UNIT 1 - SharpSchoolroselle.sharpschool.net/UserFiles/Servers/Server_3152275...Abraham Clark High...

Abraham Clark High School George/Lee – July 2013

1

UNIT 1 Relationships Between Quantities And Reasoning With Equation

Total Number of Days: 5 weeks – Instruction; 2 weeks – Assessment/Reteach Grade/Course: 9/Algebra 1

ESSENTIAL QUESTIONS ENDURING UNDERSTANDINGS

CHAPTER 1

Variable: How can you represent quantities, patterns, and relationships?

Properties: How are properties related to algebra?

CHAPTER 2

Equivalence: Can equations that appear to be different be equivalent? Solving Equations & Inequalities: How can you solve equations?

CHAPTER 1

Variable: Algebra uses symbols to represent quantities that are unknown or that vary.

You can represent mathematical phrases and real-world relationships using symbols and operations. (1.1)

Equations are used to represent the relationship between two quantities that have the same value. (1.8)

Sometimes the value of one quantity can be found if the value of another is known. The relationship between the quantities can be represented in different ways, including tables, equations, and graphs. (1.9)

Properties: Powers can be used to shorten the representation of repeated multiplication,

such as 2 x 2 x 2 x 2 x 2 x 2. When simplifying an expression operations must be performed in the correct order. (1.2)

The definition of a square root can be used to find the exact square roots of some nonnegative numbers. The square roots of other nonnegative numbers can be approximated. Numbers can be classified by their characteristics. Some types of numbers can be represented on the number line. (1.3)

Relationships that are always true for real numbers are called properties, which are rules used to rewrite and compare expressions. (1.4)

Any real numbers can be added or subtracted using a number line model or using rules involving absolute value. (1.5)

The rules for multiplying real numbers are related to the properties of real numbers and the definitions of operations. (1.6)

The distributive property can be used to simplify the product of a number and a sum or difference. An algebraic expression can be simplified by combining the parts of the expression that are alike. (1.7)

CHAPTER 2

Equivalence: Equivalent equations are equations that have the same solution(s). In these

lessons, students learn to use the properties of equality and inverse operations to find equivalent equations. (2.1-2.5)

Abraham Clark High School © George/Lee – July 2013

2


CHAPTER 3

Variable: How do you represent relationships between quantities that are not equal?

Equivalence: Can inequalities that appear to be different be equivalent? Solving Equations and Inequalities: How can you solve inequalities?

CHAPTER 4

Function: How can you represent and describe functions? Modeling: Can functions describe real-world situations?

Solving Equations & Inequalities: Equations can describe, explain, and predict various aspects of the real world.

In these lessons, students solve one-step, two-step, and multi-step linear equations, as well as equations with variables on both sides. (2.1-2.5)

CHAPTER 3

Variable: An inequality is a mathematical sentence that uses an inequality symbol to

compare the values of two expressions. Inequalities can be represented with symbols. Their solutions can be represented on a number line. (3.1)

Just as properties of equality can be used to solve equations, properties of inequality can be used to solve inequalities (including multi-step and compound inequalities). (3.2-3.6)

Equivalence: Just as equivalent equations can be used to solve equations, equivalent

inequalities can be used to solve inequalities (including multi-step and compound inequalities). (3.2-3.6)

Solving Equations & Inequalities: Just as equations can be solved using the properties of equality, inequalities

(including multi-step and compound inequalities) can be solved using the properties of inequality. (3.2-3.6)

CHAPTER 4

Function: The value of one variable may be uniquely determined by the value of another

variable. Such relationships may be represented using words, tables, equations, sets of ordered pairs, and graphs. (4.2)

Functions (linear and nonlinear) are special type of relation where each value in the domain is paired with exactly one value in the range. Some functions can be graphed or represented by equations. (4.3-4.6)

Modeling: Graphs can be used to visually represent the relationship between two

variable quantities as they change. (4.1) The set of all solutions of an equation forms its graph. A graph may include

solutions that do not appear in a table. A real-world graph should show only points that make sense in the given situation. (4.4)

Many real-world functional relationships can be represented by equations. Equations can be used to find the solution of given real-world problems. (4.5)


3

PACING (days)

CONTENT SKILLS STANDARDS

(NJCCCS/CCSS/MP)

RESOURCES LEARNING ACTIVITIES/

ASSESSMENTS Pearson

OTHER (e.g., tech)

0.5

1-1 Variables and Expressions

To write algebraic expressions

Example(s):

1. What is an algebraic express for “1 less than the product of 2 and a number x” Ans:

2. A state park charges an entrance fee of $30 plus $20 for each night of camping. Write an algebraic expression that describes the total cost of camping for n nights. Ans:

CCSS

A.SSE.A.1 Interpret expressions that represent a quantity in terms of its context. A.SSE.1.a

MP

1, 4

Text: p.4-10

Basic: Exs: 9-26, 27-38, 42-52

Average: Exs: 9-25 odd, 27-38, 42-52

Advanced: Exs: 9-25 odd , 27-52

9-15, 20-26, 42, 48

On-line Textbook

https://www.pearsonsuccessnet.com/snpapp/login/login.jsp?showLoginPage=true

Worksheets

Kuta PA1 Kuta A1 math-drills

Translating Algebraic Phrases

Teacher created materials

Video(s)

Mathispower4u

PH-A1-SR

Chapter 1:

Homework Video Tutor 1-1 www.pearsonsuccessnet.com

http://quizlet.com

/6198638/lession-

11-variables-and-

expressions-flash-

cards/

http://quizlet.com/6198638/scatter/

Algebra 1 Course PRE-TEST

Math Journal HSPA/PARCC Prep

PH-A1-TR

Activity – Game Matching Expressions

Project 1 – Checks and Balances (Chapter 1) Station Work Station 1 – Understanding variables Station 2 – Vocabulary Station 3 – using key words to form algebraic expressions Station 4 – word problems





http://www.kutasoftware.com/freeipa.html

http://www.kutasoftware.com/free.html

http://www.math-drills.com/algebra.shtml

http://mathispower4u.yolasite.com/algebra.php

http://www.pearsonsuccessnet.com/


http://quizlet.com/6198638/lession-11-variables-and-expressions-flash-cards/






4

HSPA/PARCC Prep

To simplify fractions

Example(s):

1. Write in simplest

form.

2. Are and equivalent

fractions? Why/Why-Not?

*Factoring Tree – visual learner *Greatest Common Factor *Reducing Fractions to simplest form

Text:

p.801

Standardized Test Prep p.9

Warm-Up (Include Simplifying fractions)

Math Minute Teacher Created

Handouts

PH-A1-TR

Test Prep Handout

1

1-2 Order of Operations and Evaluating Expressions

To simplify and evaluate expressions by using order of operations

Example(s):

1. What is the simplified form of the given expression: Ans:

2. What is the value of the expression:

for and

Ans:

*PEMDAS

CCSS A.SSE.A.1 Interpret expressions that represent a quantity in terms of its context.

A.SSE.1.a

MP

1, 4, 6

Text: p.11-18

Basic: Exs: 9-35, 41-47, 55, 61-80 Average: Exs: 9-35 odd, 36-55, 61-80 Advanced: Exs: 9-35 odd, 36-80

*9-35 odd

On-line Textbook


Worksheets

Kuta PA1 Kuta A1 teAchnology

(order of operations)

Teacher created materials

Video(s)

Mathispower4u MathTV

(Algebra-Positive and Negative Numbers)

PH-A1-SR

Chapter 1:


Algebra 1 Unit PRE-TEST


PH-A1-TR

Activity – Puzzle Calc-Words Negative/Positive Dice – make dice with different numbers positive and negative, students roll dice and have to add together the numbers that are rolled. *ADV – multiply and divide numbers







http://www.teach-nology.com/worksheets/math/order/


http://www.mathtv.com/




5

HSPA/PARCC Prep

To write fractions as decimals and vice versa

Example(s):

1. Write as a decimal.

2. Write 0.323232 as a fraction.

Text:

p.802

Standardized Test Prep p.15

Warm-Up (Include Basic order of operations; fractions/decimals)


Handouts

PH-A1-TR

Test Prep Handout

0.25

1-3 Real Numbers and the Number Line

To classify, graph, and compare real numbers and to estimate square roots.

Example(s):

1. Name the subset(s) of the real numbers to which the number 13 belongs. Ans: rational numbers, whole numbers, natural numbers and integers

2. Order the numbers from least to greatest:

Ans:

CCSS N.RN.B.3 Explain why the sum of 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. MP

1, 4

Text: p.19-25

Basic: Exs: 9-50, 51-56, 58,60, 62-67, 72-85 Average: Exs: 9-49 odd, 51-68, 72-85 Advanced: Exs: 9-49 odd, 51-85 *9-50 odd 51, 63-67 odd

On-line Textbook


Worksheets

Kuta PA1 Kuta A1 Teacher

created materials

Video(s)

Mathispower4u

PH-A1-SR

Chapter 1:



PH-A1-TR

Activity – Inequality Ski Trail *Jigsaw Method Students get in groups according to a number and a shape (can be on do now or notecard) all of the ones, twos etc. will get together each group will study one type of number, rational, irrational, whole, natural, real. They will then go to their shape group and be responsible of teaching that type of number to the rest of their group. *Origami Study Review – Students make origami with each name of











6

different types of numbers ex. – rational, irration, real, etc. Inside the origami they pick questions related to the chapter and play against eachother *mod students can use on test.

0.25

1-4 Properties of Real Numbers

To identify and use properties of real numbers.

Example(s):

1. Name the property illustrated by the statement:

Ans: Comm Prop of Add

2. Simplify the expression:

Ans: * Matching or multiple choice


1, 4, 6

Text: p.26-31

Basic: Exs: 7-35 all, 36-46 even, 47-48, 58-68 Average: Exs: 7-35 odd, 36-55, 58-68 Advanced: Exs: 7-35 odd, 36-68 *7-35 odd, 36-46 even

On-line Textbook


Worksheets

Kuta PA1 Kuta A1 Properties of

Real Numbers Teacher

created materials

Video(s)


(Algebra – Properties of Numbers)

PH-A1-SR

Chapter 1:



PH-A1-TR

Activity – Game You’ve Got My Property http://www.math-play.com/Algebraic-Expressions-Millionaire/algebraic-expressions-millionaire.html

HSPA/PARCC Prep

See above skills for 1-3 & 1-4

NJCCCS

4.1.A1, A2, A3

Standardized Test Prep p. 22, 28

MU Workbook

Unit 1.1 p.2-8

Warm-Up Math Minute







http://www.math.utah.edu/~gresham/F11_1010/Props_of_R_Wksht.pdf






http://www.math-play.com/Algebraic-Expressions-Millionaire/algebraic-expressions-millionaire.html







7

4.5.A1, A3, B1, B2, B4, C3, C6, D5, E1

Unit 1.6 p.42-47

Teacher Created Handouts

PH-A1-TR

Test Prep Handout

1

1-5 Adding and Subtracting Real Numbers

To find sums and differences of real numbers.

Example(s):

Evaluate the expression for , , and .

Ans:

*positive and negative tiles


1, 4, 6

Text: p.37-44

Basic: Exs: 10-43,47-61, 70-85 Average: Exs: 11-43 odd, 44-63, 70-85 Advanced: Exs: 11-43 odd, 44-85 * 11-43 odd, 44-62 even

On-line Textbook


Worksheets


created materials

Video(s)



PH-A1-SR

Chapter 1:



PH-A1-TR

Activity – Puzzle That’s Sum Puzzle! *http://www.studyzone.org/mtestprep/math8/d/Evalexpq.cf Stations Stations 1 – understanding substitution Station 2 – understanding negative and positives Station 3- substituting negatives and positives Station 4 – word problems.

HSPA/PARCC Prep

See above 1-5 skills NJCCCS

4.1.B1 4.5 A3, D5

Standardized Test Prep p. 36

MU Workbook

Unit 1.6 p.42-47

Warm-Up Math Minute

PH-A1-TR

Test Prep Handout











http://www.studyzone.org/mtestprep/math8/d/Evalexpq.cf





8

1

1-6 Multiplying and Dividing Real Numbers

To find products and quotients of real numbers.

Example(s):

Evaluate the expression for ,

Ans:


1, 4, 6

Text: p.45-51

Basic: Exs: 8-50 all, 54-64 even, 70-78

Average: Exs: 11-43 odd, 44-65, 70-78 Advanced: Exs: 11-43 odd, 44-78 *8-48 even, 54-64 even

On-line Textbook


Worksheets


created materials

Video(s)



PH-A1-SR

Chapter 1:



PH-A1-TR

Activity – A Class Divided *Student Teaching – match students according to strengths. Stronger students teaches the problem other solves problem while being guided. Switch positions.

HSPA/PARCC Prep

To Add and Subtract Fractions

Example(s):

Add or Subtract. Write each answer in simplest form.

1.

2.

Text:

p.803


Warm-Up (Include Add/Subtract Fractions)

Math Minute

PH-A1-TR

Test Prep Handout

0.25

1-7 The Distributive Property

To use the Distributive Property to simplify expressions.

CCSS A.SSE.A.1.a Interpret parts of an

Text: p.52-60

Basic:

On-line Textbook

https://www.pearsonsuccessnet.com/snpap















9

Example(s):

1. Use the Distributive Property to simplify the expression ) Ans:

2. Simplify the expression by

combining like terms. Ans:

expression, such as terms, factors, and coefficients. MP

1, 4, 5, 6

Exs: 9-40, 41-64, 66, 68-76, 91-100 Average: Exs: 9-63 odd, 65-83,91-100 Advanced: Exs: 9-63 odd, 65-100 * 9-50 odd, 64, 66

p/login/login.jsp?showLoginPage=true

Worksheets

Kuta PA1 Kuta A1 Video(s)


(Algebra-Linear Eq in 1 Variable w/Parentheses)

PH-A1-SR

Chapter 1:


PH-A1-TR

Activity – Game Algebra *M & M Distributive Property activity – See attachments at bottom

0.25

1-8 An Introduction to Equations

To solve equations using tables and mental math.

