Patterns and Functions. Write an algebraic expression for each phrase more than twice a number 2. a number divided by 4
|
|
- Hugo Freeman
- 5 years ago
- Views:
Transcription
1 - Patterns and Functions -. Plan What You ll Learn To write a function rule To understand relationships of quantities in a function... And Why To find reasonable domain and range for real-world situations, as in Example Check Skills You ll Need Part Writing Simplifying a Function and Evaluating Rule Expressions and Formulas Lesson - Write an algebraic expression for each phrase.. 0 more than twice a number. a number divided by t x minus six times a number. twice a number subtracted from 7 8-6n 7 - p New Vocabulary function function rule dependent variable independent variable domain range In Lesson -, the equation C = p p shows the relationship between the original price p of a pair of sneakers and the total cost C after the 6% sales tax is included. The relationship between these quantities is a function. A function is a relationship that assigns exactly one output value for each input value. For each input there is only one corresponding output. A function rule, such as C = p p, is an equation that describes a functional relationship. for Help Objectives To write a function rule To understand relationships of quantities in a function Examples Writing a Function Rule Writing a Function Rule Identifying Independent and Dependent Quantities Reasonable Domain and Range Math Background Any set of ordered pairs forms a relation. Only a relation in which each input (or x-value) has a unique output (or y-value) is a function. Writing a Function Rule More Math Background: p. C Laundry Suppose you are washing and drying clothes at a self-service laundry. The relationship between the number of loads (input) and the cost (output) is a function. Use the table to write a function rule. Lesson Planning and Resources Loads Cost $.75 $5.50 $8.5 $.00 See p. E for a list of the resources that support this lesson. Relate Total cost is.75? number of loads Describe how the quantities relate. Define Let n = the number of loads. The number of loads is the input. Let c = the total cost. The total cost is the output. Write c =.75? n Translate this relationship to a function rule. The function rule is c =.75n. Write a function rule for the relationship between the number of hours (input) and the number of miles (output). m 60h Hours Total Miles Bell Ringer Practice Check Skills You ll Need For intervention, direct students to: Using Variables Lesson - Extra Skills and Word Problem Practice, Ch. Lesson - Patterns and Functions 7 Special Needs L Help students understand the nature of a functional relationship by explaining that the output depends on the value of the input. Have them rephrase function rules, as in Example : the cost depends on the number of loads. learning style: verbal Below Level L Ask: Is a relationship with input as the student s last name and output as age in years a function? Yes, unless two have the same last name and different ages. learning style: verbal 7
2 . Teach Writing a Function Rule Guided Instruction One House Two Houses The relationship between the number of houses (input) and the number of toothpicks (output) is a function. Use the table to write a function rule. Special Needs Have a volunteer describe what you do at a self-service laundry, pointing out that you use each machine by inserting coins. Additional Examples Suppose you are buying apples from a vending machine. Use the table to write a function rule. c 0.5n Make a two-story house by adding one toothpick that goes from side to side. Use the table to write a function rule. c 0.5n L of Apples Cost $.5 $.70 $.05 $.0 of Houses Total Toothpicks Suppose you want to find out how much gas a trip will take, in a car that uses one gallon of gas to go about 8 miles. What are the independent quantity and the dependent quantity for this situation? independent quantity: miles in the trip; dependent quantity: gallons of gas used Three Houses b. No; you need toothpicks to make houses and 6 toothpicks to make houses. Relationships in a Function Relate Total number of toothpicks is one more than five times the number of houses. Define Let n the number of houses. Let t the total number of toothpicks. Describe how the quantities relate. The number of houses is the input. The total number of toothpicks is the output. Write t 5n Translate this relationship to a function rule. The function rule is t 5n. Houses Total Toothpicks a. How many toothpicks are needed to make seven houses? 6 b. Reasoning Could a set of houses be built with exactly toothpicks? Explain. c. Write a rule for the function represented by the data in the table. y = ± x Input x Output y 5 8 In Example, the total number of toothpicks t depends on the number of houses n. The value of the dependent variable t depends on the value of the independent variable n. In real-world situations, you must determine which varying quantity is dependent and which is independent. 6 Identifying Independent and Dependent Quantities Memory Stick The table and graph model a function relating the storage capacity of a memory stick and its cost. Identify the independent and dependent quantities. Memory (mb) Cost ($) Cost ($) Memory (megabytes) 6 Cost of Memory Sticks (8, 9) (6, 9) (, 9) (56, 55) The cost is the dependent quantity because it depends on the storage capacity of the memory stick. Memory is the independent quantity. The cooking time for an unstuffed turkey is about 0 minutes per pound. What are the independent quantity and dependent quantity for this situation? independent quantity: weight of turkey; dependent quantity: cooking time 8 Chapter Variables, Function Patterns, and Graphs 8 Advanced Learners L Students may wish to use other formulas they know to make a table and write the matching function rule. learning style: visual English Language Learners ELL Help students learn the special vocabulary of functions by having them write, compare, and discuss their own explanations of the Examples using the words in the New Vocabulary list. learning style: verbal
