Unit 2: Functions and Patterns

Size: px
Start display at page:

Download "Unit 2: Functions and Patterns"

Transcription

1 For Teacher Use Packet Score: Name: Period: Algebra 1 Unit 2: Functions and Patterns Note Packet Date Topic/Assignment Page Due Date Score (For Teacher Use Only) Warm-Ups 2-A Intro to Functions 2-B Tile Pattern Challenge 2-C Tile Pattern Challenge Continued 2-D Functions and Function Notation 2-E More on Functions 2-F Function Matrix Activity 2-G Types of Functions and Their Patterns 2-H Arithmetic Sequences 2-I Arithmetic Sequences Part 2 2-J Geometric Sequences (2 days of notes, 1 HW) Check for Understanding 2-K Arithmetic an Geometric Sequences 2-L Review (2 Days) Test This packet will be turned in on the day of the test for 100 points. Whenever you re absent, you can get these notes filled out from a classmate or at my website During the unit, I ll check off homework each day to keep track of who is doing their homework, but your homework assignments won t be scored and entered into IC until this packet is collected and graded at the end of the unit. 1

2 Warm-Up Solve each equation below for the given variable. Record all work so that your teacher can follow your legal moves. a. 2x + 2 = 8 b. 4x 2 + x = 2x x c. 3y 9 + y = 6 d. 9 (2 3y) = 6 + 2y (5 + y) Warm-Up Use the pattern you discovered last unit to complete each diamond problem. Some of these may be challenging! a. b. c. Warm-Up Use the Distributive Property to complete and simplify each expression below. a. 2(x + 5) = b. 3(2x + 1) = c. 2(x + 3) = d. 3(2x 5) = 2

3 Warm-Up Simplify the following expressions by combining like terms. a. x + 3x 3 + 2x x b. 2x + 4y 2 6y x + 3x c. 2x y 3y 2 + 4xy 14 x d xy 3xy + y y 2 Warm-Up Solve each of the following equations for x. Show your steps. a. 3x 2(5x + 3) = 14 2x b. 3(x + 1) 8 = 14 2(3x 4) c. 2(x 3) + 5x = 3x + 14 d. 5x + 3(x 4) = 24 2(x + 3) Warm-Up Compute without using a calculator. a b. 8 ( 21) c. 6 ( 8) d. 9 + ( 13) e f. 3 ( 9) 3

4 Warm-Up 1. Joe s age is three times Aaron s age and Aaron is six years older than Christina. If the sum of their ages is 149, what is Christina s age? Joe s age? Aaron s age? 2. A box of fruit has three times as many nectarines as grapefruit. Together there are 36 pieces of fruit. How many pieces of each type of fruit are there? Warm-Up 1. Write an inequality that represents the solutions on each number line below. a. b. c. d. 2. Graph the following inequalities on the number lines below. a. x 5 b. x < 3 or x 2 c. 4 x < 7 4

5 Warm-Up Solve the following equations below for x. Show all steps. a. 3(2x 5) 2x = 2(x + 7) + 5 b. 2(x 3) + 4 = 4x 14 Warm-Up Solve each of the following inequalities for the given variable. Represent your solutions on a number line. a. 3(2p 1) > 15 b. 7 < 2k Warm-Up Evaluate each expression if r = 4, s = 5, and t = 6. a. r 2 + 2s b. t r s Warm-Up 1. Complete each of the Diamond Problems below. Warm-Up 5

6 A. B. Evaluate the expression (a+c)2 a below b+c when a = 2, b = 6 and c= 8. Show all work C. D Warm-Up 1. Christian has twice as much money as Vanessa? Gonzo has ten more dollars than Vanessa. How much money does each person have it the sum of their money is $90? 2. A board that is 100 centimeters long is cut into three pieces? The first piece and the second piece have the same length. The third piece is four more than twice the length of the first piece. Find the length of each piece. Warm-Up Simplify the following expressions by combining like terms. a. -15x + 3x + 9-2x x 2 b. -4x +3y 2 + 7y 2 + 9x x - 3 Warm-Up Solve the following equations for x. Show all steps that lead to your solution. a. 3 8 x 1 12 = 3 4 b x 6 = 2 3 6

7 2-A: Intro to Functions 7

8 8

9 2-B: Tile Pattern Challenge 9

10 10

11 2-D: Functions and Function Notation What is a function? Opening Task: Think about it Is there another way you could represent these functions? Part 1: How can you determine whether a relation is a function? (Eureka Math Grade 9 Functions) 11

12 a) Table x f(x) Does this represent a function? Why or why not? b) Set of Points c) Mapping d) Graph Does this represent a function? Why or why not? {( 2 5, 1), ( 3.5, 6), (3, 10), ( 2.1, 6), ( 1, 1 5 )} Does this represent a function? Why or why not? Does this represent a function? Why or why not? Give an example of a function and not a function for the following Choose: Choose: Table or Set of Coordinates Graph or Map Part 3: The variables of a function Domain: Range: Determine the domain and range for the functions in part 1 a)-c) a) D: b) D: c) D: R: R: R: Part 3: Function Notation Ex 1. Given the coordinate: (-2, 5) Ex 3. f(x) = 3x f(x) = y Write in function notation. f(3)= input output Ex 2. Given: g(5) = 2 f(.5) = Write as a coordinate. 12

13 2-E: More on Functions Opening Task: Think about it Swine flu is attacking Porkopolis. The function S(t) = 9t 4 determines how many people have swine where t = time in days and S = the number of people in thousands. a) What would reasonable values for t (input values)? b) Graph the function Make a table of 4 different values. t S(t) c) Find S(4). d) Find t when S(t) = 23. What does S(4) mean? What does S(t) = 23 mean? Part 4: Discrete versus continuous functions. Discrete Functions: Domain and ranges of discrete functions: Continuous Functions: Domain and ranges of continuous functions: Ex1: Graphs 13

