subject(s) fts grade/course th th unit of study pacing...

Subject(s) FTS

Grade/Course 11th and 12th grade

Unit of Study #1: Linear Relations & Functions & systems of Linear Equations & Inequalities

Unit Type(s) Skills-based

Pacing 3 weeks plus 1 week re-teaching

Overarching Standards:

Math Practices: (Mathematical Practices #1 and #3 describe a classroom environment

that encourages thinking mathematically and are critical for quality teaching and

learning.)

Determine whether a given relation is a function and perform operations with

functions

Evaluate and find zeros of linear functions using function notation

Graph and write functions and inequalities

Write equation of parallel and perpendicular lines

Model data using scatter plots and write prediction equations

Identify and graph piecewise functions

Graph linear inequalities

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Priority and Supporting Standards: (CCSS/Content Standards, ELL) Explanations and Examples:

CC.9-12.A.CED.2 Create equations in two or more variables to represent relationships

between quantities; graph equations on coordinate axes with labels and scales.

(1-4) The mileage in miles per gallon (mpg) for city

and highway driving of several recent model-year cars

are given.

a) Find a linear equation that can be used to find a

car’s highway mileage based on its city mileage

b) Model J’s city mileage is 19 mpg. Use your

equation to predict its highway mileage

c) Highway mileage for Model J is 26 mpg. How well

did your equation predict the mileage? Explain.

Model City Highway

(mpg)

A 24 32

B 20 29

C 20 29

D 20 28

E 23 30

F 24 30

G 27 37

H 22 28

CC.9-12.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 its domain, then f(x) denotes the output

of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

(1-1) State the domain and range of the relation below. Then state whether the relation is

a function. Explain. {(1, 2), (2, 4), (-3, -6), (0,0)}

(1-1) The temperature of the atmosphere decreases about 5F for every 1000 ft that an

airplane ascends. Thus, if the ground-level temperature is 95F, the temperature can be

found using the function t(d) = 95 – 0.005d, where t(d) is the temperature at a height of

d feet. Find the temperature outside of an airplane at 500 ft. 750ft. 5000ft

CC.9-12.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.

(1-7) The income tax brackets for the District of Columbia are listed in the tax table.

Income Tax Bracket

Up to $10,000 5%

More than $10,000, but

no more than $30,000

7.5%

More than $30,000 9.3%

a) What type of function is described by the tax rate?

b) Write the function if x is income and f(x) is the tax rate.

c) Graph the tax brackets for different taxable incomes.

d) Alicia Davis lives in the District of Columbia. In which tax bracket is Ms. Davis if

she made $36,000 last year?

CC.9-12.F.IF.7b Graph square root, cube root, and piecewise-defined functions,

including step functions and absolute value functions

(1-7) Write the equation for the following piecewise function. State the domain and

range.

CC.9-12.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

graphs showing key features given a verbal description of the relationship. Key

features include: intercepts; intervals where the function is increasing,

decreasing, positive, or negative; relative maximums and minimums;

symmetries; end behavior; and periodicity. *

The student council is sponsoring a pancake breakfast to raise money for the senior

prom. You estimate that 200 adults and 250 student s will attend. Let x represent the

cost of an adult ticket and y represent the cost of a child’s ticket. Write an equation that

you will use to find out what ticket prices should be set at in order to raise $3,800. Also,

state the domain and range of your function.

CC.9-12.F.BF.1.b Combine standard function types using arithmetic operations (1-2) Find f(x) + g(x), f(x) - g(x), f(x) ∙ g(x), f(x) ÷ g(x), given:

1)(

x

xxf and

1)( 2 xxg .

CC.9-12.F.BF.1.c Compose functions

(1-2) A bicycle is on sale for 15% off of its regular retail price $199.99. The sale tax in

New Jersey (where the bicycle was purchased) is 5%. What is the total price? Write and

solve a composition of function that answers this question.

CC.9-12.F.IF.8 Write a function defined by an expression in different but equivalent

forms to reveal and explain different properties of the function

(1-5) What is the slope and y-intercept of this equation: 2x + y = -3?

CC.9-12.G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use

them to solve geometric problems (e.g., find the equation of a line parallel or

perpendicular to a given line that passes through a given point).

(1-5) Write an equation of the line parallel to y = ½ x + 3 through the point (-6, 1).

(1-5) Write an equation of the line perpendicular to y = -4x- 1 through the point (8, -3)

CCC.9-12.A-REI.12. Graph the solutions to a linear inequality in two variables as a

half-plane (excluding the boundary in the case of a strict inequality), and graph the

solution set to a system of linear inequalities in two variables as the intersection of the

corresponding half-planes.

(1-8) Write and graphically solve an inequality that models the situation given below.

Bridget is selling bracelets and earrings to make money for summer vacation. She

decides to sell the bracelets for $2.00 each and the earrings for $3.00 each. She wants to

make at least $500.

Essential Question(s): Enduring Understanding(s):

How do variables help you model real-world situation?

How do you solve an equation or inequality?

How can you model data with a linear function?

Does it matter which form of a linear equation you use?