Example(s):

1. Is a solution of the equation ? Ans:

2. You can read 2 pages for every page your friend can read. Write an equation that relates the number of pages p that you can read and the number of pages n that your friend can read. Ans:

CCSS A.CED.A.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.) MP

1, 4

Text: p. 61-68

Basic: Exs: 7-48 all, 50, 52-62 even, 63, 67-86 Average: Exs: 7-47 odd, 49-64, 67-86 Advanced: Exs: 7-47 odd, 49-86 * 7-47 odd, 50, 54, 63

On-line Textbook


Worksheets


created materials

Video(s)

PH-A1-SR

Chapter 1:



PH-A1-TR

Activity – Puzzle Algebra Connections *http://www.math-play.com/Inequality-Game.html















http://www.math-play.com/Inequality-Game.html





10

HSPA/PARCC Prep

See above skills for 1-7 NJCCCS

4.1.B1 4.5 A3, D5

Standardized Test Prep p. 52, 58

MU Workbook

Unit 1.6 p.44

Warm-Up Math Minute

PH-A1-TR

Test Prep Handout

1

1-9 Patterns, Equations, and Graphs

To use tables, equations, and graphs to describe relationships.

Example(s):

1. Is a solution of the equation . Ans:

2. Joe runs 6 laps before

Dany joins him at the track. They then run together at the same pace. How can you represent the relationship between the number of laps Joe runs and the number of laps Dany runs in different ways? Use a table, an equatioin, and a graph.

Ans: Table: J 1 2 3 4 5 D 7 8 9 10 11

Equation:

Graph: (plot pts. From table) x-axis = Joe’s laps, y-axis = Dany’s laps

CCSS A.REI.D.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). A.CED.2 MP

1, 4, 5

Text: p.69-75

Basic: Exs: 8-26 all, 28-33, 36-54 Average: Exs: 9-25 odd, 27-33, 36-54 Advanced: Exs: 9-25 odd, 27-54 *8-26 even, 28-32 even, 36-54 even

On-line Textbook


Worksheets


created materials

Video(s

PH-A1-SR

Chapter 1:


Math Journal HSPA/PARCC Prep Chapter 1 Test

PH-A1-TR

Activity – Sequencing Patterns

http://www.teachervision.fen.com/math/problem-solving/48897.html

teach by step by step process. Step 1 – what is the question asking for? Step 2 – Find key words Step 3 – eliminate unneeded information Step 4 – list important information given Step 5 – form an equation Step 6 – form a table to find possible answers. Step 7 – graph.














11

HSPA/PARCC Prep

To multiply and divide fractions.

Example(s):

Multiply or divide. Write your answers in simplest form.

1.

2.

Text:

p.804


Warm-Up (Include Multiply/Divide fractions)

Math Minute

PH-A1-TR

Test Prep Handout

1

2-1 Solving One-Step Equations

To solve one-step equations in one variable.

Example(s):

Solve the given equations and check your answer:

1.

2.

CCSS A.CED.A.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.REI.3

MP

1, 2, 4

Text: p.87-93

Basic: Exs: 10-54 all, 56-70 even, 71, 73, 79-88 Average: Exs: 11-51 odd, 52-76, 79-88 Advanced: Exs: 11-51 odd, 52-88 * 10-70 even 71, 73

On-line Textbook


Worksheets


created materials

Video(s)


(Algebra-Linear Equations in 1 Variable-Addition & Multiplication)

PH-A1-SR

Chapter 2:



PH-A1-TR

Activity – Game Algebra One-Step

Project 2 – The Big Dig!!

One step equations PPT * attached

Have students

answer and identify each step.

What is the

variable? What is the

operation being done?

What is the

opposite/inverse of that operation?












12

HSPA/PARCC Prep

To write numbers as fractions, decimals, and percents.

Example(s):

1. Write 3.256 as a percent.

2. Write 23.1% as a decimal.

3. Write % as a fraction

or mixed number in simplest form.

Text:

p.805


Warm-Up Math Minute

PH-A1-TR

Test Prep Handout

1

2-2 Solving Two-Step Equations

To solve two-step equations in one variable.

Example(s):

Solve each equation and justify each step. 1.

2.

CCSS A.REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. A.CED.1 A.REI.A.1

MP

1, 2, 3, 4

Text: p.94-100

Basic: Exs: 11-37 all, 38-56 even, 59, 66-78 Average: Exs: 11-37 odd, 38-60, 66-78 Advanced: Exs: 11-37 odd, 38-78 * 11-37 odd, 38-56 even, 59

On-line Textbook


Worksheets



(Algebra-Linear Equations in 1 Variable)

PH-A1-SR

Chapter 2:



PH-A1-TR

Activity – Game Equation

http://www.mathplayground.com/AlgebraEquations.html

*Use scales to illustrate two step equations Bingo -http://go.hrw.com/resources/go_msm/course3/mathables/c3ch2.pdf

HSPA/PARCC Prep

To write numbers using scientific notation

Example(s):

1. Write 1,324,000 to

Text:

p.807


Warm-Up (Include Math Minute

PH-A1-TR

Test Prep Handout














http://go.hrw.com/resources/go_msm/course3/mathables/c3ch2.pdf





13

scientific notation. 2. Write in

standard form.

1

2-3 Solving Multi-Step Equations

To solve multi-step equations in one variable.

Example(s):

Solve each equation. 1.

2.

CCSS A.CED.A.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.REI.1, 3

MP 1, 2, 4

Text: p.101-108

Basic: Exs: 10-44 all, 46-54 even, 55-59, 61, 69-80 Average: Exs: 11-45 odd, 46-64 Advanced: Exs: 11-43 odd, 45-80 *10-44 even, 55-59 odd

On-line Textbook


Worksheets



(Algebra-Linear Equations in 1 Variable)

PH-A1-SR

Chapter 2:



PH-A1-TR

Activity – Actors and Equations!

Multi-step

equations IT’S A PARTY!! Activity and lesson – project grade*

All documents

attached including ppt and student and teacher worksheet.

See me for more

information.

HSPA/PARCC Prep

See above 2-3 skills

Example(s):

Describe two ways in which you can solve

See 2-3 Standards See 2-3 Text resources


Same 2-3 “other” resources

Warm-Up Math Minute

PH-A1-TR

Test Prep Handout

1

2-4 Solving Equations With Variables on Both Sides

To solve equations with variables on both sides and identify equations that are identities or have no solution.

CCSS A.CED.A.1 Create equations and inequalities in one variable and use them to solve problems. (Include equations

Text: p.109-116

Basic: Exs: 10-32 all, 34-42 even, 43, 44, 46,

On-line Textbook


Worksheets


PH-A1-TR

Activity – Puzzle Breaking the Code
















14

Example(s):

Solve each equation and determine whether the equation is an identity or has no solution. 1. 2.

arising from linear and quadratic functions, and simple rational and exponential functions.) A.REI.1, 3

MP

1, 2, 3, 4

57-66 Average: Exs: 11-31 odd, 33-49, 57-66 Advanced: Exs: 11-31 odd, 33-66 *10 – 32 even


PH-A1-SR

Chapter 2:


Musical Activity Partner Up - attached

HSPA/PARCC Prep


4.1.B1, D1, D2, D3

4.5.A1, A2, A5, B2, B4, C3, C4


MU Workbook

Unit 4.30 p.267: Step 7 p.269: 31 p.270: 40

Warm-Up Math Minute

PH-A1-TR

Test Prep Handout

1.5

2-5 Literal Equations and Formulas

To rewrite and use literal equations and formulas.

Example(s):

Rearrange Ohm’s law to highlight

resistance R.

CCSS A.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. N.Q.1 A.CED.1 A.REI.1, 3

MP

1, 4

Text: p.117-124

Basic: Exs: 11-35 all, 36-42 even, 43, 45-47, 51-66 Average: Exs: 11-35 odd, 36-48, 51-66 Advanced: Exs: 11-35 odd, 36-66 *11-35 odd 36-42 even, 43-59 odd

On-line Textbook


Worksheets


PH-A1-SR

http://www.ment

ormob.com/learn

/i/unit-2-solving-

equations-2/25-

literal-equations-

and-formulas


PH-A1-TR

Activity – Advertising Formulas

fly swatter review game - http://mathequalslove.blogspot.com/2012/12/flyswatter-review-game-for-forms-of.html











http://www.mentormob.com/learn/i/unit-2-solving-equations-2/25-literal-equations-and-formulas






http://mathequalslove.blogspot.com/2012/12/flyswatter-review-game-for-forms-of.html






15

Chapter 2:


HSPA/PARCC Prep


Example(s):

p.113: 35 Bricklayers use the formula

to estimate the number n of bricks needed to build a wall of length l and height h, where l and h are in feet. Solve the formula for h. Estimate the height of a wall 28 ft. long that requires 1568 bricks.

See 2-5 Standards See 2-3 Text resources Standardized Test Prep p. 114


Warm-Up Math Minute

PH-A1-TR

Test Prep Handout

0.25

3-1 Inequalities and their Graphs

To write and graph inequalities.

Example(s):

1. Write an inequality to represent the verbal expression: 5 less than a is greater than 10.

2. Graph the inequality .

CCSS A.REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. MP

1, 4

Text: p.174-183

Basic: Exs: 8-39 all, 40-58 even, 65-79 Average: Exs: 9-39 odd, 40-59, 65-79 Advanced: Exs: 9-39 odd, 40-79 * 9 – 39 odd 40-48 even

On-line Textbook


Worksheets


PH-A1-SR

Chapter 3:



PH-A1-TR

Activity – Game Tic-Stack-Toe

Interactive graphing understanding graphs of inequalities. http://www.quickmath.com/webMathematica3/quickmath/graphs/inequalities/basic.jsp











http://www.quickmath.com/webMathematica3/quickmath/graphs/inequalities/basic.jsp






16

0.5

3-2 Solving Inequalities Using Addition or Subtraction

To use addition or subtraction to solve inequalities.

Example(s):

Solve and graph the given inequalities. 1. 2.

CCSS A.REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. A.CED.1 MP

1, 4, 5

Text: p.184-190

Basic: Exs: 9-44 all, 46-70 even, 81-92 Average: Exs: 9-43 odd, 45-75, 81-92 Advanced: Exs: 9-43 odd, 45-92 *9-43 odd, 46-70 even

On-line Textbook


Worksheets



(Algebra-Inequalities)

PH-A1-SR

Chapter 3:



PH-A1-TR

Activity – Which Number Am I?

http://www.mangahigh.com/en_us/maths_games/algebra/inequalities/inequalities

HSPA/PARCC Prep

See above 3-1 & 3-2 skills

NJCCCS

4.1.B1, D1, D2, D3

4.3.B1, B2, C2 4.5.A1, A2, A5,

B2, B4, C3, C4, E1, E3

Standardized Test Prep p. 170 & 177

MU Workbook

Unit 4.30 p.267 p.269: 33, 35 p.270: 41

Unit 4.31 p.278: 47

Warm-Up Math Minute

PH-A1-TR

Test Prep Handout

1

3-3 Solving Inequalities Using Multiplication or Division

To use multiplication or division to solve inequalities.

Example(s):

Solve the given inequalities. 1.

2.

CCSS A.CED.A.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

Text: p.191-198

Basic: Exs: 7-18 all, 46-48 even, 49,59 Average: Exs: 7-31 odd, 33-62, 65-76 Advanced: Exs:

On-line Textbook


Worksheets



PH-A1-TR

Activity – A Real Find

Scavenger Hunt –

Internet based. – must use laptops.

http://homepages.i






















http://homepages.ius.edu/DCURETON/lessons/hunt.htm


17

functions.) N.Q.2 A.REI.3

MP

1, 4, 5

7-31 odd, 33-76 Mathispower4u MathTV


PH-A1-SR

Chapter 3:


us.edu/DCURETON/lessons/hunt.htm

HSPA/PARCC Prep


Example(s):

p.183: 62

If and , is ? Explain.



Warm-Up Math Minute

PH-A1-TR

Test Prep Handout

1

3-4 Solving Multi-Step Inequalities

To solve multi-step inequalities.

Example(s):

Solve each inequality, if possible. If the inequality has no solution, write no solution. If the solutions are all real numbers, write all real numbers. 1. 2. 3)

CCSS A.REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. A.CED.1

MP

1, 2, 4

Text: p.199-205

Basic: Exs: 9-34 all, 36-46 even, 51, 53-54, 58-68 Average: Exs: 9-35 odd, 35-54, 58-68 Advanced: Exs: 9-33 odd, 35-68 10 – 34 even, 36-46 even

On-line Textbook


Worksheets




PH-A1-SR

Chapter 3:



PH-A1-TR

Activity – Game Points for Each Line http://www.mathway.com/problem.aspx?p=algebra















http://www.mathway.com/problem.aspx?p=algebra




18

HSPA/PARCC Prep


Example(s):

p.191: 48

Write two different inequalities that you can solve by subtracting 3 from each side and then dividing each side by -5. Solve each inequality.



Warm-Up Math Minute

PH-A1-TR

Test Prep Handout

1

4.1. Using Graphs to Relate Two Quantities

To represent mathematical relationships using graphs.

Example(s):

1. What are the variables in each graph? Describe how the variables are related at various points on the graph.

2. Sketch a graph to

represent the given situation. Label each section. Your distance from the ground as you ride a

CCSS F.IF.B.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. MP

1, 3, 4, 6

Text: p.248-254

Basic: Exs: 5-15, 17-18, 21-29 Average: Exs: 5-13 odd, 14-18, 21-29 Advanced: Exs: 5-13 odd, 14-29

On-line Textbook


Worksheets


PH-A1-SR

Chapter 4:



PH-A1-TR

Activity – Relating Quantities

PPT Attached I do, We do, You do.










