INTEGRATED ALGEBRA UNIT 1

Transcription

Unit Title: Foundations of Algebra
Enduring Understandings/Big Ideas:
 The transition from arithmetic to algebraic
representation and the introduction of
variables sometimes causes difficulty for
students
 It is important to recognize that variables
are used in a variety of applications.
Grade Level: 9th
Unit Length: 9 days
Essential Questions:
 How do you interpret, evaluate and write
algebraic expressions that model real-world
situations?
Common Core Learning Standards:
N.Q.1 Use units as a way to understand… and to guide the
solution of multi step problems…
N.Q.2 Define appropriate quantities for the purpose of
descriptive modeling.
A.SSE.1 Interpret expressions that represent a quantity in
terms of its context.
A.SSE.1a Interpret parts of an expression, such as terms,
factors, and coefficients.
A.SSE.1b Interpret complicated expressions by viewing
one or more of their parts as a single entity.
A.SSE.2 Use the structure of an expression to identify ways
to rewrite it.
A.REI.1 Explain each step in solving a simple equality of
numbers asserted at the previous step, starting from the
assumption that the original equation has a solution.
Construct a viable argument to justify a solution method.
HSN-RN.B.3. Explain why the sum or product of two
rational numbers is rational; that the sum of a rational
number and an irrational number is irrational; and that the
product of a nonzero rational number and an irrational
number is irrational.
HSA-APR.A.1. Understanding that polynomials form a
system analogous to the integers, namely, they are closed
under the operations of addition, subtraction, and
multiplication; add, subtract, and multiply polynomials.
New York State / Content Standards:
A.A.1. Translate a quantitative verbal phrase into an
algebraic expression.
A.N.1. Identify and apply the properties of real
numbers.
A.N.6. Evaluate expressions involving factorial(s),
absolute value(s), and exponential expression(s).
Skills (Students will be able to…)
 Evaluate and simplify expressions
 Translate between words and algebra
 Identify and apply the properties of real numbers
 Classify numbers within the real number system
 Use the order of operations to simplify expressions
 Identify patterns formed by points plotted in the coordinate plane
 Combine like terms
Unit Outline – Sequence of learning (AIMs):
 How do we use the symbol of algebra and how do we evaluate algebraic expressions?
 How do we add and subtract within the set of signed numbers?
 How do we multiply and divide signed numbers?
 How do we evaluate expressions containing exponents?
 How do we evaluate expressions containing square roots and how do we classify real numbers?
 How do we use order of operations to simplify expressions?

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What are the properties of real numbers?
Review
Formative Assessments:
 Quizzes
 Do Now responses
 Teacher/student exchange
 Questioning during class discussions
 Exit Slips
 Homework
 Notebook check quiz
Summative Assessment / Performance Task:
 Unit test
 Performance Task
Key Terms/Vocabulary:
Additive inverse, multiplicative inverse, coefficient, constant, coordinate plane, irrational numbers, like
terms, origin, rational numbers, variable, reciprocal, power, base, exponents, real numbers, natural
numbers, whole numbers, integers, rational numbers, terminating decimals, repeating decimals, order of
operations
Differentiation: choice of homework problems, choice on exit ticket, heterogeneous grouping
Higher Achieving - Challenge and bonus questions, accelerate pacing
SWD – small group instruction, modified assessments, skeleton – note handouts, mnemonic strategies,
computer assisted instruction, peer mediation
ELL – use of dictionaries, translated assessments, translated handouts, visuals/graphic organizer that
reinforce spoken word
Resources:
Explorations in CORE Math for Common Core
Algebra 1 Textbook – Holt
Algebra 1 MES21
Unit 1: Foundations of Algebra
(1.1)
How do we use the symbol of algebra and how do we evaluate algebraic expressions?
HW#1: Handout
(1.2)
How do we add and subtract within the set of signed numbers?
HW#2: Handout
(1.3)
How do we multiply and divide signed numbers?
HW#3: Handout
(1.4)
How do we evaluate expressions containing exponents?
HW#4: Handout
(1.5)
How do we evaluate expressions containing square roots and how do we classify real numbers?
HW#5: p.35-36/ #11-14, 15, 16-23, 28
(1.6)
How do we use order of operations to simplify expressions?
HW#6: p.43-45/ #26, 28, 36, 41, 42, 49, 50, 54, 55a-f, 72*
(1.7)
What are the properties of real numbers?
HW#7: p.49-50/ #26, 29, 30, 31, 34, 39, 40, 42, 46, 48, 49
Review
Test
Unit Title: Equations
 When solving an equation, you find the
number that makes the open sentence true.
Equations can also take several forms.
 Equations can be solved by using inverse
operations.
 Equations are termed conditional
equations. If we replace x is a certain
number then the equation will be true, and
if we replace x with a different number,
then the equation will be false
 Using the distributive property first before
applying inverse operations
Grade Level: 9th
Unit Length: 15 days
 What are some different methods for solving
linear equations?
 How can you use properties to justify
solutions to equations that involve
multiplication and division?
solutions to multi-step equations?
solutions to equations with variables on both
sides?
 How do you solve literal equations and
rewrite formulas?
 How can you use units to help solve realworld problems?
 How can you use units to write and solve
proportions?
A.REI.1 Explain each step in solving a simple equation as
following from the equality of numbers asserted at the
previous step, starting from the assumption that the original
equation has a solution. Construct a viable argument to
justify a solution method.
A.REI.3 Solve linear equations…in one variable…
A.SSE.2 Use the structure of an expression to identify ways
to rewrite it…
A.CED.2 Create equations in two or more variables to
represent relationships between quantities…
A.CED.4 Rearrange formulas to highlight a quantity of
interest, using the same reasoning as in solving equations…
N.Q.1 Use units as a way to understand…and to guide the
solution of multi-step problems.
A.SSE.1 Interpret expressions that represent a quantity in
terms of its context.
A.CED.1 Create equations…in one variable and use them
to solve problems.
A.A.22 Solve all types of linear equations in one variable
A.A.23 Solve literal equations for a given variable
A.A.24 Solve linear inequalities in one variable
A.A.25 Solve equations involving fractional expressions
Note: Expressions which result in linear equations in one
variable.
A.A.26 Solve algebraic proportions in one variable which
result in linear or quadratic equations
A.A.5. Write algebraic equations or inequalities that
represent a situation.
Solve one-step equations in one variable by using addition and subtraction.
Solve one-step equations in one variable by using multiplication and division
Solve equations in one variable that contain more than one operation
Solve equations in one variable that contain variables on both sides
Solve a formula for a given variable
Solve an equation in two or more variables for one of the variables
Write and use ratios, rates, and unit rates
Write and solve proportions
Use proportions to solve problems involving geometric figures
Use proportions and similar figures to measure objects indirectly
Solve problems involving percents
Use common applications of percents
Estimate with percents
Unit Outline:
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What are equations, and how do we solve them using mental math and tables?
How do we solve one-step equations?
How do we solve two-step equations?
How do we solve multi-step equations?
How do we solve equations we variables on both sides?
How do we solve literal equations for a variable?
How do we use LESCA to solve word problems?
How do we use LESCA to solve consecutive integer problems?
What are rates, ratios, and proportions? How do we solve proportions?
How do we use proportions to geometric and other problems?
What are percents, and how do we convert them to fractions and decimals?
How do we use percents to solve real life/word problems?