The slopes of two lines in the same plane indicate how the lines are related.

Linear functions can be represented by either the slope-intercept form, point-

slope form, or stand dorm. One version can be transformed to another as

needed

The shortest distance between a point and a line is the perpendicular distance

The slopes of perpendicular lines are negative reciprocals of each other.

Concepts (Students will…)

DOK Skills (What students need to be able to

do)

21st Century Skills/ Life and Career

Skills

Review functions and relations

and operation with functions

Evaluate, find the zeros of,

write, and graph linear functions

and inequalities.

Write equations of parallel and

perpendicular lines.

Use scatter plots and piecewise

functions to model real world

data.

Review concepts of solving

systems of linear equations and

inequalities and basic operations

with matrices

Identify different forms of linear

equations

Determine which form of a linear

equation is most easily found with

the given information

Covert between various forms of

linear equations

Make a scatter plot of linear data

Determine the correlation of

linear data

Use linear regression to find the

line of best fit of linear data with a

graphing calculator.

Use the correlation coefficient to

analyze linear data with a graphing

calculator

Assessments Evidence

Assured Assessment(s) (Performance Based/Curriculum Based)

Summer Packet Quiz

Mid-Chapter Quiz

Unit 1 Test

Other Evidence:

Entrance slips

Exit slips

Observations

Learning Plan

Days CCSS DOK Instructional Practices Ensured Assignments # of Days

per Section Differentiation/ Resources Teacher Notes

1 1-1 Relations and Function

CW: Section 1-1 Relations and

Functions Practice wkst

HW: Pg 9-11 #8-13, 15, 49,55

1

D:

R:

2 1-2 Compositions of Functions

CW: 7.4 Function Operations and

Composition of Functions Guided

Notes

HW: Pg 17-19 #3, 5, 8, 14

3

D:

R: S-B-S Homework Key

http://www.khanacademy.or

g/math/algebra/algebra-

functions/eval-function-

expressions/e/functions_3

3

CW: Operations with Functions

(Kuta) Practice

HW: Pg 17-19 #12, 16, 17, 19, 24, 31

D: Teacher chosen pairs


4

CW: Composition of Functions

HW: kuta wkst

D:


5 1-3 Graphing Linear Functions

CW: Section 1-3 Graphing Linear

Equations Practice

HW: Pg 23-25 #6, 7, 9, 10, 11, 29,

35, 38

1

D:


Graphing Linear

Functions cheat sheet

Need straightedges

6 1-4 Writing Linear Equations

CW: 10-5 Reteaching Wkst

HW: Pg 29 # 3, 11, 13, 16, 27

1

D:


7 1-5 Writing Equations of Parallel

and Perpendicular Lines

CW: Practice 6-5 Parallel and

Perpendicular Lines

HW: Pg 35 # 4-8, 28, 36

1

D:


8 CW: Mid-Chapter Quiz (pg 31)

1

Open Notes- Not

Open Book

http://www.khanacademy.org/math/algebra/algebra-functions/eval-function-expressions/e/functions_3




HW: Composition of Functions Extra

Practice wkst

9 1-6 Modeling Real-World Data with

Linear Functions

CW: Section 1.6 Modeling Real

World Data Correlation Coefficient

Wkst

HW: Pg 43-44 # 12, 13

2

D:


Need Graphing

Calculators

Need straightedges

10

CW: Scatterplot Calculator Activity

HW: Pg 44 # 14-19 all

D:


11

CW: Summer Packet Quiz Review

HW: Complete Review Packet

1

D:


12

CW: Summer Packet Quiz

HW: Graphing Lines Practice

1

D:


13 1-7 Piecewise Functions

CW: Introduction to Piecewise

Functions (Discovery Activity)

*Focus on graphing given functions

HW: Pg 48 # 4, 11, 16

2

D:


Need Patty Paper

and colored pencils

14

CW: Focus on Step Functions

HW: Pg 48 # 15, 26, 28

D:


15 1-8 Graphing Linear Inequalities

CW: Graphing linear inequalities in

all forms (standard, slope-intercept,

point-slope)

HW: Pg 55 # 5-23 odd and #8

1

D:


Remind students

the difference

between solid and

dotted lines.

16 2-6 Solving Systems of Linear

Inequalities

CW: Guided Notes on Solving

Systems of Linear Inequalities (go

along with PPT)

HW: Pg 109 # 4-6, 8, 9, 12, 23

1

D: Use color pencils to

more easily see overlapping

areas

R: S-B-S Homework Key,

PPT available

17 1-1 Relations and Functions

CW: I = PRT Review

HW: Wkst

1

D:


18

CW: Review for Unit 1 Test

HW: Chapter 1 Study Guide and

Assessment (pg57-61) #1-69 odd

1

D:


19 Unit 1 Test (Questions #1-4) 2

20 Unit 1 Test (Questions #5-11)

Interdisciplinary Connection

Sports- Find the relation between data sets

Aviation- writing temperature of the atmosphere as a function of the height in feet

Geography- Computing the distance that radio waves can travel as a function of the surrounding temperature.