3 . independent: the amount of money he can spend; dependent: number of songs he can download. domain: $.00 to $6.00; range: to 8 songs. EXERCISES The possible values for the input, or the independent variable, of a function are the domain of the function. The possible values of the output, or the dependent variable, are the range of the function. Practice and Problem Solving Reasonable Domain and Range Maria earns $7 per hour for baby-sitting after school and on Saturday. She works no more than 6 hours a week. a. Identify the independent and dependent quantities for this situation. The amount Maria earns depends on the number of hours she works in a week. So the amount Maria earns is the dependent variable. The number of hours she works is the independent variable. b. Find reasonable domain and range values for this situation. A reasonable domain is from 0 to 6 hours. If Maria works 0 hours, she earns $0. If she works 6 hours, she earns 7? $6, or $. So, a reasonable range is from $0 to $. Charlie downloads songs for $.75 each. He has between $.00 and $6.00 to spend on songs. Identify the independent and dependent quantities for this situation and find reasonable domain and range values. See above left. For more exercises, see Extra Practice. English Language Learners ELL Some students may not be familiar with the term downloads (in the for Example ). Ask a volunteer to explain. Additional Examples Ken burns 5 calories per hour when he bikes. He bikes from to 7 hours each weekend. Identify the independent and dependent quantities for this situation and find reasonable domain and range values. independent quantity: hours he bikes; dependent quantity: calories he burns; domain: to 7 hours; range:,75 to,975 calories Resources Daily Notetaking Guide - L Daily Notetaking Guide - Adapted Instruction L A Practice by Example for Help Example (page 7) Example (page 8) Example (page 8) The relationships in the tables below are functions. Write a function rule for each... Cans of Soup Servings s c. Hours Cost to Home. a Plumber Works Owner 8 6 $65 $90 $5 $0 Cans of Frozen Orange Juice Time (hours) c 0 ± 5h c ± 6t Identify the independent and dependent quantity in each situation. 5. The cost of a long-distance telephone call increases, with the number of minutes of the call. number of minutes; cost 6. Water pressure increases 0. pounds per square inch (0. psi) with each increase of one foot in depth below sea level. depth; water pressure Cost of Bike Rental $0 $6 $ $8 Total Cost $.5 $.50 $.75 $5.00 c.5n Closure Ask students to group these terms into two related lists: range, domain, x-value, y-value, dependent, independent, abscissa, ordinate. Ask them to explain their choices. Sample: List : domain, x-value, independent, abscissa List : range, y-value, dependent, ordinate Lesson - Patterns and Functions 9 9
4 . Practice Assignment Guide A B -, 9-,, 5 A B 5-8,, C Challenge 6, 7 Test Prep 8- Mixed Review 5- Homework To check students understanding of key skills and concepts, go over Exercises, 7, 9,,. GPS Enrichment Guided Problem Solving Reteaching Adapted Practice Practice Name Class Date Practice - Adding Real s Simplify each expression (-). - + (-) (-) (-) (-) (-.9) (-7.) a b a b () a b u u u u 0. u 6 u. Evaluate each expression for m.5.. -m m (-m) Simplify (-6) (-8) + (-) (-.) (-.) + (-.) a b Simplify.. c. 5 d c d.7. The temperature at 5:00 A.M. is-8 F. The temperature rises 0 by :00 A.M. What is the temperature at :00 A.M.?. A football team has possession of the ball on their own 5-yd line. The next two plays result in a loss of 7 yd and a gain of yd, respectively. On what yard line is the ball after the two plays? 5. Suppose your opening checking account balance is $.5. After you write a check for $57.9 and make a deposit of $0.9, what is your new balance? 6. During an emergency exercise, a submarine dives 7 ft, rises 6 ft, and then dives 8 ft. What is the net change in the submarine s position after the second dive? u 7 u a b a b L L L L L Pearson Education, Inc. All rights reserved. Example (page 9) 7. number of gallons of gas; distance traveled; 0 to gallons; 50 to 00 miles B Apply Your Skills a. Yes; there is one range value for each domain value. b. year, number of students nline Homework Help Visit: PHSchool.com Web Code: ate-00 b. No; you cannot have a fractional amount of a book. Yes; books can weigh fractional amounts. Identify the independent and dependent quantities for each situation, and find reasonable domain and range values. 7. Tara s car travels about 5 miles on one gallon of gas. She has between 0 and gallons of gas in the tank. 8. Sal and three friends plan to bowl one or two games each. Each game costs $.50. number of games; total cost; to 8 games; $0 to $0 Copy and complete each table. Then write a function rule for each relationship Minutes Hours of Yoga Reading Words Read Lessons Total Cost w 5m. The graph shows the average size of a school s ninth-grade class over several years. a. Does this graph represent a function? Explain. a b. See left. b. If the graph represents a function, identify the independent and dependent quantities.. a. The weight of the books carried in a backpack depends on the number of books in the backpack. Susan s books weigh from pound up to.5 pounds each and she carries at most books. Find a reasonable domain and range for the situation. 0 to books; 0 to.0 pounds b. Critical Thinking Can noninteger numbers be part of the domain? of the range? Explain.. Each side of the first figure is one unit. Copy and complete the table. Then find a GPS function rule for the relationship between a figure s number and its perimeter. Figure Perimeter 5 units 7 units 9 units units. Motorcycles The table below shows the price of several motorcycles and the size of their engines. Identify the independent and dependent quantities. Explain. See margin. Engine (cc) Price ($) 99 Students $5 $7 $9 $5 5 $6 c ± h Figure Figure Figure Figure p + n Average Size of a Ninth-Grade Class Year Chapter Variables, Function Patterns, and Graphs. size of engine; price. The greater the engine size the greater the cost of the motorcycle. 0