19

Ferris wheel.

HSPA/PARCC Prep


4.4.A2 4.5.D1-4, E1


MU Workbook

Unit 4.24 p.213-222

Warm-Up Math Minute

PH-A1-TR

Test Prep Handout

1

4-2 Patterns and Linear Functions

To identify and represent patterns that describes linear functions.

Example(s):

An automaker makes a car that can travel 40 mi on its charged battery before it begins to use gas. Then the car travels 50 mi per gallon of gas used. Represent the relationship between the amount of gas used and the distance traveled using a table, an equation, and a graph. Is total distance traveled a function of the amount of gas used? What are the independent and dependent variables? Explain.

CCSS A.REI.D.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). F.IF.4

MP

1, 2, 3, 4

Text: p.255-261


On-line Textbook


Worksheets


PH-A1-SR

Chapter 4:



PH-A1-TR

Activity – Common Themes

http://helpmewithmathproblems.com/algebra1/list-of-topics/identifying-and-representing-patterns-that-describe-linear-functions/

HSPA/PARCC Prep


Example(s):

p.244: 15

Graph the set of ordered pairs (-2, -3), (0, -1), (1, 0), (3, 2), and (4, 4). Determine whether the relationship is a linear function. Explain how you know.



Warm-Up Math Minute

PH-A1-TR

Test Prep Handout


















20

1

4-3 Patterns and Nonlinear Functions

To identify and represent patterns that describe nonlinear functions.

Example(s):

Graph the function shown by the given set of ordered pairs. Tell whether the function is linear/non-linear.

x 0 1 2 3 y 1 4 9 16

CCSS A.REI.D.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). F.IF.4

MP

1, 2, 3, 4

Text: p.262-269


On-line Textbook


Worksheets


PH-A1-SR

Chapter 4:



PH-A1-TR

Activity – Puzzle The Quadratic Code Partner to Partner – one partner graphs the point while the other determines if the function is linear or non-linear.

HSPA/PARCC Prep


Example(s):

p.251: 22

A certain function fits the following description: As the value of x increases by 1 each time, the value of y continually decreases by a smaller amount each time, and never reaches a value as low as 1. Is this function linear or non-linear? Explain your reasoning.



Warm-Up Math Minute

PH-A1-TR

Test Prep Handout

1

4-4 Graphing a Function Rule

To graph equations that represent functions.

Example(s):

1. Graph the function rule:

2. The function rule

CCSS F.IF.B.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the

Text: p.270-279

Basic: Exs: 9-33, 36-39, 42-58 Average: Exs: 9-31 odd, 33-39, 42-58

On-line Textbook


Worksheets

Kuta PA1 Kuta A1


PH-A1-TR

Activity – Graphing from Samples

http://www.mathsi

sfun.com/data/grap















http://www.mathsisfun.com/data/grapher-equation.html

http://www.mathsisfun.com/data/grapher-equation.html


21

represents the total weight W, in pounds, of a spa that contains g gallons of water. a. What is a reasonable

graph of the function rule, given that the capacity of the spa is 250 gal?

b. What is the weight of the spa when empty? Explain.

function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. N.Q.1 A.REI.10

MP

1, 2, 3, 4

Advanced: Exs: 9-31 odd, 33-58 9-33 odd 36, 38, 42-58 even

Video(s)

PH-A1-SR

Chapter 4:


her-equation.html

HSPA/PARCC Prep


Example(s):

p.258: 34

Is the point on the

graph of ? How do you know?



Warm-Up Math Minute

PH-A1-TR

Test Prep Handout

1

4-5 Writing a Function Rule

To write equations that represent functions

Example(s):

1. Write a function rule that represents the sentence: M is 10 more than half of n.

2. Write a function rule that represents the situation: A student’s earnings e are a function of the number of hours h worked at a rate of $8.25 per hour.

CCSS N.Q.A.2 Define appropriate quantities for the purpose of descriptive modeling. A.SSE.1, 1.a A.CED.2

MP

1, 4

Text: p.280-285

Basic: Exs: 8-21, 23, 26-27, 29-30, 33-56 Average: Exs: 9-21 odd, 22-30, 33-56 Advanced: Exs: 9-21 odd, 22-56

On-line Textbook


Worksheets


PH-A1-SR

Chapter 4:


Math Journal HSPA/PARCC Prep Chapter 4 Test Unit 1 Review Unit 1 Assessment

(Model Curriculum)

PH-A1-TR

Activity – Puzzle Chasing Down the Clues http://www.studyzone.org/mtestprep/math8/g/7functionrulep.cfm











http://www.studyzone.org/mtestprep/math8/g/7functionrulep.cfm





22

HSPA/PARCC Prep


Example(s):

p.266: 24

The golden ratio has been studied and used by mathematicians and artists for more than 2000 years. A golden rectangle, constructed using the golden ratio, has a length of about 1.6 times its width. Write a rule for the area of a golden rectangle as a function of its width.



Warm-Up Math Minute

PH-A1-TR

Test Prep Handout

INSTRUCTIONAL FOCUS OF UNIT 1 (Model Curriculum Student Learning Objectives)

1. Solve multi-step problems that can be represented algebraically with accurate and appropriately defined units, scales, and models (such as graphs, tables, and

data displays).

2. Interpret terms, factors, coefficients and expressions (including complex linear and exponential expression) in terms of context.

3. Solve linear equations and inequalities in one variable (including literal equations). Justify each step in the process and solution.

4. Create linear equations and inequalities in one variable and use them to solve problems. Justify each step in the process and the solution

5. Create linear equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

6. Model and describe constraints with linear equations and inequalities and systems of equations and/or inequalities to determine if solutions are viable or

non-viable.

HSPA/PARCC FRAMEWORK/ASSESSMENT – UNIT 1

PARCC EXEMPLARS: www.parcconline.org (copy & paste the url or link into search engine)

Functions: http://www.parcconline.org/samples/mathematics/high-school-functions

Solving Equations: http://www.parcconline.org/samples/mathematics/high-school-seeing-structure-equation

1. It is given that: . Find the value of p.

HSPA EXEMPLARS: http://www.nj.gov/education/assessment/hs/hspa_mathhb.pdf

Number And Numerical Operations

http://www.parcconline.org/

http://www.parcconline.org/samples/mathematics/high-school-functions

http://www.parcconline.org/samples/mathematics/high-school-seeing-structure-equation

http://www.nj.gov/education/assessment/hs/hspa_mathhb.pdf


23

1. The following are two ration numbers greater than 1 and less than 2:

Give two more rational numbers greater than 1 and less than 2. Give reasons why your numbers are rational numbers.

The following are two irrational numbers greater than 1 and less than 2.

Give two more irrational numbers greater than 1 and less than 2. Give reasons why your numbers are irrational numbers.

Patterns And Algebra

1. For each bicycle that it repairs, a repair shop charges for parts and $35 per hour for labor.

Write an equation for the total charge, C, of repair with the cost of parts, p, and the number of hours of labor, n.

The shop adds 6% tax on the total charge for each repair. Write an equation for the total charge T, after tax, of a repair with the cost of parts,

p, and the number of hours of labor, n.

The total charge after tax of a bicycle repair was $233.20. The cost of parts was $80. How many hours of labor were charged in this bicycle

repair? Show your work or provide an explanation for your answer.

Variables, Expressions, And Equations (1.1 &1.8): Exemplar from HSPA Practice booklet.

http://www.state.nj.us/education/assessment/hs/hspa_prep.pdf

1. The basketball team scored 75 points in the final game of the season. During that time, the team made twice as many field goals as they did free

throws. Each field goal is worth two points, and each free throw is worth one point. How many points did the basketball team make on free throws

during the game? Which of the following equations can be used to solve the problem given above?

a.

b.

c.

d.

21ST CENTURY SKILLS – UNIT 1 (4Cs & CTE Standards)

Career Technical Education (CTE) Standards: http://www.state.nj.us/education/aps/cccs/career/

9.1. 21st Century Life and Career Skills: All students will demonstrate the creative, critical thinking, collaboration, the problem-solving skills needed to function successfully as both global citizens and workers in diverse ethnic and organizational cultures.

9.1.12.B.1. Present resources and data in a format that effectively communicates the meaning of the data and its implications for solving problems using multiple perspectives.

PROJECT 2: THE BIG DIG! (Prentice Hall Algebra 1 Teacher Resources)

http://www.state.nj.us/education/assessment/hs/hspa_prep.pdf

http://www.state.nj.us/education/aps/cccs/career/


24

9.2. Personal Financial Literacy: All students will develop skills and strategies that promote personal and financial responsibility related to financial planning, savings, investment, and charitable giving in the global economy.

9.2.12.A.1. Analyze the relationship between various careers and personal earning goals.

PROJECT 1: CHECKS AND BALANCES (Prentice Hall Algebra 1 Teacher Resources)

4-C’s o Creativity:

Project 1: Checks & Balances (Prentice Hall Algebra 1 Teacher Resources - DVD)

Project 2: The Big Dig! (Prentice Hall Algebra 1 Teacher Resources - DVD)

o Critical Thinking:

Math Journals

Project 1 & 2

o Collaboration:

Project 1 & 2

Stations (pairs/teams)

Group-Work (pairs/teams)

Math Centers (differentiated groups)

MODIFICATIONS/ACCOMMODATIONS

Teacher directed instruction by providing students with more necessary steps in order to solve the problems

Small Group Activities - when students are given group guided practice

IEP/504 Modifications: 1. Students will be allowed to use the graphing calculator 2. Students will be provided guided notes/graphic organizers to help with organization and to build their note-taking skills in math 3. Modified assessments and assignments (classwork, homework, quizzes/tests) as needed

Math Centers (Differentiation) – Review/Revisit topics missed by absentee students

APPENDIX (Teacher resource extensions)

CCSS.Mathematical Practices:

MP1: Make sense of problems and persevere in solving them. MP2: Reason abstractly and quantitatively. MP3: Construct viable arguments and critique the reasoning of others. MP4: Model with mathematics. MP5: Use appropriate tools strategically. MP6: Attend to precision.


25

MP7: Look for and make use of structure. MP8: Look for and express regularity in repeated reasoning.

Common Core Standards Abbreviations

a. Number & Quantity 1. N-RN-The Real Number System 2. N-Q-Quantities 3. N-CN-The Complex Number System 4. N-VM-Vector and Matrix Quantities

b. Algebra 1. A-SSE-Seeing Structure in Equations 2. A-APR-Arithmetic with Polynomials and Rational Expressions 3. A-CED-Creating Equations 4. A-REI-Reasoning with Equations and Inequalities

c. Functions 1. F-IF-Interpreting Functions 2. F-BF-Building Functions 3. F-LE-Linear, Quadratic and Exponential Models 4. F-TF-Trigonometric Functions

d. Geometry 1. G-CO-Congruence 2. G-SRT-Similarity, Right Triangles, & Trigonometry 3. G-C-Circles 4. G-GPE-Expressing Geometric Properties with Equations 5. G-MG-Modeling with Geometry

e. Statistics and Probability 1. S-ID-Interpreting Categorical & Quantitative Data 2. S-IC-Making Inferences & Justifying Conclusions 3. S-CP-Conditional Probability and Rules of Probability 4. S-MD-Using Probability to Make Decisions

Kuta A1: Kuta Software – Infinite Algebra 1 (Free Worksheets) - http://www.kutasoftware.com/free.html

Kuta PA1: Kuta Software – Infinite Pre-Algebra 1 (Free Worksheets) - http://www.kutasoftware.com/freeipa.html

teAchnology: o Order of Operations: http://www.teach-nology.com/worksheets/math/order/ o

Math-drills: o Translating Algebraic Phrases: http://www.math-drills.com/algebra/algebra_translating_algebraic_phrases_001.html

The University of Utah – Department of Math (Marina Gresham) Properties of Real Numbers: http://www.math.utah.edu/~gresham/F11_1010/Props_of_R_Wksht.pdf

Mathispower4u: http://mathispower4u.yolasite.com/algebra.php

MathTV: www.mathtv.com



http://www.teach-nology.com/worksheets/math/order/

http://www.math-drills.com/algebra/algebra_translating_algebraic_phrases_001.html





26

MU: Measuring Up Workbook

PH-A1-TR: Prentice Hall – Algebra 1 – Teacher Resources (on-line & DVD)

PH-A1-SR: Prentice Hall – Algebra 1 – Teacher Resources (on-line)


27

UNIT 2 Linear Relationships

Total Number of Days: 25 days (5 weeks) Grade/Course: 9/Algebra 1


CHAPTER 4

Functions: How can you represent and describe functions?

CHAPTER 5

Proportionality: What does the slope of a line indicate about the line?

Function: What information does the equation of a line give you?

CHAPTER 6

Solving Equations and Inequalities: How can you solve a system of equations or inequalities?

Modeling: Can systems of equations model real-world situations?

CHAPTER 4

Function: Functions (linear and nonlinear) are special type of relation where each value in

the domain is paired with exactly one value in the range. Some functions can be graphed or represented by equations. (4.3-4.6)

Arithmetic sequences have function rules that can be used to find any term of the sequence. (4.7)

CHAPTER 5

Proportionality:

Ratios can be used to show a relationship between changing quantities, such as vertical and horizontal change. (5.1)

If the ration of two variables is constant, then the variables have a special relationship, called a direct variation. (5.2)

Function:

A line on a graph can be represented by a linear equation. Forms of linear equations include the Slope-Intercept, Point-Slope, and Standard Forms. (5.3-5.5)

The relationship between two lines can be determined by comparing their slopes and y-intercepts. (5.6)

CHAPTER 6

Solving Equations & Inequalities:

Systems of linear equations can be used to model problems. Systems of equations can be solved by graphing, substitution, or eliminating a variable. (6.1-6.3)

A linear inequality in two variables has an infinite number of solutions. These solutions can be represented in the coordinate plane as the set of all points on one side of a boundary line. The solutions of a system of linear inequalities can be represented by the region where the graphs of the individual inequalities


28

overlap. (6.5-6.6)


Modeling:

Some problems can be modeled by systems of linear equations. (6.1)

Solutions to a linear inequality in two variables can be represented in the coordinate plane as the set of all points on one side of a boundary line. The solutions of a system of linear inequalities can be represented by the region where the graphs of the individual inequalities overlap. (6.5-6.6)

PACING (days)

CONTENT SKILLS STANDARDS (CCSS/MP)


ASSESSMENTS Pearson

OTHER (e.g., tech)

1

4.6. Formalizing Relations and Functions

To determine whether a relation is a function and to find domain and range using function notation

Example(s):

You have 3 qt of paint to paint the trim in your house. A quart of paint covers 100

. The function represents the

area , in square feet, that q quarts of paint cover. What domain and range are reasonable for the function?