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How can we apply our skills from Unit 2?
Review
Test
 Quizzes
 Exit Slips
 Homework
Equation project
Unit Test
Equation, formula, identity, indirect measurement, literal equation, percent, percent change, proportion,
ratio, unit rate, scale, conversion factor, cross products, scale model, scale drawing, solution of an
equation, inverse operations, contradiction, similar, corresponding sides, corresponding angles, scale
factor, commission, principal, tip, interest, sales tax, percent change, percent increase, percent decrease,
discount, markup
Resources:
Algebra 1 MES21
Unit 2: Equations
(2-1)
What are equations, and how do we solve them using mental math and tables?
HW #8: Handout.
(2-2)
How do we solve one-step equations?
HW #9: Handout.
(2-3)
How do we solve two-step equations?
HW #10: p. 96/ # 2, 5, 7, 11, 14, 17, 20, 47.
(2-4)
How do we solve multi-step equations?
HW #11: p. 96-98 # 8, 23, 28, 31, 34, 50, *76, *77.
(2-5)
How do we solve equations we variables on both sides?
HW #12: p. 103-106/ # 15, 18, 19, 21, 23, 26, 27, 40, 42, *65, *66.
(2-6)
How do we solve literal equations for a variable?
HW #13: p. 109-111/ #10, 11, 12, 15, 17, 19, 48, 49. p. 103/ # 9.
(2-7)
How do we use LESCA to solve word problems?
HW #14: Handout
(2-8)
How do we use LESCA to solve consecutive integer problems?
HW #15: Handout
(2-9)
What are rates, ratios, and proportions? How do we solve proportions?
HW #16: pp. 117-119/ # 2, 5, 8, 11, 14, 17, 31, 41.
(2-10) How do we use proportions to geometric and other problems?
HW #17: p. 124/ # 3, 4, 5, 6, 7, 22, 30, 31, 32, (no calculators for 30, 31, 32).
(2-11) What are percents, and how do we convert them to fractions and decimals?
HW #18: p. 130/ # 2, 3, 6, 7, 10, 11, 28, 30, 33, 38, 40, 43.
(2-12) How do we apply our skills from Unit 2?
HW #19: Handout
Review
Test
Grade Level: 9th
Unit Length: 9 days
 How can patterns, relations, and functions be
used as tools to best describe and help explain
real-life relationships?
 How can situations be modeled as a system of
linear inequalities and how to find solutions
using all constraints?
Unit Title: Inequalities
 Patterns and relationships can be
represented graphically, numerically, and
symbolically.
 How to use the unknown, constraints and
their relationships to model a situation

