INTEGRATED ALGEBRA UNIT 1 - Manhattan Center for …mcsmportal.net/wp-content/uploads/2015/04/Algebra-Co… · · 2015-05-01INTEGRATED ALGEBRA UNIT 1 Unit Title: ... algebraic expressions

INTEGRATED ALGEBRA UNIT 1

Unit Title: Foundations of Algebra Grade Level: 9th

Unit Length: 9 days

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.

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?

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 Grade Level: 9th

Unit Length: 15 days


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


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 real-

world problems?

How can you use units to write and solve

proportions?

Common Core Learning Standards: 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.

New York State / Content Standards: 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:

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? How can we apply our skills from Unit 2?

Review

Test


Quizzes

Do Now responses



Exit Slips

Homework

Notebook check quiz


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


Unit Title: Inequalities Grade Level: 9th

Unit Length: 9 days


Patterns and relationships can be

represented graphically, numerically, and

symbolically.

How to use the unknown, constraints and

their relationships to model a situation


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?

Common Core Learning 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.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

New York State / Content 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.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

Do Now responses



Exit Slips

Homework

Notebook check quiz


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 Grade Level: 9 Unit Length: 9 days

Enduring Understandings:

What is a function?

How do functions relate to mathematics?


How can patterns, relations, and functions

be used as tools to best describe and help

explain real-life relationships?


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

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

New York State Standards:

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

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

Do Now responses



Homework

Notebook check

Summative Assessment:

Unit test


linear relationships, translate; dependent variable; independent variable; profit; co-ordinate grid; x- and y-

axis; 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 Grade Level: 9 Unit Length: 10 Days

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?


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?

Common Core Learning Standards: 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

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 x-

or 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

Skills:

Identify linear functions given a table of values

Identify linear functions given its graph

Identify linear functions given its equation

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

Do Now responses



Homework

Notebook check quiz

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

Grade Level: 9 Unit Length: 9 days


How to graph systems of equations

Which algebraic method is most useful

Translating word problems

Graph linear equations

Graph linear inequalities


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?

Common Core Learning Standards: 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…


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

Do Now responses



Homework

Notebook check quiz


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

Grade Level: 9th

Unit Length: 8 days


How to multiply and divide monomials

What parts of a polynomial represent

terms, factors and coefficients

How do exponential functions operate?


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.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.APR.6 Rewrite simple rational expressions in

different forms; write a(x)

/b(x) in the form q(x) + r(x)

/b(x),

where a(x), b(x), q(x), and r(x) are polynomials with

the degree of r(x) less than the degree of b(x), using

inspection, long division, or, for the more complicated

examples, a computer algebra system.

N.RN.1 Explain how the definition of the

meaning of rational exponents follows from the

extending properties of integer exponents to those

values, allowing for a notation for radicals in

terms of rational exponents

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


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

remainder

A.N.3 Perform the four arithmetic operations using

like and unlike radical terms and express the

result in simplest form

A.N.4 Understand and use scientific notation to

compute products and quotients of

numbers greater than 100%

A.N.6 Evaluate expressions involving factorial(s),

absolute value(s), and exponential

expression(s)

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 Grade Level: 9th

Unit Length: 8 days


Connecting knowledge of linear and

exponential functions to sequences and

patterns


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

functions

How to factor different types of

expressions


How can you find the GCF of monomials?

When factoring what numbers do we need to

find?

Can you factor expressions with more than

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 ¹1?

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 ¹1?

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 Grade Level: 9th

Unit Length: 8 days


What are characteristics of quadratic

functions?

Transformations on the standard quadratic

function


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?


CED.A.2 Graph equations in two or more

variables to represent relationships between

quantities; graph equations on coordinate axes

with labels and scales

SSE.B.3a Factor a quadratic to reveal the zeros of

the function it defines

APR.B.3 Identify zeros of polynomials when

suitable factorizations are available, and use the

zeros to construct a rough graph of the function

defined by the polynomial

IF.B.4 For a function that models a relationship

between two quantities, interpret key features of

graphs in terms of the quantities, and sketch

graphs showing key features given a verbal

description of the relationship

IF.C.7a Graph... quadratic functions and show

intercepts, maxima, and minima

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


A.R.8 Use mathematics to show and understand

mathematical phenomena

A.G.4 Identify and graph, linear, quadratic, absolute

value and exponential functions

A.G.5 Investigate and generalize how changing the

coefficients of a function affects its graph

A.G.10 Determine the vertex and axis of symmetry

of a parabola, given its graph

A.A.41 Determine the vertex and axis of symmetry

of a parabola, given its equation

A2.S.51 Determine the domain and range of a

function from its graph


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) = ax2 +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) = ax2 +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

Documents

INTEGRATED ALGEBRA UNIT 1 - Manhattan Center for …mcsmportal.net/wp-content/uploads/2015/04/Algebra-Co… · · 2015-05-01INTEGRATED ALGEBRA UNIT 1 Unit Title: ... algebraic expressions