Download Grade 6 – Expressions, Equations and Inequalitie

Lexington School District One
Curriculum Unit Plan
Mathematics
Grade Level/Course
Unit Summary
Grade 6 Course 1 Expressions, Equations, and Inequalities
Students will apply and extend previous understandings of arithmetic to algebraic expressions, reason about
and solve one-variable equations and inequalities, and represent and analyze quantitative relationships
between dependent and independent variables.
Duration
Chapter 7:​ 10 Days ​Chapter 8:​ 10 Days ​Chapter 9:​ 11 Days (​Total:​ 31 Days)
Enduring Understandings
Essential Questions
Rational numbers can be represented in multiple ways and are useful
when examining situations involving numbers that are not whole.
How can algebraic expressions and equations be used to model,
analyze, and solve mathematical situations?
Standards
6.EEI.1 Write and evaluate numerical expressions involving whole-number exponents and positive rational number bases using the Order of
Operations.
6.EEI.2 Extend the concepts of numerical expressions to algebraic expressions involving positive rational numbers.
a. Translate between algebraic expressions and verbal phrases that include variables.
b. Investigate and identify parts of algebraic expressions using mathematical terminology, including term, coefficient, constant, and
factor.
c. Evaluate real-world and algebraic expressions for specific values using the Order of Operations. Grouping symbols should be limited
to parentheses, braces, and brackets. Exponents should be limited to whole-numbers.
6.EEI.3 Apply mathematical properties (e.g., commutative, associative, distributive) to generate equivalent expressions.
6.EEI.4 Apply mathematical properties (e.g., commutative, associative, distributive) to justify that two expressions are equivalent.
6.EEI.5 Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or
inequality true.
6.EEI.6 Write expressions using variables to represent quantities in real-world and mathematical situations. Understand the meaning of the
variable in the context of the situation.
6.EEI.7 Write and solve one-step linear equations in one variable involving nonnegative rational numbers for real-world and mathematical
situations.
6.EEI.8 Extend knowledge of inequalities used to compare numerical expressions to include algebraic expressions in real-world and
mathematical situations.
x > c​a. Write
x < c​ an inequality of the form ​
or ​
and graph the solution set on a number line.
b. Recognize that inequalities have infinitely many solutions.
6.EEI.9 Investigate multiple representations of relationships in real-world and mathematical situations.
a. Write an equation that models a relationship between independent and dependent variables.
b. Analyze the relationship between independent and dependent variables using graphs and tables.
c. Translate among graphs, tables, and equations.
Learning Plan
Focus Lesson
Chapter 7:
Introduction to
Expressions
7.1 There’s a
Reason Behind
the Rhyme
(Order of
Operations)
7.2 Getting to
the Root of It
(Exploring
Squares, Cubes,
and Roots)
7.3 Things that
Vary
(Understanding
Variables)
Standard/Learning Targets
●
I can apply the order of operations
when evaluating expressions. (6.EEI.1)
OMIT LESSON
●
I can translate a relationship
given in words into an algebraic
expression. (6.EEI.2)
●
I can apply the order of
operations when evaluating algebraic
expressions. (6.EE.2)
Instructional Notes
Adequate Problems:
-Prob. 1
-Prob. 2
-Talk the Talk
Omit square roots and cube roots
Adequate Problems:
-Prob. 1
-Prob. 2 (as needed)
Language Targets
7.4 What’s My
Number?
(Writing
Algebraic
Expressions)
7.5 Different
Ways
(Multiple
Representation
s of Algebraic
Expressions)
7.6 There’s
More than One
Way
(Using Multiple
Representation
s of Problems)
Chapter 8:
Algebraic
Expressions
8.1 The Parts of
Cars You Don’t
See!
(Relationships
between
Quantities)
●
I can use a variable to write an
algebraic expression that represents a
real-world situation when a specific
number is unknown. (6.EEI.6)
●
I can translate a relationship
given in words into an algebraic
expression. (6.EEI.2)
●
I can evaluate an algebraic
expression for a given value. (6.EEI.2)
●
I can identify parts of an
algebraic expression. (6.EEI.2)
●
I can translate between
graphs, tables, and equations. (6.EEI.9)
●
I analyze the relationship
between independent and dependent
variables using tables and graphs.
(6.EEI.9)
OMIT LESSON
OMIT LESSON (Supplement terminology
from 8.4 in 7.4)
Adequate Problems:
-Prob. 1 #10-13
-Prob. 2
Supplement Lesson 8.1 , problem 2 to
address terminology.
Additional practice on terminology found
in the skill practice book
Adequate Problems:
-Prob. 2
-Prob. 3
-Prob. 4 (as needed)
OMIT Lesson
OMIT LESSON
8.2 Tile Work
(Simplifying
Algebraic
Expressions)
Introduction to
Distributive
Property
8.3 Blueprints
to Floor Plans
to Computers
(Using the
Distributive
Property to
Simplify
Algebraic
Expressions)
8.4 Are They
Saying the
Same Thing?