A.CED.1 Create equations and inequalities in one
variable and use them to solve problems. Include
equations arising from linear and quadratic functions,
and simple rational and exponential functions
A.CED.3 Represent constraints by equations or
inequalities, and by systems of equations and/or
inequalities, and interpret solutions as viable or
nonviable options in a modeling context
A.REI.1 Explain each step in solving a simple
inequality as following from the equality of numbers
asserted at the previous step, starting from the
assumption that the original equation has a solution.
Construct a viable argument to justify a solution
method
A.REI.3 Solve linear equations and inequalities in one
variable, including equations with coefficients
represented by letter
A.A.4 Translate verbal sentences into mathematical
equations or inequalities
A.A.5 Write algebraic equations or inequalities that
represent a situation
A.A.6 Analyze and solve verbal problems whose solution
requires solving a linear equation in one variable or linear
inequality in one variable
A.A.24 Solve linear inequalities in one variable
A.G.6 Graph linear inequalities
A.A.29 Use set-builder notation and/or interval notation to
illustrate the elements of a set, given the elements in roster
form
Write an inequality from a verbal description
Write and use inequalities to solve verbal problems
Write the inequality of a line parallel to the x- or y-axis
Graph linear inequalities on a number line
Use set-builder notation to write the solution set of an inequality
Solve a compound inequality
Determine solutions of compound inequality that make the inequality true
Unit Outline:
 How do we write and graph inequalities? How do we solve one-step inequalities?
 How do we solve multi-step inequalities?
 How do we solve inequalities with variables on both sides?
 How do we solve compound inequalities (Day1)?
 How do we solve compound inequalities (Day 2)?
 How do we use set-builder notation and interval notation to write the solution set of an inequality?
 How do we solve verbal problems with inequalities?
 Review
 Test
 Quizzes
 Exit Slips
 Homework
Unit Test
Inequality, Less than, greater than, less than or equal to, greater than or equal to, included, not included,
compound inequality, conjunction, intersection, set-builder notation, interval notation, sets, roster form
Resources:
Algebra 1 MES21
Unit 3: Inequalities
(3-1)
How do we write and graph inequalities? How do we solve one-step inequalities?
HW #21: pp. 171-173/ # 6,7, 29-35
pp. 177-179/ # 7-9, 13 – 15, 34
pp. 183-185/ # 23, 24, 30, 32, 67 – 69
(3-2)
How do we solve multi-step inequalities?
HW #22: pp. 191-193 # 25, 27, 31, 33, 52, 53, 55-59, 78, 79
(3-3)
How do we solve inequalities with variables on both sides?
HW #23: pp. 197-200/ # 6, 8, 12, 21, 53, 55, 60, 64, 69, 73 .
(3-4)
How do we solve compound inequalities? (Day 1)
HW #24: pp. 206-208/ #3, 6, 11, 14, 28, 30, 32, 59, 62
(3-5)
How do we solve compound inequalities? (Day 2)
HW #25: pp. 206-208/ # 9, 10, 12, 13, 31, 33, 36, 45, 48, 49, 64
(3-6)
How do we use set-builder notation and interval notation to write the solution set of an
inequality?
HW #26: Handout
(3-7)
How do we solve verbal problems with inequalities?
HW #27: Handout
Review
Test
Unit Title: Intro to Functions
Enduring Understandings:
 What is a function?

