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DURHAM PUBLIC SCHOOLS 2013-2014
UNIT 4 and 5 PLAN FOR 6TH GRADE PLUS MATHEMATICS
Unit Overview:
Instructional Time: Unit 4- 6 weeks Unit 5- 4 weeks
Quarter
One
Two
Three
Four
Grade Level: 6th Grade
Unit Theme: Expressions, Equations, and Inequalities
Depth of Knowledge: Level I, II, III, IV
Unit Summary: This unit introduces students to expressions and equations by applying and extending previous understandings of arithmetic to
algebraic expressions. Students will write and evaluate numerical expressions involving whole-number exponents. They will write, read, and
evaluate expressions in which letters stand for numbers. Students will generate equivalent expressions by applying the properties of operations
and identify when two expressions are equivalent. This unit gives students the skills to reason about and solve one-variable equations and
inequalities. Students will represent and analyze quantitative relationships between dependent and independent variables in real-world problems
that change in relationship to one another.
North Carolina Informational Technology Essential Standards:
6. TT.1 Use technology and other resources for the purpose of assessing, organizing, and sharing information.
Common Core State Standards
Apply and extend previous understandings of arithmetic to
algebraic expressions.
6. EE.1 Write and evaluate numerical expressions involving wholenumber exponents.
6. EE.2 Write, read, and evaluate expressions in which letters stand for
numbers.
a. Write expressions that record operations with numbers and with
letters standing for numbers. For example, express the
calculation
“Subtract y from 5” as 5-y.
b. Identify parts of an expression using mathematical terms (sum,
Learning Targets:
 I can write numerical expressions involving whole number
exponents. Ex. 34 = 3x3x3x3
 I can evaluate numerical expressions involving whole number
exponents. Ex. 34 = 3x3x3x3 = 81
 I can solve order of operation problems that contain exponents.
Ex. 3+22 – (2+3) = 2
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I can use numbers and variables to evaluate expressions.
I can translate written phrases into algebraic expressions.
I can translate algebraic expressions into written phrases.
I can identify parts of an expression using mathematical terms
(sum, term, product, factor, quotient, coefficient).
I can identify parts of an expression as a single entity, even if
term, product, factor, quotient, coefficient); view one or more
parts of an expression as a single entity. For example, describe
the expression 2 (8+7) as both a single entity and a sum of two
terms.
c. Evaluate expressions at specific values of their variables.
Include expressions that arise from formulas used 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). For example, use the formulas V = s^3
and A = 6 s^2 to find the volume and surface area of a cube
with sides of lengths s = ½.
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not a monomial.
I can substitute specific values for variables.
I can evaluate algebraic expressions including those that arise
from real-world problems.
I can apply order of operations when there are no parentheses
for expressions that include whole number exponents.
6. EE.3 Apply the properties of operations to generate equivalent
expressions. For example, apply the distributive property to the
expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply
the distributive property to the expression 24x + 18y to produce the
equivalent expression 6(4x + 3y); apply properties of operations to y + y
+ y to produce the equivalent expression 3y.
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6. EE.4 Identify when two expressions are equivalent (i.e. when the two
expressions name the same number regardless of which value is
substituted to them). For example, the expression y + y + y and 3y are
equivalent because they name the same number regardless of which
number y stands for.
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I can recognize when two expressions are equivalent.
I can prove (using various strategies) that two expressions are
equivalent no matter what number is substituted.
Reason about and solve one-variable equations and inequalities.
6. EE.5 Understand solving an equation or inequality as a process of
answering a question: which values from a specified set, in any, make
the equation of inequality true? Use substitution to determine whether a
given number in a specified set makes an equation or inequality true.
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I can recognize solving an equation or inequality as a process of
answering “which values from a specified set, if any, make the
equation or inequality true?”.
I can use the solution to an equation or inequality to prove that
the answer is correct.
I can use substitution to determine whether a given number in a
specified set makes an equation or inequality true.
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I can create equivalent expressions using the properties of
operations (e.g. distributive property, associative property,
adding like terms with the addition property or equality, etc.).
I can apply the properties of operations to create equivalent
expressions.
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.
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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.
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6. EE.8 Write an inequality of the form x>c or x<c to represent a
constraint or condition in a real-world of 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.
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Represent and analyze quantitative relationships between
dependent and independent variables.
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
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I can recognize that a variable can represent an unknown
number, or, depending on the scenario/situation, any number in
a specific set.
I can relate variables to a context.
I can write expressions when solving a real-world or
mathematical problem
I can define an inverse operation.
I can use inverse operations to solve one step variable
equations.
I can 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).
I can develop a rule for solving one-step equations using
inverse operations with nonnegative rational coefficients.
I can solve and write equations for real-world mathematical
problems containing one unknown.
I can identify the constraint or condition in a real-world or
mathematical problem in order to set up an inequality.
I can recognize that inequalities of the form x>c or x<c have
infinitely many solutions.
I can write an inequality of the form x>c or x<c to represent a
constraint or condition in a real-world or mathematical problem.
