Math Released Set Algebra 1 PBA Item #13 Two Real Numbers Defined M44105


 Sherman Andrews
 11 months ago
 Views:
Transcription
1 Math Released Set 2015 Algebra 1 PBA Item #13 Two Real Numbers Defined M44105
2 Prompt
3 Rubric Task is worth a total of 3 points. M44105 Rubric Score Description 3 Student response includes the following 3 elements. Reasoning component = 3 points o Correct identification of a as rational and b as irrational o Correct identification that the product is irrational o Correct reasoning used to determine rational and irrational numbers Sample Student Response: A rational number can be written as a ratio. In other words, a number that can be written as a simple fraction. a = can be written as 4. Thus, a is a 9 rational number. All numbers that are not rational are considered irrational. An irrational number can be written as a decimal, but not as a fraction. b = cannot be written as a fraction, so it is irrational. The product of an irrational number and a nonzero rational number is always irrational, so the product of a and b is irrational. You can also see it is irrational with my calculations: 4 ( ) 9 = is irrational. 2 Student response includes 2 of the 3 elements. 1 Student response includes 1 of the 3 elements. 0 Student response is incorrect or irrelevant.
4 Anchor Set A1 A8
5 A1 Score Point 3
6 Annotations Anchor Paper 1 Score Point 3 This response receives full credit. The student includes each of the three required elements: Correct identification of a as rational and b as irrational (The number represented by a is rational... The number represented by b would be irrational). Correct identification that the product is irrational (The product of the expression ab would equal an irrational number). Correct reasoning to determine rational and irrational numbers (rational because it repeats, and can be written as a fraction), (irrational... it cannot be written as a fraction), (a nonzero rational number multiplied by an irrational number can never be rational, only irrational... cannot be written as a fraction). Note: Since a is defined as a = we know that the product will not be zero, so we know the student s explanation is sufficient.
7 A2 Score Point 3
8 Annotations Anchor Paper 2 Score Point 3 This response receives full credit. The student includes each of the three required elements: Correct identification of a as rational and b as irrational (a is rational... b is irrational). Correct identification that the product is irrational (the product of a and b is irrational). Correct reasoning to determine rational and irrational numbers (rational because it is repeated... irrational because the digits have no specific pattern).
9 A3 Score Point 2
10 Annotations Anchor Paper 3 Score Point 2 This response receives partial credit. The student includes two of the three required elements: Correct identification of a as rational and b as irrational (a = rational), (b = irrational). Correct identification that the product is irrational (The product of a and b would have to be irrational). The student does not provide reasoning to determine rational and irrational numbers.
11 A4 Score Point 2
12 Annotations Anchor Paper 4 Score Point 2 This response receives partial credit. The student includes two of the three required elements: Correct identification of a as rational and b as irrational (a is rational... b is not rational). Correct reasoning to determine rational and irrational numbers (rational because it can be expressed as a fraction ( 4 )... not rational because it can t be expressed as a 9 fraction). The student does not indicate that the product of the two numbers would be irrational.
13 A5 Score Point 1
14 Annotations Anchor Paper 5 Score Point 1 This response receives partial credit. The student includes one of the three required elements: Correct identification of a as rational and b as irrational (a. is rational... b. is irrational). The response does not receive credit for correct reasoning to determine rational and irrational numbers because the explanation of the irrational number is incorrect (it will stop). The student does not identify the product as an irrational number.
15 A6 Score Point 1
16 Annotations Anchor Paper 6 Score Point 1 This response receives partial credit. The student includes one of the three required elements: Correct reasoning to determine rational and irrational numbers (rational... are able to be put into a fraction). It is only necessary for the student to provide correct reasoning for determination of either rational or irrational numbers to receive credit for this element. The reasoning for both types of numbers is not required. The student does not identify a as rational or b as irrational. In addition, the product of a and b is not identified as irrational. The response does show some understanding of the characteristics of rational numbers
17 A7 Score Point 0
18
19 Annotations Anchor Paper 7 Score Point 0 This response receives no credit. The student includes none of the three required elements: The student reverses the identification of a and b (the product of a is irrational... product b is rational). The student does not indicate that the product of the two numbers would be irrational. The reasoning used for determining whether a number is rational or irrational is incorrect. Both rational numbers and irrational numbers can be (continued).