How do functions relate to mathematics?
Grade Level: 9
Unit Length: 9 days
 How can patterns, relations, and functions
be used as tools to best describe and help
explain real-life relationships?
New York State Standards:
A.CED.1 Create equations and inequalities in one
variable and use them to solve problems. Include
equations arising from linear and quadratic functions, and
simple rational and exponential functions
A.CED.2 Create equations in two variables to represent
relationships between quantities
A.CED.3 Represent constraints by equations or
inequalities, and by systems of equations and/or
inequalities, and interpret solutions as viable or nonviable
options in a modeling context
A.REI.3 Solve linear equations and inequalities in one
variable, including equations with coefficients
represented by letter
A.REI.10 Understand that the graph of an equation in
two variables is the set of all its solutions plotted in the
A.G.3 Determine when a relation is a function,
by examining ordered pairs and
inspecting graphs of relations
A.G.4 Identify and graph linear, quadratic
(parabolic), absolute value, and
exponential functions
A.G.5 Investigate and generalize how changing
the coefficients of a function affects its
graph
A.A.5 Write algebraic equations or inequalities to
represents a situation
coordinate plane
F.LE.2 Construct linear functions given a graph, a
description of a relationship, or two input-output pairs
F.IF.4 For a function that models a relationship between
two quantities, interpret key features if graphs… and
sketch graphs showing key features given a verbal
description of the relationship
Skills:
Write an equation from a verbal description
Write an inequality from a verbal description
Write and use equations to solve verbal problems
Graph ordered pairs on a coordinate grid
Represent mathematical relationships using graphs
Determine if a relation is a function
Identify the domain and range of a function
Write equations from descriptions and tables
Write equations using function notation
Use a table of values to graph a function
Use a graphing calculator to graph a function
Analyze how different transformations affect a graph
Unit Outline:
 How do we use the coordinate plane to graph ordered pairs?
 How do we use graphs to relate two quantities?
 What is the difference between a relation and a function? How do we identify the domain and
range?
 How do we write equations of functions from tables or descriptions?
 What is a parent function?
 How do we graph functions using the table method?
 How do we graph functions using a graphing calculator?
 Review
 Test
 Quizzes
 Homework
 Notebook check
Summative Assessment:
Unit test
linear relationships, translate; dependent variable; independent variable; profit; co-ordinate grid; x- and yaxis; quadrants, domain, range,
Resources:
Algebra 1 MES21
Unit 4: Intro to Functions
ALL GRAPHS IN THE UNIT MUST BE DONE ON GRAPH PAPER
OR YOU WILL NOT RECEIVE CREDIT!
YOU WILL NEED A GRAPHING CALCULTOR FOR LESSONS 33 & 34!
(4-1)
How do we use the coordinate plane to graph ordered pairs?
HW #28: p. 57/ #17-20 (Use the same set of axes for 17-20, and label each point.),
21-26, 28, 29, 30.
(4-2)
How do we use graphs to relate two quantities?
HW #29: p. 233-235/ #10, 11, 12, 13, 14, 32, 33.
(4-3)
What is the difference between a relation and a function? How do we identify the domain and
range?
HW #30: p. 239-242/ #15, 16, 17, 18, 21, 29, 34, 39.
(4-4)
How do we write equations of functions from tables or descriptions?
HW #31: p. 249-251/ #13, 14, 15, 16, 17, 18, 20, 21, 22, 33, 38, 39.
(4-5)
What is a parent function?
HW#32: p 250-251/#32-35, 43, 44
(4-6)
How do we graph functions using the table method?
HW #33: p. 256-258/ #13, 14, 18, 19, 24, 37, 39, 40, 41, 68.
(4-7)
How do we graph functions using a graphing calculator?
HW #34: p. 256-258/ 17, 21, 22, 32, 33, 54
p. 284/1, 2, 3, 4, 5, 7
Review
Test
Unit Title: Linear Functions
Enduring Understandings:
 Patterns and relationships can be
represented graphically, numerically, and
symbolically.
 Purpose of intercepts
 How do changing the m, k and a-values
affect the graph?
A.REI. 10. Understand that the graph of an equation in two
variables is the set of all its solutions plotted in the
coordinate plane
N.Q.1 – Use units as a way to understand problems and to
guide solutions to multi-step problems;choose and interpret
scale and the origin in graphs and data displays.
F.IF.1 – Understand that a function from one set (called the
domain) to another set (called the range) assigns to each
element of the domain exactly one element of the range. If f
is a function and x is an element of the domain, then f(x) =
denotes the output of f corresponding to the input x. The
graph of f is the graph of the equation f(x) = x
F.IF.2 – Use function notation, evaluate functions for inputs
in their domains, and interpret statements that use function
notation in terms of a context.
F.IF.3 – Recognize that sequences are functions, sometimes
defined recursively, whose domain is a subset of the
integers.
F.IF.4 – For a function that models a relationship between
two quantities, interpret key features of graphs and tables in
terms of the quantities, and sketch graph showing key
features given a verbal description of the relationship
F.IF.5 – Relate the domain of a function to its graph and,
where applicable, to the quantitative relationship it
describes.
F.IF.6 – Calculate and interpret the average rate of change
of a function (presented symbolically or in a table) over a
specified interval. Estimate the rate of change from a graph
F.IF.7 – Graph functions expressed symbolically and show
key features of the graph, by hand in simple cases and using
technology for more complicated cases.
F.IF.7a – Graph linear…functions and show intercepts
F.BF.1 – Write a function that describes a relationship
between two quantities
F.LE.2 – Construct linear functions, given a graph, a
description of a relationship, or two input-output pairs
(include reading a table)
F.BF.3 – Identify the effect on the graph of replacing f(x)
by f(x) + k and f(x + k) for specific values of k; find the
value of k given the graphs
F.LE.5 – Interpret the parameters in a linear function in
terms of a context
Skills:
Identify linear functions given a table of values
Identify linear functions given its graph
Identify linear functions given its equation
Grade Level: 9
Unit Length: 10 Days
 What is a discrete linear function? How are
discrete and continuous linear functions alike
and how are they different?
 What is the slope of a linear function and how
can we use it to graph linear functions?
 How can you represent relationships using
linear functions?
New York State Standards:
A.A.4 Translate verbal sentences into mathematical
equations or inequalities
A.A.5 Write algebraic equations or inequalities that
represent a situation
A.G.3 Determine when a relation is a function, by
examining ordered pairs and inspecting graphs of relations
A.G.4 Identify and graph linear, quadratic (parabolic),
absolute value, and exponential functions
A.G.5 Investigate and generalize how changing the
coefficients of a function affects its graph
A.A.32 Explain slope as a rate of change between
dependent and independent variables
A.A.33 Determine the slope of a line, given the
coordinates of two points on the line
A.A.34 Write the equation of a line, given its slope
and the coordinates of a point on the line
A.A.35 Write the equation of a line, given the
coordinates of two points on the line
A.A.36 Write the equation of a line parallel to the xor y-axis
A.A.37 Determine the slope of a line, given its
equation in any form
A.A.38 Determine if two lines are parallel, given
their equations in any form
A.A.39 Determine whether a given point is on a line,
given the equation of the line
Determine x and y-intercepts of a given graph
Find slope using the slope formula
Plot a line given the slope
Find the slope of a line, given its equation
Write the equation of a line in y=mx + b form
Graph a line given its equation
Write the equation of a line, given its slope and the coordinates of a point on the line
Find slope of a line parallel or perpendicular to a given equation
Perform transformations of a linear function
Unit Outline:
 What are linear functions and how do we identify them? What are x-intercepts and y-intercepts
and how do we use them to graph functions?
 What is the slope of the line, and how do we find it from a graph?
 How do we find slope using the slope formula?
 How do we write and graph an equation of a line in slope-intercept form? (y = mx + b)
 How do we write and graph an equation of a line given the slope and a point?
 How do we use different forms of linear equations? What is the difference between a linear
equation and a linear function?
 How do we find slopes of parallel and perpendicular lines?
 How do we perform transformations of linear functions?
 Review
 Test
 Quizzes
 Homework
Summative Assessment:
 Unit test
 Cell Phone Project
Linear function, Rate of change, rise, run, slope, constant function, x-intercept, y-intercept, standard form
of a line, direct variation, constant, point slope form, parallel, perpendicular, transformation
Resources:
Algebra 1 MES21
Unit 5: Linear Functions
(5.1)
What are linear functions, and how do identify them?
What are x-intercepts and y-intercepts, and how do we use them to graph functions?
HW #35/36: p. 300/ #5, 7, 9-12, 15, 17; p. 306-307/ #2, 4, 6, 11, 30
(5.2)
What is the slope of a line, and how do we find it from a graph?
HW #37: pp. 314-317/# 2, 4, 5, 8-11, 25, 36-38, 41
(5.3)
How do we find slope using the slope formula?
HW #38: pp. 323-325/# 1, 3, 5, 6, 8-10, 21, 26, 27, 29, 32, 34
(5.4)
How do we write and graph an equation of a line in slope-intercept form?
HW #39: pp. 338-340/# 1, 4-8, 10, 11, 20, 24, 25, 50, 53
(5.5)
How do we write and graph an equation of a line given the slope and a point?
HW #40: pp. 345-347/# 4-6, 13-15, 51, 54, 59
(5.6)
How do we use different forms of linear equations? What is the difference between a linear
equation and a linear function?
HW #41: Worksheet
(5.7)
How do we find slopes of parallel and perpendicular lines?
HW #42: pp. 353-355/# 9, 10, 13, 15, 18, 19, 21, 23, 26, 33, 46, 47
(5.8)
How do we perform transformations of linear functions?
HW #43: pp. 361-363/# 3, 6, 8, 10, 12, 13, 19, 55, 57, 58, 60
Review
Test
Unit Title: Systems of Equations and
Inequalities
 How to graph systems of equations