Business- I=PRT

Unit Vocabulary Technology Resources

Best fit line

Boundary

Coinciding lines

Composite

Composition of functions

Correlation coefficient

Domain

Function

Function notation

Goodness of fit

Half plane

Linear equation

Linear function

Linear inequality

Model

Parallel lines

Perpendicular lines

Piecewise function

Point-slope form

Prediction equation

Range

Regression line

Relation

Scatter plot

Slope

Slope-intercept form

Standard form

Step function

x-intercept

y-intercept

Interactive Smartboard

https://www.pearsonsuccessnet.com

My Math Video

Solve It!

Student Companion

o Vocabulary Support

o Got It? Support

Dynamic Activity

Online Problems

Additional problems

English Language Learner Support (TR)

Activities, Games, and Puzzles

Teaching with TI Technology with CD-Rom

Ti-Nspire Support CD-Rom

http://www.poweralgebra.com

http://www.purplemath.com

http://smarterbalanced.org

http://www.map.mathshell.org.uk/materials/index.php

http://illustrativemathematics.org/

http://insidemathematics.org/index.php/tools-for-teachers/problems-of-the-month

http://www.ets.org/k12/commonassessments

http://www.ccebos.org/qpa/publications-products/common-core/

http://www.corestandards.org

http://www.sharemylesson.com/

http://www.mathplayground.com

Kuta Infinite Software

Pre-Algebra

Algebra I

Geometry

Algebra II

https://www.pearsonsuccessnet.com/

http://www.poweralgebra.com/

http://www.purplemath.com/

http://smarterbalanced.org/






http://www.corestandards.org/


http://www.mathplayground.com/

Subject(s) FTS


Unit of Study #2: Systems of Linear Equations and Inequalities


Pacing 3weeks plus 1 week re-teaching

Overarching Standards: Math Practices: (Mathematical Practices #1 and #3 describe a classroom environment


learning.) Solve systems of equations graphically and algebraically

Solve systems involving three variables using the calculator

Solve two variable systems of equations graphically and algebraically

Graph systems of inequalities

Using linear programming to solve applications (optional)

Find determinants and inverses of matrices








8. Look for and express regularity in repeated reasoning. Priority and Supporting Standards: (CCSS/Content Standards, ELL) Explanations and Examples: CC.9-12.A.CED.2 Create equations in two or more variables to represent

relationships between quantities; graph equations on coordinate axes with labels

and scales.

Plant A and Plant B are on different watering schedules. This affects their rate of growth.

Compare the growth of the two plants to determine when their heights will be the same.

Let W = number of weeks

Let H = height of the plant after W weeks

Given each set of coordinates, graph their corresponding lines.

Solution:

Write an equation that represent the growth rate of Plant A and Plant B.

Solution:

Plant A: H = 2W + 4

Plant B: H = 4W + 2

• At which week will the plants have the same height?

Solution:

The plants have the same height after one week.

Plant A: H = 2W + 4 Plant B: H = 4W + 2

Plant A: H = 2(1) + 4 Plant B: H = 4(1) + 2

Plant A: H = 6 Plant B: H = 6

After one week, the height of Plant A and Plant B are both the same. CC.9-12.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.

Write and graph a piecewise function, f(x), that representative

of the table shown to the left.

Solution:

5 if 5

99.4x2 if 6

99.1x0 if 8

)(

x

xf

CC.9-12. N.VM.6 Use matrices to represent and manipulate data You’re going to the mall with your friends and you have $200 to spend from your recent

birthday money. You discover a store that has all jeans for $25 and all dresses for $50.

You must use your money to purchase exactly 6 items of clothing.

Solution:

Let J = number of jeans and D = number of dresses.

System of Equations:

J + D = 6

25J + 50D = 200

Corresponding Matrix:

Final Answer: You must purchase 4 pairs of jeans and 2 dresses.

CC.9-12. N.VM.7. Multiply matrices by scalars to produce new matrices

Find

720

1462

Solution:

1440

2812

CC.9-12. N.VM.8. Add, subtract, and multiply matrices of appropriate dimensions.

Complete the indicated operation below. If not possible write ‘not possible’ and explain

why.

A =

1440

2812 B =

254

321

(a) A + B (b) B – A (c) AB

Solution:

(a)

1694

51013 (b)

1214

1611 (c) DNE

CC.9-12. N.VM.9. Understand that, unlike multiplication of numbers, matrix

multiplication for square matrices is not a commutative operation, but still satisfies the

associative and distributive properties. A =

254

321 B =

4156

2763

3481

Why is AB possible, yet BA is not?

Solution: When multiplying matrices the number of columns in the first matrix must

match the number of rows in the second matrix. Multiplication of matrices is not

commutative like multiplication of integers are. CC.9-12. A.REI.5 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.

Solve the system of equations below using the substitution and elimination approaches.

Compare your answers.

2x + 5y = 16

3x + 2y = 13

Solution: x = 3 and y = 2 CC.9-12. A.REI.6 Solve systems of linear equations exactly and approximately (e.g.,

with graphs), focusing on pairs of linear equations in two variables.