14 Ex2: Real World Situations For each of the context situations 1-3 described in the opening task from last class: 1) Tell whether it describes a discrete or continuous situation 2) Tell which variable represents the domain and which variable represents the range. 1) Discrete or Continuous? Why? 2) Discrete or Continuous? Why? 3) Discrete or Continuous? Why? Description of the domain: Description of the domain: Description of the domain: Description of the range: Description of the range: Description of the range: Bringing it all together Function? Function? Discrete/Continuous? Discrete/Continuous? Domain: Range: f(0) = f(6) = Domain: Range: 14

15 Function? Give a real world example of a situation modeled by a continuous function. Discrete/Continuous? Domain: f(-2) = Range: If v(t) = 3x 2 2x + 1, find the value of v(5). If h(x) = x2 9, find the value of h(5). x 5 15

16 Equation Word Rule Chart of Values Ordered Pairs Graph f(x) f(x) = x 2 +3 Domain: Range: To find the output, you square the input and add 3. x f(x) Domain: x Range: f(x) x f(x) x Domain: Range: page 1 16

17 Equation Word Rule Chart of Values Ordered Pairs Graph f(x) Domain: Range: (-1,1/4) (2,16) (1,4) (-2, 1/16) (3,64) x f(x) Domain: x Range: To find the output, square the input and subtract 1 f(x) x Domain: Range: page 2 17

18 2-G: Types of Functions and Their Patterns Linear Functions (arithmetic pattern) Algebraically Numerically y = f(x) = 1 x f(x) 2 x Graphically I noticed I wonder Summary of important things I heard from my classmates Exponential Functions (geometric pattern) Algebraically y = f(x) = 1 2 x I noticed Numerically x f(x) -2 ¼ -1 ½ I wonder Graphically Summary of important things I heard from my classmates 18

19 Quadratic Functions Algebraically y = f(x) = x Numerically x f(x) Graphically I noticed I wonder Summary of important things I heard from my classmates Identifying types of functions Type/Eqaution Pattern Look fors Vocabulary Linear x y Constant 1 st Difference Exponential x y 2/ Common Ratio Quadratic x y Constant 2 nd Difference 19

20 Practice: Identify the type function from the pattern given or described. Justify your answer using correct mathematical language Bacteria can multiply at an alarming rate when each bacteria splits into two new cells, thus doubling. For example, if we start with only one bacteria which can double every hour, by the end of one day we will have over 16 million bacteria. 5. I get a $100 itunes gift card for my birthday and then start buying $1 songs. What type of function describes the amount of money, m, I have left on the card after buying s songs? 20

21 2-H: Arithmetic Sequences Today s Goal: Identify arithmetic sequences and write recursive and explicit formulas for arithmetic sequences. Warm-up: Find the next 3 terms in the patterns below So what is a sequence?!? A sequence is a list or an ordered arrangement of numbers, figures, or objects. The members, which are also elements, are called the terms of sequences. A general sequence can be written using the following 2 different notations: Subscript Notation: Function Notation: a 1, a 2, a 3, a 4, a 5, a 6, a 7, a 8, f(1), f(2), f(3), f(4), f(5), where a 1 or f(1) is the first term, a 2 or f(2) is the second term, and so on. The n th term is denoted with a n or f(n) Try this Find the missing terms in the sequences using correct notation. a. a1, a2, a3,, a, a56, a,, an-1, a, an+1, b. f( ), f(2), f(3),, f(98), f( ), f( ),, f( ), f( ), f(n+1), What is an arithmetic sequence? Describe how you know if a sequence is arithmetic in your own words: Let s look back at the warm-up Which of the following are arithmetic sequences? How do you know? 21

22 How do you write formulas of arithmetic sequences? Recursive Formulas: use terms to find the term Verbal Subscript Function Notation Previous term f(n-1) a n Next term Helpful hint: Ex1: Write the recursive formula for the following sequence; 14, 17, 20, 23, Verbal: 1) = 2) = + Subscript: 1) =, 2) = + Functions: 1) =, 2) = + IMPORTANT IDEA: A recursive formula always consists of 2 parts. 1) the value of the 1 st term 2) the formula to find the current term based on the previous term. rely on previous terms to find Arithmetic sequences have a structure so writing a formula is easy! Explicit Formulas: Do not the n th term. specific Connection Time! This structure is just like + m x Slope Intercept Form y = b Output 0-term vs. 1 st term Slope vs. common dif. Input Explicit Forms of Arithmetic Seq. a n = a 1 + d (n 1) f(n) = f(1) + d (n 1) Ex2: Write an explicit formula in both subscript and function notation for the following arithmetic sequence 76, 72, 68, 64,. Subscript Notation: Function Notation: 22

23 2-I: Arithmetic Sequences Part 2 Warm-up: 1. Write a recursive formula in subscript notation for the following sequence. 2 5, 4 5, 1 1 5, 1 3 5, 2. Write an explicit formula in function notation for the following sequence. 76.3, 75.5, 74.7, 73.9, Lesson Activity: Card Sort With a partner sort the cards into matching pairs. You will have 20 minutes to complete this task Good Luck! While you are working on the card sort, think about the class discussion questions. Class Discussion Questions: 1. Which pair of cards were easiest to match and why? 2. Which pair of cards were hardest to match and why? 3. How are arithmetic sequences similar to linear functions 4. How are arithmetic sequences different to linear functions 5. Is an arithmetic sequence a function? 23

24 2-J: Geometric Sequences (2 days of notes, 1 HW) Doctors need to know approximately how long medications stay in a person s body. A half-life is the approximate time it takes for the body to remove 1/2 of the active ingredient in a medicine. Caffeine is in medications, foods, and energy supplements. The half-life of caffeine is about 4 hours. A student drinks an energy drink that contains 16 mg of caffeine. a. Complete the table showing the amount of caffeine in the body over time Time (hr.) Caffeine in body (mg) b. Create a graph showing the relationship between the time in hours and the amount of caffeine in the body c. Describe the domain and range of the relationship. d. Does this represent a continuous or discrete situation? Explain. e. What type of graph describes this relationship? What are geometric Sequences? Find the next 3 terms in the sequences below. Explain how you found these terms. a. 48, 24, 12, 6,,,, b. 7, 10, 15, 22,.,, c. 18, 14, 10, 6,,,, d. 2, 6, 18, 54,,,, Which two sequences in number 2 are geometric sequences? How do you know? 24