Which algebraic method is most useful

Translating word problems

Graph linear equations

Graph linear inequalities
A.REI.4
Prove that, given a system of two
equations in two variables, replacing one equation by
the sum of that equation and a multiple of the other
produces a system with the same solutions.
A.REI.5 Solve systems of linear equations exactly
and approximately (e.g., with graphs), focusing on
pairs of linear equations in two variables.
A.REI.6 Solve systems of linear
equations…approximately (e.g. with graphs), focusing
on pairs of linear equations in two variables.
AREI.12 Graph the solutions to a linear inequality in
two variables as half-place (excluding the boundary in
the case of a strict inequality)…
.N.Q.1 Use units as a way to understand problems and
to guide the solution of multi-step problems; choose
and interpret units consistently….
N.Q.2 Define appropriate quantities for the purpose of
descriptive modeling. *
A.CED.2 Create equations in two or more variables to
represent relationships between quantities…
Grade Level: 9
Unit Length: 9 days
 What does it mean to be the solution of a
system of equations?
 How do we graph linear equations?
 How can we determine if a value/point is in the
solution set?
 Look at the graphs of the two equations. Does
the linear system have exactly one solution?
How do you know?
 How do we graph linear inequalities?
 How can we determine if a value/point is in the
solution set?
A.A.21 Determine whether a given value is a
solution to a given linear equation in one variable or
linear inequality in one variable
A.G.7
Graph and solve systems of linear
equations and inequalities with rational coefficients
in two variables
A.G.6
Graph linear inequalities
A.A.40 Determine whether a given point is in the
solution set of a system of linear inequalities
Skills:
 Graph linear equations
 Solve systems of equations by substitution
 Solve systems of equations by elimination
 Solve systems of equations from word problems
 Graph linear inequalities
 Identify the solution set of linear inequalities
 Solve systems of linear inequalities
Unit Outline:
 What are systems of equations? How do we solve systems of linear equations by graphing?
 How do we solve systems of linear equations by Substitution?
 How do we solve systems of linear equations by Elimination?
 What are special systems?
 How do we solve verbal problems leading to solving a system of linear equations algebraically?
 How do we graph and solve linear inequality in two variables?
 How do we graph and solve systems of linear inequalities in two variables?
 Review
 Test
 Quizzes
 Homework
 Unit test
 Performance Task, National Treasure
Key Terms/Vocabulary: intersection, systems of equations, linear, solution set, substitution
Resources:
Algebra 1 MES21
Unit 6: Systems of Equations and Inequalities
ALL GRAPHS MUST BE DONE ON GRAPH PAPER
(6.1)
What are systems of equations? How do we solve systems of linear equations by graphing?
HW #44 : pp. 386-388 /# 1-8, 34, 36, 37, 41
(6.2) How do we solve systems of linear equations by Substitution?
HW #45: pp. 394-396 /# 1-7, 38, 39, 46
(6.3)
How do we solve systems of linear equations by Elimination?
HW #46: pp. 401-403 /# 11, 12, 14, 15, 18-20, 24, 25, 39, 44, 45
(6.4)
What are special systems?
HW #47: pp. 409-411 /# 12, 14, 16, 20-22, 26, 29, 42-44
(6.5)
How do we solve verbal problems leading to solving a system of linear equations
algebraically?
HW #48: Worksheet
(6.6) How do we graph and solve linear inequality in two variables?
HW #49: pp. 418-420 /#12-14, 16, 18, 20-22, 27, 42
(6.7)
How do we graph and solve systems of linear inequalities in two variables?
HW #50: pp. 424-426 /# 6, 10, 12, 14, 29, 35-37, 41, 54-57
Review
Test
INTGRATED ALGEBRA UNIT 7
Unit Title: Exponents and Exponential
Functions
 How to multiply and divide monomials