5 C Challenge 5. a. Copy the table at the right. Evaluate the expression x for x,,, and. Record your results in the second column. b. Critical Thinking Do the numbers in the table represent a function? Explain. Yes, there is one range value (x + ) for each domain value (x). 6. a. Look at the pattern below. Make a table that relates the figure number n to the number of hexagons h. x x Assess & Reteach Lesson Quiz Copy and complete each table. Then write a function rule for each relationship.. of Lemons Cups of Punch.5.5 Test Prep Multiple Choice Figure Figure Figure b. Predict What will be the number of hexagons in Figure? 7 c. Does your table represent a function? Explain. Yes, there is one range value (h) for each domain value (figure number). 7. a. Complete the table for the side lengths and areas of squares. b. Identify the independent and the Side length Area.5.5 dependent quantities c. Graph the data. Show the data for the independent quantity on the 9 horizontal axis and the data for the dependent quantity on the vertical axis. b. side length; area c. See margin. 8. The graph at the right represents the temperature of water that was boiled and then left to cool. Which statement is true? B A. Time depends on the water temperature. B. The water temperature depends on time. C. The cooling time depends on how long the water boils. D. The water temperature depends on the boiling time. 9. The function c = (n ) + 7 represents Time the cost c in cents for mailing a letter weighing n ounces. Which statement is true? H F. The weight of a letter depends on its cost. G. The number of letters mailed depends on the total number of ounces of the letters. H. The cost to mail a letter depends on its weight. J. Each letter costs 7 an ounce. 0. Evaluate the expression x 5 for x =, 0,, and 5. Which value of x produces the greatest value from the expression? D A. B. 0 C. D. 5 Water Temperature c.5n. Minutes in Phone Call Cost of Call $.5 $.0 $.5 c.5m ± Identify the independent and dependent quantity in each situation and find reasonable domain and range values.. Gerald rents movies for each day of the -day holiday weekend. Each rental costs between $.50 and $5. independent quantity: number of movies; dependent quantity: cost of rental; domain: 6 movies; range: $5 to $0. The weight of each kitten in the litter of 5 is between 0 and ounces. Jill chooses a basket that can support the total weight of the litter. independent quantity: hours he bikes; dependent quantity: calories he burns; domain: to 7 hours; range:,75 to,975 calories 7. c. 8 y lesson quiz, PHSchool.com, Web Code: ata-00 Lesson - Patterns and Functions Area 6 6. a. Figure n Hexagons h 7 O Side length x 9
6 Alternative Assessment Have students make a table with 5 sets of values, and write the function rule for their table. Have them identify the dependent and independent variables, and the domain and range. Test Prep Resources For additional practice with a variety of test item formats: Standardized Test Prep, p. 5 Test-Taking Strategies, p. 6 Test-Taking Strategies with Transparencies. Simplify u 7 8 u u 9 u. G F. 6 G. 0 H. 6 J. 8. Jacob recorded the height of a sunflower each week for 5 weeks. Week Height (cm) 5 0 Which function best describes the relationship, if w represents the week and h represents the height? A A. h = 5w B. w = 5h C. h = w + 5 D. w = h + 5. Monica s basketball team is playing an exhibition game against a local college. After the first half of the game, Monica sees that her team has points, and the college team has points. How many more points does Monica s team need to tie the game? G F. 6 G. 8 H. J. 56. A collection of quarters and nickels is worth $.0. There are coins. How many of the coins are quarters? B A. 9 B. C. D Mixed Review for Help Lesson - Are whole numbers, integers, or rational numbers the most reasonable for each situation? 5 7. Answers may vary. Samples are given. 5. your height rational numbers 6. the number of pages in your math text whole numbers 7. the overnight low temperature in degrees Celsius for Barrow, Alaska, on January 5 rational numbers Lesson - Evaluate each expression for c = 5 and d = d - c 6 9. cd 0 0. dc 00. (cd),00. cd - c 5. (c) d 00 Algebra at Work Cartographer A cartographer, or mapmaker, makes measurements of an area being mapped. The cartographer uses these measurements to create the scale of the map showing the ratio of map distance to actual distance. Knowing the scale of a map means that you can use a proportion to calculate any distance on the map. PHSchool.com For: Information about cartographers Web Code: atb-0 Chapter Variables, Function Patterns, and Graphs
New Vocabulary equivalent inequalities. x 1 4, 7 and x, 3 are equivalent inequalities.
-. Plan - Solving Inequalities Using Addition and Subtraction Objectives To use addition to solve To use subtraction to solve Eamples Using the Addition Property of Inequality Solving and Checking Solutions
More informationWhat You ll Learn. or irrational. New Vocabulary perfect square, square root, irrational numbers, real numbers. Why Learn This?
-. Plan - Exploring Square Roots and Irrational Numbers Objective To find and estimate square roots and to classify numbers as rational or irrational Examples Finding Square Roots of Perfect Squares Estimating
More informationWrite in simplest form. New Vocabulary rate of change
-. Plan bjectives To find rates of change from tables and graphs To find slope Eamples Finding Rate of Change Using a Table Finding Rate of Change Using a Graph Finding Slope Using a Graph Finding Slope
More informationLesson 1. Unit 6 Practice Problems. Problem 1. Solution
Unit 6 Practice Problems Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17 Lesson 18 Lesson
More informationLINEAR EQUATIONS Modeling Linear Equations Common Core Standards
E Linear Equations, Lesson 1, Modeling Linear Functions (r. 2018) LINEAR EQUATIONS Modeling Linear Equations Common Core Standards F-BF.A.1 Write a function that describes a relationship between two quantities.
More informationSkills Practice Skills Practice for Lesson 1.1
Skills Practice Skills Practice for Lesson. Name Date Tanks a Lot Introduction to Linear Functions Vocabulary Define each term in your own words.. function 2. linear function 3. independent variable 4.
