Course Title: ALGEBRA I
Grade Level(s): 7-12
Objectives:
●
Represent numbers and number systems in different ways to solve problems.
●
Analyze real-world data numerically, graphically, and algebraically.
●
Solve and represent linear equations using different methods.
●
Write and graph linear equations when provided with two points or a point and the slope.
●
Create a line-of-best-fit to make predictions given a set of data.
●
Solve systems of inear equations and inequalities algebraically and graphically.
Essential Questions:
●
Number Sense and Algebraic Thinking
○
How can you use a picture to represent a problem situation?
○
How do you find the LCM of two or more numbers?
○
How do the terms “multiple” and “divisibility” relate to factor pairs?
○
How do prime factorization help us find the GCF of two or more numbers?
○
How can you tell if a fraction is simplified?
○
How can you compare and order fractions?
○
How are fractions related to decimals?
○
How does place value help with estimating and rounding decimals?
○
Why is it necessary to represent and/or convert numbers to different forms?
○
How are mathematical operations used in order to simplify and evaluate expressions involving real numbers?
●
Patterns and Multiple Representations
○
How do you find the nth term of a sequence?
○
How do you model real world data with an expression?
○
How do you model data given an initial value?
○
How do you compare two problem situations?
○
How do you use proportions to make predictions?
○
How can you compare recipes using ratios?
●
Solving Equations
○
How do we classify numbers?
○
How do you solve a one-step equation?
○
How do you transform two-step equations into one-step equations?
○
How do we solve equations with variables on both sides?
○
How do you know when to use the distributive property?
○
How can you determine the better deal?
○
●
○
○
○
○
○
○
○
○
●
○
○
○
●
○
○
○
○
○
○
○
How can you use graphs to estimate values?
Writing and Graphing Linear Functions
What are the similarities and differences between relations and functions?
How can you write a linear equation using function notation?
How do you find domain and range of a function?
How do we find intercepts algebraically and graphically?
How do we find slope?
How do you write the equation of a line in slope-intercept form?
How do we go from standard form to slope-intercept form and vice versa?
How do we solve for a variable in an equation?
Lines of Best Fit
How can you model a situation using a line of best fit?
How can you perform an experiment and use the data to create a prediction equation?
How do you find the correlation of a set of data?
Systems of Equations and Inequalities
How do you solve a system using substitution?
How do you solve a system using elimination?
How do you know which method is most efficient?
How do you solve and graph an inequality in one variable?
How do you graph a linear inequality?
How do you solve a system of linear inequalities?
How do you write equations of parallel and perpendicular lines?
How do we find the break-even point
Title: Number Sense and Algebraic Thinking
Standards
Content
(Students will know)
Performance
(Students will Do)
Activities/
Assessments
Essential Questions
How to represent
Use picture algebra to represent a
problem situations using a problem
CC.2.3.HS.A.6 picture, diagram, or
CC.2.3.HS.A.14 symbols
Apply the order of operations to
simplify and evaluate expressions
G.1.3.1.1
How to write algebraic
G.1.3.1.2
expressions based on
Choose correct operations for
G.2.2.4.1
problem scenarios
solving mathematical problems
G.2.3.1.1
G.2.3.1.2
Order of operations
G.2.3.1.3
Order of operations
graphic organizer
How can you use a picture to
represent a problem
situation?
M.11.A.1.2
Hot dogs and buns
problem
How do you find the LCM of
two or more numbers?
M.11.A.3.1
CC.2.1.6.E.3
How to work with
multiples and divisibility
in a problem situation
Find the least common multiple of
two numbers
Collaborative grouping
M06.A-N.2.2.1 Least common multiple
M06.A-N.2.2.2
A1.1.1.2.1
M.11.A.1.2
CC.2.1.6.E.3
Prime and composite
numbers
Determine if a number is prime or
composite
Sieve of Eratosthenes
How to create a factor
tree for a number using
prime factorization
Find the prime factorization of a
number
Photo hunt for common
features
Use prime factorization to find GCF
of two numbers
Quiz on multiples and
factors
Write fractions in simplest form
Create groups using
M06.A-N.2.2.1 Relationship between
M06.A-N.2.2.2 multiples and factors
A1.1.1.2.1
M.11.A.1.1
When a fraction is
How do the terms “multiple”
and “divisibility” relate to
factor pairs?