CCSS F.IF.A.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). F.IF.2

MP

1, 2, 4

Text: p.268-273

Basic: Exs: 8-24 all, 26, 28, 29, 41-50 Average: Exs: 9-23 odd, 24-35, 41-50 Advanced: Exs: 9-23 odd, 24-50

On-line Textbook


Worksheets

Kuta PA1 Kuta A1 Video(s) http://www.b

rightstorm.com/math/algebra/graphs-and-functions/relations-and-determining-whether-a-relation-is-a-function/


PH-A1-TR

Activity – Game: Home on the Range

Review definitions, make a study guide, take the tests, email to teacher, and do practice games. *SEND ALL RESULTS TO TEACHER!

http://quizlet.com/3453397/relations-functions-graphs-flash-cards/

HSPA/PARCC

Prep


4.3.B1, B2, C2 4.5.A1, A2, A5,

C3, C4, E1, E3


MU Workbook

Unit 4.31 p.272: Step 2 p.276: 31-37

Warm-Up Math Minute Teacher Created

Handouts







http://www.brightstorm.com/math/algebra/graphs-and-functions/relations-and-determining-whether-a-relation-is-a-function/
















29

p.278: 48 PH-A1-TR

Test Prep Handout

1

4.7. Arithmetic Sequences

To identify and extend patterns in sequences and to represent arithmetic sequences using function notation

Example(s):

Describe a pattern in the given sequence. Then find the next two terms of the sequence.

CCSS F.IF.A.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1. A.SSEE.1.a, b F.BF.1.a, 2 F.LE.2

MP

1, 4, 8

Text: p.274-281

Basic: Exs: 9-53, 54-62 even, 68, 70, 76-87 Average: Exs: 9-53 odd, 76-87 Advanced: Exs: 9-53 odd, 54-87 * 9-53 odd, 54-62 even, 68, 70

On-line Textbook


Worksheets



(Algebra-Sequences and Series)

Online

Activity in Illuminations - The Devil and Daniel Webster


PH-A1-TR

Activity – Game: Walking the Walk

*Hands on introduction – attached. *Arithmetic Sequence – Powerpoint - attached

HSPA/PARCC

Prep

See above 4.7 skills NJCCCS

4.3.A1,A3 4.5.A2, B1, C1-C4,

E1


MU Workbook

Unit 4.29 p.259 p. 261: 25, 26


Handouts

PH-A1-TR

Test Prep Handout









http://illuminations.nctm.org/LessonDetail.aspx?id=L288



30

1

5.1. Rate of Change and Slope

To find rates of change from tables and to find slope.

Example(s):

Find the slope of the line that passes through the points (1, 2) and (3, 8).

CCSS F.LE.A.1b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. F.IF.6

MP

1, 4, 8

Text: p.294-299

Basic: Exs: 8-25 all, 26-38 even, 39, 41, 42-48 even, 59-74 Average: Exs: 9-25 odd, 26-49, 59-74 Advanced: Exs: 9-25 odd, 26-74 *9-25 odd, 26-38 even

On-line Textbook


Worksheets

Kuta PA1 Kuta A1 Counting for

Slope Video(s) Mathispower4u MathTV

(Algebra-Linear Equations in 2 Variables)


PH-A1-TR

Activity – Activity: Finding Slope by the Book

* Tick Tock Toothpick – Think, Pair, Share Activity - attached

HSPA/PARCC

Prep


4.3.A1, A3 4.5.A2, B1, C1-C4,

E1


MU Workbook

Unit 4.32 p.280-81


Handouts

PH-A1-TR

Test Prep Handout

0.25

5.2. Direct Variation

To write and graph an equation of a direct variation

Example(s):

Write a direct variation equation that relates x and y given and

CCSS A.CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. N.Q.2

MP

1, 4, 6

Text: p.301-306

Basic: Exs: 9-29 all, 30-34 even, 35-42, 48-59 Average: Exs: 9-29 odd, 30-43, 48-59 Advanced: Exs: 9-29 odd, 30-59 9-29 odd, 30-34 even

On-line Textbook


Worksheets



(Algebra-Sequences and Series)

Warm-Up Math Journal HSPA/PARCC Prep

PH-A1-TR

Activity – Puzzle: The Origin of the Origin

Walk around activity – attached




















31

HSPA/PARCC

Prep


4.3.B1, C1 4.5.C1, C2, C6, E1,

E2, E3, F3


MU Workbook

Unit 4.33 p.294


Handouts

PH-A1-TR

Test Prep Handout

1.25

5.3. Slope-Intercept Form

To write and graph linear equations using slope-intercept form.

Example(s):

1. Write an equation in slope-intercept form of the line with the slope

and y-intercept

2. Write an equation in

slope-intercept form of the line that passes through the points (1, 3) and (-2, 5).

3. Graph the equation

CCSS F.IF.C.7a Graph linear and quadratic functions and show intercepts, maxima, and minima. A.SSE.1.a, 2 A.CED.2 F.IF.4 F.BF.1.a, 3 F.LE.2, 5

MP

1, 4, 5

Text: p.307-314

Basic: Exs: 7-35 all, 38-44 even, 45-47 all, 48-56 even, 58, 63-77 Average: Exs: 7-35 odd, 36-58, 63-77 Advanced: Exs: 7-37 odd, 38-77 *7-35 odd, 38-44 even, 45, 47 EXTRA CREDIT PROJECT – Slope intercept form ec attached

On-line Textbook


Worksheets



(Algebra-Linear Equations in 2 Variables)


PH-A1-TR

Activity – Game: It’s Your Turn

Group work – one person writes equation given m and b – lower leveled

Second person

writes equation of slope when passing through two points – higher level

Third person

graphs the equations – middle level

* do not let students decide their roles assign roles and groups based on skill levels.

HSPA/PARCC

Prep

See above 5.3 skills

Example(s):

See 5.3 Standards See 5.3 Text resources Standardized Test Prep

Same 5.3 “other” resources


Handouts










32

p.313: 45

Polar bears are listed as a threatened species. In 2005, there were about 25,000 polar bears in the world. If the number of polar bears declines by 1000 each year, in what year will polar bears become extinct? a. What equation models

the number of polar bears?

b. How can graphing the equation help you solve the problem?

p. 314

PH-A1-TR

Test Prep Handout

1

5.4. Point-Slope Form

To write and graph linear equations using point-slope form.

Example(s):

1. Write an equation in point-slope form of the line that passes through the point (3, -2) and with the slope

2. Graph the equation

3. Write an equation in

point-slope form of the line that passes through the points (1, 2) and (-2, 3). Then write the equation in slope-intercept form.

CCSS F.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 (include reading these from a table). A.SSE.A.1.a, 2 A.CED.2 F.IF.4, 7.a F.BF.1.a, 3 F.LE.5

MP

1, 4, 5

Text: p.315-321

Basic: Exs: 8-24, 26, 27, 29, 33, 42 Average: Exs: 9-23 odd, 24-32 Advanced: Exs: 9-23 odd, 24-42

On-line Textbook


Worksheets



PH-A1-TR

Activity – Puzzle: Slippery Slope

Group work – one person writes equation given m and b – lower leveled

Second person

writes equation of slope when passing through two points – higher level

Third person

graphs the equations – middle level

* do not let students decide their roles assign roles and groups based on skill levels.








33

HSPA/PARCC

Prep


Example(s):

p.319:29

The relationship between altitude and the boiling point of water is linear. At an altitude of 8000 ft., water boils at . At an altitude of 4500 ft., water boils at . Write an equation giving the boiling point b of water, in degrees Fahrenheit, in terms of the altitude a, in feet. What is the boiling point of water at 2500 Ft.?

See 5.4 Standards See 5.4 Text resources Standardized Test Prep p. 320



Handouts

PH-A1-TR

Test Prep Handout

1

5.5. Standard Form

To graph linear equations using intercepts and write linear equations in standard form

Example(s):

1. Find the x- and y-intercepts of the graph of

2. Graph using x-

and y-intercepts. 3. Graph the equation

4. Write the equation

in standard form using integers.

CCSS A.CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. N.Q.2 A.SSE.2 F.IF.4, 7.a, 9 F.BF.1.a F.LE.2, 5

MP

1, 4, 5, 6

Text: p.322-329

Basic: Exs: 8-44 all, 52-58 even, 64-77 Average: Exs: 9-39 odd, 40-58, 64-77 Advanced: Exs: 9-39 odd, 40-77

On-line Textbook


Worksheets



PH-A1-TR

Activity – Game: It’s All Downhill From Here

Outlining - Students work in pairs and go to website http://www.mathwarehouse.com/algebra/linear_equation/standard-form-equation-of-a-line.php

Students must

outline the information and complete all of the activities on a separate sheet of







http://www.mathwarehouse.com/algebra/linear_equation/standard-form-equation-of-a-line.php







34

paper to be handed in to the teachers. Outlines must be complete and answers to each question must be answered. One person will be the researcher the other the writer and the teacher will have them switch at a certain point.

HSPA/PARCC

Prep


Example(s):

p.326: 39 (Writing)

The three forms of linear equations you have studied are slope-intercept form, point-slope form, and standard form. Explain when each form is most useful?




Handouts

PH-A1-TR

Test Prep Handout

1

5.6. Parallel and Perpendicular Lines

To determine whether lines are parallel, perpendicular, or neither and to write the equations of parallel and perpendicular lines.

Example(s):

Identify each pair of parallel and perpendicular lines.

CCSS G.GPE.B.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). MP

1, 3, 4

Text: p.330-335

Basic: Exs: 7-30, 32-33, 35, 38-47 Average: Exs: 7-25 odd, 27-35, 38-47 Advanced: Exs: 7-25 odd, 27-47 8-30 even, 38-46 even

On-line Textbook


Worksheets

Kuta PA1 Kuta A1 Video(s) http://www.y

outube.com/watch?v=PIAP4gnu2Ic


PH-A1-TR

Activity – Game: Dot Plot

Stations - http://highschool.wapak.org/Portals/46/Parallel%20and%20Perpendicular%20Lines%20Investigation.pdf *explained in website https://www.jths.org/assets/2/staff_assets/dn







http://highschool.wapak.org/Portals/46/Parallel%20and%20Perpendicular%20Lines%20Investigation.pdf





https://www.jths.org/assets/2/staff_assets/dnewell/7_STATIONS.pdf

https://www.jths.org/assets/2/staff_assets/dnewell/7_STATIONS.pdf


35

ewell/7_STATIONS.pdf - chapter 5 review

HSPA/PARCC

Prep


Example(s):

p.334: 32

Will the graph of the line represented by the table

x -1 0 1 2 y -1 3 7 11

intersect the graph of ? Explain.




Handouts

PH-A1-TR

Test Prep Handout

2

6.1. Solving Systems by Graphing

To solve systems of equations by graphing and analyze special systems

Example(s):

Solve the system of equations below by graphing on a coordinate plane.

CCSS A.REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. MP

1, 4, 5

Text: p.364-370

Basic: Exs: 10-34, 36, 38, 43-57 Average: Exs: 11-29 odd, 31-40, 43-57 Advanced: Exs: 11-29 odd, 31-57 10-34 even, 36, 38

On-line Textbook


Worksheets



(Algebra-Systems of Equations)

Online

Activity in


PH-A1-TR

Activity –Game: Name That Quadrant

Math scavenger hunt, worksheets, math lab http://literacy.kent.edu/eureka/EDR/9/Math%20SolvingSystemsofLinearEquationsGraphing.pdf Graphic Org system of equations for note taking









http://literacy.kent.edu/eureka/EDR/9/Math%20SolvingSystemsofLinearEquationsGraphing.pdf







36

Illuminations - Game Cartridges and Silver Dollars

attached**

HSPA/PARCC

Prep


4.3.B2, B4 4.5.A1, A2, A5 B1,

B2, C4


MU Workbook

Unit 4.32 p.283: 18-20 p.290-91: 52-54


Handouts

PH-A1-TR

Test Prep Handout

2

6.2. Solving Systems Using Substitution

To solve systems of equations using substitution

Example(s):

Solve the system of equations below algebraically.

CCSS A.REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. MP

1, 4, 5

Text p.372-377


On-line Textbook


Worksheets





PH-A1-TR

Activity – Puzzle: The Shortest Path

Step by Step Process – Solving using Sub. PPT Attached. Graphic Org system of equations for note taking attached**

HSPA/PARCC

Prep


Example(s):

p.376: 33

What would your first step be in solving the system below? Explain.




Handouts

PH-A1-TR

Test Prep Handout












37

2

6.3. Solving Systems Using Elimination

To solve systems by adding or subtracting to eliminate a variable

Example(s):

Solve the system of equations below algebraically.

CCSS A.REI.C.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. A.REI.6

MP

1, 4

Text p.378-386


On-line Textbook


Worksheets



(Algebra-Systems of Equations-Matrix Method)


PH-A1-TR

Activity – Toss the Variables

Graphic Organizer Elim – attached

Graphic Org system

of equations for note taking attached**

HSPA/PARCC

Prep


Example(s):

p.383: 28

A toy store worker packed two boxes of identical dolls and plush toys for shipping in boxes that weigh 1 oz. when empty. One box held 3 dolls and 4 plush toys. The worker marked the weight as 12 oz. The other box held 2 dolls and 3 plush toys. The worker marked the weight as 10 oz. Explain why the worker must have made a mistake.