More informationMeasures of Central Tendency and Range
8-2 Measures of Central Tendency and Range MAIN IDEA Describe a set of data using mean, median, mode, and range. The number of pennies in each cup represents Jack s scores for five math quizzes. New Vocabulary
More informationGrade 8. Functions 8.F.1-3. Student Pages
THE NEWARK PUBLIC SCHOOLS THE OFFICE OF MATHEMATICS Grade 8 Functions 8.F.1-3 Student Pages 2012 2012 COMMON CORE CORE STATE STATE STANDARDS ALIGNED ALIGNED MODULES Grade 8 - Lesson 1 Introductory Task
More informationSolving Multi-Step Inequalities
- What You ll Learn To solve multi-step inequalities with variables on one side To solve multi-step inequalities with variables on both sides... And Why To find the measurements of a banner, as in Eample
More informationNew Vocabulary inductive reasoning conjecture counterexample. Using Inductive Reasoning
-. Plan - Patterns and Inductive Reasoning Objectives To use inductive reasoning to make conjectures Examples Finding and Using a Patternn Using Inductive Reasoning 3 Finding a Counterexample Real-World
More informationA function is a rule that establishes a relationship between two quantities, called
1.7 An Introduction to Functions What you should learn GOAL 1 Identify a function and make an input-output table for a function. GOAL 2 Write an equation for a real-life function, such as the relationship
More informationGrade 8 + DIGITAL. EL Strategies. DOK 1-4 RTI Tiers 1-3. Flexible Supplemental K-8 ELA & Math Online & Print
Standards PLUS Flexible Supplemental K-8 ELA & Math Online & Print Grade 8 SAMPLER Mathematics EL Strategies DOK 1-4 RTI Tiers 1-3 15-20 Minute Lessons Assessments Consistent with CA Testing Technology
More informationIntensive Math-Algebra I Mini-Lesson MA.912.A.3.1
Intensive Math-Algebra I Mini-Lesson MA.912.A.3.1 Summer 2013 Solving Linear Equations Student Packet Day 3 Name: Date: Benchmark MA.912.A.3.1 Solve linear equations in one variable that include simplifying
More informationEXAMPLE EXAMPLE. Simplify. Simplify each expression. See left. EXAMPLE Real-World Problem Solving EXAMPLE. Write = xa1 1!5 B = 162 Cross multiply.
-. Plan Lesson Preview Check Skills You ll Need Operations With Radical Epressions Lesson -: Eamples,, 7 Eercises, Etra Practice, p. 7 Lesson Preview What You ll Learn - To simplify sums and differences
More informationTest 3 Practice. 1) Solve the following equations. A)! " #$"% 24) = + ( x) Date Class
Test 3 Practice Name 1) Solve the following equations. A)! " #$"% 24) = + ( 16 + 4x)!!, Date Class B) $ (32 40x) 5x = 11 ( 14 + 20x) + 9, C) 2(5x 7) + 15 = 2(4 8x) + 7 2) Write an algebraic equation for
More informationName Period Date DRAFT
Name Period Date Equations and Inequalities Student Packet 4: Inequalities EQ4.1 EQ4.2 EQ4.3 Linear Inequalities in One Variable Add, subtract, multiply, and divide integers. Write expressions, equations,
More informationThe Top 11 Keystones of Algebra 1
The Top 11 Keystones of Algebra 1 The Top Eleven Keystones of Algebra 1 You should be able to 1) Simplify a radical expression. 2) Solve an equation. 3) Solve and graph an inequality on a number line.
More informationAsk questions such as If you ate a total of 30 cookies, some in the morning and 12 in the afternoon, how many crackers did you eat in the morning?
Welcome to Summer Vacation! Your child has worked hard this school year to strengthen their ability as a young Mathematician. Remember that learning does not stop outside the classroom. Daily routines
More informationWriting Equations in One Variable
7.1 Writing Equations in One Variable solve the word problem? How does rewriting a word problem help you 1 ACTIVITY: Rewriting a Word Problem Work with a partner. Read the problem several times. Think
More informationLesson Lesson Tutorials
7.4 Lesson Lesson Tutorials An equation in two variables represents two quantities that change in relationship to one another. A solution of an equation in two variables is an ordered pair that makes the
More informationAlgebra Supplement Homework Packet #1
Algebra Supplement Homework Packet #1 Day 1: Fill in each blank with one of the words or phrases listed below. Distributive Real Reciprocals Absolute value Opposite Associative Inequality Commutative Whole
More informationQuestions # 1-53 Provide review for the Mid-Term Questions # Provide review for the Final
Central Carolina Technical College MAT 031 - Developmental Math Exam Review Questions # 1-53 Provide review for the Mid-Term Questions # 1-105 Provide review for the Final SHORT ANSWER. Write the word
More informationWinter-Break Packet 7 th grade mathematics
M.S. 181 PABLO CASALS CHRISTOPHER WARNOCK, PRINCIPAL 800 BAYCHESTER AVENUE, BRONX, NY 10475 PHONE: 718-904-5600 Conceive, it, Believe it, Achieve it! Winter-Break Packet 7 th grade mathematics Student:
More informationMATH 081. Diagnostic Review Materials PART 2. Chapters 5 to 7 YOU WILL NOT BE GIVEN A DIAGNOSTIC TEST UNTIL THIS MATERIAL IS RETURNED.
MATH 08 Diagnostic Review Materials PART Chapters 5 to 7 YOU WILL NOT BE GIVEN A DIAGNOSTIC TEST UNTIL THIS MATERIAL IS RETURNED DO NOT WRITE IN THIS MATERIAL Revised Winter 0 PRACTICE TEST: Complete as
More informationCircles in the Coordinate Plane. Find the length of each segment to the nearest tenth y. Distance Formula Square both sides.