20 A8 Score Point 0
21 Annotations Anchor Paper 8 Score Point 0 This response receives no credit. This response does not satisfy any of the three required elements. It is not true that both numbers are irrational; therefore, this statement demonstrates a lack of understanding of differentiating between rational and irrational numbers. There is no attempt to provide the last two elements of the prompt.
22 Practice Set P101  P105
23 P101
24 P102
25 P103
26 P104
27 P105
28
29 Practice Set Paper Score P101 3 P102 2 P103 2 P104 1 P105 3
Math Spring Operational 2015. Grade 3 PBA Item #13 Carpet and Walkways M00553
Math Spring Operational 2015 Grade 3 PBA Item #13 Carpet and Walkways M00553 Prompt Rubric Task is worth a total of 4 points. M00553 Rubric Score Description 4 Student response includes the following 4
More informationMath Spring Operational Grade 4 PBA Item #13 Multiplication Number Line Model M00778
Math Spring Operational 2015 Grade 4 PBA Item #13 Multiplication Number Line Model M00778 Prompt Rubric M00778 Rubric Score Description 3 Student response includes the following 3 elements. Reasoning component
More informationMath Spring Operational Algebra 2 PBA Item #18 Property of an Even Function 2092M40742
Math Spring Operational 2015 Algebra 2 PBA Item #18 Property of an Even Function 2092M40742 Prompt Rubric Task is worth a total of 4 points. 2092M40742 Rubric Part A Score Description 1 Student response
More informationMath Spring Operational Grade 7 PBA Item #15 Bags of Oranges VF654249
Math Spring Operational 2015 Grade 7 PBA Item #15 Bags of Oranges VF654249 Task is worth a total of 6 points. VF654249 Rubric Part A Score Description 1 Student response includes the following element.
More informationMath Spring Operational Grade 5 Total Volume for Both Figures 0161M00840
Math Spring Operational 2015 Grade 5 Total Volume for Both Figures 0161M00840 Prompt Rubric Task is worth a total of 4 points. 0161M00840 Rubric Part A Score Description 1 Student response includes the
More informationMath Spring Geometry PBA Item #12 MerryGoRound Rate 2159M40884
Math Spring 2015 Geometry PBA Item #12 MerryGoRound Rate 2159M40884 Prompt Rubric Task is worth a total of 3 points 2159M40884 Rubric Part A Score Description 2 Student response includes the following
More informationMath Fall Block Algebra 2 PBA Item #13 System of Inequalities M44085
Math Fall Block 2015 Algebra 2 PBA Item #13 System of Inequalities M44085 Prompt Task is worth a total of 3 points. M44085 Rubric Score Description 3 Student response includes the following 3 elements.
More informationMath Released Item Grade 4. Pet Store Gave Away Goldfish M03520
Math Released Item 2016 Grade 4 Pet Store Gave Away Goldfish M03520 Prompt Task is worth a total of 3 points. Rubric Pet Store Gave Away Goldfish Score 3 Description Student response includes the following
More informationMath Spring Operational Geometry PBA Item #17 Perimeter of Isosceles Triangle 2221M41124P
Math Spring Operational 2015 Geometry PBA Item #17 Perimeter of Isosceles Triangle 2221M41124P Prompt Task is worth a total of 4 points 2221M41124 Rubric Part A Score Description 1 Student response includes
More informationMath Spring Operational Geometry PBA Item #13 Hexagon Claims M41170
Math Spring Operational 2015 Geometry PBA Item #13 Hexagon Claims M41170 Prompt Rubric Task is worth a total of 3 points M41170 Rubric Score Description 3 Student response includes the following 3 elements.
More informationMath Spring Operational Grade 8 PBA Item #14 Amount of Gasoline M20534
Math Spring Operational 2015 Grade 8 PBA Item #14 Amount of Gasoline M20534 . Based on the unit prices, Gas Station P charges more for gasoline. The unit price for Gas Station P is $4.00 per gallon since
More informationLesson Plan. N.RN.3: Use properties of rational and irrational numbers.
