Download Foundations of Algebra

Teacher: CORE Algebra Foundations
Year: 2014-15
Month: All
Months
Course: Algebra Foundations
Foundations of Algebra
Standards
Essential Questions Assessments
Skills
Content
Lessons
Resources
A1.1.1.1-Represent
and/or use numbers in
equivalent forms (e.g.,
integers, fractions,
decimals, percent’s,
square roots, and
exponents).
A1.1.1.4-Use estimation
strategies in problemsolving situations.
How are math vocabulary Teacher created quizzes 10/1/2014
and symbols used to
translate between
Teacher created tests 10/1/2014
equation and verbal
sentences to help us
communicate effectively
about mathematics?
translate phrases into
variable expressions
variable
Order of Operations
Approved algebra I
textbook
Why is the order of
operations a necessary
component of math?
algebraic expression
translate word sentences into
equations
equation
Writing Algebraic
Expressions
Supplemental resources
Number line
simplify expressions using the simplify
correct order of operations
evaluate
evaluate expressions for the
given value of the variable
order of operation
solve real life problems
grouping symbols
classify numbers
substitution principle
compare numbers
natural numbers
whole numbers
find the absolute value of
rational numbers
integers
write a function rule
rational number
irrational numbers
real numbers
inequality
opposite
absolute value
function
functional rule
domain
range
Manipulatives
Real Numbers
Standards
Essential Questions Assessments
A1.1.1.1-Represent
and/or use numbers in
equivalent forms (e.g.,
integers, fractions,
decimals, percent’s,
square roots, and
exponents).
A1.1.1.2-Apply number
theory concepts to show
relationships between
real numbers in problem
solving settings.
What are some real life
number lines?
How do integers
represent situations in
the real world?
How are integer
operations relevant in
real-world situations?
Skills
Teacher created quizzes add, subtract, multiply, and divide
integers
Teacher created tests
simplify and evaluate expressions
involving absolute value
simplify and evaluate expressions
involving the addition, subtraction,
multiplication, and division of
integers
Content
Lessons
Resources
rules for addition with integers
Algebraic Properties
Approved algebra I
textbook
rules for subtraction with integers
Rules of Operations with
Integers
rules for multiplication and division with
integers
simplify expressions using the
distributive property
simplify expressions by combining
like terms
coefficient
like terms
closure property
simplify expressions using real
number properties
name an algebraic property that is
illustrated
Manipulatives
Number line
the distributive property
term
How can algebraic
properties assist you in
performing mental
operations?
Supplemental resources
commutative property
associative property
identity property
solve real life problems
inverse property
reflexive property
symmetric property
transitive property
multiplicative property of zero
multiplicative property of negative one
Solving Equations
Standards
Essential Questions
Assessments
A1.1.1.2-Apply number
theory concepts to show
relationships between real
numbers in problem
solving settings.
A1.1.2.1-Write, solve,
and/or graph linear
equations using various
methods.
How can a real world
Teacher created quizzes
problem be represented by
an equation and how does Teacher created tests
the solution relate to the
problem?
How do properties of
equality assist in solving
equations?
Skills
Content
Lessons
Resources
solve two step equation
inverse operations
One, No, Many Solutions
Practice
Approved algebra I
textbook
solve multi-step equations
including the distributive
property, combining like terms,
and equations with variables on
both sides
solve
Solving Equations Review
Supplemental resources
addition property of equality
Manipulatives
subtraction property of equality
justify steps in solving equations multiplication property of equality
by using properties of equalities
division property of equality
write and solve an equation
consecutive integers
identify an equation as an identity
or one with no solution
distance formula
solve real life problems
uniform motion
Solving proportions
same direction travel
round trip travel
opposite direction travel
Solving Equations (continued)
Standards
Essential Questions Assessments
Skills
Content
Lessons
Resources
A1.1.1.2-Apply number
theory concepts to show
relationships between real
numbers in problem
solving settings.
A1.1.2.1-Write, solve,
and/or graph linear
equations using various
methods.