Solve the following system of equations graphically.

4x + 6y = 12

2x + 2y = 6

Solution: (3, 0)

CC.9-12. A.REI.9 Find the inverse of a matrix if it exists and use it to solve systems of

linear equations (using technology for matrices of dimension 3 × 3 or greater).

A group took a trip on a bus, at $3 per child and $3.20 per adult for a total of $118.40.

They took the train back at $3.50 per child and $3.60 per adult for a total of $135.20.

How many children, and how many adults?

Solution:

Let C = number of children and A= number of adults.

Find the inverse of the matrrix.

Use the inverse matrix to solve the problem

Final Answer: There are 16 children and 22 adults. CC.9-12. A-REI 11. Explain why the x-coordinate of the points where the graphs of

y=f(x) and y =g(x) intersect are the solutions of the equation f(x) = g(x); find the

solutions approximately, or find successive approximations.

Charlene makes $10 per hour babysitting and $5 per hour gardening. She wants to make

at least $80 a week, but can work no more than 12 hours a week.

(a) Write a system of linear equations

(b) Graph the solution to the system.

(c) Describe at least two possible combinations of hours that Charlene could work at each

job.

(d) What does the intersection of the two lines represent?

Solution:

(a) 10x + 5y > 80

x + y < 12

(b)

(c) 8 hours babysitting and 2 hours gardening or 6 hours

babysitting and 4 hours gardening.

(d) 4 hours of babysitting and 8 hours of gardening is the

maximum number hours that she can work at both jobs

at the same time and still stay within her criteria.

CC.9-12.A-REI.12. Graph the solutions to a linear inequality in two variables as a half-

plane (excluding the boundary in the case of a strict inequality), and graph the solution

set to a system of linear inequalities in two variables as the intersection of the

corresponding half-planes

Students are raising money for a field trip by selling scented candles and specialty soap.

The candles cost $0.75 each and will be sold for $1.75, and the soap costs $1.25 per bar

and will be sold for $3.25. The students need to raise at least $200 to cover their trip

costs.

a. Write an inequality that relates the number of candles c and the number of bars of soap

s to the needed income.

b. The wholesaler can supply no more than 80 bars of soap and no more than 140

candles. Graph the inequality from part a and these constraints, using number of candles

for the vertical axis.

c. What does the shaded area of your graph represent?


What methods can be used to solve systems of equations?

How can a system of equations be solved graphically versus algebraically?

How can data be modeled with a matrix?

What operations can be used to solve matrices?

What does the graphical representation of system of inequalities represent?

How is a maximum or minimum value of a function defined for a polygonal

convex set be determined?

How do you solve a system of inequalities?

How does representing functions graphically help you solve a system of

equations?

How does a writing equivalent equation help you solve a system of equations?

A variety of representations of linear systems of equations, including matrices,

are used to model and solve real-world

problems.

The characteristics of linear inequalities and their representations are useful in

solving real-world problems.

Systems of linear equations and/or inequalities are used to model and solve real-

world problems involving 2 variables.

A system of equations is solved by finding a set of values that replace the

variables in the equations and make each equation true.

A point of intersection (x, y) of the graphs of the functions f and g is a solution

of the system y = f(x) , y =g(x)

A system of inequalities can be solved in more than one way. Graphing is

usually the most appropriate method.

Concepts (Students will…) DOK Skills (What students need to be able to

do) 21st Century Skills/ Life and Career

Skills Solve systems of equations

graphically

Solve systems of equations

algebraically

Solve systems of equations involving

three variables

Model data using matrices

Add, subtract, and multiply matrices

Evaluate determinants

Find inverses of matrices

Solve systems of equations by using

inverses of matrices

Graph systems of inequalities

Find the maximum and minimum

value of a function defined for a

polygonal convex set.

Use linear programming procedures

to solve applications

Recognize situations where exactly

one solution to a linear programming

application may not exist

Students will use substitution and

elimination methods to write equivalent

equations until they get an equation with

only one variable.

Solve a system of linear equations by

graphing the equations to find the point(s)

of intersection

Identify the best approach to use in order to

solve a system of equations

Determine the maximization or

minimization factor

Explain why producing a specific number

of objects in a given scenario is a profitable

or not

Assessment Evidence Assured Assessments: (Performance Based/Curriculum Based)

Quiz System of Equations

Quiz Matrices

Quiz Systems of Equations and Matrices

Linear Programming Evaluation of Process

Unit 2 Test

Other Evidence:

Entrance slips

Exit slips

Observations

At home practice

Learning Plan

Days CCSS DOK Instructional Practices Ensured Assignments

# of

Days per

Section

Differentiation/

Resources Teacher Notes

21 2-1 Solving Systems of

Equations in Two

Variables: Substitution

Method

CW: 2-1 Study Guide: Solving Systems

of Equations in Two Variables

HW: pg 70-71 # 5, 6, 7, 11, 12, 14, 15

5 D: S-B-S guided notes

R:

http://www.mathwarehous

e.com/algebra/linear_equat

ion/systems-of-

equation/index.php

Do not follow directions in book

for hw only use substitution

method.

http://www.mathwarehouse.com/algebra/linear_equation/systems-of-equation/index.php




22 Elimination Method CW: Solving Systems of equations Kuta

HW: pg 71 #13, 16-19, 21, 22

D: S-B-S guided notes

R:

http://learnzillion.com/less

ons/162-solve-systems-of-

equations-using-

elimination-4

Do not follow directions in book

for hw only use elimination

method.