N.RN.3: Use properties of rational irrational numbers. N.RN.3: Use Properties of Rational Irrational Numbers Use properties of rational irrational numbers. 3. Explain why the sum or product of two rational
More informationSimplifying Radical Expressions
Section 9 2A: Simplifying Radical Expressions Rational Numbers A Rational Number is any number that that expressed as a whole number a fraction a decimal that ends a decimal that repeats 3 2 1.2 1.333
More information1. The algebra of exponents 1.1. Natural Number Powers. It is easy to say what is meant by a n a (raised to) to the (power) n if n N.
CHAPTER 3: EXPONENTS AND POWER FUNCTIONS 1. The algebra of exponents 1.1. Natural Number Powers. It is easy to say what is meant by a n a (raised to) to the (power) n if n N. For example: In general, if
More informationN.RN.3: Use properties of rational and irrational numbers.
N.RN.3: Use properties of rational irrational numbers. NUMBERS, OPERATIONS, AND PROPERTIES N.RN.B.3: Use Properties of Rational Irrational Numbers B. Use properties of rational irrational numbers. 3. Explain
More informationMath Spring Operational Geometry PBA Item #11 KingSized Mattress VF800122
Math Spring Operational 2015 Geometry PBA Item #11 KingSized Mattress VF800122 Prompt Rubric VF800122 Rubric Part A Score Description 1 Student response includes the following element. Modeling component
More informationMath Released Item Grade 6. Precipitation in Plainville VH094567
Math Released Item 2016 Grade 6 Precipitation in Plainville VH094567 Rubric Part A Score Description 2 Student response includes the following 2 elements. Reasoning component = 1 point o The student explains
More informationExample 1 Example 2 Example 3. The set of the ages of the children in my family { 27, 24, 21, 19 } The set of Counting Numbers
Section 0 1A: The Real Number System We often look at a set as a collection of objects with a common connection. We use brackets like { } to show the set and we put the objects in the set inside the brackets
More informationGuide to Mathematics Released Items: Understanding Scoring
2015 Guide to Mathematics Released Items: Understanding Scoring 1.0 Task Types, Scoring Rubrics, Anchor Sets and Annotations Overview Section 1.0 1.1 Background The 20142015 administrations of the PARCC
More informationA rational number is a number that can be written as where a and b are integers and b 0.
S E L S O N Rational Numbers Goal: Perform operations on rational numbers. Vocabulary Rational number: Additive inverse: A rational number is a number that can be a written as where a and b are integers
More informationQ N R. Sep 5 7:55 AM THE NUMBER SYSTEM
Q W I TITLE: Q N R Sep 5 7:55 AM THE NUMBER SYSTEM N NATURAL NUMBERS All positive non zero numbers; in other words, all positive numbers. This does not include zero. These are the numbers we use to count.
More information1.3. Properties of Real Numbers Properties by the Pound. My Notes ACTIVITY
Properties of Real Numbers SUGGESTED LEARNING STRATEGIES: Create Representations, Activating Prior Knowledge, Think/Pair/Share, Interactive Word Wall The local girls track team is strength training by
More informationAlgebra I Notes Review Real Numbers and Closure Unit 00a
Big Idea(s): Operations on sets of numbers are performed according to properties or rules. An operation works to change numbers. There are six operations in arithmetic that "work on" numbers: addition,
More informationAlgebra 1: Topic 1 Notes
Algebra 1: Topic 1 Notes Review: Order of Operations Please Parentheses Excuse Exponents My Multiplication Dear Division Aunt Addition Sally Subtraction Table of Contents 1. Order of Operations & Evaluating
More informationLesson 4: The Number System
Lesson 4: The Number System Introduction The next part of your course covers math skills. These lessons have been designed to provide an overview of some basic mathematical concepts. This part of your
More informationGraphing Radicals STEM 7
Graphing Radicals STEM 7 Radical functions have the form: The most frequently used radical is the square root; since it is the most frequently used we assume the number 2 is used and the square root is
More informationDetermining When an Expression Is Undefined
Determining When an Expression Is Undefined Connections Have you ever... Tried to use a calculator to divide by zero and gotten an error Tried to figure out the square root of a negative number Expressions
More informationShrtAns OpenEnded III 1. Student Name:
Student Name: Date: Please read the following and complete the task in order to prepare for this section of the Ontario Secondary School Literacy Test (OSSLT). Before Refer to pages 2 and discuss the following
More informationFRACTIONS, DECIMALS, PERIODS, (IR)RATIONALS
FRACTIONS, DECIMALS, PERIODS, (IR)RATIONALS MATH CIRCLE (BEGINNERS) 10/09/2011 (1) Here is a slightly different way to do long division and convert a fraction to a decimal. Let s try it with 3/7. First,
More informationWhat are features of a good explanation of a mathematical line of reasoning?