Handouts

PH-A1-TR

Test Prep Handout










38

2

6.4. Applications of Linear Systems

To choose the best method for solving a system of linear equations

Example(s):

A carpenter makes and sells bookshelves. The material for each bookshelf costs $45.50. The bookshelves sell for $100. If the carpenter spends $450 on advertising, how many bookshelves must he sell to break even?

CCSS A.REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. N.Q.2, 3 A.CED.3

MP

1, 3, 4

Text p.387-392

Basic: Exs: 7-16, 18-21, 23, 25, 29-37 Average: Exs: 7-11 odd, 13-26, 29-37 Advanced: Exs: 7-11 odd, 13-37 7-31 odd

On-line Textbook


Worksheets




Online

Activity in Illuminations – Talk or Text


PH-A1-TR

Activity – A Real-World Application

*Refresher on key words and understanding word problems

HSPA/PARCC

Prep


Example(s):

p.392: 25

A student claims that the best way to solve the system below is by substitution. Do you agree? Explain.




Handouts

PH-A1-TR

Test Prep Handout











39

2

6.5. Linear Inequalities

To graph linear inequalities in two variables and to use linear inequalities when modeling real-world situations

Example(s):

1. What is the equation of the graph shown?

2. Graph the solution to the

system of inequalities in a coordinate plane.

3. A fish market charges $9

per pound for Cod and $12 per pound for Flounder. If the fish store has to sell each type of fish today to reach a daily quota of at least $120, then

. a. Graph the

inequality.

b. Give three different combinations of Cod and Flounder sales that meets the daily quota.

CCSS A.REI.D.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. A.CED.3

MP

1, 4

Text p.394-399

Basic: Exs: 8-37, 42-49 Average: Exs: 9-33 odd, 35-38, 42-49 Advanced: Exs: 9-35 odd, 36-49

On-line Textbook


Worksheets



PH-A1-TR

Activity – Game: Above, On, or Below?

Linear Inequalities – project – students must answer questions and graph word problems – groups of 3 or 4 – attached Inequalities Jeopardy PPT - attached








40

HSPA/PARCC

Prep


4.3.B1, B2, C2 4.5.A1, A2, A5 B1,

B2, C4


MU Workbook

Unit 4.31 p.278: 47


Handouts

PH-A1-TR

Test Prep Handout

2

6.6. Systems of Linear Inequalities

To solve systems of linear inequalities by graphing and to model real-world situations using systems of linear equalities

Example(s):

You want to build a fence for a rectangular dog run. You want the run to be at least 10 ft. wide. The run can be at most 50 ft. long. You have 126 ft. of fencing.

CCSS A.REI.D.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. MP

1, 4

Text p.400-405

Basic: Exs: 7-27, 28, 30, 31, 33, 39-48 Average: Exs: 7-27 odd, 28-35, 39-48 Advanced: Exs: 7-27 odd, 28-48 7-41 odd

On-line Textbook


Worksheets



PH-A1-TR

Activity – Puzzle: Figure Me Out Project

http://alex.state.al.us/lesson_view.php?id=24038

All worksheets are

available on website as well as directions

HSPA/PARCC

Prep


Example(s):

p.404: 29

a. Graph the system and .

b. Will the boundary lines and ever intersect?

How do you know? c. Do the shaded regions in

the graph from part(a) overlap?

d. Does the system of




Handouts

PH-A1-TR

Test Prep Handout











41

inequalities have any solutions? Explain.


1. Solve systems of linear equations in two variables graphically and algebraically. Include solutions that have been found by replacing one equation by the sum of

that equation and a multiple of the other.

2. Find approximate solutions of linear equations by making a table of values, using technology to graph and successive approximations.

3. Graph equations, inequalities, and systems of inequalities in two variables and explain that the solution to an equation is all points along the curve, the

solution to a system of linear functions is the point of intersection, and the solution to a system of inequalities is the intersection of the corresponding half-

planes.

4. Explain and interpret the definition of functions including domain and range and how they are related; correctly use function notation in a context and

evaluate functions for inputs and their corresponding outputs.

5. Write a function for a geometric sequence defined recursively, whose domain is a subset of the integers.

6. Graph functions by hand (in simple cases) and with technology (in complex cases) to describe

linear relationships between two quantities and identify, describe, and compare domain and other key features in one or multiple representations.

7. Compare properties of two functions each represented in a different way (algebraically,

graphically, numerically in tables, or by verbal descriptions).

PARCC FRAMEWORK/ASSESSMENT – UNIT 2

PARCC EXEMPLARS: www.parcconline.org (copy & paste the url or link into search engine)

Best Buy Tickets from http://map.mathshell.org/materials/tasks.php?taskid=286#task286

HSPA EXEMPLARS: http://www.nj.gov/education/assessment/hs/hspa_mathhb.pdf

Patterns And Algebra: Exemplar from HSPA booklet

http://www.woodbridge.k12.nj.us/SchoolsHS/Colonia-HS/pdfs/hspa/2012_hspa_student_preparation_booklet.pdf

1. The graph below represents which of the following inequalities?


http://map.mathshell.org/materials/tasks.php?taskid=286#task286

http://www.nj.gov/education/assessment/hs/hspa_mathhb.pdf

http://www.woodbridge.k12.nj.us/SchoolsHS/Colonia-HS/pdfs/hspa/2012_hspa_student_preparation_booklet.pdf


42

a.

b.

c.

d.

Geometry and Measurement: Exemplars from http://www.regentsprep.org/Regents/math/geometry/GCG1/PracLine.htm

1. What is the slope of a line perpendicular to ?

a.

b.

c.

d.



9.1. 21st Century Life and Career Skills: All students will demonstrate the creative, critical thinking, collaboration, the problem-solving skills needed to function successfully as both global citizens and workers in diverse ethnic and organizational cultures. 9.1.12.A.1 Apply critical thinking and problem-solving strategies during structured learning experiences.

http://www.regentsprep.org/Regents/math/geometry/GCG1/PracLine.htm

http://www.state.nj.us/education/cccs/standards/9/9.pdf


43

PROJECT 2: LETS DANCE! (Prentice Hall Algebra 1 Teacher Resources: Chapter 6)


9.2.12.A.1 Analyze the relationship between various careers and personal earning goals.

PROJECT 1: THE CHOICE IS YOURS (Prentice Hall Algebra 1 Teacher Resources: Chapter 5)

9.3. Career Awareness, Exploration, and Preparation: All students will apply knowledge about and engage in the process of career awareness, exploration, and preparation in order to navigate the globally competitive work environment of the information age.

9.4. Career and Technical Education: All students who complete a career and technical education program will acquire academic and technical skills for careers in emerging and established professions that lead to technical skill proficiency, credentials, certificates, licenses, and/or degrees.


Project 1: The Choice is Yours (Chapter 5)

Project 2: Let’s Dance! (Chapter 6)


Math Journals

Project 1 & 2

o Collaboration:

Project 1 & 2







IEP/504 Modifications: f. Students will be allowed to use the graphing calculator g. Students will be provided guided notes/graphic organizers to help with organization and to build their note-taking skills in math h. Modified assessments and assignments (classwork, homework, quizzes/tests) as needed



CCSS Mathematical Practices:

MP1: Make sense of problems and persevere in solving them.


44

MP2: Reason abstractly and quantitatively. MP3: Construct viable arguments and critique the reasoning of others. MP4: Model with mathematics. MP5: Use appropriate tools strategically. MP6: Attend to precision. MP7: Look for and make use of structure. MP8: Look for and express regularity in repeated reasoning.

Common Core Standards Abbreviations a. Number & Quantity

1. N-RN-The Real Number System 2. N-Q-Quantities 3. N-CN-The Complex Number System 4. N-VM-Vector and Matrix Quantities





Kuta A1: Kuta Software – Infinite Algebra 1 (Free Worksheets)

Kuta PA1: Kuta Software – Infinite Pre-Algebra 1 (Free Worksheets)



45

UNIT 3 Expressions and Equations

Total Number of Days: 25 days (5 weeks) Grade/Course: 9/Algebra 1


CHAPTER 7

Equivalence: How can you represent numbers less than 1 using exponents?

Properties: How can you simplify expressions involving exponents?

Function: What are the characteristics of exponential functions? CHAPTER 8

Equivalence: Can two algebraic expressions that appear to be different be equivalent?

Properties: How are the properties of real numbers related to polynomials?

CHAPTER 7

Equivalence: The idea of exponents can be extended to include zero and negative

exponents. (7.1) Properties: Properties of exponents make it easier to simplify products or quotients of

powers with the same base or powers raised to a power or products raised to a power. (7.2-7.4)

You can use rational exponents to represent radicals. (7.5) Function: The parent of the family of exponential functions is . The

independent variable is an exponent. This family of functions can model growth or decay of an initial amount. (7.6-7.7)

CHAPTER 8

Equivalence:

Monomials can be used to form larger expressions called polynomials. Polynomials can be added and subtracted. (8.1)

There are several ways to find the product of two binomials, including models, algebra, and tables. (8.3-8.4)

Some trinomials of the form and some polynomials of a degree greater than 2 can be factored to equivalent forms which are the product of two binomials. (8.5-8.8)

Properties

The properties of real numbers can be used to multiply a monomial by a polynomial or simplify the product of binomials. (8.2-8.4)

The properties of real numbers can also be used to factor some trinomials of the form and some polynomials of a degree greater than 2. (8.5-8.8)


46

PACING (days)



ASSESSMENTS Pearson

OTHER (e.g., tech)

1.5

7.1. Zero and Negative Exponents

To simplify expressions involving zero and negative exponents

Example(s):

1. Simplify each expression. a. b.

2. Is the value of

positive or negative?

CCSS N.RN.A.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5. N.RN.2

MP

1, 4

Text p.418-423

Basic: Exs: 9-46 all, 48-58 even, 60, 62, 64, 73-91 Average: Exs: 9-45 odd, 47-65, 73-91 Advanced: Exs: 9-45 odd, 47-91 9-45 odd, 48-58 even

On-line Textbook


Worksheets



(Algebra-Exponents)

Warm-Up (Include review question from 3.4)


PH-A1-TR

Activity – Puzzle: Find the power of 2

Think Pair Share and partner to partner http://www.acoe.org/acoe/files/EdServices/Math/DiscoveringAeroAndNegativeExponentsLessonV4.pdf http://www.rapidtables.com/calc/math/Exponent_Calculator.htm

HSPA/PARCC

Prep


4.3.A1, B2, B4 4.5.A1, B1, B2, B3


MU Workbook

Unit 1.2 p.9-11 p.15: 29, 30 p.17: 50


Handouts

PH-A1-TR

Test Prep Handout

1

7.2. Multiplying Powers with the Same Base

To multiply powers with the same base

Example(s):

Simplify each expression.

1.

CCSS N.RN.A.1 Explain how the definition of the meaning of rational exponents follows from extending the

Text p.424-431

Basic: Exs: 8-30 all, 37, 42, 44, 46, 54-68 Average:

On-line Textbook


Worksheets



PH-A1-TR









http://www.acoe.org/acoe/files/EdServices/Math/DiscoveringAeroAndNegativeExponentsLessonV4.pdf





http://www.rapidtables.com/calc/math/Exponent_Calculator.htm








47

2. properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5. MP

1, 4

Exs: 9-29 odd, 31-46, 54-68 Advanced: Exs: 9-31 odd, 32-68



(Algebra-Exponents)

Activity – Game: From Very Small to Very Large

Spinner Game – MultipExpAct - attached

HSPA/PARCC

Prep


4.1.A1, B2, B4 4.5.A1, B1, B2, B3


MU Workbook

Unit 1.2 p.10-12 p.15: 29, 30 p.16:49


Handouts

PH-A1-TR

Test Prep Handout

1.5

7.3. More Multiplication Properties of Exponents

To raise a power to a power and a product to a power

Example(s):

Simplify each expression.

1.

2.

CCSS N.RN.A.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.

Text p.432-438

Basic: Exs: 10-42 all, 48-66 even, 70, 74-89 Average: Exs: 11-41 odd, 47-89 Advanced: Exs: 11-41 odd, 42-89

On-line Textbook


Worksheets



(Algebra-Exponents)

Warm-Up (Include review question from T426)


PH-A1-TR

Activity – Puzzle: A Hidden Fruit

Bingo and Puzzle – MultExpAct -attached














48

MP

1, 4

HSPA/PARCC

Prep


4.1.A1, B2, B4 4.5.A1, B1, B2, B3


MU Workbook

Unit 1.2 p.12 p.15: 32, 33, 34, 38


Handouts

PH-A1-TR

Test Prep Handout

1

7.4. Division Properties of Exponents

To divide powers with the same base and to raise a quotient to a power

Example(s):

Simplify the given expression:

CCSS N.RN.A.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5. MP

1, 4

Text p.439-446

Basic: Exs: 8-48 all, 50-54 even, 60-72 even, 78-80, 84, 86, 94-110 Average: Exs: 9-47 odd, 49-87, 94-110 Advanced: Exs: 9-47 odd, 49-110 8-54 even 60-72 even

On-line Textbook


Worksheets



(Algebra-Exponents)



PH-A1-TR

Activity – Playing with Properties

Exponent powers graphic organizer - attached Connecting Exponents to real life samples – attached

HSPA/PARCC

Prep


4.1.A1, B2, B4 4.5.A1, B1, B2, B3


MU Workbook

Unit 1.2 p.10-11 p.15: 31, 37 p.17: 50


Handouts

PH-A1-TR

Test Prep Handout










49

1

7.5. Rational Exponents and Radicals

To rewrite expressions involving radicals and rational exponents

Example(s):

Simplify the given expression using the properties of exponents, and then write the expression in radical form.

