 –Nov 7
Professional Learning: 11/4 / Unit 3
Expressions / MCC6.EE.1
MCC6.EE.2a
MCC6.EE.2b
MCC6.EE.2c
MCC6.EE.3
MCC6.EE.4 / “How can we use variables?” / • Represent repeated multiplication with exponents
• Evaluate expressions containing exponents to solve mathematical and real world problems
• Translate verbal phrases and situations into algebraic expressions
• Identify the parts of a given expression
• Use the properties to identify equivalent expressions
• Use the properties and mathematical models to generate equivalent expressions / * Ga OAS System
* NAEP Questions
* Performance and
Culminating Tasks
*Common Unit Tests
* Formative Assess.
NOVEMBER/
DECEMBER
Nov 10 –Dec 19
Thanksgiving: 11/24-28 / Unit 4
One-Step Equations and Inequalities / MCC6.EE.5
MCC6.EE.6
MCC6.EE.7
MCC6.EE.8
MCC6.EE.9
MCC6.RP.3a
MCC6.RP.3b
MCC6.RP.3c
MCC6.RP.3d
(equations) / “How do equations and inequalities represent real life situations?” / • Determine if an equation or inequality is appropriate for a given situation
• Represent and solve mathematical and real world problems with equations and inequalities
• Interpret the solutions to equations and inequalities
• Represent the solutions to inequalities on a number line
• Analyze the relationship between dependent and independent variables through the use of tables, equations and graphs / * Ga OAS System
* NAEP Questions
* Performance and
Culminating Tasks
*Common Unit Tests
* Formative Assess.
HENRY COUNTY SCHOOLS
2014-2015Curriculum Map (Yearly Overview)
Second Semester
Course: 6th Grade Mathematics Grade Level: 6
DATES /UNIT
/STANDARD
/ ESSENTIAL QUESTION /ENDURING UNDERSTANDINGS
The students will… /ASSESSMENTS
JANUARY
Jan 6 –Jan 30
Professional Learning: 1/5
MLK: 1/19 / Unit 5
Area and Volume / MCC6.G.1
MCC6.G.2
MCC6.G.4 / “When is it appropriate to use area, surface area, and volume?” / • Find areas of right, equilateral, isosceles, and scalene triangles, and special quadrilaterals
• Find areas of composite figures and polygons by composing into rectangles and decomposing into triangles and other shapes
• Solve real-world and mathematical problems involving area
• Decipher and draw views of rectangular and triangular prisms from a variety of perspectives
• Recognize and construct nets for rectangular and triangular prism
• Find the surface area of rectangular and triangular prisms by using manipulatives and by constructing nets
• Determine the surface area of rectangular and triangular prisms by substituting given values for their dimensions into the correct formulas;
• Solve real-world that require determining the surface area of rectangular and triangular prisms
• Measure and compute volume with fractional edge length using cubic units of measure
• Find the volumes of right rectangular prisms by substituting given values for their dimensions into the correct formulas
• Make the connection that finding the volume given the length (l) x width (w) is the same as the base (B)
• Solve real-world problems that require determining the volume of right rectangular prism / * Ga OAS System
* NAEP Questions
* Performance and
Culminating Tasks
*Common Unit Test
* Formative Assess.
FEBRUARY/
MARCH
Feb 2–March 6Winter Break:
2/16 - 2/20
PL: 2/23 / Unit 6
Statistics / MCC6.SP.1
MCC6.SP.2
MCC6.SP.3
MCC6.SP.4
MCC6.SP.5 / “How do we represent and analyze data?” / • Analyze data from many different sources such as organized lists, box-plots, bar graphs and stem-and-leaf plots
• Understand that responses to statistical questions may vary
• Understand that data can be described by a single number
• Determine quantitative measures of center (median and/or mean)
• Determine quantitative measures of variability (interquartile range and/or mean absolute deviation) / * Ga OAS System
* NAEP Questions
* Performance and
Culminating Tasks
*Common Unit Test
* Formative Assess.
HENRY COUNTY SCHOOLS
2014-2015 Curriculum Map (Yearly Overview)
Second Semester Continued
Course: 6th Grade Mathematics Grade Level: 6
DATES /UNIT
/STANDARD
/ ESSENTIAL QUESTION /ENDURING UNDERSTANDINGS
The students will… /ASSESSMENTS
March
Mar 9 –April 3
Professional Learning:
3/23 / Unit 7
Rational Explorations: Numbers and their Opposites / MCC6.NS.5
MCC6.NS.6a
MCC6.NS.6b
MCC6.NS.6c
MCC6.NS.7a
MCC6.NS.7b
MCC6.NS.7c
MCC6.NS.7d
MCC6.NS.8
MCC6.G.3 / “Why are signed numbers important? How do we use positive and negative numbers in real world situations?” / • understand that pos. and neg. numbers are used together to describe quantities having opposite directions or values.