What are features of a good explanation of a mathematical line of reasoning? We will discuss this packet on Monday evening. Please make sure to read through this carefully by then, and to submit responses
More informationDay 2: Numbers and Quantities MAFS.912.NRN.1.1, MAFS.912.NRN.1.2, MAFS.912.NRN.2.3
Day 2: Numbers and Quantities MAFS.912.NRN.1.1, MAFS.912.NRN.1.2, MAFS.912.NRN.2.3 I CAN write algebraic proofs that show that a sum or product of two rational numbers is rational; that the sum of a
More informationRational Numbers Comparing Rational Numbers ~ Lesson Plan
Rational Numbers Comparing Rational Numbers ~ Lesson Plan I. Topic: Comparing Rational Numbers II. III. Goals and Objectives: A. The students will demonstrate an understanding of rational numbers. B. The
More informationWhen you find the square root of a perfect square there will not be a square root in the answer.
Section 7 A: Simplifying Radical Expressions When you find the square root of a perfect square there will not be a square root in the answer. 9 = 25 = 5 6 49 = 6 7 Most of the time the number under the
More informationTom wants to find two real numbers, a and b, that have a sum of 10 and have a product of 10. He makes this table.
Sum and Product This problem gives you the chance to: use arithmetic and algebra to represent and analyze a mathematical situation solve a quadratic equation by trial and improvement Tom wants to find
More informationHFCC Math Lab Intermediate Algebra  17 DIVIDING RADICALS AND RATIONALIZING THE DENOMINATOR
HFCC Math Lab Intermediate Algebra  17 DIVIDING RADICALS AND RATIONALIZING THE DENOMINATOR Dividing Radicals: To divide radical expression we use Step 1: Simplify each radical Step 2: Apply the Quotient
More informationArithmetic and Algebra of Matrices
Arithmetic and Algebra of Matrices Math 572: Algebra for Middle School Teachers The University of Montana 1 The Real Numbers 2 Classroom Connection: Systems of Linear Equations 3 Rational Numbers 4 Irrational
More informationSquare Roots and Irrational Numbers
Square Roots and Irrational Numbers Grade 7 PreAlgebra Copyright Ed2Net Learning, Inc. 1 Let s warm up : 1) Find the area of a trapezoid with Bases: 10 cm and 16 cm Height: 10 cm 2) Find the area of a
More informationHFCC Math Lab Intermediate Algebra  7 FINDING THE LOWEST COMMON DENOMINATOR (LCD)
HFCC Math Lab Intermediate Algebra  7 FINDING THE LOWEST COMMON DENOMINATOR (LCD) Adding or subtracting two rational expressions require the rational expressions to have the same denominator. Example
More informationMath 2: Algebra 2, Geometry and Statistics Ms. SheppardBrick
Math : Algebra, Geometry and Statistics Ms. SheppardBrick 617.596.41 http://lps.lexingtonma.org/page/44 Math Chapter 1 Review Exponents and Radicals Exponent definitions and rules: For the expression,
More informationSolving Linear Equations in One Variable
Lesson #70 Mathematics Assessment Project Formative Assessment Lesson Materials Solving Linear Equations in One Variable MARS Shell Center University of Nottingham & UC Berkeley Alpha Version Please Note:
More informationMATH Algebra for High School Teachers Units and Zero Divisors
MATH 57091  Algebra for High School Teachers Units and Zero Divisors Professor Donald L. White Department of Mathematical Sciences Kent State University D.L. White (Kent State University) 1 / 9 Examples
More information( ) 4, how many factors of 3 5
Exponents and Division LAUNCH (9 MIN) Before Why would you want more than one way to express the same value? During Should you begin by multiplying the factors in the numerator and the factors in the denominator?