-5 ircles in the oordinate Plane -5. Plan What You ll Learn To write an equation of a circle To find the center and radius of a circle... nd Wh To describe the position and range of three cellular telephone
More informationEvaluate and Simplify Algebraic Expressions
TEKS 1.2 a.1, a.2, 2A.2.A, A.4.B Evaluate and Simplify Algebraic Expressions Before You studied properties of real numbers. Now You will evaluate and simplify expressions involving real numbers. Why? So
More information7) 24% of the lawyers in a firm are female. If there are 150 lawyers altogether, how many lawyers are female?
Math 110 Sample Final Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the perimeter (or circumference) and area of the figure. 1) Give the exact
More informationImmaculate Heart Academy Summer Math Assignment for Algebra I Honors Course Code: 5130
Immaculate Heart Academy Summer Math Assignment for Algebra I Honors Course Code: 10 LEARN PRACTICE EXCEL You are taking Algebra I Honors in the fall. A mastery of and proficiency in performing the following
More informationGoal: Write variable expressions and equations. a. A number increased by 3. c. 1 more than three times a number
S E S N Writing Expressions and Equations Goal: Write variable expressions and equations. Vocabulary Verbal model: EXAMPE 1 Translating Verbal Phrases Verbal phrase Expression a. A number increased by
More informationMathematics. Standards Plus. Grade COMMON CORE INTERVENTION SAMPLER
Mathematics Standards Plus COMMON CORE INTERVENTION Grade 7 SAMPLER Standards Plus COMMON CORE INTERVENTION Available for Grades 1-8 Language Arts and Math Standards Plus COMMON CORE INTERVENTION Mathematics
More informationName Class Date. Essential question: How do you interpret, evaluate and write algebraic expressions that model real-world situations?
Name Class Date 1-1 1 Variables and Expressions Going Deeper Essential question: How do you interpret, evaluate and write algebraic expressions that model real-world situations? A-SSE.1.1a ENGAGE Interpreting
More informationSample. Test Booklet. Subject: MA, Grade: 08 STAAR Grade 8 Math signup at to remove - Student name:
Test Booklet Subject: MA, Grade: 08 STAAR Grade 8 Math 2013 Student name: Author: Texas District: Texas Released Tests Printed: Wednesday January 31, 2018 STAAR GRADE 8 MATHEMATICS REFERENCE MATERIALS
More information1.) The number of points a basketball player scored each game for one week is recorded. Which is a not a statistical question for the situation?
6 th Grade Math Common Assessment: Chapter 6 Name: Date 6.SP.1 1.) The number of points a basketball player scored each game for one week is recorded. Which is a not a statistical question for the situation?
More informationWriting Equations to Represent Situations
11-1 Writing Equations to Represent Situations Practice and Problem Solving: A/B Determine whether the given value is a solution of the equation. Write yes or no. 1. x + 11 = 15; x = 4 2. 36 w = 10; w
More informationSolving Inequalities Using Addition or Subtraction 7.6. ACTIVITY: Writing an Inequality. ACTIVITY: Writing an Inequality
7.6 Solving Inequalities Using Addition or Subtraction How can you use addition or subtraction to solve an inequality? 1 ACTIVITY: Writing an Inequality Work with a partner. In 3 years, your friend will
More informationALGEBRA 1 SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: Algebra 1 S1 (#2201) and Foundations in Algebra 1 S1 (#7769)
Multiple Choice: Identify the choice that best completes the statement or answers the question. 1. Ramal goes to the grocery store and buys pounds of apples and pounds of bananas. Apples cost dollars per
More informationExpressions and. equation. Algebra Expressions 3.2 Adding and Subtracting Linear Expressions. Descartes, if you solve for. in the equation, what do
Expressions and Equations.... Algebra Algebraic Algebra Expressions. Adding and Subtracting Linear Expressions. Solving Equations Using Addition or Subtraction. Solving Equations Using Multiplication or
More information7 LESSON 7.1 Writing and Solving One-Step Inequalities
Inequalities? MODULE ESSENTIAL QUESTION How can you use inequalities to solve real-world problems? 7 LESSON 7.1 Writing and Solving One-Step Inequalities 7.EE.4b LESSON 7.2 Writing Two-Step Inequalities
More informationWrite an equation for each relationship. Then make a table of input-output pairs and tell whether the function is proportional.
Functions Reteaching 41 Math Course, Lesson 41 A function is a rule that identifies a relationship between a set of input numbers and a set of output numbers. A function rule can be described in words,
More informationAlgebra 1 S1 (#2201) Foundations in Algebra 1 S1 (#7769)
Instructional Materials for WCSD Math Common Finals The Instructional Materials are for student and teacher use and are aligned to the Course Guides for the following courses: Algebra 1 S1 (#2201) Foundations
More information2-1 Writing Equations
Translate each sentence into an equation. 1. Three times r less than 15 equals 6. Rewrite the verbal sentence so it is easier to translate. Three times r less than 15 equals 6 is the same as 15 minus 3
More informationSection 2.2 Objectives
Section 2.2 Objectives Solve multi-step equations using algebra properties of equality. Solve equations that have no solution and equations that have infinitely many solutions. Solve equations with rational
More informationLesson 8: Using If-Then Moves in Solving Equations
Student Outcomes Students understand and use the addition, subtraction, multiplication, division, and substitution properties of equality to solve word problems leading to equations of the form and where,,
More informationTopic 1. Solving Equations and Inequalities 1. Solve the following equation
Topic 1. Solving Equations and Inequalities 1. Solve the following equation Algebraically 2( x 3) = 12 Graphically 2( x 3) = 12 2. Solve the following equations algebraically a. 5w 15 2w = 2(w 5) b. 1
More informationALGEBRA 1 UNIT 3 WORKBOOK CHAPTER 6
ALGEBRA 1 UNIT 3 WORKBOOK CHAPTER 6 FALL 2014 0 1 Algebra 1 Section 6.1 Notes: Graphing Systems of Equations System of Equations: a set of two or more equations with the same variables, graphed in the
More informationModeling with Functions
Practice and Problem Solving: A/B Identify the dependent and independent s in each situation. 1. The cost of a dozen eggs depends on the size of the eggs. dependent: 2. Ally works in a shop for $18 per
More information4) A high school graduating class is made up of 550 students. There are 144 more boys than girls. How many girls are in the class?