25 A geometric sequence is a sequence of numbers where each successive number is determined by multiplying by a constant value, called the common ratio. Consider the sequence 2, 6, 18, 54,,,,. a. Write the recursive form of the sequence: now = previous, starting at b. Write the recursive form in sequence notation: a n = a n-1, = 2 c. Write the recursive form in function notation: f(n) =, = 2 Practice: Find the first four terms of this sequence: f(n + 1) = f(n) 2, f(1) = 9 Explict Form of Geometric Sequences. How would you find the explicit form? 2, 6, 18, 54,. x 3 x 3 x 3 Term 1 = 2 Term 2 = 2 x 3 Term 2 is multiplied by one 3 Term 3 = 2 x 3 x 3 Term 3 is multiplied by two 3s Term 4 = 2 x 3 x 3 x 3 Term 4 is multiplied by three 3s Term n is multiplied by 3s So, f(n) = 2 (3) Does it work? Is f(1) = 2? f(2) = 6? f(3) = 18? More Practice: Write each sequence below in recursive and explicit form. For each sequence, find the given term. a. 48, 24, 12, 6, Find a 15 b. -90, -30, -10,. Find f(6) c. 6, -18, 54, -162,.. Find f(10) 25

26 2-K: Arithmetic and Geometric Sequences 26

27 27

28 28

29 2-L: Review 29

30 30

Unit 9: Quadratics Intercept Form

Unit 9: Quadratics Intercept Form For Teacher Use Packet Score: Name: Period: Algebra 1 Unit 9: Quadratics Intercept Form Note & Homework Packet Date Topic/Assignment HW Page 9-A Graphing Parabolas in Intercept Form 9-B Solve Quadratic

More information

Functions in Tables 2.0

Functions in Tables 2.0 Ns Activate Prior Knowledge Function Table Game Topic: Functions Functions in Tables 2.0 Date: Objectives: SWBAT (Identify patterns in Tables) Main Ideas: Assignment: What is a relation? What is a function?

More information

Mathematics Success Grade 8

Mathematics Success Grade 8 T538 Mathematics Success Grade 8 [OBJECTIVE] The student will compare functions represented algebraically, graphically, with verbal descriptions or in tables and identify functions as linear or non-linear.

More information

Name: 4-1 P a g e Teacher:

Name: 4-1 P a g e Teacher: Name: 4-1 Teacher: P a g e Problem 5: What Drinking Box Design Is Most Efficient MPM1D1 Grade 9 Academic Mathematics: Principles of Mathematics Tool Number Lesson Title & Topics Topics Homework 1 Exponents

More information

Algebra 1 Spencer Unit 4 Notes: Inequalities and Graphing Linear Equations. Unit Calendar

Algebra 1 Spencer Unit 4 Notes: Inequalities and Graphing Linear Equations. Unit Calendar Algebra 1 Spencer Unit 4 Notes: Inequalities and Graphing Linear Equations Unit Calendar Date Topic Homework Nov 5 (A ) 6.1 Solving Linear Inequalities +/- 6.2 Solving Linear Inequalities x/ 6.3 Solving

More information

Algebra 1. Mathematics Course Syllabus

Algebra 1. Mathematics Course Syllabus Mathematics Algebra 1 2017 2018 Course Syllabus Prerequisites: Successful completion of Math 8 or Foundations for Algebra Credits: 1.0 Math, Merit The fundamental purpose of this course is to formalize

More information

Mathematics Success Grade 6

Mathematics Success Grade 6 T632 Mathematics Success Grade 6 [OBJECTIVE] The students will draw polygons in the coordinate plane given the coordinates for the vertices and use the coordinates to find the length of the sides in mathematical

More information

GRADE 7 MATH LEARNING GUIDE. Lesson 26: Solving Linear Equations and Inequalities in One Variable Using

GRADE 7 MATH LEARNING GUIDE. Lesson 26: Solving Linear Equations and Inequalities in One Variable Using GRADE 7 MATH LEARNING GUIDE Lesson 26: Solving Linear Equations and Inequalities in One Variable Using Guess and Check Time: 1 hour Prerequisite Concepts: Evaluation of algebraic expressions given values

More information

C. Graph the solution to possibilities for Sharmara s number and give the solution in interval notation.

C. Graph the solution to possibilities for Sharmara s number and give the solution in interval notation. Homework Problem Set Sample Solutions S.77 Homework Problem Set 1. Shamara is thinking of a number. A. Could Shamara be thinking of 8? Explain. No, if Shamara thought of 8, the answer would equal 2. B.

More information

Name: for students entering. Algebra 2/Trig* For the following courses: AAF, Honors Algebra 2, Algebra 2

Name: for students entering. Algebra 2/Trig* For the following courses: AAF, Honors Algebra 2, Algebra 2 Name: Richard Montgomery High School Department of Mathematics Summer Math Packet for students entering Algebra 2/Trig* For the following courses: AAF, Honors Algebra 2, Algebra 2 (Please go the RM website

More information

Algebra Performance Level Descriptors

Algebra Performance Level Descriptors Limited A student performing at the Limited Level demonstrates a minimal command of Ohio s Learning Standards for Algebra. A student at this level has an emerging ability to A student whose performance

More information

HW# Date In Class Homework. Sections 11.1 and 11.2: Simplifying Rational Expressions, Multiplying and Dividing Rational Expressions

HW# Date In Class Homework. Sections 11.1 and 11.2: Simplifying Rational Expressions, Multiplying and Dividing Rational Expressions Algebra 1 Chapter 11 Notes Spragg Spring 010 Name: Algebra Homework: Chapter 11 (Homework is listed by date assigned; homework is due the following class period) HW# Date In Class Homework 33 Th 6/ Sections

More information

Algebra II. In this technological age, mathematics is more important than ever. When students

Algebra II. In this technological age, mathematics is more important than ever. When students In this technological age, mathematics is more important than ever. When students leave school, they are more and more likely to use mathematics in their work and everyday lives operating computer equipment,