More informationFirst Degree Equations First degree equations contain variable terms to the first power and constants.
Section 4 7: Solving 2nd Degree Equations First Degree Equations First degree equations contain variable terms to the first power and constants. 2x 6 = 14 2x + 3 = 4x 15 First Degree Equations are solved
More information1.1. Basic Concepts. Write sets using set notation. Write sets using set notation. Write sets using set notation. Write sets using set notation.
1.1 Basic Concepts Write sets using set notation. Objectives A set is a collection of objects called the elements or members of the set. 1 2 3 4 5 6 7 Write sets using set notation. Use number lines. Know
More informationFactorization in Rings
Factorization in Rings Our algebra sequence (Math 3500/4510/4520) covers the three main algebraic structures: rings, groups, and fields, roughly in that order. This course focuses on the theory of rings.
More informationWE SAY THAT A SQUARE ROOT RADICAL is simplified, or in its simplest form, when the radicand has no square factors.
SIMPLIFYING RADICALS: 12 th Grade Math & Science Summer Packet WE SAY THAT A SQUARE ROOT RADICAL is simplified, or in its simplest form, when the radicand has no square factors. A radical is also in simplest
More informationScientific Notation and Exponentiation
Scientific Notation and Exponentiation This handout will: Explain significant figures Explain exponentiation and some of its properties. Explain scientific notations. Provide examples that show techniques
More informationELEMENTARY MATHEMATICS is concerned mainly with certain elements called numbers and with certain operations defined on them.
ELEMENTARY MATHEMATICS is concerned mainly with certain elements called numbers and with certain operations defined on them. NUMERALS Arabic: 0, 1, 2, 3, 4 Roman: I, II. III. IV, X, L, C, D, M Numerical
More informationTo write a whole number as a fraction, write the whole number over 1. So, 12 =.
11. Write each number as a fraction. To write a mixed number as a fraction, multiply the whole number by the denominator and then add the numerator. Write the result over the denominator. 12. 12 To write
More informationCOMPLEX NUMBERS. Algebra 2 & Trigonometry
COMPLEX NUMBERS Algebra & Trigonometry Name: Topic Pages Day 1 Imaginary Numbers / Powers of i 3 4 Day Graphing and Operations with Complex Numbers 8 13 Day 3 Dividing Complex Numbers 14 17 Day 4 Complex
More informationChapter 2 Section 1 Lesson Kinds of Numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12...
Chapter Section Lesson Kinds of Numbers Introduction This lesson briefly reviews the real numbers and introduces variables. Digits Digits are the ten number symbols used to write any number. These are
More information3.2 Equivalent Fractions: Simplifying and Building
3.2 Equivalent Fractions: Simplifying and Building Two fractions are said to be equivalent if they have the same value. Naturally, one approach we could use to determine if two fractions are equivalent
More informationGrade 7 Mathematics Item Specification C1 TB Task Model 1
Task Model 1 Graphing DOK Level 2 7.NS.A.1b Understand p + q as the number located a distance q from p, in the positive or negative direction depending on whether q is positive or negative. Show that a
More informationHow To Scientific Notation
What Is Scientific Notation And How Is It Used? Scientific notation is also referred to as exponential notation. It is based on the Law of Exponents. The notation is based on powers of base number 10.
More informationPractice Test Answer and Alignment Document Mathematics: Algebra I Performance Based Assessment  Paper
The following pages include the answer key for all machinescored items, followed by the rubrics for the handscored items.  The rubrics show sample student responses. Other valid methods for solving
More information8 is 8 divided by 3.