Math 110 FYC chapter and 4 Practice The actual text is different Solve. 1) The difference of four times a number and seven times the same number is 9. Find the number. 1) 2) x - 1 = 1 15 2) ) 5 4 x = 15
More informationEureka Math. Grade 8, Module 4. Student File_B. Contains Exit Ticket, and Assessment Materials
A Story of Ratios Eureka Math Grade 8, Module 4 Student File_B Contains, and Assessment Materials Published by the non-profit Great Minds. Copyright 2015 Great Minds. No part of this work may be reproduced,
More informationSection 2.1 Objective 1: Determine If a Number Is a Solution of an Equation Video Length 5:19. Definition A in is an equation that can be
Section 2.1 Video Guide Linear Equations: The Addition and Multiplication Properties of Equality Objectives: 1. Determine If a Number Is a Solution of an Equation 2. Use the Addition Property of Equality
More informationAnswer to chapter 1-4
Answer to chapter 1-4 MULTIPLE CHOICE 1. ANS: C Substitute each value for y into the equation. 22 = y 6 22 = 28 6? Substitute 28 for y. 22 = 22 So 28 is a solution. A B C D Feedback Check the sign of your
More informationReteaching Using Deductive and Inductive Reasoning
Name Date Class Reteaching Using Deductive and Inductive Reasoning INV There are two types of basic reasoning in mathematics: deductive reasoning and inductive reasoning. Deductive reasoning bases a conclusion
More informationCOMMON CORE MATHEMATICS CURRICULUM
COMMON CORE MATHEMATICS CURRICULUM Lesson 1 8 4 Lesson 1: Writing Equations Using Symbols Write each of the following statements using symbolic language. 1. When you square five times a number you get
More informationName: Class: Date: ID: A
Name: Class: Date: ID: A 6A Short Answer Solve the equation. 1.!5d! 24 =!4(d + 6)! d Write the inequality for the graph. 2. 3. 4. 5. Solve the inequality. 6. p + 7
More informationTeacher Resource Sampler. Algebra 1. Common Core. MatPri111484CCSSAlg1ResourceSampler.indd 1
Teacher Resource Sampler Algebra 1 Common Core MatPri111484CCSSAlg1ResourceSampler.indd 1 6/3/11 :04 PM Going beyond the textbook with Pearson Algebra 1 Common Core Edition provides the teacher with a
More informationNegative Exponents Scientific Notation for Small Numbers
Negative Exponents Scientific Notation for Small Numbers Reteaching 51 Math Course 3, Lesson 51 The Law of Exponents for Negative Exponents An exponential expression with a negative exponent is the reciprocal
More informationFor full credit, show all work.
Accelerated Review 1: Decimals/Exponents/Algebraic Thinking Name: For full credit, show all work. 1.. 3. 4. 5. Which statement is false? A Some integers are irrational. B Some integers are whole numbers.
More informationAlgebra 1 Winter Break Extra Credit Fall Semester 2013
Algebra Winter Break Extra Credit Fall Semester ( Homework Points Maximum) Due: Monday January, at the start of class Directions: Answer all questions, showing work for each problem on your own separate
More informationWhich of the following is an irrational number? a) 2.8 b) 19
Which of the following is an irrational number? a) 2.8 b) 19 c)!! d) 81 A discounted ticket for a football game costs $12.50 less than the original price p. You pay $63 for a discounted ticket. Write and
More informationSHOW ALL WORK ON SEPARATE PAPER Answers will be provided at a later date. REAL NUMBER SYSTEM Go back and try problems on Review 1 and Test 1.