23 Substitution vs

Elimination Method

CW: Solving Systems of Equations-

Which Strategy Works Best?

HW: pg 70-71 # 9, 20, 23-26

D:

R:

Focus on why one will use one

method over the other.

*encourage students to solve

each problem using both

methods and ask themselves

after each question, ‘which

method was simpler?’

24 Word problems CW: Writing and Solving Systems of

Equations

HW: pg 70-71 # 10, 32, 33


R:

http://www.shmoop.com/li

near-equation-

systems/translating-word-

problems.html

25 Review of Solving

Systems of Equations

CW: System of Linear Equations-

Exercises

HW: Complete Review Packet

D:

R:

http://www.quia.com/cb/79

607.html

Encourage students to think

about which method is easier for

each type of problem

26 CW: Quiz Solving Systems of

Equations

HW: TBD based on how much is

completed in class

1 *This Quiz will not take the

entire period. After Quiz review

how to enter a system into a

matrix.

27 2-3 Matrices CW: Introduction to Matrices wkst

HW: pg 82 # 2, 4, 15-20 all

4 D:

R:

http://coolmath.com/algebr

a/24-matrices/02-adding-

subtracting--01.htm

Terminology (row, column,

elements)

How to write a system of

equations as a matrix

28 2-3 Add. Subtract Matrices CW: 13-2 Introduction to Matrices

(www.algebra1.com/extra_examples)

HW: pg 83 # 8, 9, 10, 28, 32

D:

R: http://www.mathsisfun.co

m/algebra/matrix-

calculator.html

Show students online matrix calc

so they can check their work at

home.

http://learnzillion.com/lessons/162-solve-systems-of-equations-using-elimination-4




http://www.shmoop.com/linear-equation-systems/translating-word-problems.html




http://www.quia.com/cb/79607.html

http://www.quia.com/cb/79607.html

http://coolmath.com/algebra/24-matrices/02-adding-subtracting--01.htm



http://www.algebra1.com/extra_examples

http://www.mathsisfun.com/algebra/matrix-calculator.html



29 2-3 Multiply Matrices CW: 2-3 Practice: Modeling Real-

World Data with Matrices wkst

HW: 83 # 27, 31, 33, 34, 38, 43

D: PPT sides available that

coincide with practice

worksheet

R:

http://www.glencoe.com/se

c/math/studytools/cgi-

bin/msgQuiz.php4?isbn=0-

02-834135-

X&chapter=2&lesson=3&t

itle=scq (self check quiz)

Scaler Multiple and 2x2 matrices

30 2-2, 2-

3

RREF CW: Using Technology to help solve

matrix problems with more than two

variables.

HW: pg 106 #1-4 only

D:

R: TI calculator guide for

step-by-step directions how

to input/ solve matrices.

Focus on using the TI-83 to

solve

http://www.glencoe.com/sites/co

mmon_assets/mathematics/TN_2

012/Alg2_se/CH04_895267.pdf

(pg55)

31 CW: Quiz: Systems of Equations and

Matrices

HW: pg 60 # 59-66 all

1 Quiz is 2 parts: calc and no calc.

32 2-6 Solving Systems of

Linear Inequalities

CW: Kuta practice “Solving Systems of

Inequalities”

HW: pg 110 # 9-12


R: TI- 83 graphing

calculators

Need graph paper for homework

assignment

33 Graphing systems of

inequalities, finding

vertices, calculating min

and max values.

CW: “Notes: Linear Programming”

HW: pg 110 # 13-16


R: TI- 83 graphing

calculators


assignment

*Partner work encouraged

34 CW: continue notes from day last class

HW: pg 110# 17-19


R: TI- 83 graphing

calculators


assignment

35 CW: 2-7 Study Guide: linear

programming

HW: pg 110 # 20-22


R:

http://prejudice.tripod.com/

ME30B/LP_Steps.htm


assignment

36 2-7 Linear Programming CW: Linear Programming practice

HW: Complete in class assignment

3 D: Small Groups activity

R: Extra practice examples

are available with s-b-s

answer keys (3.4 Linear

Programming Application

Problem)