More information

Math 3 Variable Manipulation Part 7 Absolute Value & Inequalities

Math 3 Variable Manipulation Part 7 Absolute Value & Inequalities Math 3 Variable Manipulation Part 7 Absolute Value & Inequalities 1 MATH 1 REVIEW SOLVING AN ABSOLUTE VALUE EQUATION Absolute value is a measure of distance; how far a number is from zero. In practice,

More information

CURRICULUM CATALOG. Algebra II (3135) VA

CURRICULUM CATALOG. Algebra II (3135) VA 2018-19 CURRICULUM CATALOG Algebra II (3135) VA Table of Contents COURSE OVERVIEW... 1 UNIT 1: STRUCTURE AND FUNCTIONS... 1 UNIT 2: LINEAR FUNCTIONS... 2 UNIT 3: INEQUALITIES AND ABSOLUTE VALUE... 2 UNIT

More information

Mathematics. Algebra Course Syllabus

Mathematics. Algebra Course Syllabus Prerequisites: Successful completion of Math 8 or Foundations for Algebra Credits: 1.0 Math, Merit Mathematics Algebra 1 2018 2019 Course Syllabus Algebra I formalizes and extends the mathematics students

More information

evaluate functions, expressed in function notation, given one or more elements in their domains

evaluate functions, expressed in function notation, given one or more elements in their domains Describing Linear Functions A.3 Linear functions, equations, and inequalities. The student writes and represents linear functions in multiple ways, with and without technology. The student demonstrates

More information

Argyle Magnet Middle School Summer Math Packet ANSWERS

Argyle Magnet Middle School Summer Math Packet ANSWERS Argyle Magnet Middle School Summer Math Packet ANSWERS For Students Entering Algebra Prep and C2.0 Algebra 1 ANSWERS MAY VARY FOR MANY OF THESE QUESTIONS. IF YOU HAVE DIFFERENT ANSWERS, TRY TO SEE IF YOU

More information

GSE Algebra 1. Unit Two Information. Curriculum Map: Reasoning with Linear Equations & Inequalities

GSE Algebra 1. Unit Two Information. Curriculum Map: Reasoning with Linear Equations & Inequalities GSE Algebra 1 Unit Two Information EOCT Domain & Weight: Equations 30% Curriculum Map: Reasoning with Linear Equations & Inequalities Content Descriptors: Concept 1: Create equations that describe numbers

More information

Lesson: Slope. Warm Up. Unit #2: Linear Equations. 2) If f(x) = 7x 5, find the value of the following: f( 2) f(3) f(0)

Lesson: Slope. Warm Up. Unit #2: Linear Equations. 2) If f(x) = 7x 5, find the value of the following: f( 2) f(3) f(0) Warm Up 1) 2) If f(x) = 7x 5, find the value of the following: f( 2) f(3) f(0) Oct 15 10:21 AM Unit #2: Linear Equations Lesson: Slope Oct 15 10:05 AM 1 Students will be able to find the slope Oct 16 12:19

More information

Agile Mind Algebra I Scope and Sequence, Texas Essential Knowledge and Skills for Mathematics

Agile Mind Algebra I Scope and Sequence, Texas Essential Knowledge and Skills for Mathematics In the three years prior to Algebra I, students have already begun their study of algebraic concepts. They have investigated variables and expressions, solved equations, constructed and analyzed tables,

More information

Honors Math 2 Unit 5 Exponential Functions. *Quiz* Common Logs Solving for Exponents Review and Practice

Honors Math 2 Unit 5 Exponential Functions. *Quiz* Common Logs Solving for Exponents Review and Practice Honors Math 2 Unit 5 Exponential Functions Notes and Activities Name: Date: Pd: Unit Objectives: Objectives: N-RN.2 Rewrite expressions involving radicals and rational exponents using the properties of

More information

Topic: Solving systems of equations with linear and quadratic inequalities

Topic: Solving systems of equations with linear and quadratic inequalities Subject & Grade: Mathematics, 9 th Grade Topic: Solving systems of equations with linear and quadratic inequalities Aim: How would you find the solution set of a linear and quadratic inequality? Materials:.

More information

Algebra I Assessment. Eligible Texas Essential Knowledge and Skills

Algebra I Assessment. Eligible Texas Essential Knowledge and Skills Algebra I Assessment Eligible Texas Essential Knowledge and Skills STAAR Algebra I Assessment Mathematical Process Standards These student expectations will not be listed under a separate reporting category.

More information

Banneker Middle School. Summer Math Packet C2.0 Algebra 1

Banneker Middle School. Summer Math Packet C2.0 Algebra 1 Banneker Middle School Summer Math Packet C2.0 Algebra 1 Dear Student and Parent, The purpose of this packet is to provide a review of objectives that were taught the previous school year and provide tasks

More information

Unit 3 Day 4. Solving Equations with Rational Exponents and Radicals

Unit 3 Day 4. Solving Equations with Rational Exponents and Radicals Unit Day 4 Solving Equations with Rational Exponents and Radicals Day 4 Warm Up You know a lot about inverses in mathematics we use them every time we solve equations. Write down the inverse operation

More information

Prentice Hall Algebra 1, Foundations Series 2011 Correlated to: Washington Mathematics Standards, Algebra 1 (2008)

Prentice Hall Algebra 1, Foundations Series 2011 Correlated to: Washington Mathematics Standards, Algebra 1 (2008) Algebra 1 A1.1. Core Content: Solving problems (Algebra) Students learn to solve many new types of problems in Algebra 1, and this first core content area highlights the types of problems students will

More information

AQR Unit 4: Using Recursion in Models and Decision Making Sequence Notes. Name: Date: Sequences

AQR Unit 4: Using Recursion in Models and Decision Making Sequence Notes. Name: Date: Sequences Name: Date: Sequences A number sequence is a set of numbers, usually separated by commas, arranged in an order. The first term is referred to as t 1, the second term as t 2, the third term as t 3 and so

More information

MS Algebra 1 Scope and Sequence Quarter 1 Overview

MS Algebra 1 Scope and Sequence Quarter 1 Overview Quarter 1 Overview Equations, Inequalities, Absolute Value Students must master creating, solving, and In 7 th grade, students will have developed a Write, solve, and interpret multi-step equations analyzing

More information

Alignment This course is aligned to the California Common Core State Standards for Algebra 1. Suggested Video/DVDs//Films 3. TBD Web Sites 4.