How can a real world
Teacher created quizzes
problem be represented
by an equation and how Teacher created tests
does the solution relate to
the problem?
solve two step equation
inverse operations
One, No, Many Solutions
Practice
Approved algebra I
textbook
solve multi-step equations
including the distributive
property, combining like terms,
and equations with variables on
both sides
solve
Solving Equations Review
Supplemental resources
How do properties of
equality assist in solving
equations?
addition property of equality
Manipulatives
subtraction property of equality
justify steps in solving equations multiplication property of equality
by using properties of equalities
division property of equality
write and solve an equation
consecutive integers
identify an equation as an identity
or one with no solution
distance formula
solve real life problems
uniform motion
Solving proportions
same direction travel
round trip travel
opposite direction travel
Solving Inequalities
Standards
Essential Questions Assessments
Skills
Content
Lessons
Resources
A1.1.1.3-Use exponents,
roots, and/or absolute
values to solve problems.
A1.1.3.1-Write, solve,
and/or graph linear
inequalities using various
methods.
How are inequalities
similar to and different
from equations?
Teacher created quizzes
identify solutions of inequalities
inequalities
Solving Compound
Inequalities
Approved algebra I
textbook
Teacher created tests
graph inequalities
solve
Solving Inequalities
Supplemental resources
write inequalities when given a
graph
solution of an inequality
When would writing,
solving, and graphing an
inequality be useful in the
real world?
What role does the graph
of an inequality solution
play?
Manipulatives
solve, graph, and check the
addition property of inequality
solutions of inequalities (one
step, multi-step, and variables on subtraction property of inequality
both sides)
multiplication properties of
write, solve, and graph compound inequality, c>0 and c<0
inequalities
Number line
justify steps in solving inequalities division property of inequality
by using properties of inequalities
compound inequality containing
solve real world problems using "and"
inequalities
compound inequality containing
"or"
Relations and Functions
Standards
Essential Questions Assessments
Skills
Content
Lessons
A1.2.1.1-Analyze and/or
use patterns or relations.
A1.2.1.2-Interpret and/or
use linear functions and
their equations, graphs, or
tables.
How can a graph represent Teacher created quizzes
an event in your life?
Teacher created tests
How are relations and
functions similar and how
are they different?
determine if a relation is a
function
relation
Name that Function Game Approved algebra I
textbook
Function Notation
Supplemental resources
How can patterns assist
you in making
conjectures?
domain
evaluate functions using function
notation
range
Resources
Manipulatives
model functions using a rules,
tables, and graphs
vertical line test
Graph paper
function notation
write a function rule given a table
of values or a real world situation function rule
describe an arithmetic sequence sequence
complete an arithmetic sequence arithmetic sequence
Linear Equations and Their Graphs
Standards
A1.1.2.1-Write, solve,
and/or graph linear
equations using
various methods.
A1.2.2.1-Describe,
compute, and/or use
the rate of change
(slope) of a line.
Essential
Questions
Assessments
Skills
How can the rate Teacher created
determine if an ordered pair is a solution to an
of change be
quizzes
equation
found in various
representations of Teacher created tests determine if lines are parallel or perpendicular
linear data?
calculate rate of change using tables and graphs
How are graphs of
linear equation
calculate the slope of a line graphed on a
helpful in
coordinate plane
visualizing a real
world application?
calculate the slope of a line given two ordered
pairs
How can a real
world linear graph
determine the slope and y-intercept of an
assist you in
equation
solving a
problem?