(Multiple
Representation
of Equivalent
Expressions)
8.5 Like and
Unlike
(Combining Like
Terms)
8.6 DVDs and
Songs: Fun with
Expressions
(Using
Algebraic
Expressions to
Analyze and
Solve
Problems)
●
●
●
I can apply the associative and
commutative properties to justify that
two expressions are equivalent
(6.EEI.4)
●
I can apply the associative and
commutative properties to generate
equivalent expressions. (6.EEI.3)
I can use the distributive property to
factor out a common factor of two
whole number addends. (6.NS.4)
●
I can apply the distributive
property to justify that two
expressions are equivalent (6.EEI.4)
●
I can apply the distributive
property to generate equivalent
expressions. (6.EEI.3)
Adequate Problems:
-Prob. 1 (use as review)
*Vocab. to introduce on 541
-Prob. 2
I can evaluate an algebraic expression
for a given value. (6.EEI.2)
●
I can use mathematical
properties to justify that two
expressions are equivalent. (6.EEI.4)
Adequate Problems:
-Prob. 1
-Prob. 2
OMIT LESSON
●
I can translate a relationship
given in words into an algebraic
expression. (6.EEI.2)
●
I can evaluate an algebraic
expression for a given value. (6.EEI.2)
●
I can use a variable to write an
algebraic expression that represents a
real-world situation when a specific
number is unknown. (6.EEI.6)
Lesson is found on the Google Drive
Adequate Problems:
-Prob. 1
-Prob. 2
-Prob. 3 # 4- # 6
OMIT LESSON
Adequate Problems:
-Prob. 1 # 1-3 (others as needed)
-Prob. 2 (as needed)
Chapter 9:
Inequalities and
Equations
9.1 Call to
Order
(Inequalities)
9.2 Opposites
Attract to
Maintain a
Balance
(Solving
One-Step
Equations Using
Addition and
Subtraction)
9.3 Statements
of Equality
Redux
(Solving
One-Step
Equations Using
Multiplication
and Division)
9.4 There Are
Many Ways
(Representing
Situations in
Multiple Ways)
●
I can write a simple inequality
to represent a real-world or
mathematical problem. (6.EEI.8)
●
I can explain what the solution
set of an inequality represents.
(6.EEI.8)
●
I can show the solution set of
an inequality by graphing it on a
number line. (6.EEI.8)
●
I can explain that solving an
equation leads to finding the value(s)
that make a true mathematical
statement. (6.EEI.5)
●
I can substitute a given value
into an algebraic equation or
inequality to determine whether it is a
solution. (6.EEI.5)
●
I can solve one-step equations.
(6.EEI.7)
●
I can explain that solving an
equation leads to finding the value(s)
that make a true mathematical
statement. (6.EEI.5)
●
I can substitute a given value
into an algebraic equation or
inequality to determine whether it is a
solution. (6.EEI.5)
●
I can solve one-step equations.
(6.EEI.7)
●
I can explain that solving an
equation leads to finding the value(s)
that make a true mathematical
statement. (6.EEI.5)
●
I can substitute a given value
into an algebraic equation or
Adequate Problems:
-Prob. 1
-Prob. 3
-Talk the Talk
Adequate Problems:
-Prob. 1
-Prob. 2
-Prob. 3
-Talk the Talk (incorporate throughout the
lesson)
Adequate Problems:
-Prob. 1 & 2 (teacher discretion)
-Prob. 3
-Talk the Talk (incorporate throughout the
lesson)
●
●
●
Adequate Problems:
-Prob. 1
-Prob. 2 (if needed)
9.5 Measuring
Short
(Using Multiple
Representation
s to Solve
Problems)
9.6 Variables
and More
Variables
(The Many Uses
of Variables in
Mathematics)
9.7 Quantities
that Change
(Independent
and Dependent
Variables)
inequality to determine whether it is a
solution. (6.EEI.5)
●
I can solve one-step equations.
(6.EEI.7)
OMIT LESSON (can be used for additional
practice to supplement 9.4 if needed)
OMIT LESSON
OMIT LESSON
OMIT LESSON
●
I can translate between
graphs, tables, and equations. (6.EEI.9)
●
I can determine the
independent and dependent variable
in a relationship. (6.EEI.9)
●
I can analyze the relationship
between the dependent and
independent variables by comparing
the table, graph, and equation.
(6.EEI.9)
Adequate Problems:
-Prob. 1
-Prob. 2
-Prob. 3 (if needed)
**Make sure to have students discuss
how y changes as a result of x based on
the graph.
Key Academic Vocabulary
Key academic vocabulary comes directly from the standards. Students should be immersed in this language through instruction and assessment. These terms are not to be
taught as a vocabulary “list” but used on a daily basis so students are literate in the content area of Mathematics.
base, exponent, evaluate, sum, difference, term, product, factor, quotient, coefficient, arithmetic expression, algebraic expression, substitute,
evaluate, equivalent expressions, commutative property, distributive property, equation, inequality, solve, solution, variable, constant,
algebraic equation, independent variable, dependent variable, coordinate plane
Additional Teaching Resources