Strand IV: Number Sense and Numeration Standard 1: Concepts and Properties of Numbers  Students experience counting and measuring activities to develop intuitive sense about numbers, develop understanding
More informationChapter 1. Real Numbers Operations
www.ck1.org Chapter 1. Real Numbers Operations Review Answers 1 1. (a) 101 (b) 8 (c) 1 1 (d) 1 7 (e) xy z. (a) 10 (b) 14 (c) 5 66 (d) 1 (e) 7x 10 (f) y x (g) 5 (h) (i) 44 x. At 48 square feet per pint
More informationMATH 113 Section 5.4: Decimals, Exponents, and Real Numbers
MATH 113 Section 5.4: Decimals, Exponents, and Real Numbers Prof. Jonathan Duncan Walla Walla University Winter Quarter, 2008 Outline 1 Introduction 2 Modeling with Decimals 3 Irrational Numbers 4 Conclusion
More informationa. State the integer that corresponds to a real world situation. c. Convert from fraction notation to decimal notation for a rational number.
1.2 THE REAL NUMBERS Objectives a. State the integer that corresponds to a real world situation. b. Graph rational numbers on a number line. c. Convert from fraction notation to decimal notation for a
More information12 Properties of Real Numbers
12 Properties of Real Numbers Warm Up Lesson Presentation Lesson Quiz 2 Warm Up Simplify. 1. 5+5 0 2. 1 3. 1.81 4. Find 10% of $61.70. $6.17 5. Find the reciprocal of 4. Objective Identify and use properties
More informationExploring Scientific Notation
Exploring Scientific Notation LAUNCH (8 MIN) Before How many different forms of numbers are shown in this problem? Describe each form. When ordering rational and irrational numbers, why did you need to
More informationMath Review. for the Quantitative Reasoning Measure of the GRE revised General Test
Math Review for the Quantitative Reasoning Measure of the GRE revised General Test www.ets.org Overview This Math Review will familiarize you with the mathematical skills and concepts that are important
More informationKhan Academy Algebra I Summer Preparation. Instructions for creating a Khan Academy account and selecting a coach:
Summer Math Prep Algebra I Mrs. Love Westbury Christian School mlove@westburychristian.org Website: www.khanacademy.org Khan Academy Algebra I Summer Preparation Instructions for creating a Khan Academy
More informationMathematics Scoring Guide for Sample Test 2005
Mathematics Scoring Guide for Sample Test 2005 Grade 5 Contents Strand and Performance Indicator Map with Answer Key................. 2 Holistic Rubrics......................................................
More informationSection 1.3 Systems of Linear Equations
Section 1.3 Systems of Linear Equations A system of linear equations is a set of two or more linear equations. It is also called a linear system. In this section we will study 2 2 linear systems, which
More informationC1: Surds. Learning objectives
B_Chap0_007.qxd 5/6/0 0: am Page CHAPTER C: Surds Learning objectives After studying this chapter, you should be able to: distinguish between rational and irrational numbers understand what is meant by
More informationNumbers, Operations, and Expressions. 1) Determine the classification(s) for each number below. List all that apply. 3
Numbers, Operations, and Expressions Review of Natural Numbers, Whole Numbers, Integers, and Rational Numbers 1) Determine the classification(s) for each number below. List all that apply. a) 11 b) 9.8
More informationMATH 90 CHAPTER 1 Name:.
MATH 90 CHAPTER 1 Name:. 1.1 Introduction to Algebra Need To Know What are Algebraic Expressions? Translating Expressions Equations What is Algebra? They say the only thing that stays the same is change.