I can represent solutions to inequalities or the form x>c or x<c,
with infinitely many solutions, on the number line diagrams.
I can define independent and dependent variables
I can use variables to represent two quantities in a real-world
problem that change in relationship to one another.
I can write an equation to express one quantity (dependent) in
terms of the other quantity (independent).
I can analyze the relationship between the dependent variable
and independent variable using tables and graphs.
graphs and tables, and relation 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.
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I can relate the data in a graph and table to the corresponding
equation.
Expressions and Equations: Solve real-life and mathematical
problems using numerical and algebraic expressions and equations.
7.EE.3 Solve multi-step real-life and mathematical problems posed with
positive and negative rational numbers in any form (whole numbers,
fractions, and decimals), using tools strategically. Apply properties of
operations as strategies to calculate with numbers in any form; convert
between forms as appropriate; and assess the reasonableness of
answers using mental computation and estimation strategies Use
variables to represent quantities in a real- world or mathematical
problem, and construct simple equations and inequalities to solve
problems by reasoning about the quantities.
a. Solve word problems leading to equations of the form px + q = r
and p(x + q) = r, where p, q, and r are specific rational numbers.
Solve equations of these forms fluently. Compare an algebraic
solution to an arithmetic solution, identifying the sequence of the
operations used in each approach.
b. Solve word problems leading to inequalities of the form px + q >
r or px + q < r, where p, q, and r are specific rational numbers.
Graph the solution set of the inequality and interpret it in the
context of the problem.
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I can apply strategic tools to solve multi-step problems involving
both positive and negative rational numbers.
I can evaluate expressions utilizing mental math and estimation
strategies.
I can solve real world problems utilizing properties of operations
converting between fractions, decimals and percent.
7.EE4 Use variables to represent quantities in a real-world or
mathematical problem, and construct simple equations and inequalities
to solve problems by reasoning about the quantities.
 Solve word problems leading to equations of the form px + q = r
and p(x + q) = r, where p, q, and r are specific rational numbers.
Solve equations of these forms fluently. Compare an algebraic
solution to an arithmetic solution, identifying the sequence of the
operations used in each approach. For example, the perimeter
of a rectangle is 54 cm. Its length is 6 cm. What is its width?
Solve word problems leading to inequalities of the form px + q > r or px
+ q < r, where p, q, and r are specific rational numbers. Graph the
solution set of the inequality and interpret it in the context of the
problem. For example: As a salesperson, you are paid $50 per week
plus $3 per sale. This week you want your pay to be at least $100.
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I can create equations and inequalities to solve real world
problems.
I can solve and graph inequalities with rational numbers to find
the minimum and maximum of a real world situation.
Write an inequality for the number of sales you need to make, and
describe the solutions.
Essential Question(s):
 When can you substitute a variable for a number in a mathematical equation?
 How can exponents shorten equations?
 What is the difference between doubling a number and squaring a number?
 How can I read information and represent it as a mathematical equation?
 How do the algebraic properties help me write equivalent equations?
 How does an expression differ from an equation?
 What strategies can be used to solve for unknowns in an expression/equation?
 Why would you use an inequality instead of an equation?
Enduring Understanding(s):
 The purpose of this unit is to apply and extend previous understandings of arithmetic to algebraic expressions, reason about and solve
one-variable equations and inequalities, represent and analyze quantities relationships between dependent and independent variables.
Through investigation and self-inquiry, students will apply this knowledge in real-world mathematical problems.
Vocabulary:
Expressions
Exponents
Coefficient
Factor
Terms
Order of Operations
Distributive
Property
Equivalent
Expressions
Equality
Inequality
Substitution
Specified Set
Variable
Nonnegative
Rational Numbers
Constraint
Dependent
Variables
Independent
Variables
Language: Conventions of Standard English
L.6.1 Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.
L.6.2 Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.
Writing: Text Types and Purposes
W.6.1 Write arguments to support claims with clear reasons and relevant evidence.
Writing: Production and Distribution of Writing
W.6.6 Use technology, including the Internet, to produce and publish writing as well as to interact and collaborate with others; demonstrate
sufficient command of keyboarding skills to type a minimum of three pages in a single sitting.
Evidence of Learning (Formative Assessment):
 Teacher Observation
 Exit Slips
 Small Quizzes
 Durham Public Schools’ Small Goal Assessment
Summative Assessment:
 Teacher-made Test
Unit Implementation:
Expressions (6.EE.1-2) Write and evaluate numerical expressions involving whole-number exponents. Write, read, and evaluate expressions in which letters stand for
numbers.
a. Introduce key vocabulary and formulas (word wall, flashcards, graphic organizers, foldable, etc)
b. Prime Time Inv. 4
c. Bits and Pieces II Inv. 2-4
d. Bits and Pieces III Inv. 1-4
e. Patterns in Numbers and Shapes (MathScape) Lesson 4
Expressions (6.EE.2.a) Write expressions that record operations with numbers and with letters standing for numbers.