Alignment This course is aligned to the California Common Core State Standards for Algebra 1. Suggested Video/DVDs//Films 3. TBD Web Sites 4. High School Course Description for Algebra 1 Course Title: Algebra 1 Course Number: MTH 101, 102, 131, 132, 181, 182, 1011, 1012, 1013, 1014 Grade Level: 9-12 Meets a UC a-g Requirement: Yes C Curricular

More information

ALGEBRA GRADE 7. Do not open this booklet until instructed to do so. Mark your answer on the answer sheet by FILLING in the oval.

ALGEBRA GRADE 7. Do not open this booklet until instructed to do so. Mark your answer on the answer sheet by FILLING in the oval. Kansas City Area Teachers of Mathematics 2014 KCATM Math Competition ALGEBRA GRADE 7 INSTRUCTIONS Do not open this booklet until instructed to do so. Time limit: 20 minutes You may NOT use calculators.

More information

Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Algebra 2

Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Algebra 2 4-5 Warm Up Lesson Presentation Lesson Quiz Algebra 2 Warm Up Solve. 1. log 16 x = 3 2 64 2. log x 1.331 = 3 1.1 3. log10,000 = x 4 Objectives Solve exponential and logarithmic equations and equalities.

More information

Algebra 1 Semester 2. Instructional Materials for the WCSD Math Common Finals

Algebra 1 Semester 2. Instructional Materials for the WCSD Math Common Finals 014-015 Algebra 1 Semester Instructional Materials for the WCSD Math Common Finals The Instructional Materials are for student and teacher use and are aligned to the Math Common Final blueprint for this

More information

6th Grade. Dependent & Independent Variables

6th Grade. Dependent & Independent Variables Slide 1 / 68 Slide 2 / 68 6th Grade Dependent & Independent Variables 2014-10-28 www.njctl.org Slide 3 / 68 Table of Contents Translating to Equations Dependent and Independent Variables Click on a topic

More information

Student Performance Analysis. Algebra I Standards of Learning

Student Performance Analysis. Algebra I Standards of Learning Student Performance Analysis Algebra I Standards of Learning Practice for SOL A.1 Select each phrase that verbally translates this algebraic expression: One fourth times the cube root of x less five. One

More information

Algebra 1. Correlated to the Texas Essential Knowledge and Skills. TEKS Units Lessons

Algebra 1. Correlated to the Texas Essential Knowledge and Skills. TEKS Units Lessons Algebra 1 Correlated to the Texas Essential Knowledge and Skills TEKS Units Lessons A1.1 Mathematical Process Standards The student uses mathematical processes to acquire and demonstrate mathematical understanding.

More information

Using the Laws of Exponents to Simplify Rational Exponents

Using the Laws of Exponents to Simplify Rational Exponents 6. Explain Radicals and Rational Exponents - Notes Main Ideas/ Questions Essential Question: How do you simplify expressions with rational exponents? Notes/Examples What You Will Learn Evaluate and simplify

More information

Algebra 1 Khan Academy Video Correlations By SpringBoard Activity and Learning Target

Algebra 1 Khan Academy Video Correlations By SpringBoard Activity and Learning Target Algebra 1 Khan Academy Video Correlations By SpringBoard Activity and Learning Target SB Activity Activity 1 Investigating Patterns 1-1 Learning Targets: Identify patterns in data. Use tables, graphs,

More information

Unit 2, Ongoing Activity, Little Black Book of Algebra II Properties

Unit 2, Ongoing Activity, Little Black Book of Algebra II Properties Unit 2, Ongoing Activity, Little Black Book of Algebra II Properties Little Black Book of Algebra II Properties Unit 2 - Polynomial Equations & Inequalities 2.1 Laws of Exponents - record the rules for

More information

Materials: Hw #9-6 answers handout; Do Now and answers overhead; Special note-taking template; Pair Work and answers overhead; hw #9-7

Materials: Hw #9-6 answers handout; Do Now and answers overhead; Special note-taking template; Pair Work and answers overhead; hw #9-7 Pre-AP Algebra 2 Unit 9 - Lesson 7 Compound Interest and the Number e Objectives: Students will be able to calculate compounded and continuously compounded interest. Students know that e is an irrational

More information

Algebra. Robert Taggart

Algebra. Robert Taggart Algebra Robert Taggart Table of Contents To the Student.............................................. v Unit 1: Algebra Basics Lesson 1: Negative and Positive Numbers....................... Lesson 2: Operations

More information

Equations and Inequalities in One Variable

Equations and Inequalities in One Variable Name Date lass Equations and Inequalities in One Variable. Which of the following is ( r ) 5 + + s evaluated for r = 8 and s =? A 3 B 50 58. Solve 3x 9= for x. A B 7 3. What is the best first step for

More information

Math 2 Variable Manipulation Part 7 Absolute Value & Inequalities

Math 2 Variable Manipulation Part 7 Absolute Value & Inequalities Math 2 Variable Manipulation Part 7 Absolute Value & Inequalities 1 MATH 1 REVIEW SOLVING AN ABSOLUTE VALUE EQUATION Absolute value is a measure of distance; how far a number is from zero. In practice,

More information

Semester Review Packet

Semester Review Packet MATH 110: College Algebra Instructor: Reyes Semester Review Packet Remarks: This semester we have made a very detailed study of four classes of functions: Polynomial functions Linear Quadratic Higher degree

More information

Exponential function review and practice Day 1

Exponential function review and practice Day 1 February 9, 2009 Exponential review: Day 1 page 1 Exponential function review and practice Day 1 Test this Friday 2/13. Bring your calculator every day, but especially Friday! Today s problems emphasize

More information

Algebra 1. Unit 3: Quadratic Functions. Romeo High School

Algebra 1. Unit 3: Quadratic Functions. Romeo High School Algebra 1 Unit 3: Quadratic Functions Romeo High School Contributors: Jennifer Boggio Jennifer Burnham Jim Cali Danielle Hart Robert Leitzel Kelly McNamara Mary Tarnowski Josh Tebeau RHS Mathematics Department