write an equation of a line when given the slope
and y-intercept or from a graph
Content
Lessons
Resources
coordinate plane
Slope-Intercept Form
Approved algebra I
textbook
origin
Review of Graphing Linear
Equations using the
Supplemental resources
Graphing Calculator
Manipulatives
axis
ordered pair
rate of change
slope
rise
run
positive slope
negative slope
graph a linear equation using the slope and yintercept
slope of horizontal lines
slope of vertical lines
interpret real life graphs
linear equation
find the x and y-intercepts when given an equation
y-intercept
graph a linear equation in two variable using
intercepts
slope-intercept form
graph horizontal and vertical lines
standard form of a linear equation
transform an equation into standard form
x-intercept
graph a linear equation using point-slope form
graphs of horizontal lines
write a linear equation when given the slope and a graph of vertical lines
point, a graph, or a table
point-slope form
write equations of parallel and perpendicular lines
parallel lines
write an equation for a line of best fit on a
scatterplot
perpendicular lines
make predictions about a scatter plot using the
line of best fit
slopes of parallel lines
slopes of perpendicular lines
Graph paper
Graphing calculator
negative reciprocal
scatter plots
line of best fit
positive, negative, and no correlation
Linear Equations and Their Graphs (continued)
Standards
A1.1.2.1-Write, solve,
and/or graph linear
equations using
various methods.
A1.2.2.1-Describe,
compute, and/or use
the rate of change
(slope) of a line.
Essential
Questions
Assessments
Skills
How can the rate Teacher created
determine if an ordered pair is a solution to an
of change be
quizzes
equation
found in various
representations of Teacher created tests determine if lines are parallel or perpendicular
linear data?
calculate rate of change using tables and graphs
How are graphs of
linear equation
calculate the slope of a line graphed on a
helpful in
coordinate plane
visualizing a real
world application?
calculate the slope of a line given two ordered
pairs
How can a real
world linear graph
determine the slope and y-intercept of an
assist you in
equation
solving a
problem?
write an equation of a line when given the slope
and y-intercept or from a graph
Content
Lessons
Resources
coordinate plane
Slope-Intercept Form
Approved algebra I
textbook
origin
Review of Graphing
Linear Equations using
the Graphing Calculator
axis
Manipulatives
ordered pair
Graph paper
rate of change
Graphing calculator
slope
rise
run
positive slope
negative slope
graph a linear equation using the slope and yintercept
Supplemental resources
slope of horizontal lines
slope of vertical lines
interpret real life graphs
linear equation
find the x and y-intercepts when given an equation
y-intercept
graph a linear equation in two variable using
intercepts
slope-intercept form
graph horizontal and vertical lines
standard form of a linear equation
transform an equation into standard form
x-intercept
graph a linear equation using point-slope form
graphs of horizontal lines
write a linear equation when given the slope and a graph of vertical lines
point, a graph, or a table
point-slope form
write equations of parallel and perpendicular lines parallel lines
write an equation for a line of best fit on a
scatterplot
perpendicular lines
slopes of parallel lines
make predictions about a scatter plot using the
line of best fit
slopes of perpendicular lines
negative reciprocal
scatter plots
line of best fit
positive, negative, and no correlation
Systems of Equations and Inequalities
Standards
Essential
Questions
Assessments
Skills
A1.1.2.2-Write, solve, In what real world Teacher created
solve system of equations by graphing
and/or graph systems situations could quizzes
of linear equations
systems of linear
analyze solutions of systems of equations in real
using various methods. equations or
Teacher created tests world solutions
A1.1.3.2-Write, solve, inequalities assist
and/or graph systems you in finding
determine when systems of equations have no
of linear inequalities solutions?
solution or infinitely many solutions
using various
methods.
How can I best
solve systems using substitution
determine which
method to use to
solve systems by elimination, including systems in
solve systems of
which the first term must be multiplied
linear equations?
write and solve real world systems of equations
Content
Lessons
Resources
system of linear equations
Solving Systems of
Equations by Graphing
Approved algebra I
textbook
Systems of Equations (3
methods)
Supplemental resources
solution of system of linear equations
no solution
Manipulatives
infinitely many solutions
Graph paper
elimination method
Graphing calculator
substitution method
linear inequality
solutions of an inequality
graph linear inequalities
system of linear inequalities
write and find solutions for linear inequalities
when modeling real world situations
solve systems of linear inequalities by graphing
solve real world systems of inequalities
solution of a system of linear inequalities