More informationAP CALCULUS AB 2006 SCORING GUIDELINES (Form B) Question 5
AP CALCULUS AB 2006 SCORING GUIDELINES (Form B) Question 5 dy 2 Consider the differential equation = ( y 1) cos ( π x). dx (a) On the axes provided, sketch a slope field for the given differential equation
More informationALGEBRA STANDARDS BASED RUBRIC Revised July 2003
ALGEBRA STANDARDS BASED RUBRIC Revised July 2003 IDENTIFY AND USE MATH OPERATIONS AND PROPERTIES OVER REAL NUMBERS, MONOMIALS AND POLYNOMIALS. Unable to accurately manipulate expressions using addition,
More informationSupplemental Worksheet Problems To Accompany: The PreAlgebra Tutor: Volume 1 Section 1 Real Numbers
Supplemental Worksheet Problems To Accompany: The PreAlgebra Tutor: Volume 1 Please watch Section 1 of this DVD before working these problems. The DVD is located at: http://www.mathtutordvd.com/products/item66.cfm
More informationNovember 01, S4.4p Theorems about Zeros of Polynomial Functions. 4.4 Theorems about Zeros of Polynomial Functions
MAT 171 Precalculus Algebra CHAPTER 4: Polynomial and Rational Functions 4.1 Polynomial Functions and Models 4.2 Graphing Polynomial Functions 4.3 Polynomial Division; The Remainder and Factor Theorems
More informationLesson 13: Solving Quadratic Equations by Completing the Square
Lesson 3 Solving Quadratic Equations by Completing the Square MP.7 Student Outcomes Students solve complex quadratic equations, including those with a leading coefficient other than, by completing the
More informationPerfect Cubes, Cube Roots, and Equations of the form x³ = p
Perfect Cubes, Cube Roots, and Equations of the form x³ = p LAUNCH (8 MIN) Before What is the same about the figures and measurements shown? What is different? During Could the 64 in. measurement refer
More informationTCAP/CRA Phase II Rectangle Task Anchor Set. SECURE MATERIAL  Reader Name: Tennessee Comprehensive Assessment Program
SECURE MATERIAL  Reader Name: Tennessee Comprehensive Assessment Program TCAP/CRA 2014 6 Phase II Rectangle Task Anchor Set Copyright 2014 by the University of Pittsburgh and published under contract
More informationSample Diagnostic Test
Sample Diagnostic Test for Mathematics A r i t h m e t i c E l e m e n t a r y A l g e b r a C o l l e g e L e v e l M a t h WHAT IS THE PURPOSE OF THIS BOOKLET? Most students who enroll at Merced College
More informationUnit 03: Decimals and Inequalities
Unit 03: Decimals and Inequalities Content Area: Mathematics Course(s): Mathematics Time Period: Week 7 Length: 3 Weeks Status: Published Unit Overview Students will begin this chapter by comparing and
More informationHawkes Learning Systems: College Algebra
Hawkes Learning Systems: College Algebra Section 1.1: The Real Number System Objectives o Common subsets of real numbers. o The real number line. o Order on the real number line. o Setbuilder notation
More informationSimplifying Radical Expressions
9.2 Simplifying Radical Expressions 9.2 OBJECTIVES. Simplify expressions involving numeric radicals 2. Simplify expressions involving algebraic radicals In Section 9., we introduced the radical notation.
More informationInequalities. Learning objectives
CHAPTER Inequalities Learning objectives After studying this chapter, you should be able to: use sign diagrams to solve inequalities solve inequalities involving rational expressions. This chapter covers
More informationEquations with Rational Expressions. Integers in the denominators. x 2. 1 Original equation. 1 2 x 2
0 (8) Chapter Rational Epressions In this section Equations with Rational Epressions Etraneous s. SOLVING EQUATIONS WITH RATIONAL EXPRESSIONS Many problems in algebra can be solved by using equations
More informationAlgebra Revision Sheet Questions 2 and 3 of Paper 1
Algebra Revision Sheet Questions and of Paper Simple Equations Step Get rid of brackets or fractions Step Take the x s to one side of the equals sign and the numbers to the other (remember to change the
More informationMULTIPLICATION AND DIVISION OF REAL NUMBERS In this section we will complete the study of the four basic operations with real numbers.
1.4 Multiplication and (125) 25 In this section Multiplication of Real Numbers Division by Zero helpful hint The product of two numbers with like signs is positive, but the product of three numbers with
More information2.3 Solving Equations Containing Fractions and Decimals
2. Solving Equations Containing Fractions and Decimals Objectives In this section, you will learn to: To successfully complete this section, you need to understand: Solve equations containing fractions
More information5.4 The Quadratic Formula
Section 5.4 The Quadratic Formula 481 5.4 The Quadratic Formula Consider the general quadratic function f(x) = ax + bx + c. In the previous section, we learned that we can find the zeros of this function
More informationMath 10 Lesson 14 Irrational Numbers
I. Classifying numbers Math 0 Lesson  Irrational Numbers All numbers are classified into different groups or sets. There are natural numbers, whole numbers, integers, rational numbers, irrational numbers
More informationThe wavelength of infrared light is meters. The digits 3 and 7 are important but all the zeros are just place holders.