1.

2.

CCSS N.RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. MP

1, 4

Text p.447-452

Basic: Exs: 11-36, 38-48 even, 50-53, 55-77 Average: Exs: 11-35 odd, 37-53, 55-77 Advanced: Exs: 11-35 odd, 37-77 11-35 odd, 38-50 even

On-line Textbook


Worksheets

Kuta PA1 Kuta A1 Video(s) https://www.youtube.com/watch?v=wp2Ho985DyI&feature=player_embedded

Warm-up (Include review of addition of fractions)


PH-A1-TR

Activity – Puzzle: Frontward and Backward Code

HSPA/PARCC

Prep


4.1.A1, B2, B4 4.5.A1, B1, B2, B3


MU Workbook

Unit 1.2 p.12-14 p.15: 39-40 p.16: 41-47 p.17: 51


Handouts

PH-A1-TR

Test Prep Handout

1

7.6. Exponential Functions

To evaluate and graph exponential functions

Example(s):

A city’s population, P, in thousands, can be modeled by the equation

, where t is the number of years since the year 2000. 1. In the given equation,

what does the number 225 represent?

2. In the given equation, what does the number 1.03 represent?

CCSS F.IF.C.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. F.IF.4, 5, 9 F.LE.2 A.REI.11 A.CED.2

Text p.453-459 Basic: Exs: 8-31 all, 32-50 even, 56-69 Average: Exs: 9-31 odd, 32-50, 56-69 Advanced: Exs: 9-31 odd, 32-69

On-line Textbook


Worksheets



PH-A1-TR

Activity – Expansion and Contraction

Exponential Dice Growth. Students will watch as teacher does and then perform activity by themselves.

http://media.mivu.org/mvu_pd/a4a/resources/applets/exp







https://www.youtube.com/watch?v=wp2Ho985DyI&feature=player_embedded











http://media.mivu.org/mvu_pd/a4a/resources/applets/exponential_dice.html




50

3. What is the city’s population in 3 years?

MP

1, 4

onential_dice.html Exponential Functions Stations Wksht - Attached

HSPA/PARCC

Prep

Analyze and identify continuous function graphs

Example(s):

What are the differences between the graphs of a linear, quadratic and exponential function? Explain by giving an example of each graph and by clearly labeling them.

NJCCCS

4.3.B1, B2, B4, C1 4.5.A1, A2, A5,

B1, B2, C1, C2, C6, E1-3, F3


MU Workbook

Unit 4.32 p.284-287

Unit 4:33 p.297: 26


Handouts

PH-A1-TR

Test Prep Handout

1

7.7. Exponential Growth and Decay

To model exponential growth and decay

Example(s):

In an experiment, a colony of bacteria is growing at a rate or 25% per hour. The function represents the population of bacteria t hours after the start of the experiment, where P is the initial population at the start of the experiment. The researcher wants to determine the growth rate per minute instead of per hour. If the function is rewritten in the form , what is the value of a?

CCSS F.IF.C.8b Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay. F.IF.B.4 A.SSE.1.b, 3 A.CED.2 F.BF.3 F.LE.1.c, 5

MP

Text p.460-466

Basic: Exs: 9-27 all, 28-38 even, 39, 43-55 Average: Exs: 9-27 odd, 28-40, 43-55 Advanced: Exs: 9-27 odd, 28-55 9-45 odd

On-line Textbook


Worksheets



PH-A1-TR

Activity – Game: Getting Lager or Getting Smaller?

M&M lab –exponential growth and decay –attached








51

1, 4

HSPA/PARCC

Prep


4.1.A1, B2, B4 4.5.A1, B1, B2, B3


MU Workbook

Unit 4.33 p.292-293 p.296: 21 p.297: 25, 26


Handouts

PH-A1-TR

Test Prep Handout

1

8.1. Adding and Subtracting Polynomials

To classify, add, and subtract polynomials

Example(s):

1. Simplify the given polynomial.

2. The perimeter of a triangular park is

. What is the missing length? a. What is the sum of

the two given side lengths?

b. What operation should you use to find the remaining side length?

CCSS A.APR.A.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. MP

1, 4

Text p.486-491

Basic: Exs: 8-44, 52-56 Average: Exs: 9-39 odd, 41-48, 52-56 Advanced: Exs: 9-39 odd, 41-56 8-56 even

On-line Textbook


Worksheets



(Algebra-Polynomials)

Warm-Up (Include review of adding/subtracting integers)


PH-A1-TR

Activity – Puzzle: Polynomial Search Adding and Subtract Polynomials flashcards – attached *see me for details

HSPA/PARCC

Prep

See above skills for 8.1 NJCCCS

4.1.B1, D1-3 4.5.A1, A2, A5,

C3, C4, E1, E3


MU Workbook

Unit 4.30 p.265: 4-6 p.268: 23, 26, 29, 30


Handouts

PH-A1-TR

Test Prep Handout










52

1

8.2. Multiplying and Factoring

To multiply a monomial by a polynomial and to factor a monomial from a polynomial

Example(s):

1. Simplify and write in standard form.

2. Factor the given polynomial.


1, 4

Text p.492-497

Basic: Exs: 9-28 all, 30-36, 38, 40, 44-58 Average: Exs: 9-25 odd, 27, 29-41, 44-58 Advanced: Exs: 9-29 odd, 30-58 10-28 even, 30-46 even

On-line Textbook


Worksheets




Warm-Up (Include review question from T426)


PH-A1-TR

Activity – Puzzle: Getting Back Home

Factoring polynomials graphic organizers – attached key and blank

HSPA/PARCC

Prep


4.1.B1, D1-3 4.5.A1, A2, A5,

C3, C4, E1, E3


MU Workbook

Unit 4.30 p.266: 7-9 p.268: 24, 25, 27, 28


Handouts

PH-A1-TR

Test Prep Handout

1.5

8.3. Multiplying Binomials

To multiply two binomials or a binomial by a trinomial

Example(s):

Simplify the given product and write in standard form: 1.

2.


1, 4

Text p.498-503


On-line Textbook


Worksheets





PH-A1-TR

Activity – Puzzle: The Binomial Code Binomial tiles online

http://nlvm.usu.edu/en/nav/frames_asid_189_g_1_t_2.html?open=activities&from=topic_t_2.html

HSPA/PARCC

Prep


4.1.B1, D1-3 4.5.A1, A2, A5,

C3, C4, E1, E3


MU Workbook

Unit 4.30 p.270: 39


Handouts























53

PH-A1-TR

Test Prep Handout

1.5

8.4. Multiplying Special Cases

To find the square of a binomial and to find the product of a sum and difference

Example(s):

1. Simplify the expression:

2. Simplify each product:

a.

b.


1, 4

Text p.504-511

Basic: Exs: 9-35 all, 36-50 even, 51-52, 59-71 Average: Exs: 9-35 odd, 36-55, 59-71 Advanced: Exs: 9-35 odd, 36-71 9-57 odd

On-line Textbook


Worksheets





PH-A1-TR

Activity – Game: Special Cases

FOIL

HSPA/PARCC

Prep

See above skills for 8.4

Example(s):

Write and simplify the expression for the area of a square with a side length of

. (Draw a diagram that depicts this problem)

NJCCCS

4.1.B1, D1-3 4.5.A1, A2, A5,

C3, C4, E1, E3


MU Workbook

Unit 4.30 p.270: 39


Handouts

PH-A1-TR

Test Prep Handout

1

8.5. Factoring

To factor trinomials of the form

Example(s):

Factor the given expressions

1.

2.

CCSS A.SSE.A.1.a Interpret parts of an expression, such as terms, factors, and coefficients. MP

1, 4

Text p.512-517

Basic: Exs: 10-40 all, 42-44 all, 50-54 even, 61-73 Average: Exs: 11-39 odd, 41-54, 61-73 Advanced: Exs: 11-39 odd, 41-73

On-line Textbook


Worksheets



(Algebra-

Warm-Up (Include questions on GCF)


PH-A1-TR

Activity – Game: Factoring

Factoring Frenzy PPT - Attached


















54

Factoring)

HSPA/PARCC

Prep


4.1.B1, D1-3 4.5.A1, A2, A5,

C3, C4, E1, E3


MU Workbook

Unit 4.30 p.267: 18 p.270: 40


Handouts

PH-A1-TR

Test Prep Handout

1

8.6. Factoring

To factor trinomials of the form

Example(s):

1. Factor the given expressions a. b.

2. The top of a rectangular table has an area of

. The width of the table is

. What is the length of the table?

CCSS A.SSE.A.1.a Interpret parts of an expression, such as terms, factors, and coefficients. MP

1, 4

Text p.518-522

Basic: Exs: 8-27 all, 28-34 even, 35-36, 38-46 even, 52-67 Average: Exs: 9-27 odd, 28-47, 52-67 Advanced: Exs: 9-27 odd, 28-67 8-45 odd

On-line Textbook


Worksheets



(Algebra-Factoring)

Warm-Up (Include general Area problem)


PH-A1-TR

Activity – Game: One From Column A, One From Column B Factoring Frenzy PPT - Attached

HSPA/PARCC

Prep

To estimate the area of a figure

NJCCCS

4.1.A2, C1 4.2.D1, D2, E2 4.5.A2, B1, B2,

C4, D2, E1, E2


MU Workbook

Unit 2.15 p.126-128 p.134: 62, 63 p.135: 66 p.136: 69, 70


Handouts

PH-A1-TR

Test Prep Handout

1.5

8.7. Factoring Special Cases

To factor perfect-square trinomials and the difference of two squares

Example(s):

CCSS A.SSE.A.1a Interpret parts of an expression, such as terms, factors, and coefficients.

Text p.523-528

Basic: Exs: 9-40, 42-43, 49, 58-67 Average:

On-line Textbook


Worksheets

Warm-Up (Include question on prime factors)


PH-A1-TR














55

Factor each expression.

1.

2.

A.SSE.A.1b, 2

MP

1, 4

Exs: 9-37 odd, 39-50, 58-67 Advanced: Exs: 9-37 odd, 39-67 9-49 odd



(Algebra-Factoring)

Activity – Grid-Paper Factoring

Factoring special cases battleship – laptops http://www.quia.com/ba/356108.html

HSPA/PARCC

Prep


Example(s):

a. Factor by removing the common monomial factor and them using the difference of squares rule to factor the remaining expression.

b. Factor by using the difference of squares rule and then removing the common monomial factors.

c. Why can you factor in two

different ways? d. Can you factor

in the two ways you factored in parts (a) and (b)? Explain your answer

See above standards for 8.7

See above text resources for 8.7 Standardized Test Prep p. 528

See above “other” resources for 8.7


Handouts

PH-A1-TR

Test Prep Handout

2

8.8. Factoring by Grouping

To factor higher-degree polynomials by grouping

Example(s):

Factor completely

1.

2.

CCSS A.SSE.A.1.a Interpret parts of an expression, such as terms, factors, and coefficients.

A.SSE.A.1b, 2

MP

Text p.529-533

Basic: Exs: 9-30, 32, 34, 35, 38, 40, 47-61 Average: Exs: 9-29 odd, 31-40, 47-61

On-line Textbook


Worksheets

Kuta PA1 Kuta A1

Warm-Up (Include problem on Distributive Property)


PH-A1-TR

Activity – Game: Common Binomial





http://www.quia.com/ba/356108.html

http://www.quia.com/ba/356108.html








56

1, 4 Advanced: Exs: 9-29 odd, 31-61 10-40 even

Video(s)


(Algebra-Factoring)

Factors

Factoring step by step http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut27_gcf.htm

HSPA/PARCC

Prep


Example(s):

Describe how to factor the polynomial:

See above standards for 8.8

See above text resources for 8.8 Standardized Test Prep p. 533

See above “other” resources for 8.8


Handouts

PH-A1-TR

Test Prep Handout


1. Interpret parts of expressions in terms of context including those that represent square and cube roots; use the structure of an expression to identify ways to

rewrite it.

2. Manipulate expressions using factoring, completing the square and properties of exponents to produce equivalent forms that highlight particular properties

such as the zeros or the maximum or minimum value of the function.

3. Perform addition, subtraction and multiplication with polynomials and relate it to arithmetic operations with integers.

4. Write linear and exponential functions (e.g. growth/decay and arithmetic and geometric sequences) from graphs, tables, or a description of the relationship,

recursively and with an explicit formula, and describe how quantities increase linearly and exponentially over equation intervals.

5. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, simple

rational and exponential functions and highlighting a quantity of interest in a formula.

6. Create linear and quadratic equations that represent a relationship between two or more variables. Graph equations on the coordinate axes with labels and

scale.

7. Derive the quadratic formula by completing the square and recognize when there are no real solutions.

8. Solve quadratic equations in one variable using a variety of methods [including inspection (e.g. ), factoring, completing the square, and the quadratic

formula].


PARCC

1. QUADRATIC EQUATIONS: Exemplar from www.PARCConline.org



http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut27_gcf.htm






57

f. Solve the following equation: 2. Rabbit Populations from http://www.ccsstoolbox.com/parcc/PARCCPrototype_main.html

HSPA

Patterns and Algebra

1. Applications of Factoring from http://www.regentsprep.org/Regents/math/ALGEBRA/AV6/PracFact7.htm The room that is shown in the figure bellow has a floor space of square feet. If the width of the room is feet, what is the length?

a. b. c. d.

2. http://map.mathshell.org/materials/tasks.php

On the grid are eight points from two different functions. A certain linear function passes through exactly four of the points shown and a certain quadratic function passes through the remaining four points.

a. For the linear function:

Write the coordinate pairs of its four points. Draw the line on the grid Write an equation for the function and show your work.

b. For the quadratic function:

Write the coordinate pairs of its four points.

http://www.ccsstoolbox.com/parcc/PARCCPrototype_main.html

http://www.regentsprep.org/Regents/math/ALGEBRA/AV6/PracFact7.htm

http://map.mathshell.org/materials/tasks.php


58

Draw the graph of the function on the grid Write an equation that fits the quadratic function and show your work.