*exit slip: Linear Programming

Evaluation of progress

http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-02-834135-X&chapter=2&lesson=3&title=scq






http://www.glencoe.com/sites/common_assets/mathematics/TN_2012/Alg2_se/CH04_895267.pdf



http://prejudice.tripod.com/ME30B/LP_Steps.htm

http://prejudice.tripod.com/ME30B/LP_Steps.htm

37 CW: Linear Programming practice #2

HW: pg 115 # 6

D: S-B-S guided practice

R:

http://www.youtube.com/w

atch?v=Z_aDBs9LWRY

38 CW: Linear Programming Using a Ti-

83 wkst

HW: pg 115 # 7

D: S-B-S guided practice

R:

http://www.math.ncsu.edu/

ma114/PDF/2.2.pdf

39 CW: Review for Unit 2 Test

HW: Chapter 2 Study Guide (pg 119-

123) # 1-16

1 D: S-B-S examples are

available

R:

http://www.cpalms.org/Pub

lic/PreviewResourceLesso

n/Preview/39920 (matrix

review activities)

Soft copies and keys are

available from the resource files

online

40 CW: Unit 2 Test (Part 1)

HW: Chapter 2 Study Guide (pg 119-

123) #20-27, 49-54

2

41 CW: Unit 2 Test (Part 2)

HW: Parent Functions packet

HW packet create a table of

values to graph each function

Interdisciplinary Connections

Financial Literacy: When is one cell phone plan cheaper than another?

Marketing/ Sales: Maximize profits or Minimizing costs

Critical Thinking/ Problem Solving


Additive Identity Matrix

Alternate Optiomal Solutions

Column Matrix

Consistent

Constraints

Dependent

Dimensions

Element

Elimination Method

Equal Matrices

Inconsistent

Independent

Infeasible

Linear Programming

m x n matrix

Matrix

Nth Order

Polygonal Convex Set

Row Matrix

Scalar

Square Matrix

Substitution Method

System of Equations

System of Linear Inequalities

Unbounded

Vertex Theorem

Zero Matrix

Texas Instrument Graphing Calculator



My Math Video

Solve It!

Student Companion


o Got It? Support

Dynamic Activity

Online Problems

Additional problems




http://www.youtube.com/watch?v=Z_aDBs9LWRY

http://www.youtube.com/watch?v=Z_aDBs9LWRY

http://www.math.ncsu.edu/ma114/PDF/2.2.pdf

http://www.math.ncsu.edu/ma114/PDF/2.2.pdf

http://www.cpalms.org/Public/PreviewResourceLesson/Preview/39920
















https://www.desmos.com/calculator - must use Google Chrome

http://www.glencoe.com/sec/math/studytools/amclblr.shtml


Pre-Algebra

Algebra I

Geometry

Algebra II












https://www.desmos.com/calculator


Subject(s) FTS


Unit of Study #3: The Nature of Graphs with a Concentration on Polynomials and Rational Functions


Pacing 3weeks plus 1 week re-teaching

Overarching Standards: Math Practices: (Mathematical Practices #1 and #3 describe a classroom environment


learning.) Graph functions, relations, inverses, and inequalities

Analyze families of graphs

Investigate symmetry, continuity, end behavior, and transformations of graphs

Find asymptotes and extrema of functions

Solve problems involving direct, inverse, and joint variation








8. Look for and express regularity in repeated reasoning. Priority and Supporting Standards: (CCSS/Content Standards, ELL) Explanations and Examples: CC.9-12.A.CED.2 Create equations in two or more variables to represent relationships

between quantities; graph equations on coordinate axes with labels and scales.

Find a formula for the volume of a single-scoop ice cream cone in terms of the

radius and height of the cone. Rewrite your formula to express the height in

terms of the radius and volume. Graph the height as a function of radius when

the volume is held constant.

CC.9-12. F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x),

f(kx), and 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. Include recognizing even and odd functions from their

graphs and algebraic expressions for them.

Compare the shape and position of the graphs of (𝑥) = 𝑥2 and 𝑔(𝑥) = 2𝑥2 , and

explain the differences in terms of the algebraic expressions for the functions.

CC.9-12. 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

Sketch the graph and identify the key characteristics of the function described below.

CC.9-12.A.APR.1 Understand 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.

Simplify:

(a)

(b) (x3 + 3x2 -2x + 5)(x -7)

CC.9-12.A.APR.2 Know and apply the Remainder Theorem: For a polynomial p(x)

and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x -

a) is a factor of p(x).

(a) Let p(x) = x3-3x4+8x2- 9x + 30 Evaluate p(–2).

What does your answer tell you about the factors of p(x)?

(b) Consider the polynomial function: P(x) = x4 − 3x3 + ax2-6x+14, where a is an

unknown real number.

If (x-2) is a factor of this polynomial, what is the value of a?

CC.9-12.A.APR.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

Factor the expression x3 + 4x2 - 59x -126 and explain how your answer can be

used to solve the equation x3 + 4x2 - 59x -126 = 0.

CC.9-12.F.BF.B.4 Find inverse functions.

Example: Draw the graph of the inverse of f(x) = - 3/2 x - 3 on the coordinate grid

below.

Solution:

CC.9-12.A.CED.3 Represent constraints by equations or inequalities, and by systems

of equations and/or inequalities, and interpret solutions as viable or non-viable options

in a modeling context

A club is selling hats and jackets as a fundraiser. Their budget is $1500 and they

want to order at least 250 items. They must buy at least as many hats as they

buy jackets. Each hat costs $5 and each jacket costs $8.