How do prime factorization
help us find the GCF of two
or more numbers?
How can you tell if a fraction
completely simplified
Compare and order fractions
How to use a number line
to order fractions
M.11.A.3.2
Place value chart
Human number line for
fractions
Write decimals as fractions
How to compare decimals Write decimals in word form
Identify place value of given digit
Compare and order decimals
Round decimals
M.11.A.3.1
Rules for operations for
the following:
CC.2.1.6.E.1
- Integers
M06.A-N.1.1.1 - Fractions
- Decimals
equivalent fractions index
cards
Add, subtract, multiply, and divide
any rational number
is simplified?
How can you compare and
order fractions?
Place value chart organizer How are fractions related to
decimals?
Real world estimation
examples
How does place value help
with estimating and
Human number line for all rounding decimals?
rational numbers
Why is it necessary to
represent and/or convert
numbers to different forms?
Flip charts for operation
rules
Number line for integer
operations
Flash cards
Supplemental worksheets
How are mathematical
operations used in order to
simplify and evaluate
expressions involving real
numbers?
Title: Patterns and Multiple Representations
Standards
Content
(Students will know)
Performance
(Students will do)
M.11.A.3.1.1
Definitions of sequence,
term, pattern, order of
operations, numeric and
algebraic expression
Write an algebraic expression to find
the nth term of the sequence
CC.2.2.HS.C.3
A1.1.2.1.1
A1.1.2.1.2
A1.1.2.1.3
A1.2.1.1.1
A1.2.1.1.2
A1.2.1.1.3
A1.2.1.2.1
A1.2.1.2.2
A1.2.2.1.3
A1.2.2.1.4
A2.1.3.1.1
A2.1.3.1.2
A2.1.3.1.3
A2.1.3.1.4
A2.1.3.2.1
A2.1.3.2.2
A2.2.1.1.1
A2.2.1.1.2
A2.2.1.1.3
A2.2.1.1.4
A2.2.2.1.1
A2.2.2.1.2
A2.2.2.1.3
A2.2.2.1.4
Activities/
Assessments
Essential Questions
How do you find the nth
term of a sequence?
CC.2.2.5.A.1
Order of operations
Simplify expressions using the order Evaluating expressions
of operations
organizer
The difference between a
numeric and algebraic
expression and the
procedure for evaluating
each
Evaluate numeric and algebraic
expressions
M05.B-O.1.1.1
M05.B-O.1.1.2
M.11.D.1.1.1
CC.2.2.HS.D.2
A1.1.1.5.1
A1.1.1.5.2
A1.1.1.5.3
A2.1.2.1.1
A2.1.2.1.1
A2.1.2.1.3
A2.1.2.1.4
A2.1.2.2.1
A2.1.2.2.2
M.11.D.1.1.1
CC.2.4.HS.B.2
A1.2.1.1.1
A1.2.1.1.2
A1.2.1.1.3
A1.2.1.2.1
A1.2.1.2.2
A1.2.2.2.1
A2.2.1.1.1
A2.2.3.1.1
A2.2.3.1.2
M.11.D.1.1.1
CC.2.1.HS.F.3
A1.1.2.1.1
Group presentation
Write and compare different
representations to model problem
situations
Determine whether a given value is
a solution to an equation
How to analyze a set of
data for an existing
pattern and represent it
algebraically and
graphically
Identify the advantages
and disadvantages of each
form of representing the
problem situation
Determine values for a variable from Collaborative grouping
a graph
How do you model real
world data with an
expression?
Write an equation
Classify variables as dependent or
independent
Identify a rate of change Compare and analyze two problem
and initial value from a set situations
of data
Jigsaw activity
How do you model data
given an initial value?
Consumer report
How do you compare two
problem situations?