07 Accelerated Fall Exam Review Name: SHOW ALL WORK ON SEPARATE PAPER Answers will be provided at a later date. REAL NUMBER SYSTEM Go back and try problems on Review and Test.. Name the set(s) of numbers
More informationThe Keystones of Algebra 1
The Keystones of Algebra 1 The Top Ten Keystones of Algebra 1 You should be able to 1) Simplify a radical expression. 2) Solve an equation. 3) Solve and graph an inequality on a number line. 4) Manipulate
More informationQuiz For use after Section 4.2
Name Date Quiz For use after Section.2 Write the word sentence as an inequality. 1. A number b subtracted from 9.8 is greater than. 2. The quotient of a number y and 3.6 is less than 6.5. Tell whether
More informationGrade K-Algebra 2. Diagnostic and Placement Tests for Grades K through 8, Algebra 1, Geometry, and Algebra 2
Grade K-Algebra 2 Diagnostic and Placement Tests for Grades K through 8, Algebra 1, Geometry, and Algebra 2 Scoring Guide Sco ide Diagnostic Chart Intervention/Remediation simplify placement decisions
More informationQuiz For use after Section 3.2
Name Date Quiz For use after Section.2 Identify the terms, coefficients, and constants of the expression. 2 1. 5h + 9 2. a + 2 + 7b Answers 1. Write the expression using exponents.. r r r r r r 4. 4 d
More informationRelationships Between Quantities
Algebra 1 Relationships Between Quantities Relationships Between Quantities Everyone loves math until there are letters (known as variables) in problems!! Do students complain about reading when they come
More informationInstructional Materials for WCSD Math Common Finals
Instructional Materials for WCSD Math Common Finals The Instructional Materials are for student and teacher use and are aligned to the Course Guides for the following courses: High School Algebra 1 S1
More informationPre-Algebra Semester 1 Practice Exam A
. Evaluate y when = 0 and y = 6. 5 6 80. Which epression is equivalent to 5 5 + + + + + 5?. In math class, we follow the order of operations when evaluating epressions. Which is the second operation a
More informationChapter 1. Exercise Set 1.1
Chapter Exercise Set.. To prepare properly for this class, you need to do all the homework carefully and preview the new material that is to be covered in class.. At least hours of study and homework time
More informationSpring Break Assignment
B Spring Break Assignment Name: Class: Due: Answer Sheet Directions: Record your answers for Part A on the lines provided. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Part A: Multiple Choice (1) There are 150 boys
More informationInequalities. Writing and Solving One-Step Inequalities COMMON CORE. Writing Two-Step Inequalities COMMON CORE
? Inequalities 7 MODULE ESSENTIAL QUESTION How can you use inequalities to solve real-world problems? LESSON 7.1 Writing and Solving One-Step Inequalities 7.EE.4b LESSON 7.2 Writing Two-Step Inequalities
More informationCIE-USA/DFW. MathComp Grade questions. Time: One Hour
CIE-USA/DFW MathComp 2015 Grade 4 40 questions Time: One Hour Note: Make sure to write all your answers on the answer sheet. Only the answer sheet will be graded. Each question only has one correct answer.
More informationAlgebra Terminology Part 1
Grade 8 1 Algebra Terminology Part 1 Constant term or constant Variable Numerical coefficient Algebraic term Like terms/unlike Terms Algebraic expression Algebraic equation Simplifying Solving TRANSLATION
More informationMath 1 Variable Manipulation Part 4 Word Problems
Math 1 Variable Manipulation Part 4 Word Problems 1 TRANSLATING FROM ENGLISH INTO ALGEBRA (PLUG IN) The next part of variable manipulation problems is to figure out the problem from real life situations.
More informationUNIT 5 INEQUALITIES CCM6+/7+ Name: Math Teacher:
UNIT 5 INEQUALITIES 2015-2016 CCM6+/7+ Name: Math Teacher: Topic(s) Page(s) Unit 5 Vocabulary 2 Writing and Graphing Inequalities 3 8 Solving One-Step Inequalities 9 15 Solving Multi-Step Inequalities
More informationThe Thomas family went for a Sunday drive. Before they left, Mr. Thomas noticed the gas tank
North arolina Testing Program EOG Mathematics Grade Sample Items Goal. Susie earns $4.90 per hour. If she earned $90.7 last pay period, about how many hours did she work during the pay period? 5 0 75 70
More informationWrite an inequality for the graph. Then, in words, describe all the values of x that make the inequality true
Name Date. Practice A Write an inequality for the graph. Then, in words, describe all the values of that make the inequality true... 6 8 0 6 Write the word sentence as an inequality.. A number is at most..
More informationLesson 1. Problem 1. Solution. Problem 2. Solution. Problem 3
Lesson 1 Tyler reads of a book on Monday, of it on Tuesday, of it on Wednesday, and of the remainder on Thursday. If he still has 14 pages left to read on Friday, how many pages are there in the book?
More information4. Solve for x: 5. Use the FOIL pattern to multiply (4x 2)(x + 3). 6. Simplify using exponent rules: (6x 3 )(2x) 3
SUMMER REVIEW FOR STUDENTS COMPLETING ALGEBRA I WEEK 1 1. Write the slope-intercept form of an equation of a. Write a definition of slope. 7 line with a slope of, and a y-intercept of 3. 11 3. You want
More informationModel Direct Variation. You wrote and graphed linear equations. You will write and graph direct variation equations.
2.5 Model Direct Variation a.3, 2A.1.B, TEKS 2A.10.G Before Now You wrote and graphed linear equations. You will write and graph direct variation equations. Why? So you can model animal migration, as in
More informationEureka Math. Grade, Module 4. Student File_B Contains Sprint and Fluency, Exit Ticket, and Assessment Materials
A Story of Eureka Math Grade, Module 4 Student File_B Contains Sprint and Fluency,, and Assessment Materials Published by the non-profit Great Minds. Copyright 2015 Great Minds. No part of this work may
More informationGeometry Pre-Test. Name: Class: Date: ID: A. Multiple Choice Identify the choice that best completes the statement or answers the question.