• 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.
• recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line.
• recognize that the opposite of the opposite of a number is the number itself.
• understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane.
• recognize that when 2 ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
• 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.
• understand ordering and absolute value of rational numbers.
• interpret statements of inequality as statements about the relative position of 2 numbers on a number line diagram.
• write, interpret, and explain statements of order for rational numbers in real-world contexts.
• 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.
• distinguish comparisons of absolute value from statements about order.
• solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. / * Ga OAS System
* NAEP Questions
* Performance and
Culminating Tasks
*Common Unit Test
* Formative Assess.
APRIL/MAY
April 13 - May 29Spring Break:
4/6 – 4/10
Memorial Day: 5/25 / Unit 8
Show What We Know / ALL /
- Review for the Georgia Milestones
- Administer Georgia Milestones
- Begin seventh grade curriculum
- Review for final exam
- Complete culminating task and final exam
* NAEP Questions
* Performance and
Culminating Tasks
*Common Unit Test
* Formative Assess.
First Semester
Unit 1Number System Fluency / Unit 2
Rate, Ratio and Proportional Reasoning: Using Equivalent Fractions
Common Core Georgia Performance Standards
Apply and extend previous understandings of multiplication and division to divide
fractions by fractions.
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.
Compute fluently with multi-digit numbers and find common factors and multiples.
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. Usethe 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 / Understand ratio concepts and use ratio reasoning to solve problems.
MCC6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
MCC6.RP.2 Understand the concept of a unit rate ?/? associated with a ratio ?: ? with? ≠ 0, (b not equal to zero), and use rate language in the context of a ratio relationship.
MCC6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
MCC6.RP.3a Make tables of equivalent ratios relating quantities with whole-number
measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
MCC6.RP.3b Solve unit rate problems including those involving unit pricing and constant speed.
MCC6.RP.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means
30/100 times the quantity); solve problems involving finding the whole given a part and the percent.
MCC6.RP.3d Use ratio reasoning to convert measurement units; manipulate and transformunits appropriately when multiplying or dividing quantities.
Enduring Understandings (Students will…)
• Find the greatest common factor of two whole numbers less than or equal to 100
• Find 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.
• Interpret and compute quotients of fractions
• Solve word problems involving division of fractions by fractions using visual fraction models and equations to represent the problem.
• Fluently divide multi-digit numbers using the standard algorithm
• Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. / • gain a deeper understanding of proportional reasoning through instruction and practice
• will develop and use multiplicative thinking
• develop a sense of proportional reasoning
• develop the understanding that ratio is a comparison of two numbers or quantities
• find percents using the same processes for solving rates and proportions
• solve real-life problems involving measurement units that need to be converted
First Semester
Unit 3Expressions / Unit 4
One-Step Equations and Inequalities
Common Core Georgia Performance Standards
Apply and extend previous understandings of arithmetic to algebraic expressions.
MCC6.EE.1 Write and evaluate numerical expressions involving whole-number
exponents.
MCC6.EE.2 Write, read, and evaluate expressions in which letters stand for
numbers.
MCC6.EE.2a Write expressions that record operations with numbers and with letters
standing for numbers.
MCC6.EE.2b Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.
MCC6.EE.2c Evaluate expressions at specific values for their variables. Include expressions that arise from formulas in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
MCC6.EE.3 Apply the properties of operations to generate equivalent expressions.
MCC6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). / Reason about and solve one-variable equations and inequalities.
MCC6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
MCC6.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.
MCC6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form ? + ? = ? and ?? = ?for cases in which p, q and x are all non-negative rational numbers.
MCC6.EE.8 Write an inequality of the form ?? or ?? to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form ?? or ?? have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
Represent and analyze quantitative relationships between dependent and independent variables.
MCC6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the otherquantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.
Understand ratio concepts and use ratio reasoning to solve problems.
MCC6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
MCC6.RP.3a Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
MCC6.RP.3b Solve unit rate problems including those involving unit pricing and constant speed.
MCC6.RP.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole given a part and the percent.
MCC6.RP.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
Enduring Understandings (Students will…)
• Represent repeated multiplication with exponents
• Evaluate expressions containing exponents to solve mathematical and real world problems
• Translate verbal phrases and situations into algebraic expressions
• Identify the parts of a given expression
• Use the properties to identify equivalent expressions
• Use the properties and mathematical models to generate equivalent expressions / • Determine if an equation or inequality is appropriate for a given situation
• Represent and solve mathematical and real world problems with equations and inequalities
• Interpret the solutions to equations and inequalities
• Represent the solutions to inequalities on a number line
• Analyze the relationship between dependent and independent variables through the use of tables, equations and graphs
Second Semester