What parts of a polynomial represent
terms, factors and coefficients

How do exponential functions operate?
A.APR.1 Understand that polynomials form a
system of analogous to the integers, namely, they
are closed under the operations of addition,
subtraction and multiplication; add, subtract, and
multiply polynomials
Grade Level: 9th
Unit Length: 8 days
 What are like terms?
 When we multiply monomials what do we do
with the exponents?
 When we divide monomials what do we do with
the exponents?
A.A.12 Multiply and divide monomial expressions
with a common base, using the properties of
exponents
A.A.14 Divide a polynomial by a monomial or
binomial, where the quotient has no
A.APR.6 Rewrite simple rational expressions in
remainder
different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x),
A.N.3 Perform the four arithmetic operations using
where a(x), b(x), q(x), and r(x) are polynomials with
like and unlike radical terms and express the
the degree of r(x) less than the degree of b(x), using
result in simplest form
inspection, long division, or, for the more complicated
examples, a computer algebra system.
A.N.4 Understand and use scientific notation to
N.RN.1 Explain how the definition of the
compute products and quotients of
meaning of rational exponents follows from the
numbers greater than 100%
extending properties of integer exponents to those A.N.6 Evaluate expressions involving factorial(s),
values, allowing for a notation for radicals in
absolute value(s), and exponential
terms of rational exponents
expression(s)
N.RN.2 Rewrite expressions involving radicals
and rational exponents using the properties of
exponents
A.SSE.1a Interpret parts of an expression, such
as terms, factors, and coefficients
Skills:
 Combine like terms
 Simplify expressions with exponents (integer and rational)
 Evaluate expressions with rational exponents
 Multiply monomials
 Divide monomials
 Distribute
 Evaluate growth and decay problems
 Evaluate compound interest
Unit Outline:
 How do we evaluate and simplify numeric expressions with integer exponents?
 How can we write and evaluate an nth root of a number?
 How do we use multiplication properties of exponents to simplify expressions?
 How do we use division properties of exponents to simplify expressions?
 How do we solve problems involving exponential growth and decay?
 How do we compute compound interest?
 Review
 Test
Homework assignments
Quizzes
Exit Tickets
Unit test
Like terms, Coefficient, Constant, Rational exponent, Expression, Variable, Exponent, Monomial,
Exponential growth/decay, compound interest, principal
Resources:
Algebra 1 MES21
Unit 7: Exponents and Exponential Functions
(7.1)
How do we evaluate and simplify numeric expressions with integer exponents?
HW #51 : pp. 449-451 /#1-6, 41, 42, 68, 70, 86-88, 107, 109, 113
(7.2) How can we write and evaluate an nth root of a number?
HW #52: Handout
(7.3)
How can we use multiplication properties of exponents to simplify expressions?
HW #53: pp. 464-466 /#2, 4, 7, 10, 11, 21, 36, 39, 41, 48, 77-79
(7.4)
How do we use division properties of exponents to simplify expressions?
HW #54: pp. 471-473 /#1, 2, 5, 11, 14, 15, 46, 50, 52, 57, 64, 66
(7.5) How do we solve problems involving exponential growth and decay?
HW #55: pp. 785-786 /#10, 11, 13, 21-24, 29, 34
(7.6) How do we compute compound interest?
HW #56: pp. 785-786 /#14, 15, 17, 30-32, 36, 54 (copy chart)
Review
Test
INTGRATED ALGEBRA UNIT 8
Unit Title: Patterns and Sequences
 Connecting knowledge of linear and
exponential functions to sequences and
patterns
Grade Level: 9th
Unit Length: 8 days
 How can you use a geometric of arithmetic
sequence to describe a pattern?
 How can you define a sequence recursively?
IF.A.3 Recognize that sequences are functions,
sometimes defined recursively, whose domain is a
subset of the integers
BF.A.1a Determine an explicit expression, a
recursive process, or steps for calculation from a
context
BF.A.2 Write arithmetic and geometric
sequences both recursively and with an explicit
formula, use them to model situations, and
translate between the two forms
LE.A.2 Construct linear and exponential
functions, including arithmetic and geometric
sequences, given a graph, a description of a
relationship, or two input-output pairs
A.PS.3 Observe and explain patterns to formulate
generalizations and conjectures
A2.A.29 Identify an arithmetic or geometric
sequence and find the formula for its nth term
A2.A.30 Determine the common difference in an
arithmetic sequence
A2.A.31 Determine the common difference in a
geometric sequence
A2.A.32 Determine a specified term of an arithmetic
or geometric sequence
A2.A.33 Specify terms of a sequence, given its
recursive definition
Skills:
 Determining whether a sequence is geometric, arithmetic or neither
 Find an nth term of a given sequence
 Creating an explicit formula for a given sequence
 Creating a recursive formula for a given sequence
 Converting between recursive and explicit rules
Unit Outline:
 What is an arithmetic sequence?
 How do we solve arithmetic sequences problems?
 What are geometric sequences?
 How do we solve geometric sequences problems?
 How do we define sequences using recursive formula?
 Practice with Patterns
 Review
 Test
Quizzes
Exit Tickets
Unit test
Pattern Task
Sequence Project
Common difference, Common ratio, Explicit formula, Recursive formula, Arithmetic sequence,
Geometric sequence, Term, Sequence
Resources:
Big Ideas – Algebra 1 Textbook
Algebra 1 MES21
Unit 8: Patterns and Sequences
(8.1)
What is an arithmetic sequence?
HW #57 : pp. 275 /#2-5, 16-18, 22-25, 28-31
(8.2) How do we solve arithmetic sequence problems?
HW #58: pp. 275-276 /#15, 33, 39, 40
(8.3)
What are geometric sequences?
HW #59: pp. 769-770 /#8-13, 17-22, 26-28, 34-36
(8.4)