More information

Spring 2012 Student Performance Analysis

Spring 2012 Student Performance Analysis Spring 2012 Student Performance Analysis Algebra I Standards of Learning Presentation may be paused and resumed using the arrow keys or the mouse. 1 Representing and Evaluating Cube Roots and Square Roots

More information

LHS Algebra Pre-Test

LHS Algebra Pre-Test Your Name Teacher Block Grade (please circle): 9 10 11 12 Course level (please circle): Honors Level 1 Instructions LHS Algebra Pre-Test The purpose of this test is to see whether you know Algebra 1 well

More information

Algebra Summer Review Packet

Algebra Summer Review Packet Name: Algebra Summer Review Packet About Algebra 1: Algebra 1 teaches students to think, reason, and communicate mathematically. Students use variables to determine solutions to real world problems. Skills

More information

HADDONFIELD PUBLIC SCHOOLS Curriculum Map for Algebra II

HADDONFIELD PUBLIC SCHOOLS Curriculum Map for Algebra II Curriculum Map for Algebra II September Solving problems involving number operations and algebraic expressions. Solving linear equations, literal equations, formulas and inequalities. Solving word problems

More information

In case (1) 1 = 0. Then using and from the previous lecture,

In case (1) 1 = 0. Then using and from the previous lecture, Math 316, Intro to Analysis The order of the real numbers. The field axioms are not enough to give R, as an extra credit problem will show. Definition 1. An ordered field F is a field together with a nonempty

More information

Writing Exponential Equations Day 2

Writing Exponential Equations Day 2 Writing Exponential Equations Day 2 MGSE9 12.A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, simple rational,

More information

One box per group ( star group of 6)

One box per group ( star group of 6) 4 markers 2 erasers One box per group ( star group of 6) 1 pencil (just in case) Some small post-it notes 1 glue stick One person from each group collect all items and place them back into the box. Concept

More information

Math 8 Notes Units 1B: One-Step Equations and Inequalities

Math 8 Notes Units 1B: One-Step Equations and Inequalities Math 8 Notes Units 1B: One-Step Equations and Inequalities Solving Equations Syllabus Objective: (1.10) The student will use order of operations to solve equations in the real number system. Equation a

More information

Module 1: Equations and Inequalities (30 days) Solving Equations: (10 Days) (10 Days)

Module 1: Equations and Inequalities (30 days) Solving Equations: (10 Days) (10 Days) Module 1: Equations and Inequalities (30 days) Word Problems Literal Equations (Scientific Applications) Justifying solutions Algebraic Proofs Represent constraints by equations and inequalities Graphing

More information

Function Junction: Homework Examples from ACE

Function Junction: Homework Examples from ACE Function Junction: Homework Examples from ACE Investigation 1: The Families of Functions, ACE #5, #10 Investigation 2: Arithmetic and Geometric Sequences, ACE #4, #17 Investigation 3: Transforming Graphs,

More information

Unit 5. Linear equations and inequalities OUTLINE. Topic 13: Solving linear equations. Topic 14: Problem solving with slope triangles

Unit 5. Linear equations and inequalities OUTLINE. Topic 13: Solving linear equations. Topic 14: Problem solving with slope triangles Unit 5 Linear equations and inequalities In this unit, you will build your understanding of the connection between linear functions and linear equations and inequalities that can be used to represent and

More information

Day 1~ 2-1 Relations & Functions

Day 1~ 2-1 Relations & Functions NOTES: Honors Algebra Unit 1: Linear Equations Day 1~ -1 Relations & Functions Part 1: Use the following words to complete the sentences below: Inputs Dependent Range Range Domain Independent Relation

More information

Mathematics Curricular Guide SEVENTH GRADE SCHOOL YEAR

Mathematics Curricular Guide SEVENTH GRADE SCHOOL YEAR Mathematics Curricular Guide SEVENTH GRADE 2013-2014 SCHOOL YEAR MATHEMATICS SCOPE & SEQUENCE Unit Title Dates Page 1. Ratios and Proportion... IBD... 4 2. Rational Numbers & Prime Factorization... IBD...

More information

Unit 1: Functions, Equations, & Graphs

Unit 1: Functions, Equations, & Graphs Honors Algebra ~ Spring 014 Name: 0 Unit 1: Functions, Equations, & Graphs At the end of this unit, you will know how to: Identify functions Analyze transformations of functions Graph piecewise functions

More information

Complete Week 18 Package

Complete Week 18 Package Complete Week 18 Package Jeanette Stein Table of Contents Unit 4 Pacing Chart -------------------------------------------------------------------------------------------- 1 Day 86 Bellringer --------------------------------------------------------------------------------------------

More information

COE Algebra Syllabus. Desired Results

COE Algebra Syllabus. Desired Results COE Algebra Syllabus School Year: 2015-2016 Certificated Teacher: Desired Results Course Title): COE Algebra Credit: x one semester (.5) two semesters (1.0) Prerequisites and/or recommended preparation:

More information

UNIT 2: REASONING WITH LINEAR EQUATIONS AND INEQUALITIES. Solving Equations and Inequalities in One Variable

UNIT 2: REASONING WITH LINEAR EQUATIONS AND INEQUALITIES. Solving Equations and Inequalities in One Variable UNIT 2: REASONING WITH LINEAR EQUATIONS AND INEQUALITIES This unit investigates linear equations and inequalities. Students create linear equations and inequalities and use them to solve problems. They

More information

Algebra 1 Prince William County Schools Pacing Guide (Crosswalk)

Algebra 1 Prince William County Schools Pacing Guide (Crosswalk) Algebra 1 Prince William County Schools Pacing Guide 2017-2018 (Crosswalk) Teacher focus groups have assigned a given number of days to each unit based on their experiences and knowledge of the curriculum.

More information

The steps in Raya s solution to 2.5 (6.25x + 0.5) = 11 are shown. Select the correct reason for line 4 of Raya s solution.