- Write a system of inequalities to represent the situation.

- Graph the inequalities.

- If the club buys 150 hats and 100 jackets, will the conditions be

satisfied?

- What is the maximum number of jackets they can buy and still

meet the conditions?

CC.9-12.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

graphs showing key features given a verbal description of the relationship. Key

features include: intercepts; intervals where the functions is increasing, decreasing,

positive, or negative; relative maxima and minima; symmetries; end behavior; and

periodicity

A rocket is launched from 180 feet above the ground at time t = 0. The function

that models this situation is given by h = – 16t2 + 96t + 180, where t is measured

in seconds and h is height above the ground measured in feet.

o What is a reasonable domain restriction for t in this context?

o Determine the height of the rocket two seconds after it was launched.

o Determine the maximum height obtained by the rocket.

o Determine the time when the rocket is 100 feet above the ground.

o Determine the time at which the rocket hits the ground.

o How would you refine your answer to the first question based on your response to the

second and fifth questions?

CC.9-12.F.BF.1 Write a function that describes a relationship between two quantities.

a. Determine an explicit expression, a recursive process, or steps for calculation

from a context.

b. Combine standard function types using arithmetic operations.

You are making an open box out of a rectangular piece of cardboard with dimensions

40 cm by 30 cm, by cutting equal squares out of the four corners and then folding up the

sides. How big should the squares be to maximize the volume of the box? Draw a

diagram to represent the problem and write an appropriate equation to solve.


How do you use transformations to help graph absolute value functions?

What does the degree of a polynomial tell you about its related polynomial

function?

For a polynomial function, how are factors, zero(s), and x-intercepts related?

How are a function and its inverse function related?

How do you use factors to solve a polynomial?

What is an extraneous solutions?

Just as the absolute value of x is its distance from 0, the absolute value of f(x),

or |f(x)|, gives the distance from the line y = 0 for each value of f(x).

The simplest example of an absolute value function is f(x) = |x|.

The values a, b, and k, in the form y = a |x – h| + k determine how the parent

function y = |x| can be transformed.

The graph of a non-linear inequality contains all points on one side of a function

and may or may not include the points on the function itself.

The inverse of a function may or may not be a function

When you square each side of an equation, the resulting equation may have

more solutions than the original equation

If f and f-1 are functions and if either maps a to b, then the other maps b to a, ie:

(f◦f-1)(a) = (f-1◦ f)(a) = a.

The range of the relation is the domain of the inverse. The domain of the

relation is the range of the inverse.

A square root function is the inverse of a quadratic function that has a restricted

domain.

When you square each side of an equation, the resulting equation may have

more solutions than the original equation.

Some quantities are in a relationship where the ratio of corresponding values is

constant

The formula says that the ratio of all out-put pairs equals the constant k,

the constant of variation.

Factors of numbers can be used to factor and solve equations

(x - a) is a linear factor if and only if a is a root of the related polynomial

equation.

Solving an equation containing rational expression begins by multiplying each

side by the least common denominator of the rational expressions. (Introduce

extraneous solutions)

Concepts (Students will…) DOK Skills (What students need to be able to

do) 21st Century Skills/ Life and Career

Skills Review the concepts of

symmetry of graphs.

Identify and sketch families of

graph that include polynomials,

absolute value functions, greatest

integer functions, rational

functions, and square root

functions.

Identify the critical points and

end behavior of the graphs of

polynomial functions and solve

problems involving direct,

inverse, and joint variation.

Use various methods, including

technology, to locate and

approximate the zeros of

polynomial functions.

Examine the relationship of

locating zeros of a function to

solving for the rots of an

equation.

The strand of modeling real-

word data is extended to include

polynomial functions.

Level 1: Recall/Reproduction

Use algebraic tests to determine if

the graph of a relation is

symmetrical

Level 2: Skills/Concepts

Classify functions as even or odd

Identify transformations of simple

graphs

Graph polynomial, absolute value,

and radical inequalities in two

variables. Solve absolute value inequalities

Determine inverse of relations and

functions

Graph functions and their inverses

Determine whether a function is

continuous or discontinuous

Identify the end behavior of

functions

Determine whether a function is

increasing or decreasing on an

interval.

Construct and graph functions with

gap discontinuities

Find the extrema of a function

Graph rational functions

Determine vertical, horizontal, and

slant asymptotes Solve problems involving direct,

inverse and joint variation

Write a polynomial function given

a polynomial equation

Identify the degree of a polynomial

equation

Identify the highest power of a

polynomial function Write polynomial given its factors

and zeros

Identify the zeros of a polynomial

function by finding the x-intercepts

of its graph.

