MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 6
Unit Description
Big Idea(s)
What enduring
understandings are
essential for application to
new situations within or
beyond this content?
Unit: 6
Title: Equations and Inequalities
Suggested Length: 4 weeks
Enduring Understandings
Writing, solving, and understanding variables in mathematical expressions
and equations.
Enduring Skills Rubric measures competency of the following skills:
Equivalence:
 A given equation can be represented in an infinite number of different
ways that have the same solution (e.g., 3x – 5 = 16 and 3x = 21 are
equivalent equations; they have the same solution, 7).
Comparison:
 Numerical and algebraic expressions can be compared using greater
then, less than, or equal.
Operation Meanings & Relationships:
 Adding x is the inverse of subtracting x.
 Multiplying by x is the inverse of dividing by x.
Variable:
 Letters are used in mathematics to represent generalized properties,
unknowns in equations, and relationships between quantities.
Relations & Functions:
 Mathematical relationships can be represented and analyzed using
words, table, graphs, and equations.
 In mathematical relationships, the value for one quantity depends on
the value of the other quantity.
 The graph of a relationship can be analyzed with regard to the
change in one quantity relative to the change in the other quantity.
Essential Question(s)
What questions will
provoke and sustain
Curriculum and Instruction
Equations & Inequalities:
 A solution to an equation is a value of the unknown or unknowns that
make the equation true.
 Properties of equality and reversible operations can be used to
generate equivalent equations and find solutions.
 Techniques for solving equations can be applied to solving
inequalities, but the direction of the inequality sign needs to be
considered when negative numbers are involved (7th grade).
• How is an equation like a balance? How can the idea of
balance help me solve an equation?
• What strategies can I use to help me understand and represent
2015-2016
Page 1 of 7
MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 6
student engagement
while focusing learning?
Standards
real situations using equations and inequalities?
 How can I write, interpret and manipulate equations and inequalities?
• How can I solve an equation?
• How can I tell the difference between an expression, equation and an
inequality?
• How are the solutions of equations and inequalities different?
• What does an equal sign mean mathematically?
• How does a change in one variable affect the other variable in a given
situation?
• Which tells me more about the relationship I am investigating, a
table, a graph or a formula?
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them. Students choose
the appropriate algebraic representations for given contexts and can create
contexts given equations or inequalities.
2. Reason abstractly and quantitatively. Students represent a wide variety of
real world contexts through the use of real numbers and variables in
mathematical expressions, equations, and inequalities. Students
contextualize to understand the meaning of the number or variable as
related to the problem and decontextualize to manipulate symbolic
representations by applying properties of operations.
3. Construct viable arguments and critique the reasoning of others. Students
construct arguments using verbal or written explanations accompanied by
expressions, equations, inequalities, models, graphs, and tables.
4. Model with mathematics. Students model problem situations in
symbolic, graphic, tabular, and contextual formats. Students form
expressions, equations, and inequalities from real world contexts and
connect symbolic and visual representations.
5. Use appropriate tools strategically. Students use number lines to graph
equations and inequalities. Students use tables to organize information to
write equations and inequalities.
6. Attend to precision. Students precisely define variables.
7. Look for and make use of structure. Students seek patterns or structures to
model and solve problems using tables, and equations. Students seek
patterns or structures to model problems using tables and inequalities.
Students apply properties to generate equivalent expressions (i.e. 6 + 2x = 3 (2
+ x) by distributive property) and solve equations (i.e. 2c + 3 = 15, 2c = 12 by
subtraction property of equality, c = 6 by division property of equality).
8. Look for and express regularity in repeated reasoning. Students generalize
effective processes for representing equations and inequalities based upon
experiences. Students will be solving for equations.
Standards for Mathematical Content
6.EE.5
Understand solving an equation or inequality as a process of
Curriculum and Instruction
2015-2016
Page 2 of 7
MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 6
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.
Supporting
Standard(s)
Which related standards
will be incorporated to
support and enhance the
enduring standards?
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.
6.EE.7
Solve real-world and mathematical problems by writing and
solving equations of the form x + p = q and px = q for cases in
which p, q and x are all nonnegative rational numbers.
6.EE.8
Write an inequality of the form x > c or x < c to represent a
constraint or condition in a real-world or mathematical problem.