Class: Date: Geometry Pre-Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. An equilateral triangle has three sides of equal length. What is the equation
More informationDecimal Multiplication and Division 1) ) ) ) ) 5.4 x ) x 2
Level B Review Packet This packet briefly reviews the topics covered on the Level A Math Skills Assessment. If you need additional study resources and/or assistance with any of the topics below, please
More informationEureka Math. Grade, Module. Student _B Contains Sprint and Fluency, Exit Ticket, and Assessment Materials
A Story of Eureka Math Grade, Module Student _B Contains Sprint and Fluency,, and Assessment Materials Published by the non-profit Great Minds. Copyright 2015 Great Minds. All rights reserved. No part
More informationMath 8 Unit 5. Writing Equations. Tuesday, November 27; 7:30am Tuesday, December 4; 7:30am. Date Lesson Topic Homework
Math 8 Unit 5 Writing Equations Extra Help: Tuesday, November 20; 2:40pm Tuesday, November 27; 7:30am Tuesday, December 4; 7:30am Date Lesson Topic Homework M 11/19 1 Types of Slope Lesson 1 -Page 6 T
More informationREVIEW: HSPA Skills 2 Final Exam June a) y = x + 4 b) y = 2x + 5 c) y = 3x +2 d) y = 2x + 3
Part I- Multiple Choice: 2 points each: Select the best possible answer. 1) The nutrition label of cookies states that there are 20 servings in a box and that one serving contains 1.5 grams of fat. Kyle
More informationStandards of Learning Content Review Notes. Grade 7 Mathematics 2 nd Nine Weeks,
Standards of Learning Content Review Notes Grade 7 Mathematics 2 nd Nine Weeks, 2018-2019 Revised October 2018 1 2 Content Review: Standards of Learning in Detail Grade 7 Mathematics: Second Nine Weeks
More informationCourse 1 Benchmark Test End of Year
Course 1 Benchmark Test End of Year 1. Which rule best describes the relationship shown in the function table below? Input A. subtract 2 Output 1 3 2 6 3 9 4 12 5 15 4. What is the least common multiple
More informationYear 4 Term 3 Homework
Yimin Math Centre Year 4 Term 3 Homework Student Name: Grade: Date: Score: Table of contents 4 Year 4 Term 3 Week 4 Homework 1 4.1 Topic 1 Volume.................................... 1 4.2 Topic 2 Mass......................................
More informationChapter 1 ( )? Chapter 1 Opener. Section 1.1. Worked-Out Solutions. 2π π = π. Try It Yourself (p. 1) So, x = 95.3.
Chapter Chapter Opener Try It Yourself (p. ). + ( ) 7.. + 8. ( ) +. 7. ( 7) + 7 7. 8 () 0 + 8. 7. ( 7) 8 0.. 8. Section.. Activity (pp. ). Triangle Angle A (degrees) Angle B (degrees). a. The sum of the
More informationUsing Graphs to Relate Two Quantities
- Think About a Plan Using Graphs to Relate Two Quantities Skiing Sketch a graph of each situation. Are the graphs the same? Explain. a. your speed as you travel from the bottom of a ski slope to the top
More informationACCUPLACER Sample Questions for Students
ACCUPLACER Sample Questions for Students Math Sample Questions for Students (ANSWER KEYS ARE FOUND AT THE END OF THIS DOCUMENT) 0 The College Board. College Board, ACCUPLACER, WritePlacer and the acorn
More informationGrade 7, Unit 2 Practice Problems - Open Up Resources. Lesson 1. Problem 1. Problem 2. Yes, since 3 times 1.5 is 4 and 2 times 1.5 is 3.
9//7, 0) AM Lesson Problem Which one of these shapes is not like the others? Explain what makes it different by representing each width and height pair with a ratio. C is different from A and B. For both
More informationFoundations for Algebra. Introduction to Algebra I
Foundations for Algebra Introduction to Algebra I Variables and Expressions Objective: To write algebraic expressions. Objectives 1. I can write an algebraic expression for addition, subtraction, multiplication,
More informationPre-Algebra 8 Semester 1 Practice Exam
. Evaluate xy when x = 0 and y = 6. 6 80. Which expression is equivalent to x + x x + x+ x+ x+ x x x x x x x?. In math class, we follow the order of operations when evaluating expressions. Which is the
More informationPre-Algebra Semester 1 Practice Exam A
. Evaluate xy when x 0 and y 6. 6 80. Which expression is equivalent to x x x xxx x x xxx x x?. In math class, we follow the order of operations when evaluating expressions. Which is the second operation
More informationKEYSTONE ALGEBRA I REVIEW
1. Which graph represents a linear function 4. The faces of a cube are numbered from 1 to 6. If the cube is tossed once, what is the probability that a prime number or a number divisible by 2 is obtained
More informationSTUDENT NAME DATE ID TAKS-M BENCHMARK. Grade 7 Math
STUDENT NAME DATE ID TEACHER NAME CLASSROOM PERIOD TAKS-M BENCHMARK Grade 7 Math Students, This assessment will measure your progress in the material you have covered in your class and readiness for upcoming
More information8 th Grade - Math 8 Summer Letter
8 th Grade - Math 8 Summer Letter Woodstown Middle School Class of 208: We know that you are preparing for the summer and September is far from your mind, but in order to be successful for 8 th Grade Math,
More informationAlgebra 1 Unit 3 Practice
Lesson 1-1 Use the table for Items 1 and. Canoe Rental Days Cost ($) 1 5 3 78 5 1 7 13 1. Use function notation to write a linear function that gives the cost C in dollars of renting a canoe for t days.
More informationEssential Question How can you use substitution to solve a system of linear equations?
5.2 Solving Systems of Linear Equations by Substitution Essential Question How can you use substitution to solve a system of linear equations? Using Substitution to Solve Systems Work with a partner. Solve
More informationAlgebra I. Midterm Review
Algebra I Midterm Review Class: Date: Algebra 1 Midterm Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1 Use the vertical-line test to determine which
More information