A1.1.2.1.2
A1.1.2.1.3
A1.2.1.2.1
A1.2.1.2.2
A2.2.2.1.1
A2.2.2.1.2
A2.2.3.1.1
A2.2.3.1.2
M.11.A.2.1.2
M.11.A.2.1.3
CC.2.2.8.B.2
M08.B-E.2.1.1
M08.B-E.2.1.2
M08.B-E.2.1.3
A1.2.1.2.2
M.11.A.2.1.1
M.11.A.2.1.3
CC.2.2.8.B.2
M08.B-E.2.1.1
M08.B-E.2.1.2
M08.B-E.2.1.3
A1.2.1.2.2
How labels play a valuable Set up and solve proportions
role in setting up
proportions
Translate real life problems into
proportions
Proper procedure for
solving a proportion
Left hand/right hand
survey
How to set up a mixture
problem
Supplemental recipes
Determine the amount needed of
each ingredient
Write and compare ratios of
ingredients
Use ratios and proportions to solve
mixture problems
How do you use proportions
to make predictions?
Music survey
How can you compare
recipes using ratios?
Title: Solving Equations
Standards
Content
(Students will know)
Performance
(Students will do)
Activities/
Assessments
Essential Questions
CC.2.1.8.E.1
How numbers are
classified
Classify numbers
Number taxonomy
How do we classify
numbers?
How to solve equations
Solve one-step equations
Solving equations flip chart How do you solve a one-step
or graphic organizer
equation?
M08.A-N.1.1.1
M08.A-N.1.1.2
A1.1.1.1.1
A1.1.1.1.2
CC.2.2.HS.D.8
CC.2.2.HS.D.9
Solve two-step equations
A1.1.1.4.1
A1.1.2.1.1
A1.1.2.1.2
A1.1.2.1.3
A1.1.2.2.1
A1.1.2.2.2
A1.1.3.1.1
A1.1.3.1.3
A2.1.3.1.1
A2.1.3.1.2
A2.1.3.1.3
A2.1.3.1.4
A2.1.3.2.1
A2.1.3.2.2
CC.2.2.HS.D.2
A1.1.1.5.1
A1.1.1.5.2
A1.1.1.5.3
A2.1.2.1.1
A2.1.2.1.1
Solve multi-step equations
How do you transform twostep equations into one-step
equations?
How do we solve equations
with variables on both sides?
How to use the
distributive property
Write equivalent expressions and
equations using the distributive
property
Represent the distributive How do you know when to
property using algebra tiles use the distributive
property?
A2.1.2.1.3
A2.1.2.1.4
A2.1.2.2.1
A2.1.2.2.2
How to solve systems of
linear equations
CC.2.4.HS.B.3
A1.2.2.2.1
A1.2.3.1.1
A1.2.3.2.1
A1.2.3.2.2
A1.2.3.2.3
A2.2.3.1.1
A2.2.3.1.2
Compare two deals and determine
which is better
How to interpret graphical Use a graph to make estimations
data
Phone plan activity
How can you determine the
better deal?
Shoe vs height activity
How can you use graphs to
estimate values?
Title: Writing and Graphing Linear Functions
Standards
Content
(Students will know)
CC.2.2.HS.C.1
CC.2.2.HS.C.2
The meaning of functional Determine whether a relation is a
relationships
functional
A1.2.1.1.1
A1.2.1.1.2
A1.2.1.1.3
A1.2.1.2.1
A1.21.2.2
A1.2.2.1.1
A1.2.2.1.2
A1.2.2.1.3
A1.2.2.1.4
A2.1.3.1.4
A2.1.3.2.1
A2.1.3.2.2
A2.2.1.1.1
A2.2.1.1.2
A2.2.1.1.3
A2.2.1.1.4
G.2.2.2.1
G.2.2.2.2
G.2.2.2.3
G.2.2.2.4
G.2.2.2.5
CC.2.2.HS.C.2
A1.2.1.1.1
A1.2.1.1.2
A1.2.1.1.3
A1.2.1.2.1
Performance
(Students will do)
Activities/
Assessments
Essential Questions
The soda machine
What are the similarities and
differences between
relations and functions?
Write an equation using function
notation
How can you write a linear
equation using function
notation?
Determine the domain and range of
a function
How do you find domain and
range of a function?
The meaning of intercepts Identify intercepts given a graph or
an equation
The meaning of slope
Identify slope given a graph or an
How to write an equation equation or a pair of points
of a line in slope-intercept
The big race
How do we find intercepts
algebraically and graphically?
How do we find slope?