9.1. 21st Century Life and Career Skills: All students will demonstrate the creative, critical thinking, collaboration, the problem-solving skills needed to function successfully as both global citizens and workers in diverse ethnic and organizational cultures. 9.1.12.B.1 Present resources and data in a format that effectively communicates the meaning of the data and its implications for solving problems, using

multiple perspectives 9.1.12.B.2 Create and respond to feedback loop when problem solving. 9.1.12.B.3 Assist in the development of innovative solutions to an onsite problem by incorporating multiple perspectives and applying effective problem-

solving strategies during structured learning experiences, service learning, or volunteering. 9.1.12.C.4 Demonstrate leadership and collaborative skills when participating in online learning communities and structured learning experiences.

PROJECT 1: CHAIN LETTERS (Prentice Hall Algebra 1 Teacher Resources – Chapter 7)

PROJECT 2: CSI ALGEBRA 1 STEM PROJECT ON POLYNOMIALS

(http://www.teacherspayteachers.com/Product/CSI-Algebra-1-STEM-Project-Complete-eBook-300691)





Project 1: Chain Letters

Project 2: CSI Algebra 1 – STEM Project on Polynomials

(http://www.teacherspayteachers.com/Product/CSI-Algebra-1-STEM-Project-Complete-eBook-300691)


Math Journals

o Collaboration:

Project 1 & 2





http://www.teacherspayteachers.com/Product/CSI-Algebra-1-STEM-Project-Complete-eBook-300691

http://www.teacherspayteachers.com/Product/CSI-Algebra-1-STEM-Project-Complete-eBook-300691


59




IEP/504 Modifications: a. Students will be allowed to use the graphing calculator b. Students will be provided guided notes/graphic organizers to help with organization and to build their note-taking skills in math c. Modified assessments and assignments (classwork, homework, quizzes/tests) as needed




MP1: Make sense of problems and persevere in solving them. MP2: Reason abstractly and quantitatively. MP3: Construct viable arguments and critique the reasoning of others. MP4: Model with mathematics. MP5: Use appropriate tools strategically. MP6: Attend to precision. MP7: Look for and make use of structure. MP8: Look for and express regularity in repeated reasoning.





d. Geometry 1. G-CO-Congruence 2. G-SRT-Similarity, Right Triangles, & Trigonometry 3. G-C-Circles


60

4. G-GPE-Expressing Geometric Properties with Equations 5. G-MG-Modeling with Geometry






61

UNIT 4 Quadratic Functions and Modeling

Total Number of Days: days (5 weeks) Grade/Course: 9/Algebra 1


CHAPTER 9

Function: What are the characteristics of quadratic functions? Solving Equations and Inequalities: How can you solve a quadratic

equation? Modeling: How can you use functions to model real-world situations?

CHAPTER 9

Function: The family of quadratic functions models certain situations where the rate of

change is not constant. These functions are graphed by a symmetric curve with a highest or lowest point corresponding to a maximum of minimum value. (9.1)

In the quadratic function , the value of b translates the position of the axis of symmetry. (9.2)

Solving Equations and Inequalities: Quadratic equations can be solved by a variety of methods, including graphing

and finding the square root, using the Zero-Product Property, writing the equation in the form , or using the Quadratic Formula. (9.3-9.6)

Modeling: Linear, quadratic, or exponential functions can be used to model various sets

of data. (9.7)

PACING (days)



ASSESSMENTS Pearson

OTHER (e.g., tech)

2.5

9.1. Quadratic Graphs and Their Properties

To graph quadratic functions of the form

Example(s):

Graph the given function and identify its domain and range.

CCSS F.IF.C.7a Graph linear and quadratic functions and show intercepts, maxima, and minima. F.IF.4, 5 A.CED.2 F.BF.3

MP

1, 4, 6

Text p.546-552

Basic: Exs: 7-28 all, 30-32 even, 33, 34-40 even, 46, 48, 50-63 Average: Exs: 7-27 odd, 28-46, 50-63 Advanced: Exs:

On-line Textbook


Worksheets


Mathispower4u

Warm-Up (Include Review Question from 7.5 & 7.6)


PH-A1-TR

Activity – Puzzle: Add ‘em Up

Quadratic Function Graph Matching









62

7-27 odd, 28-63 8-50 even

PH-A1-SR

Chapter 9:


HSPA/PARCC

Prep

To analyze and interpret quadratic graphs

Example(s):

The graph of is shown

below. What is the solution of the equation?

NJCCCS

4.1.B1, D1, D2, D3

4.5.A1, A2, A5, B2, B4, C3, C4


MU Workbook

Unit 4.30 p.269: 37


Handouts

PH-A1-TR

Test Prep Handout

2.5

9.2. Quadratic Functions

To graph quadratic functions of the form

Example(s):

1. Graph the function. Label the axis of symmetry and the vertex.

2. Given the table of values below;

x -4 -3 -2 -1 0

CCSS F.IF.C.7a Graph linear and quadratic functions and show intercepts, maxima, and minima. F.IF.4, 8a, 9 A.CED.2 F.BF.3

MP

1, 2, 4, 6

Text p.553-560

Basic: Exs: 7-27 all, 28, 30-34, 37-48 Average: Exs: 7-27 odd, 28-34, 37-48 Advanced: Exs: 7-27 odd, 28-48 7-27 odd, 28-34 even,

On-line Textbook


Worksheets


Mathispower4u

PH-A1-SR

Warm-Up (Include Review Question from 7.5)


PH-A1-TR

Activity – Puzzle: On Odd Riddle

Quadratic Functions Activity Bundle Attached











63

y 3 -3 -5 -3 -3

The function f is defined by:

Which function has the greater maximum value? Show your work.

37-45 odd Chapter 9:


HSPA/PARCC

Prep


Example(s):

Use the graph below to answer the given questions:

What is the domain of

the function? What is the range of the

function? What is the minimum of

the function? What type of function is

represented by the graph?

NJCCCS

4.3.B2, B4 4.5.A1, A2, A5,

B1, B2, C4


MU Workbook

Unit 4.32 p.282 p.289: 43-46


Handouts

PH-A1-TR

Test Prep Handout

2.5

9.3. Solving Quadratic Equations

To solve quadratic equations by graphing and using square roots

Example(s):

Solve the given equation and

CCSS A.REI.B.4b Solve quadratic equations by inspection (e.g., for x2 = 49), taking

Text p.561-567

Basic: Exs: 8-36 all, 38-48 even, 51, 58-74

On-line Textbook











64

graph its related function. If the equation has no real-number solution, write no solution. 1. 2.

square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. N.Q.2 A.APR.3 A.CED.1, 4

MP

1, 4

Average: Exs: 9-35 odd, 37-55, 58-74 Advanced: Exs: 9-35 odd, 37-74 8-48 even

Worksheets



(Algebra-Quadratic Equations)

PH-A1-SR

Chapter 9:


PH-A1-TR

Activity – Which is Which?

http://www.mathsisfun.com/quadratic-equation-solver.html

HSPA/PARCC

Prep


4.1.B1, D1, D2, D3

4.5.A1, A2, A5, B2, B4, C3, C4


MU Workbook

Unit 4.30 p.269: 32, 34, 36, 37 p.270: 40


Handouts

PH-A1-TR

Test Prep Handout

2.5

9.4. Factoring to Solve Quadratic Equations

To solve quadratic equations by factoring

Example(s):

1. Solve.

2. What are the x- and y-intercepts of the graph in the coordinate plane of the polynomial function:

CCSS A.REI.B.4b Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize

Text p.568-575


On-line Textbook


Worksheets



Warm-Up (Include Review question from 5.8)


PH-A1-TR

Activity – Game: The Winning

Layered look book - attached



















65

3. What are the zeros/roots of the function:

when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. A.SSE.3.a A.CED.1 F.IF.8.a

MP

1, 4

8-58 even


PH-A1-SR

Chapter 9:


HSPA/PARCC

Prep


Example(s):

Use the graph below to answer the given questions:

What are the roots of the

function? What is the maximum of

the function? What is the domain of

the function? Is the function

increasing/decreasing on the interval where

?

NJCCCS

4.3.B2, B4 4.5.A1, A2, A5,

B1, B2, C4


MU Workbook

Unit 4.32 p.290: 47-51


Handouts

PH-A1-TR

Test Prep Handout

2.5

9.5. Completing the Square

To solve quadratic equations by completing the square

CCSS A.REI.B.4a Use the method of

Text p.576-581

On-line Textbook

https://www.pearsonsuccessnet.com/snpap

Warm-Up (Include review questions from 5.3-5.5)






66

Example(s):

1. What are the solutions of the equation

2. Find the vertex of

completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form. A.REI.A.1, B.4b N.Q.3 A.SSE.1.a, b, 3.b A.CED.1 F.IF.8.a

MP

1, 4, 5

Basic: Exs: 7-33 all, 34-42 even, 43-44, 50-66 Average: Exs: 7-31 odd, 32-47, 50-66 Advanced: Exs: 7-31 odd, 32-66 8-42 even

p/login/login.jsp?showLoginPage=true

Worksheets




PH-A1-SR

Chapter 9:



PH-A1-TR

Activity – Square Patterns

Hollywood squares – ppt factoring squares - attached

HSPA/PARCC

Prep

To compare linear functions

Example(s):

The graph of the linear function f(x) is shown in the coordinate plane below. A second function h(x) is

defined by .

Compare the slope, x- and y-

NJCCCS

4.3.B1, B2, C2 4.5.A1, A2, A5,

C3, C4, E1, E3


Model Curriculum Unit 4 Assessment

MU Workbook

Unit 4.31 p.279: 49


Handouts

PH-A1-TR

Test Prep Handout








67

intercepts and for each function.

2.5

9.6. The Quadratic Formula and the Discriminant

To solve quadratic equations using the quadratic formula and to find the number of solutions of a quadratic equation

Example(s):

1. Use the quadratic formula to solve the given equation.

2. How many real number solutions does

have?

CCSS A.REI.B.4a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form. A.REI.B.4b N.Q.3 A.CED.1

MP

1, 4, 5

Text p.582-588

Basic: Exs: 7-34 all, 36-40 even, 41-44 all, 50-61 Average: Exs: 7-35 odd, 36-45, 50-61 Advanced: Exs: 7-35 odd, 36-61 8-44 even

On-line Textbook


Worksheets




PH-A1-SR

Chapter 9:


Warm-Up (Include review questions from 5.1 & 5.3)


PH-A1-TR

Activity – Game: Start your Engines Exploring the quadratic formula stations - attached

HSPA/PARCC

Prep


4.1.B1, D1, D2, D3

4.5.A1, A2, A5, B2, B4, C3, C4


MU Workbook

Unit 4.30 p.267: Step 2


Handouts

PH-A1-TR

Test Prep Handout












68

2.5

9.7. Linear, Quadratic, and Exponential Models

To choose a linear, quadratic, or exponential model for data

Example(s):

1. If , what is

the value of x? Explain your reasoning.

2. Graph the set of points and determine which model is most appropriate.

(0, 2), (-1,4), (1, 1), (2, 0.5)

CCSS F.LE.A.1a Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. F.IF.4 F.LE.A.2, 3 S.ID.6.a

MP

1, 2, 3, 4, 7

Text p.589-595

Basic: Exs: 6-20, 22-24, 28-37 Average: Exs: 7-19 odd, 20-25, 28-37 Advanced: Exs: 7-19 odd, 20-37 6-36 even

On-line Textbook


Worksheets


PH-A1-SR

Chapter 9:


Warm-Up (Include review question from 4.5 & 1.4)


PH-A1-TR

Activity – Game: Function Junction MARS – Sorting Functions Project - attached

HSPA/PARCC

Prep


4.3.B1, C1 4.5.C1, C2, C6, E1,

E2, E3, F3


MU Workbook

Unit 4.33 p.292-299


Handouts

PH-A1-TR

Test Prep Handout


1. 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.

2. Use properties of integer exponents to explain and convert between expressions involving radicals and rational exponents, using correct notation. For

example, we define to be the cube root of 5 because we want to hold, so must equal 5.

3. Use the properties of rational and irrational numbers to explain why the sum or product of two rational numbers is rational; the sum of a rational number and

an irrational number is irrational; and the product of a nonzero rational number and an irrational number is irrational.

4. Sketch the graph of a function that models a relationship between two quantities (expressed symbolically or form a verbal description) showing key features

(including intercepts, minimums/maximums, domain, and rate of change) by hand in simple cases and using technology in more complicated cases and relate

the domain of the function to its graph.










69

5. Compare properties of two functions each represented in different ways (algebraically, graphically, numerically in tables, or by verbal descriptions). For

example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

6. Calculate (over a specified period if presented symbolically or as a table) or estimate (if presented graphically) and interpret the average rate of change of a

function.

7. Write functions in different but equivalent forms by manipulating quadratic expressions using methods such as factoring and completing the square.

8. Write a function that describes a linear or quadratic relationship between two quantities given in context using an explicit expression, a recursive process, or

steps for calculation and relate these functions to the model.

9. Identify the effects of translations on a function, find the value of k given the graphs.


PARCC

Transforming of graphs of quadratic functions from http://www.ccsstoolbox.com/parcc/PARCCPrototype_main.html

HSPA EXEMPLAS: http://www.mathopolis.com/questions/q.php?id=7193

Number and Numerical Operation: http://www.regentsprep.org/Regents/math/ALGEBRA/AO5/indexAO5.htm

1. = ? Patterns and Algebra:

2. The volumes of the cube and the rectangular prism are equal. What is the value of ?



9.1. 21st Century Life and Career Skills: All students will demonstrate the creative, critical thinking, collaboration, the problem-solving skills needed to function successfully as both global citizens and workers in diverse ethnic and organizational cultures. 9.1.12.A.1 Apply critical thinking and problem-solving strategies during structured learning experiences. 9.1.4.B.1 Participate in brainstorming sessions to seek information, ideas, and strategies that foster creative thinking. 9.1.12.B.1 Present resources and data in a format that effectively communicates the meaning of the data and its implications for solving problems, using

http://www.ccsstoolbox.com/parcc/PARCCPrototype_main.html

http://www.mathopolis.com/questions/q.php?id=7193

http://www.regentsprep.org/Regents/math/ALGEBRA/AO5/indexAO5.htm



70

multiple perspectives.