Recognize that inequalities of the form x > c or x < c have infinitely
many solutions; represent solutions of such inequalities on number
line diagrams.
6.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 other quantity, 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. For example, in a problem involving motion at
constant speed, list and graph ordered pairs of distances and
times, and write the equation d = 65t to represent the relationship
between distance and time.
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. For example, express 36 + 8 as 4 (9 + 2).
6.NS.7
Understand ordering and absolute value of rational numbers.
a. Interpret statements of inequality as statements about the
Curriculum and Instruction
2015-2016
Page 3 of 7
MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 6
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.
6.NS.8
Solve real-world and mathematical problems by graphing points in
all four quadrants of the coordinate plane. Include use of
coordinates and absolute value to find distances between points
with the same first coordinate or the same second coordinate.
6.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.
a. 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.
6.EE.1
Write and evaluate numerical expressions involving whole-number
exponents.
5th grade Standards
5.OA.1: Use parentheses, brackets, or braces in numerical expressions, and
evaluate expressions with these symbols.
Instructional
Outcomes
What must students learn
and be able to do by the
end of the unit?
Curriculum and Instruction
I am learning to….
 Recognize solving an equation or inequality as a process of answering
“which value from a specified set, if any, make the equation or
inequality true?”
 Know that the solutions of an equation or inequality are the values
that make the equation or inequality true.
 Use substitution to determine whether a given number in a specified
set makes an equation or inequality true.
 Recognize that a variable can represent an unknown number or any
number in a specified set.
 Relate variables to context.
 Define inverse operation.
 Know how inverse operations can be used in solving one-variable
equations.
 Apply rules of the form x + p = q and px = q, for cases in which p, q
and x are all nonnegative rational numbers, to solve real world and
mathematical problems. (There is only one unknown quantity.)
 Develop a rule for solving one-step equations using inverse operations
2015-2016
Page 4 of 7
MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 6










Essential Vocabulary
What vocabulary must
students know to
understand and
communicate effectively
about this content?
Curriculum and Instruction
with nonnegative rational coefficients.
Solve and write equations for real-world mathematical problems
containing one unknown (Include whole numbers and decimals).
Identify the constraint or condition in a real-world or mathematical
problem in order to set up an inequality.
Recognize that inequalities of the form x >c or x < c have infinitely
many solutions.
Write an inequality of the form x > c or x < c to represent a constraint
or condition in a real-world or mathematical problem.
Represent solutions to inequalities or the form x > c or x < c, with
infinitely many solutions, on number line diagrams.
Define independent and dependent variables.
Use variables to represent two quantities in a real-world problem that
change in relationship to one another. (Ex., d=rt)
Write an equation to express one quantity (dependent) in terms or the
other quantity (independent).
Analyze the relationship between the dependent variable and
independent variable using tables and graphs.
Relate the data in a graph and table to the corresponding equation.
Essential Vocabulary
Additive Inverse
Constraint (for an inequality)
Dependent Variable
Equation
Evaluate
Independent Variable
Inequality
Inverse Operations
Multiplicative Inverse
Solution of an Equation
Solution of an Inequality
Substitution
Variable
Supporting Vocabulary
Axis
Equivalent
Greater than (>)
Less than (<)
Rational number (nonnegative)
2015-2016
Page 5 of 7
MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 6
Resources/Activities
What resources could we
use to best teach this unit?
Resources/Activities
https://www.georgiastandards.org/CommonCore/Common%20Core%20Frameworks/CCGPS_Math_6_6thGrade_Unit4.pdf
The following website is a website with lessons to address CCSS:
https://www.engageny.org/resource/grade-6-mathematics
Khan Academy – www.khanacademy.org
IXL – www.ixl.com
http://www.insidemathematics.org/common-core-resources/mathematicalcontent-standards/standards-by-grade/6th-grade
http://www.mathchimp.com/6th-grade-math-resources
Remember there are other sources in your school that may not be listed on
this resources list due to variation in each individual school. If you have a
good resource that you would be willing to share, please let Mendy Mills
know so that she can share with other math teachers.
Mendy.Mills@madison.kyschools.us
Curriculum and Instruction
2015-2016
Page 6 of 7
Curriculum and Instruction
2015-2016
Page 7 of 7