How do you write the
A1.2.1.2.2
A1.2.2.1.1
A2.1.3.1.4
A2.1.3.2.1
A2.1.3.2.2
A2.2.1.1.1
A2.2.1.1.2
A2.2.1.1.3
A2.2.1.1.4
form
CC.2.2.HS.D.2
How to convert between
various forms of
equations
A1.1.1.5.1
A1.1.1.5.2
A1.1.1.5.3
A2.1.2.1.1
A2.1.2.1.1
A2.1.2.1.3
A2.1.2.1.4
A2.1.2.2.1
A2.1.2.2.2
equation of a line in slopeintercept form?
Write equations in slope-intercept
form
How do we go from standard
form to slope-intercept form
and vice versa?
Write equations in standard form
Solve literal equations
How do we solve for a
variable in an equation?
Title: Lines of Best Fit
Standards
Content
(Students will know)
Performance
(Students will do)
CC.2.4.HS.B.1
CC.2.4.HS.B.3
How to model a real life
situation using a line of
best fit
Model real life situations using a line Burning candle
of best fit
Shoe size vs height
Conduct an experiment and use the
data collected to make predictions
A1.2.2.1.2
A1.2.2.2.1
A1.2.3.1.1
A1.2.3.2.1
A1.2.3.2.2
A1.2.3.2.3
A2.2.3.1.1
A2.2.3.1.2
How to conduct an
experiment and use data
to make predictions
How to determine the
correlation of a set of data
Determine the correlation of a set of
data
Activities/
Assessments
Essential Questions
How can you model a
situation using a line of best
fit?
How can you perform an
experiment and use the data
to create a prediction
equation?
How do you find the
correlation of a set of data?
Title: Systems of Equations and Inequalities
Standards
Content
(Students will know)
Performance
(Students will do)
Activities/
Assessments
Essential Questions
CC.2.2.HS.D.10 How to solve systems of
linear equations
A1.1.2.1.1
A1.1.2.1.2
A1.1.2.1.3
A1.1.2.2.1
A1.1.2.2.2
A1.1.3.1.1
A1.1.3.1.2
A1.1.3.1.3
A1.1.3.2.1
A1.1.3.2.2
A2.1.3.1.1
A2.1.3.1.2
A2.1.3.1.3
A2.1.3.1.4
Solve linear systems using
substitution
World Records
How do you solve a system
using substitution?
CC.2.2.HS.D.10 How to solve and graph
linear inequalities
A1.1.2.1.1
A1.1.2.1.2
A1.1.2.1.3
A1.1.2.2.1
A1.1.2.2.2
A1.1.3.1.1
A1.1.3.1.2
A1.1.3.1.3
A1.1.3.2.1
A1.1.3.2.2
A2.1.3.1.1
A2.1.3.1.2
Solve linear systems using
elimination
How do you solve a system
using elimination?
Determine the best method for a
given linear system
How do you know which
method is most efficient?
Solve linear inequalities
How do you solve and graph
an inequality in one
variable?
Graph linear inequalities
How do you graph a linear
inequality?
How do you solve a system
of linear inequalities?
A2.1.3.1.3
A2.1.3.1.4
CC.2.2.HS.C.5
A1.2.2.1.1
A1.2.2.1.2
A1.2.2.1.3
A1.2.2.1.4
A2.1.3.1.1
A2.1.3.1.2
A2.1.3.1.3
A2.1.3.1.4
A2.2.1.1.1
A2.2.1.1.2
A2.2.1.1.3
A2.2.1.1.4
A2.2.2.1.1
A2.2.2.1.2
A2.2.2.1.3
A2.2.2.1.4
A2.2.2.2.1
How slope is related to
Write the equation of a line parallel
parallel and perpendicular to a given one
lines
Write the equation of a line
perpendicular to a given one
CC.2.2.HS.D.10 How to determine the
break-even point
A1.1.2.1.1
A1.1.2.1.2
A1.1.2.1.3
A1.1.2.2.1
A1.1.2.2.2
A1.1.3.1.1
A1.1.3.1.2
A1.1.3.1.3
A1.1.3.2.1
A1.1.3.2.2
A2.1.3.1.1
A2.1.3.1.2
Determine the break-even point in a
problem situation
How do you write equations
of parallel and perpendicular
lines?
How do we find the breakeven point?
A2.1.3.1.3
A2.1.3.1.4