Assessment Evidence Assured Assessments: (Performance Based/Curriculum Based)

Daily Transformation Quizzes

Quiz #1: Transformations of Functions

Quiz #2 Inverse Functions and Relations (section 3.4)

Quiz #3: End Behavior and Critical Points (2 Parts: Calc and No Calc)

Unit 3 Test

Unit 3 PBA

Other Evidence:

Entrance slips

Exit slips

Observations

At home practice

Learning Plan

Days CCSS DOK Instructional Practices Ensured Assignments

# of

Days per

Section

Differentiation/

Resources Teacher Notes

42 3.1

Symmetry and Coordinate

Graphs

Guided Notes: 3.1 Symmetry and

Coordinate Graphs 1

D: Copy of Powerpoint

available

Pg 134 #14-36

R: http://cnx.org/content/m11

470/latest/

43

3.2

Linear Functions

Quadratic Functions

Graphing Families of Functions Practice

Packet

Transformations of Functions Practice

Pg 142 # 11, 13, 14, 20,

5

D: Graphing Quadratic

Functions Exploration

R: Families of Functions

Handout

Use colored pencils and/or

tracing paper to show

transformations

Give students daily quizzes (1

question) to ensure that they are

practicing the transformations.

44 Square Root Functions

Absolute Value Functions

Graphing Absolute Value

Pg 142 #6, 15, 19, 21, 23

D:

R: Transformations of

Square Root Functions

45 Cubic Function

Cube Root Function

Pg 142 # 5, 7, 9, 10, 16, 22

D: Guided notes and PPT

available

R:

http://community.plu.edu/~

heathdj/java/algtrig/Trans.

html

The website is a great visual tool

for students to see what vertical

stretches and shrinks do to a

function.

46 Inverse Function

Piecewise Function

Pg 142 #12, 17, 18, 24, 25, 27

D: Patty Paper activity

R:

47 Review Chapter 3 Transformations of Parent

Functions Review Packet

Pg 143 # 28-37

D:

R:

Algebra II

Equations

Guidelines for

Transformations

of Functions

48 Quiz #1: Transformations of Functions

49 3.4 Inverse Functions and

Relations

Inverse Relations and Functions wkst

Pg 156 # 15-33 odd 2

D: Guided Notes:

Introduction to Functions

and their inverses

R:

50 Practice 7-7 Inverse Relations and D:

http://cnx.org/content/m11470/latest/

http://cnx.org/content/m11470/latest/

http://community.plu.edu/~heathdj/java/algtrig/Trans.html



Functions

R:

51 3.4 Quiz Inverse Functions and Relations

52 3.5 Continuity and End

Behavior

Pg 165 #5, 6, 11, 12 ,13, 18

2

D: 3.5 Continuity and End

Behavior Guided Notes

R: PPT available

53 3.5 Continuity and End Behavior

Practice

Pg 165 # 7-10 all , 20-22 all

D: Investigating: Even and

Odd Functions

R:

54 3.6 Critical Points and

Extrema

Pg 176 # 5-17 odd only

2

D:

R: 3-6 Study Guide:

Critical Points and

Extrema

55 Pg 185 # 5, 6, 14-20 all

D:

R:

56 Quiz: 3.5 and 3.6 : End Behavior and Critical Points (2 Parts: Calc and No Calc)

57 Optimization Problems Chapter 3 Applications

Pg 178 #35 3

D:

R:

http://www.youtube.com/w

atch?v=Zq7g1nc2MJ8

Hand out Optimization PBA-

due day after unit test.

Lesson 3-6 Optimization

Calculator Guide

58

Optimization Area and Volume- The

Fence

D:

R:

http://mathvids.com/lesson

/mathhelp/413-applied-

optimization-problems

59 Optimization Problem Sets: Volume

D:

R:

60 3.7 Graphs of Rational

Functions

Pg 186 # 15-23 odd, 30, 31, 34

2

D:

R: Enrichment 3-7 Slant

http://www.youtube.com/watch?v=Zq7g1nc2MJ8

http://www.youtube.com/watch?v=Zq7g1nc2MJ8

http://mathvids.com/lesson/mathhelp/413-applied-optimization-problems



Asymptotes

61

Pg 186 # 24-29 all, 35-40

D:

R:

62

Chapter 3 Study Guide and Assessment.

Page 197-200 #1-57 odd 1

D:

R:

63

Unit 3 Test 1

D:

R:

64 Unit 3 PBA Oral Presentations

Interdisciplinary Connections

Geometry

Marketing

Chemistry


Absolute maximum

Absolute minimum

Asymptotes

Constant function

Constant of variation

Continuous

Critical point

Decreasing function

Discontinuous

End behavior

Even function

Everywhere discontinuous

Extremum

Horizontal asymptote

Horizontal line test

Infinite discontinuity

Inverse function

Inverse process

Jump discontinuity

Line symmetry

Maximum

Minimum

Monotonicity

Odd function

Parent graph

Point of discontinuity

Point of inflection

Point of symmetry

Rational function

Relative extremum

Relative maximum

Relative minimum

Slant asymptote

Symmetry with respect to the origin

Vertical asymptote

Texas Instrument Graphing Calculator



My Math Video

Solve It!

Student Companion


o Got It? Support

Dynamic Activity

Online Problems

Additional problems


























https://www.desmos.com/calculator - must use Google Chrome



Pre-Algebra

Algebra I

Geometry

Algebra II



https://www.desmos.com/calculator


subject(s) fts grade/course th th unit of study pacing...

Documents