Section 6 2A: A common use of positive and negative exponents is writing numbers in scientific notation. In astronomy, the distance between 2 objects can be very large and the numbers often contain many
More informationGroups 1. Definition 1 A Group G is a set with an operation which satisfies the following: e a = a e = e. a a 1 = a 1 a = e.
Groups 1 1 Introduction to Groups Definition 1 A Group G is a set with an operation which satisfies the following: 1. there is an identity element e G, such that for every a G e a = a e = e 2. every element
More informationAlgebra 1 Chapter 3 Vocabulary. equivalent  Equations with the same solutions as the original equation are called.
Chapter 3 Vocabulary equivalent  Equations with the same solutions as the original equation are called. formula  An algebraic equation that relates two or more reallife quantities. unit rate  A rate
More informationAlgebra 1 Lesson 13. Real Numbers
Algebra 1 Lesson 1 Common Core Real Numbers and the Number Line Real Numbers Rational Numbers Integers Whole Numbers Irrational Numbers Natural Numbers 1 Natural Numbers what you see in nature counting
More informationMath. Fraction, Decimal & Percent (Visual) Answers. Name: Determine the value written as a fraction, decimal & a percent. Ex) Fraction.
, Decimal & Percent (Visual) ) ) 0. 0%. 0. % ) Decimal 0. Percent 0% Decimal 0. Percent % ) Decimal 0. Percent %... 0. % 0. 0% 0. % 0. %. 0. %. 0. 0% ) Decimal 0. Percent 0% ) Decimal 0. Percent % ) Decimal
More informationSquare Roots. Learning Objectives. PreActivity
Section 1. PreActivity Preparation Square Roots Our number system has two important sets of numbers: rational and irrational. The most common irrational numbers result from taking the square root of nonperfect
More informationRational and Irrational Numbers 2
Lesson 31 Mathematics Assessment Project Formative Assessment Lesson Materials Rational and Irrational Numbers 2 MARS Shell Center University of Nottingham & UC Berkeley Alpha Version If you encounter
More informationYear 11 Math Homework
Yimin Math Centre Year 11 Math Homework Student Name: Grade: Date: Score: Table of contents 3 Year 11 Topic 3 Basic Algebra Part 3 1 3.1 Equations and Inequations................................ 1 3.1.1
More informationLawrence Middle School s 2016 Summer Math Packet Algebra I Course/Class
Lawrence Middle School s 2016 Summer Math Packet Algebra I Course/Class LMS Algebra 1 Page 1 Algebra 1 Summer Math Packet Directions You are expected to complete this Summer Math Packet to be best prepared
More informationSimplifying Numerical Square Root Expressions
10.1.1 Simplifying Numerical Square Root Expressions Definitions 1. The square of an integer is called a perfect square integer. Since 1 2 =1, 2 2 = 4, 3 2 = 9, 4 2 =16, etc..., the perfect square integers
More informationAbout Fractions. Introduction
About Fractions TABLE OF CONTENTS About Fractions... 1 What is a FRACTION?... 1 Introduction... 1 Introduction... 1 Forms of Fractions... 1 Different Forms of Fractions... 1 Proper Fractions... 2 Improper
More informationAxioms for the Real Number System
Axioms for the Real Number System Math 361 Fall 2003 The Real Number System The real number system consists of four parts: 1. A set (R). We will call the elements of this set real numbers, or reals. 2.
More informationCommon Core Mathematics Challenge
Level: Domain: Cluster: Grade Five Number and Operations Fractions Use equivalent fractions as a strategy to add and subtract fractions. Standard Add and subtract fraction with unlike denominators (including
More informationPercents and Applications
Percents and Applications Meaning of Percents Percent means per hundred or parts of one hundred. For example, percent means fifteen parts out of a hundred or, and percent can be written 00 %. Examples
More information