How do we solve geometric sequence problems?
HW #60: pp. 769-770 /#32, 33, 37-39, 42, 43
(8.5) How do we define sequences using a recursive formula?
HW #61: Handout
(8.5)
Practice with Sequences
HW #62: Handout
Review
Test
Unit Title: Polynomials and Factoring
Grade Level: 9th
Unit Length: 12 days
 How do perform operations on polynomial
 How can you find the GCF of monomials?
functions
 When factoring what numbers do we need to
find?
 How to factor different types of
 Can you factor expressions with more than
expressions
one variable?
A.SSE.1a Interpret parts of an expression, such
as terms, factors, and coefficients
A.SSE.1b Interpret complicated expressions by
viewing one or more of their parts as a single
entry
A.SSE.2 Use the structure of an expression to
identify ways to rewrite it
A.SSE.3 Choose and produce an equivalent form
of an expression to reveal and explain properties
of the quantity represented by the expression
A.APR.1 Understand that polynomials form a
system of analogous to the integers, namely, they
are closed under the operations of addition,
subtraction and multiplication; add, subtract, and
multiply polynomials
A.A.13
Add, subtract, and multiply monomials
and polynomials
A.A.19 Identify and factor the difference of two
perfect squares
A.A.20 Factor algebraic expressions completely,
including trinomials with a lead coefficient of one
(after factoring a GCF)
 Add/subtract polynomials
 Multiply polynomials
 Use prime factorization
 Identify GCF
 Factor quadratic trinomials
 Apply multiple types of factoring
 What are polynomials and how do we classify them?
 How do we add and subtract polynomials?
 How do we multiply polynomials?
 What are special products of polynomials?
 What is prime factorization? How do we factor polynomials?
 How do we factor trinomials?
 How do we factor trinomials where a ¹ 1?
 How do we factor using special products?
 How do we factor polynomials completely?
 How do we factor polynomials completely? (Day 2)
 Review
 Test
Quizzes
Exit Tickets
Hanger project
Unit 9 Test
Binomial, trinomial, polynomial, quadratic, standard form, leading coefficient, FOIL, difference of two
squares, GCF, prime factorization, expression, factor, factoring, perfect-square trinomial,
Resources:
Big Ideas Textbook
Algebra 1 MES22
Unit 9: Polynomials and Factoring
(9.1)
What are polynomials and how do we classify them?
HW #1: pp. 362-364/ #5 – 12, 13 – 20
(9.2) How do we add and subtract polynomials?
HW #2: pp. 362 – 364/ #23 – 40 (evens), 55, 57
(9.3)
How do we multiply polynomials?
HW #3: pp. 369 – 371/ #21 – 30, 35 – 40
(9.4)
What are special products of polynomials?
HW #4: pp. 375 /# 3 – 10, 11, 13, 15 – 19, 31, 39, 40
(9.5)
What is prime factorization? How do we factor polynomials using the GCF?
HW #5: pp. 381 – 383/ #25 – 30, 49 – 52
(9.6)
How do we factor trinomials?
HW #6: pp. 389 – 391 / #3 – 5, 11 – 14, 20 – 24
(9.7)
How do we factor trinomials where a ¹ 1?
HW #7: pp. 395 – 397/ #3, 5, 7, 11, 14, 16, 18, 20, 24, 37, 38
(9.8)
How do we factor using special products?
HW #8: pp. 401 – 403/ #2, 3 – 5, 15 – 21, 23, 25*, 43
(9.9)
How do we factor polynomials completely?
HW #9: pp. 407 – 409/ #1, 11 – 22 (evens), 37, 39
(9.10) How do we factor polynomials completely (Day 2)
HW #10: pp. 407 – 409/ #2, 11 – 22 (odds), 35a, 40
Review
Test
Unit Title: Graphing Quadratic Functions
 What are characteristics of quadratic
functions?
 Transformations on the standard quadratic
function
Grade Level: 9th
Unit Length: 8 days
 How do different transformations affect the
parabola?
 When is each type of form of a quadratic
equation necessary?
 Can we compare growth rates of each type of
function we have studied?
A.R.8 Use mathematics to show and understand
mathematical phenomena
CED.A.2 Graph equations in two or more
variables to represent relationships between
quantities; graph equations on coordinate axes
with labels and scales
A.G.4 Identify and graph, linear, quadratic, absolute
SSE.B.3a Factor a quadratic to reveal the zeros of value and exponential functions
the function it defines
APR.B.3 Identify zeros of polynomials when
A.G.5 Investigate and generalize how changing the
suitable factorizations are available, and use the
coefficients of a function affects its graph
zeros to construct a rough graph of the function
defined by the polynomial
A.G.10 Determine the vertex and axis of symmetry
IF.B.4 For a function that models a relationship
of a parabola, given its graph
between two quantities, interpret key features of
graphs in terms of the quantities, and sketch
A.A.41 Determine the vertex and axis of symmetry
graphs showing key features given a verbal
of a parabola, given its equation
description of the relationship
IF.C.7a Graph... quadratic functions and show
A2.S.51 Determine the domain and range of a
intercepts, maxima, and minima
function from its graph
IF.B.3 Identify the effect on the graph of
replacing f(x) by kf(x), f(x)+k, f(x+k) for specific
values of k (both positive and negative); find the
value of k given the graphs. Experiment with
cases and illustrate an explanation of the effects
on the graph using technology
IF.C.8a Use the process of factoring in a
quadratic function to show zeros, extreme values,
and symmetry of the graph, and interpret in terms
of a context
IF.C.9 Compare properties of two functions each
represented in a different way (algebraically,
graphically…)
IF.B.6 Calculate and interpret the average rate of
change of a function over a specified interval.
Estimate the rate of change from a graph.
LE.A.3 Observe using graphs and tables that a
quantity increasing exponentially eventually
exceeds a quantity increasing linearly,
quadratically, or as a polynomial function
 Identify characteristics of a quadratic function
 Graph quadratic equations from standard form