The steps in Raya s solution to 2.5 (6.25x + 0.5) = 11 are shown. Select the correct reason for line 4 of Raya s solution. A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear functions. Unit 2: Reasoning with Linear Equations and Inequalities The perimeter

More information

Relations and Functions

Relations and Functions Algebra 1, Quarter 2, Unit 2.1 Relations and Functions Overview Number of instructional days: 10 (2 assessments) (1 day = 45 60 minutes) Content to be learned Demonstrate conceptual understanding of linear

More information

SOLVING LINEAR INEQUALITIES

SOLVING LINEAR INEQUALITIES Topic 15: Solving linear inequalities 65 SOLVING LINEAR INEQUALITIES Lesson 15.1 Inequalities on the number line 15.1 OPENER Consider the inequality x > 7. 1. List five numbers that make the inequality

More information

Mathematics High School Algebra I

Mathematics High School Algebra I Mathematics High School Algebra I All West Virginia teachers are responsible for classroom instruction that integrates content standards and mathematical habits of mind. Students in this course will focus

More information

Please allow yourself one to two hours to complete the following sections of the packet. College Integrated Geometry Honors Integrated Geometry

Please allow yourself one to two hours to complete the following sections of the packet. College Integrated Geometry Honors Integrated Geometry Incoming Integrated Geometry Summer Work Dear Incoming Integrated Geometry Students, To better prepare for your high school mathematics entry process, summer work is assigned to ensure an easier transition

More information

Final Review. Non-calculator problems are indicated. 1. (No calculator) Graph the function: y = x 3 + 2

Final Review. Non-calculator problems are indicated. 1. (No calculator) Graph the function: y = x 3 + 2 Algebra II Final Review Name Non-calculator problems are indicated. 1. (No calculator) Graph the function: y = x 3 + 2 2. (No calculator) Given the function y = -2 x + 3-1 and the value x = -5, find the

More information

Algebra 1 Third Quarter Study Guide

Algebra 1 Third Quarter Study Guide Algebra 1 Third Quarter Study Guide 1. Evaluate:. 2. Evaluate: 8 5 5 t. 2 s t when s = 5 and 7 Simplify. 3. 2 0 5 3 2x y x y 4. 4 3 54xy 5. 4 24 6. 3x 2 y 3 7. Is 3 a solution of? 8. A store that sells

More information

Tennessee s State Mathematics Standards - Algebra I

Tennessee s State Mathematics Standards - Algebra I Domain Cluster Standards Scope and Clarifications Number and Quantity Quantities The Real (N Q) Number System (N-RN) Use properties of rational and irrational numbers Reason quantitatively and use units

More information

Unit 5: Representations of Linear Relations

Unit 5: Representations of Linear Relations Time Frame: Approximately 3-5 weeks Connections to Previous Learning: Students build upon previous understandings of linear equations and functions and apply them to various representations of linear relationships,

More information

Algebra I High School Math Solution Alignment to Oklahoma Academic Standards

Algebra I High School Math Solution Alignment to Oklahoma Academic Standards High School Math Solution A1.N.1 Extend the understanding of number and operations to include square roots and cube roots A1.A.1 Represent and solve and real-world problems using linear equations, absolute

More information

Dublin City Schools Mathematics Graded Course of Study Algebra I Philosophy

Dublin City Schools Mathematics Graded Course of Study Algebra I Philosophy Philosophy The Dublin City Schools Mathematics Program is designed to set clear and consistent expectations in order to help support children with the development of mathematical understanding. We believe

More information

Section 8 Topic 1 Comparing Linear, Quadratic, and Exponential Functions Part 1

Section 8 Topic 1 Comparing Linear, Quadratic, and Exponential Functions Part 1 Section 8: Summary of Functions Section 8 Topic 1 Comparing Linear, Quadratic, and Exponential Functions Part 1 Complete the table below to describe the characteristics of linear functions. Linear Functions

More information

Warm Up. Current: CST Released Test Question. Draw three different models to solve 3 x 5 =.

Warm Up. Current: CST Released Test Question. Draw three different models to solve 3 x 5 =. Warm Up CST Released Test Question What number can be multiplied by 5768 to give the answer 5768? Current: Draw three different models to solve 3 x 5 =. 5768 = 5768 A 0 B 1 C 2 D 10 Challenge: Find product.

More information

Unit 5. Linear equations and inequalities OUTLINE. Topic 13: Solving linear equations. Topic 14: Problem solving with slope triangles

Unit 5. Linear equations and inequalities OUTLINE. Topic 13: Solving linear equations. Topic 14: Problem solving with slope triangles Unit 5 Linear equations and inequalities In this unit, you will build your understanding of the connection between linear functions and linear equations and inequalities that can be used to represent and

More information

New Mexico Curriculum Framework Correlated to Merit Software Mathematics Programs

New Mexico Curriculum Framework Correlated to Merit Software Mathematics Programs New Mexico Curriculum Framework Correlated to Merit Software Mathematics Programs Middle School 5-8 Benchmark: Use mathematical models to represent and understand quantitative relationships Grade Performance

More information

Algebra 2 and Trigonometry

Algebra 2 and Trigonometry Algebra 2 and Trigonometry Chapter 7: Exponential Functions Name: Teacher: Pd: 1 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs.

More information

Midterm Review Fall 2018

Midterm Review Fall 2018 Midterm Review Fall 018 Topics List: Unit 1 Simplifying Expressions Evaluating Linear Equations Dimensional Analysis Consecutive Number Equations Linear Equation Word Problems Representing Linear Equations

More information

Mathematics Curriculum

Mathematics Curriculum New York State Common Core Mathematics Curriculum ALGEBRA I MODULE 3 Linear Functions Module Overview... 3 Topic A: Linear Sequences (F-IF.A.1, F-IF.A.2, F-IF.A.3, F-IF.B.6, F-BF.A.1a, F-LE.A.1, F-LE.A.2,

More information

ADVANCED ALGEBRA/ ADVANCED ALGEBRA HONORS SUMMER ASSIGNMENT 2018

ADVANCED ALGEBRA/ ADVANCED ALGEBRA HONORS SUMMER ASSIGNMENT 2018 ADVANCED ALGEBRA/ ADVANCED ALGEBRA HONORS SUMMER ASSIGNMENT 018 Name In the attached packet, complete all of the questions on each page. Bring your completed packet with shown work to class on the first

