Grade 6
Unit 4
Table of Contents
Algebraic Equations
Section
Unit Description
Unit Standards
Unit Essential Questions
Unit Proficiencies (Learning Targets)
Unit Vocabulary and Language Support
Sample Unit Calendar and Possible Supporting Materials
Student Proficiencies Handout
Unit Assessments and Rubric/Commentary
Page Number
Grade 6
Content Unit 4
Dates of Unit:
01/20/2015 – 02/20/2015
Unit Title:
Stage 1
Unit
Description:
Algebraic Equations
Identify Desired Results
Standards:
6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specific 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?
6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem;
understanding 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.
Essential
Question:
Standard
Proficiencies
How do you use variables to solve equations when there are one or two unknown values?
How do you represent inequalities?
(Learning Targets)
Students will understand solving an equation or inequality as answering a question and will use substitution to determine whether a given a
number in a specified set makes an equation or inequality true. They will write and solve equations and inequalities, use dependent and
independent variables to solve real-world and mathematical problems, and analyze the relationship between the dependent and independent
variables using graphs and tables.
6.EE.5
I can choose the values that
make an equation or
inequality true.
6.EE.6
I can use variables to
represent numbers and
write expressions.
6.EE.7
6.EE.8
I can write and solve
I can write an
equations that contain inequality.
nonnegative numbers.
6.EE.9
I can represent and
analyze quantitative
relationships
between dependent
and independent
variables.
I can translate written
phrases into algebraic
expressions using
numbers and variables.
I can identify parts of an
expression using
mathematical terms (sum,
term, product, factor,
quotient, coefficient.)
I can describe one or
more parts of an
expression as a single
entity.
I can evaluate expressions
using order of operations.
I can use formulas to
solve real-world
problems.
I can represent a
constraint or condition
in a real-world or
mathematical problem.
I can recognize that
solutions can be
infinite.
I can represent
solutions through
graphs, number lines
and visual displays.
Stage 2
Determine Assessment Evidence
Academic Language Function(s):
Academic Language (What language will students need to sound like experts?)
Academic Language Stems:
Easy for Beginners
Academic Vocabulary:


Medium for Intermediate
Difficult for Advanced and Fluent
Assessment
Tools:
 Goals Rubric
 Assessment Checklist
Student
Name
B = Beginning
Developing
Vocabulary
I can represent and analyze
quantitative relationships
between dependent and
independent variables.
I can represent solutions
through graphs, number lines
and visual displays.
I can recognize that solutions
can be infinite.
I can represent a constraint or
condition in a real-world or
mathematical problem.
I can write an inequality.
I can write and solve equations
that contain nonnegative
numbers.
I can use formulas to solve realworld problems.
I can evaluate expressions using
order of operations.
I can describe one or more parts
of an expression as a single
entity.
I can identify parts of an
expression using mathematical
terms (sum, term, product,
factor, quotient, coefficient.)
I can translate written
phrases into algebraic
expressions using
numbers and variables.
I can use variables to
represent numbers and
write expressions.
I can choose the values
that make an equation or
inequality true.
Unit of Study Assessment Checklist
D=
P = Proficient
M=Mastery
Stage 3
Plan Learning Experiences and Instruction
SAMPLE UNIT CALENDAR
I can choose the values that I can use variables to
make an equation or
represent numbers and
inequality true.
write expressions.
I can translate written
phrases into algebraic
expressions using numbers
and variables.
I can identify parts of an
expression using
mathematical terms (sum,
term, product, factor,
quotient, coefficient.)
Assessment:
Materials
I can describe one or more
parts of an expression as a
single entity.
I can evaluate expressions
using order of operations.
I can use formulas to solve
real-world problems.
I can write and solve
equations that contain
nonnegative numbers.
Assessment:
I can write an inequality.
I can represent a constraint
or condition in a real-world
or mathematical problem.
I can recognize that
solutions can be infinite.
I can represent solutions
through graphs, number
lines and visual displays.
Assessment:
I can represent and analyze
quantitative relationships
between dependent and
independent variables.
Vocabulary
Assessment:
Assessment:
ALGEBRAIC EXPRESSIONS Name ______________________________
Date ________________________ Period _____
PROFICIENCIES
My Proficiency Assessment Scores
Proficiency #1 – I can choose the values that make an equation
or inequality true.
Proficiency #2 – I can use variables to represent numbers and
write expressions.
Proficiency #3 – I can translate written phrases into algebraic
expressions using numbers and variables.
Proficiency #4 – I can identify parts of an expression using
mathematical terms (sum, term, product, factor, quotient,
coefficient.
Proficiency #5 – I can describe one or more parts of an expression
as a single entity.
Proficiency #6 – I can evaluate expressions using order of
operations.
Proficiency #7 – I can use formulas to solve real-world problems.
Proficiency #8 – I can write and solve equations that contain
non-negative numbers.
Proficiency #9 - I can write an inequality.
Proficiency #10 – I can represent a constraint or condition in a
real-world or mathematical problem.
Proficiency #11 - I can recognize that solutions can be infinite.
Proficiency #12 - I can represent solutions through graphs,
number lines and visual displays.
Proficiency #13 - I can represent and analyze quantitative
relationships between dependent and independent variables.
algebraic equation
numerical expression
inequality
base (of an exponent)
exponent
power
substitution
infinite
term
coefficient
variable
constraint
equivalent
evaluate
given number
solution
greater than
less than
formula
specified set
quantity
independent variable
dependent variable
⧠ I know how to add, subtract, multiply and divide single digit numbers efficiently.
⧠ I know how to add, subtract, multiply and divide multi- digit whole numbers, decimals, and
fractions.
⧠ I know how to stick with a problem until it’s finished.
⧠ I know how to substitute a number for a variable and use a formula.
⧠ I understand and know how to use math vocabulary appropriately.
⧠ I know how to correctly use the order of operations.
add
sum
subtract
difference
factor
multiply
product
divide
quotient
See me if you look at this list and think, “uh, oh…”
Proficiency Assessment…
Name _________________________________
Date _______________________ Period ____
Proficiency # – “I can ….”
Proficiency
Score
4
Percentage
3
83%
2
67%
1
50%
100%
Description
WOW!
I have shown proficiency and deeper understanding by:

You got it 
I have shown proficiency by:

Help is needed
I have shown partial understanding by:

Uh-oh…
I have not yet shown my understanding of the math.
Name _________________________________
Date _______________________ Period ____
Proficiency # – “I can .”
Proficiency
Score
4
Percentage
3
83%
2
67%
1
50%
100%
Description
WOW!
I have shown proficiency and deeper understanding by:

You got it 
I have shown proficiency by:

Help is needed
I have shown partial understanding by:

Uh-oh…
I have not yet shown my understanding of the math.