Determine how the value of a coefficient affects a quadratic function
Find the vertex of a quadratic function
Graph quadratic equations from vertex form

 What are the characteristics of quadratic functions? How do we graph quadratic functions?
 How does the value of c affect the graph of a quadratic function?
 How can we find the vertex of the graph of f (x) = ax 2 + bx + c ?
 How can we describe the graph of a quadratic in vertex form?
 What are characteristics of the graph f (x) = (x - p)(x - q)?
 How can we compare the growth rates of linear, exponential, and quadratic functions?
 Review
 Test
Quizzes
Exit Tickets
Unit 10 Test
Revolution K12
Quadratic function, vertex, axis of symmetry, parabola, standard form, vertex form, zeros, translation,
maximum, minimum, intercept form, average rate of change
Resources:
Big Ideas Textbook
Algebra 1 MES22
Unit 10: Graphing Quadratic Functions
ALL GRAPHS MUST BE ON GRAPH PAPER
(10.1) What are the characteristics of quadratic functions? How do we graph quadratic functions?
HW #11: pp. 423 #1 – 4, 5, 9, 21 – 23, 33, 34
(10.2) How does the value of c affect the graph of a quadratic function?
HW #12: pp. 429 #3, 5, 7, 9, 11, 18
(10.3) How can we find the vertex of the graph of f (x) = ax 2 + bx + c ?
HW #13: pp. 436 #3, 5, 7, 9, 13, 14, 19, 21, 22
(10.4) How can we describe the graph of a quadratic in vertex form?
HW #14: pp. 446 #31 – 34, 35 – 38, 39, 41
(10.5) What are characteristics of the graph f (x) = (x - p)(x - q)?
HW #15: pp. 455 #7, 9, 11, 21, 22, 31 – 36
(10.6) How can we compare the growth rates of linear, exponential, and quadratic functions?
HW #16: pp. 465 #4, 9 – 11, 15 – 18, 23, 24, 36
Review
Test

INTEGRATED ALGEBRA UNIT 1

Transcription

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