More information

Unit Name: Unit 2: Quadratic Functions and Modeling. Lesson Plan Number & Title: Lesson 5: I See Where You Are Coming From

Unit Name: Unit 2: Quadratic Functions and Modeling. Lesson Plan Number & Title: Lesson 5: I See Where You Are Coming From Unit Name: Unit 2: Quadratic Functions and Modeling Lesson Plan Number & Title: Lesson : I See Where You Are Coming From Grade Level: High School Math II Lesson Overview: Given a linear, quadratic, or

More information

Math K-1 CCRS Level A Alignment College & Career Readiness Standards Version: April 2017

Math K-1 CCRS Level A Alignment College & Career Readiness Standards Version: April 2017 Math K-1 CCRS Level A Alignment Standard Math K Lessons Math 1 Lessons Number and Operations: Base Ten Understand place value 6 Compare 1, 26 Compare 50, 33 Skip Count 5s and 10s, 35 Group 10s, 36 Compare

More information

Looking Ahead to Chapter 10

Looking Ahead to Chapter 10 Looking Ahead to Chapter Focus In Chapter, you will learn about polynomials, including how to add, subtract, multiply, and divide polynomials. You will also learn about polynomial and rational functions.

More information

Student Guide: Chapter 1

Student Guide: Chapter 1 Student Guide: Chapter 1 1.1 1.1.1 I can solve puzzles in teams 1-4 to 1-8 1.1 1.1.2 1.1 1.1.3 I can investigate the growth of patterns 1-13 to 1-17 1-18 to 1-22 I can investigate the graphs of quadratic

More information

Sequenced Units for Arizona s College and Career Ready Standards MA27 Algebra I

Sequenced Units for Arizona s College and Career Ready Standards MA27 Algebra I Sequenced Units for Arizona s College and Career Ready Standards MA27 Algebra I Year at a Glance Semester 1 Semester 2 Unit 1: Solving Linear Equations (12 days) Unit 2: Solving Linear Inequalities (12

More information

When they compared their results, they had an interesting discussion:

When they compared their results, they had an interesting discussion: 27 2.5 Making My Point A Solidify Understanding Task Zac and Sione were working on predicting the number of quilt blocks in this pattern: CC BY Camille King https://flic.kr/p/hrfp When they compared their

More information

North Seattle Community College Math 084 Chapter 1 Review. Perform the operation. Write the product using exponents.

North Seattle Community College Math 084 Chapter 1 Review. Perform the operation. Write the product using exponents. North Seattle Community College Math 084 Chapter 1 Review For the test, be sure to show all work! Turn off cell phones. Perform the operation. Perform the operation. Write the product using exponents.

More information

Semester 2 Final Exam Review Guide for AMS I

Semester 2 Final Exam Review Guide for AMS I Name: Semester 2 Final Exam Review Guide for AMS I Unit 4: Exponential Properties & Functions Lesson 1 Exponent Properties & Simplifying Radicals Products of Powers: when two powers with the same base

More information

Unit 6 Quadratic Relations of the Form y = ax 2 + bx + c

Unit 6 Quadratic Relations of the Form y = ax 2 + bx + c Unit 6 Quadratic Relations of the Form y = ax 2 + bx + c Lesson Outline BIG PICTURE Students will: manipulate algebraic expressions, as needed to understand quadratic relations; identify characteristics

More information

TransMath Third Edition Correlated to the South Carolina High School Credential Courses: Essentials of Math I, II, and III

TransMath Third Edition Correlated to the South Carolina High School Credential Courses: Essentials of Math I, II, and III TransMath Third Edition Correlated to the South Carolina High School Credential Courses: Essentials of Math I, II, and III TransMath correlated to the South Carolina High School Credential Courses: Essentials

More information

Curriculum Map Algebra I Quarter 1

Curriculum Map Algebra I Quarter 1 Quarter 1 How can algebra describe the relationship between sets of numbers? Algebra Creating Equations AI.A.CED.1 * Create equations and inequalities in one variable and use them to solve problems. Include

More information

In this lesson, students model filling a rectangular

In this lesson, students model filling a rectangular NATIONAL MATH + SCIENCE INITIATIVE Mathematics Fill It Up, Please Part III Level Algebra or Math at the end of a unit on linear functions Geometry or Math as part of a unit on volume to spiral concepts

More information

California Common Core State Standards for Mathematics Standards Map Algebra I

California Common Core State Standards for Mathematics Standards Map Algebra I A Correlation of Pearson CME Project Algebra 1 Common Core 2013 to the California Common Core State s for Mathematics s Map Algebra I California Common Core State s for Mathematics s Map Algebra I Indicates

More information

Algebra II Notes Quadratic Functions Unit Applying Quadratic Functions. Math Background

Algebra II Notes Quadratic Functions Unit Applying Quadratic Functions. Math Background Applying Quadratic Functions Math Background Previously, you Graphed and solved quadratic functions. Solved literal equations for a given variable. Found the inverse for a linear function. Verified by

More information

Note: A file Algebra Unit 09 Practice X Patterns can be useful to prepare students to quickly find sum and product.

Note: A file Algebra Unit 09 Practice X Patterns can be useful to prepare students to quickly find sum and product. Note: This unit can be used as needed (review or introductory) to practice operations on polynomials. Math Background Previously, you Identified monomials and their characteristics Applied the laws of

More information

Farquhar Middle School. Summer Math Packet for Geometry

Farquhar Middle School. Summer Math Packet for Geometry Farquhar Middle School Summer Math Packet for Geometry Dear Student and Parent, The purpose of this packet is to provide a review of objectives that were taught the previous school year and provide tasks

More information

Unit 3A Modeling with Exponential Functions

Unit 3A Modeling with Exponential Functions Common Core Math 2 Unit A Modeling with Exponential Functions Name: Period: Estimated Test Date: Unit A Modeling with Exponential Functions 1 2 Common Core Math 2 Unit A Modeling with Exponential Functions

More information