a. Introduce key vocabulary (word wall, flashcards, graphic organizers, foldable, etc)
b. Stretching and Shrinking Inv. 2
c. Comparing and Scaling Inv. 4
d. Quiz on 6.EE.1-2 (Use the results from the quiz to determine if any corrective instruction is needed)
Expressions (6.EE.2.b-c.) Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one ore more parts of an
expression as a single entity. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used 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).
a. Introduce key vocabulary (word wall, flashcards, graphic organizers, foldable, etc)
b. Looking for Pythagoras Inv. 3
c. Frogs, Fleas, and Painted Cubes Inv. 1-4
d. Say It With Symbols Inv. 1-5
e. Covering and Surrounding Inv. 1-5
Properties (6.EE.3-4) Apply the properties of operations to generate equivalent expressions. Identify when two expressions are equivalent (i.e. when the two expressions
name the same number regardless of which is substituted into them).
a. Introduce key vocabulary (word wall, flashcards, graphic organizers, foldable, etc)
b. The Shapes of Algebra Inv. 1-5, 5
c. Samples and Populations Inv. 4
d. Accentuate the Negative Inv. 2-4
e. The Shapes of Algebra Inv. 3
f. Patterns in Numbers and Shapes (MathScape) Lesson 5
g. Quiz on 6.EE.3-4 Use the results from the quiz to determine if any corrective instruction is needed)
Inequalities (6.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.
a.
b.
c.
Introduce key vocabulary (word wall, flashcards, graphic organizers, foldable, etc)
Moving Straight Ahead Inv. 1-4
Shapes and Designs Inv. 2
Variables (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.
a. Introduce key vocabulary (word wall, flashcards, graphic organizers, foldable, etc)
b. Variables and Patterns Inv. 1-3
c. Shapes and Designs Inv. 3-4
Equations/Inequalities (6.EE.7-8) Solve real-world 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. 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 of x<c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
a. Introduce key vocabulary (word wall, flashcards, graphic organizers, foldable, etc)
b. Covering and Surrounding Inv. 5
c. Moving Straight Ahead Inv. 3
d. The Shapes of Algebra Inv. 2, 5
Dependent/Independent Variables (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 relation these to the equation.
a. Introduce key vocabulary (word wall, flashcards, graphic organizers, foldable, etc)
b. Data About Us Inv. 2
c. Thinking with Mathematical Models Inv. 2-3
d. Growing, Growing, Growing Inv. 1-5
e. Patterns in Numbers and Shapes (MathScape) Phase Three
Review, Assess, Remediate, Enrich (6.EE.1-9)
a.
b.
c.
d.
e.
Review key vocabulary (word wall, flashcards, graphic organizers, foldable, etc)
Review materials covered from Weeks 1-9.
Use Unit Test Parallel questions as a study guide
Summative Assessment
Intervention/Extension Activities: Students who show mastery will complete enrichment activities (example: Learning Contracts, Peer Tutoring, and Independent
Studies). Students who did not show mastery will complete remediation activities and be reassessed to show mastery.
Supportive Unit Resources: (Please note that these are resources that can be used to supplement instruction before or during a lesson.)
Scaffolding Option 1:
Intervention
Instructional
Activities:
6.EE.1-9
-Struggling students can draw pictures and diagrams
to help identify what the variable in an expression
means. (Example: x + 5 = 7. Draw shapes or designs
to replace the 5 and the 7. What does x have to be in
order for the equation to be balanced?)
(6.EE.8)
-Students who are struggling with graphing
inequalities can practice graphing positive and
negative numbers on a number line
Scaffolding Option 2:
Maintenance
Scaffolding Option 3:
Extension
6.EE.1-9
-Have students come up with real-world mathematical
word problems that involve an unknown (variable).
Students can then write an expression for each other’s
word problems and solve(if applicable)
6.EE.6
-Solve two-step expressions and equalities
-Graph ordered pairs to represent the relationship
between x and y (example: graph the relationship
between distance and time)
6.EE.3
-Create a graphic organizer to illustrate the distributive
property and equivalent expressions
6.EE.1-9
-Patterns in Numbers and Shapes (MathScape) Phase
4. Students extend patterns in different situations.
6.EE.8
-Students can graph several different
equalities/inequalities on a number line using crayons
or colored pencils
Technology Integration: (Please note that these are resources that can be used to supplement instruction before or during a lesson.)
Multimedia
Activities:
6. EE. 1-4
This Algebraic Expressions Millionaire Game can be
played online alone or in two teams. For each
question you have to identify the correct mathematical
expression that models a given word expression.
http://www.math-play.com/Algebraic-ExpressionsMillionaire/algebraic-expressions-millionaire.html
6. EE. 1-4
Solving one-step equations. http://www.mathplay.com/One-Step-Equation-Game.html
6.EE.1-9
Algebra Math Games
http://www.math-play.com/Algebra-Math-Games.html
6.EE. 5-8 Inequality Game http://www.mathplay.com/Inequality-Game.html
Algebra Review Jeopardy
http://www.math-play.com/7th-Grade-AlgebraJeopardy/7th-Grade-Algebra-Jeopardy.html
6.EE.1-9 Review Games
http://www.ehow.com/info_8419424_interactive-gamesalgebra-inequalities.html