PROJECT: FULL STOP AHEAD (Prentice Hall Algebra 1 Teacher Resources – Chapter 9)





Project: Full Stop Ahead (Chapter 9)


Project

Math Journals

o Collaboration:

Project







IEP/504 Modifications: a. Students will be allowed to use the graphing calculator b. Students will be provided guided notes/graphic organizers to help with organization and to build their note-taking skills in math c. Modified assessments and assignments (classwork, homework, quizzes/tests) as needed




MP1: Make sense of problems and persevere in solving them. MP2: Reason abstractly and quantitatively. MP3: Construct viable arguments and critique the reasoning of others. MP4: Model with mathematics.


71

MP5: Use appropriate tools strategically. MP6: Attend to precision. MP7: Look for and make use of structure. MP8: Look for and express regularity in repeated reasoning.











72

UNIT 5 Quadratic Functions and Modeling

Total Number of Days: days (5 weeks) Grade/Course: 9/Algebra 1


CHAPTER 5

Modeling: How can you use functions to model real-world situations? CHAPTER 12

Data Collection and Analysis: How can collecting and analyzing data help you make decisions or predictions?

Data Representation: How can you make and interpret different representations of data?

Probability: How is probability related to real-world events?

CHAPTER 5

Modeling: Two sets of numerical data can be graphed as ordered pairs. If the two sets of

data are related, a line on the graph can be used to estimate or predict values. (5.7)

CHAPTER 12

Data Collection and Analysis: Different measures can be used to interpret and compare sets of data. (12.3)

Data Representation:

Data can be organized in matrices or in intervals. Different measures can be used to interpret and compare sets of data. Separating data into subsets is a useful way to summarize and compare data sets. (12.1-12.4)

Probability:

The probability of an event, of , tells how likely it is that the event will occur. Probabilities can be found by reasoning mathematically or by using experimental data. The probability of a compound event can sometimes be found from expressions of the probabilities of simpler events. (12.7-12.8)

PACING (days)



ASSESSMENTS Pearson

OTHER (e.g., tech)

2.5

5.7. Scatter Plots and Trend Lines

To write and use an equation of a trend line and of a line of best fit to make predictions.

Example(s):

Use the table below. (p.340)

CCSS N.Q.1 F.LE.5 S.ID.6, 6a, 6c, 7, 8, 9

MP

1, 4, 7

Text p.546-552

Basic: Exs: 7-28 all, 30-32 even, 33, 34-40 even, 46, 48, 50-63

On-line Textbook


Worksheets

Kuta PA1

Warm-Up (Review Question from 5.1)

Math Journal Unit 5 Pre-

Assessment (one-block prior to lesson)







73

1. Make a scatter plot of

the data. What type of relationship does the scatter plot show?

2. Draw a trend line and write its equation.

3. Predict the average maximum daily temperature in January at a latitude of N.

Average: Exs: 7-27 odd, 28-46, 50-63

Advanced: Exs: 7-27 odd, 28-63

Kuta A1 shamokinmath cheney268 Video(s)

PH-A1-SR

Chapter 5:


Technology

Advanced Data Grapher

Line of Best Fit

PH-A1-TR

Activity – Quick to React

Illuminations: Barbie Bunge

Project – Music to my Ears

Scatterplots foldable - attached

HSPA/PARCC

Prep


4.4.A4, A5 4.5.E1, F1-F3


MU Workbook

Unit 3.22 p.190-197


Handouts

PH-A1-TR

Test Prep Handout

2.5

12. 2 Frequency and Histograms

To make and interpret frequency tables and histograms

Example(s):

The given data shows battery life, in hours, for different brands of cell phones. 12, 9, 10, 14, 10, 11, 10, 18, 21, 10, 14, 22 1. Make a frequency table

of the data. 2. Make a histogram of the

data.

CCSS S.ID.A.1 Represent data with plots on the real number line (dot plots, histograms, and box plots). N.Q.1

MP

1, 4

Text p.732-737

Basic: Exs: 7-20 all, 22-30 even, 31 34-41

Average: Exs: 7-19 odd, 21-31, 34-41


On-line Textbook


Worksheets

Kuta PA1 Kuta A1 swadvantage Video(s)

PH-A1-SR

Chapter 12:

Homework Video



PH-A1-TR

Activity – Puzzle: Order in the Court

Histograms – PPT attached


http://www.cheney268.com/chs/Math/Jones%20Folder/MakeUp1/9.9%20Scatter%20Plot%20WS_Correlation.pdf



http://illuminations.nctm.org/ActivityDetail.aspx?ID=220










http://ebookbrowse.com/gdoc.php?id=490197655&url=6e4dc05b31edad44adf671cde22097cf


74

3. Make a cumulative frequency table of the data.

8-36 even Tutor 12-2 www.pearsonsuccessnet.com

Technology


Histogram Tool

HSPA/PARCC

Prep

To interpret data and graphs

Example(s):

Mr. Lloyd’s class does an experiment with a faucet and two sinks. Sink A is filled with 10 gallons of water and allowed to drain freely. Sink B starts out empty and is filled (with its drain closed) until it reaches 10 gallons of water. The chart below shows the amount of water in each sink at various times.

# min Gal. Sink A

Gal. Sink B

0 10.0 0.0 1 7.5 2.0 2 5.0 4.0 3 2.5 6.0 4 0.0 8.0 5 0.0 10.0

Which sink is draining

faster? Explain how you know.

Draw a graph that shows the filling of Sink B. After how many minutes would the

NJCCCS

4.4.A2 4.5.D1-4, E1


Book:

Kaplan Advantage: HSPA Math – p.217-241

On-line:

Interpreting Graphs – Thatquiz.org

MU Workbook

Unit 3.24 p.214, p.216 p.219, p.221: 39 p. 222


Handouts

PH-A1-TR

Test Prep Handout







http://www.thatquiz.org/tq/previewtest?OQVJ7144


75

water level in Sink B be 5 gallons? Explain how you know.

1.5

12.3 Measures of Central Tendency and Dispersion

To find mean, median, mode, and range

Example(s):

Over the past 8 seasons, one baseball player’s batting averages were .265, .327, .294, .319, .281, .318, .279, and .314. A second player’s batting averages were .304, .285, .312, .291, .303, .314, .280, .312. What are the range and mean of each players’ batting averages? Use your results to compare the players’ batting skills.

CCSS S.ID.A.2 Use statistics to appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. S.ID.3 N.Q.2

MP

1, 4

Text p.738-744

Basic: Exs: 7-21 all, 22, 24, 27, 31-41

Average: Exs: 7-21 odd, 22-28, 31-41


On-line Textbook


Worksheets


PH-A1-SR

Chapter 12:



PH-A1-TR

Activity – Puzzle: One Mean Puzzle CMT quiz with rubric – attached Card game

HSPA/PARCC

Prep


4.4.A1-A3 4.5.B1-B3, D2


MU Workbook

Unit 3.21 p.182-184 p.186-188


Handouts

PH-A1-TR

Test Prep Handout

2.5

12.4 Box-and-Whisker Plots

To make and interpret box-and-whisker plots by finding quartiles and percentiles

Example(s):

Students taking a make-up test receive the following grades: 77, 88, 85, 67, 91, 96, 82, 78, 81, and 65. Which grade has a percentile rank of 70?

CCSS S.ID.A.2 Use statistics to appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

Text p.745-751

Basic: Exs: 8-21 all, 24, 27-33

Average: Exs: 9-17 odd, 19-24, 27-33


On-line Textbook


Worksheets


PH-A1-SR


PH-A1-TR

Activity – Game: Show and Tell http://www.mathwarehouse.com/charts/box-and-whisker-plot-maker.php















http://www.mathwarehouse.com/charts/box-and-whisker-plot-maker.php





76

N.Q.1 S.ID.1

MP

1, 4

Chapter 12:


Technology


Box Plotter Mean and

Median

HSPA/PARCC

Prep


4.4.A5 4.5.A1, B1, C3-C4,

F1, F2, F4


MU Workbook

Unit 3.23 p.198-200


Handouts

PH-A1-TR

Test Prep Handout

2.5

12.7 Theoretical and Experimental Probability

To find theoretical and experimental probabilities

Example(s):

The table below shows the ratings for a new ride in an amusement park from a group of 500 riders, by age-group. A researcher is trying to see whether the ratings and the age-group of riders are related.

Rating E F P

Age

-gr

ou

p

<30 60 110 85

95 70 75

1. How many riders under

the age of 30 rated the ride fair?

CCSS S.CP.A.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). S.CP.4

MP

1, 4

Text p.769-774

Basic: Exs: 10-36 all, 38, 47-59

Average: Exs: 11-33 odd, 34-41, 47-59


On-line Textbook


Worksheets


PH-A1-SR

Chapter 12:



Math Journal HSPA/PARCC Prep Jeopardy Review

Game Unit 5 Model

Curriculum Assessment (after lesson is taught)

PH-A1-TR

Activity – Probability and Area

Experimental and theoretical activity – coin toss- laptops needed - attached

















77

2. What percent of the riders over the age of 30 rated the ride as poor?

HSPA/PARCC

Prep


4.4.B1-B6 4.5.A1-A5, C4,

D1-D3, E1, E3


MU Workbook

Unit 3.20 p.168-171


Handouts

PH-A1-TR

Test Prep Handout


1. Write linear and exponential functions (e.g. growth/decay and arithmetic and geometric sequences) from graphs, tables, or a description of the relationship,

recursively and with an explicit formula, and describe how quantities increase linearly and exponentially over equal intervals.

2. Represent data on the real number line (i.e. dot plots, histograms, and box plots) and use statistics to compare and interpret differences in shape, center, and

spread in the context of the data (account for effects for outliers).

3. Use the mean and standard deviation of a data set to fit it to a normal distribution, estimate population percentages, and recognize that there are dta sets for

which such a procedure is not appropriate (use calculators, spreadsheets, and tables to estimate areas under the normal curve).

4. Summarize and interpret categorical data for two categories in two-way frequency tables; recognize associations and trends in the data.

5. Represent and describe data for two variables on a scatter plot, fit a function to the data, analyze residuals (in order to informally assess fit), and use the

function to solve problems.

a. Uses a given function or choose a function suggested by the context. Emphasize linear and exponential models.

6. Interpret the slope, intercept and correlation coefficient (compute using technology) of a linear model.

7. Distinguish between correlation and causation in a data context.


PARCC

Interpreting categorical and quantitative data from http://map.mathshell.org/materials/tasks.php

1. Jane collected some red and yellow roses. She measured the lengths of their stems, and drew the following box plots.

http://map.mathshell.org/materials/tasks.php


78

Write down the median lengths of both the yellow and red roses to the nearest centimeter. Which color rose would you buy for a 40 cm tall vase?

2. 2. Bob looked up the value of his car in a users guide, and plotted the value after different numbers of years. Write a statement about what the graph

shows.

HSPA EXEMPLAS: http://www.pointpleasant.k12.nj.us/highschool/Guidance/2012_HSPA_Student_Preparation_Booklet.pdf Data Analysis, Probability and Discrete Mathematics

1. The data provided show test scores for twelve students and the number of hours they studied for the test during the three days prior to taking it. Hours

Studied 1.0 1.25 1.5 1.75 2.0 2.25 2.5 2.75 3.0 3.25 3.5 3.75

Test Score

60 70 68 85 90 98 85 92 91 87 85 72

o On the grid provided in your answer folder, construct a scatter plot of these data. o Does there appear to be a relationship between a student’s test score and the time spent studying? Use the scatter plot to support your answer. o Do any of the points appear to be outliers? Explain.

2. Stacy has 6 marbles in a bag: a red, an orange, a yellow, a blue, a green, and a white. She randomly picks 2 marbles out of the bag one at a time without replacement. What is the probability that she will first pick the orange marble and then pick the blue marble?

a.

b.

c.

d.



9.1. 21st Century Life and Career Skills: All students will demonstrate the creative, critical thinking, collaboration, the problem-solving skills needed to function successfully as both global citizens and workers in diverse ethnic and organizational cultures.

9.1.8.E.2 Analyze the role of digital media in sales and marketing and in delivering cultural, political, and other societal messages.

PROJECT: MUSIC TO MY EARS (Prentice Hall Algebra 1 Teacher Resources – Chapter 12)

http://www.pointpleasant.k12.nj.us/highschool/Guidance/2012_HSPA_Student_Preparation_Booklet.pdf



79





Project: Music to my Ears


Project

Math Journals

o Collaboration:

Project







IEP/504 Modifications: f. Students will be allowed to use the graphing calculator g. Students will be provided guided notes/graphic organizers to help with organization and to build their note-taking skills in math h. Modified assessments and assignments (classwork, homework, quizzes/tests) as needed




MP1: Make sense of problems and persevere in solving them. MP2: Reason abstractly and quantitatively. MP3: Construct viable arguments and critique the reasoning of others. MP4: Model with mathematics. MP5: Use appropriate tools strategically. MP6: Attend to precision. MP7: Look for and make use of structure.


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MP8: Look for and express regularity in repeated reasoning.










NOTES FOR TEACHER (NOT TO BE INCLUDED IN YOUR FINAL DRAFT):

4 Cs Three Part Objective Creativity: projects Behavior Critical Thinking: Math Journal Condition Collaboration: Teams/Groups/Stations Demonstration of Learning (DOL) Communication – Powerpoints/Presentations

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