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

Save this PDF as:

Size: px
Start display at page:

Download "Math Released Set 2015. Algebra 1 PBA Item #13 Two Real Numbers Defined M44105"

## 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 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

### 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

### Math 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.

### Math Spring Operational Grade 5 Total Volume for Both Figures 0161-M00840

Math Spring Operational 2015 Grade 5 Total Volume for Both Figures 0161-M00840 Prompt Rubric Task is worth a total of 4 points. 0161-M00840 Rubric Part A Score Description 1 Student response includes the

### Math Spring Geometry PBA Item #12 Merry-Go-Round Rate 2159-M40884

Math Spring 2015 Geometry PBA Item #12 Merry-Go-Round Rate 2159-M40884 Prompt Rubric Task is worth a total of 3 points 2159-M40884 Rubric Part A Score Description 2 Student response includes the following

### Math 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.

### Math Spring Operational Geometry PBA Item #17 Perimeter of Isosceles Triangle 2221-M41124P

Math Spring Operational 2015 Geometry PBA Item #17 Perimeter of Isosceles Triangle 2221-M41124P Prompt Task is worth a total of 4 points 2221-M41124 Rubric Part A Score Description 1 Student response includes

### Lesson 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

### Guide 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 2014-2015 administrations of the PARCC

### Simplifying 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

### Math 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

### 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.

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

### Algebra 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,

### Practice Test Answer and Alignment Document Mathematics: Algebra I Performance Based Assessment - Paper

The following pages include the answer key for all machine-scored items, followed by the rubrics for the hand-scored items. - The rubrics show sample student responses. Other valid methods for solving

### Algebra 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

### 1.3. 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

### Mathematics 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......................................................

### MATH 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.

### Arithmetic 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

### Tom 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

### Mathematics Scoring Guide for Sample Test 2005

Mathematics Scoring Guide for Sample Test 2005 Grade 3 Contents Strand and Performance Indicator Map with Answer Key........................ 2 Holistic Rubrics.............................................................

### HFCC 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

### Square Roots. Learning Objectives. Pre-Activity

Section 1. Pre-Activity 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 non-perfect

### Copy in your notebook: Add an example of each term with the symbols used in algebra 2 if there are any.

Algebra 2 - Chapter Prerequisites Vocabulary Copy in your notebook: Add an example of each term with the symbols used in algebra 2 if there are any. P1 p. 1 1. counting(natural) numbers - {1,2,3,4,...}

### Math 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

### HFCC 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

### Math: Essentials+ (GN105A) 4 Credit Hours Spring 2015

Math: Essentials+ (GN105A) 4 Credit Hours Spring 2015 Course Description: A college math course geared for the eyes and sensibilities of visual artists. Topics include Non-Euclidean and projective geometry,

### Chapter 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

### TCAP/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

### PERCENTS. Percent means per hundred. Writing a number as a percent is a way of comparing the number with 100. For example: 42% =

PERCENTS Percent means per hundred. Writing a number as a percent is a way of comparing the number with 100. For example: 42% = Percents are really fractions (or ratios) with a denominator of 100. Any

### First 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

### 1-2 Properties of Real Numbers

1-2 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

### 7.2 Translating and Solving Percent Problems

7.2 ranslating and Solving Percent Problems In this section we will study how to solve percent problems. Percent problems usually have a phrase in the question in one of the following forms: Percent of

### Autumn 1 Maths Overview. Year groups Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 1 Number and place value. Counting. 2 Sequences and place value.

Autumn 1 Maths Overview. Year groups Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 1 Number and place Counting. 2 Sequences and place Number facts and counting. Money and time. Length, position and

### COGNITIVE TUTOR ALGEBRA

COGNITIVE TUTOR ALGEBRA Numbers and Operations Standard: Understands and applies concepts of numbers and operations Power 1: Understands numbers, ways of representing numbers, relationships among numbers,

### March 29, 2011. 171S4.4 Theorems about Zeros of Polynomial Functions

MAT 171 Precalculus Algebra Dr. Claude Moore Cape Fear Community College CHAPTER 4: Polynomial and Rational Functions 4.1 Polynomial Functions and Models 4.2 Graphing Polynomial Functions 4.3 Polynomial

### SECTION 0.6: POLYNOMIAL, RATIONAL, AND ALGEBRAIC EXPRESSIONS

(Section 0.6: Polynomial, Rational, and Algebraic Expressions) 0.6.1 SECTION 0.6: POLYNOMIAL, RATIONAL, AND ALGEBRAIC EXPRESSIONS LEARNING OBJECTIVES Be able to identify polynomial, rational, and algebraic

### Released Test Answer and Alignment Document Mathematics Grade 5 Performance Based Assessment

Released Test Answer and Alignment Document Mathematics Grade 5 Performance Based Assessment The following pages include the answer key for all machine-scored items, followed by the rubrics for the hand-scored

### Math. 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

### GRADE 6 MATH: RATIOS AND PROPORTIONAL RELATIONSHIPS

GRADE 6 MATH: RATIOS AND PROPORTIONAL RELATIONSHIPS UNIT OVERVIEW This 4-5 week unit focuses on developing an understanding of ratio concepts and using ratio reasoning to solve problems. TASK DETAILS Task

### 2.3 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

### Common Core Standards for Fantasy Sports Worksheets. Page 1

Scoring Systems Concept(s) Integers adding and subtracting integers; multiplying integers Fractions adding and subtracting fractions; multiplying fractions with whole numbers Decimals adding and subtracting

### MULTIPLICATION 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 (1-25) 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

### Common 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

### Algebra 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 real-life quantities. unit rate - A rate

### To discuss this topic fully, let us define some terms used in this and the following sets of supplemental notes.

INFINITE SERIES SERIES AND PARTIAL SUMS What if we wanted to sum up the terms of this sequence, how many terms would I have to use? 1, 2, 3,... 10,...? Well, we could start creating sums of a finite number

### Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 1 Section 1 Real Numbers

Supplemental Worksheet Problems To Accompany: The Pre-Algebra 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

### Chapter 1.1 Rational and Irrational Numbers

Chapter 1.1 Rational and Irrational Numbers A rational number is a number that can be written as a ratio or the quotient of two integers a and b written a/b where b 0. Integers, fractions and mixed numbers,

### Zero and Negative Exponents. Section 7-1

Zero and Negative Exponents Section 7-1 Goals Goal To simplify expressions involving zero and negative exponents. Rubric Level 1 Know the goals. Level 2 Fully understand the goals. Level 3 Use the goals

### The 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

### Practice Test Answer and Alignment Document Mathematics: Grade 7 Performance Based Assessment - Paper

The following pages include the answer key for all machine-scored items, followed by the rubrics for the hand-scored items. - The rubrics show sample student responses. Other valid methods for solving

### SUBJECTABLE MATHMATICS

SUBJECTABLE MATHMATICS PREFACE (A NOTE TO THE READER) This book, A COMPLETE BOOK ON SUBJECTIVE (CONVEN- TIONAL) ARITHMETIC has been specially prepared for candidates appearing for competitive entrance

### QUADRATIC EQUATIONS Use with Section 1.4

QUADRATIC EQUATIONS Use with Section 1.4 OBJECTIVES: Solve Quadratic Equations by Factoring Solve Quadratic Equations Using the Zero Product Property Solve Quadratic Equations Using the Quadratic Formula

### Released Test Answer and Alignment Document Mathematics Grade 3 Performance Based Assessment

Released Test Answer and Alignment Document Mathematics Grade 3 Performance Based Assessment The following pages include the answer key for all machine-scored items, followed by the rubrics for the hand-scored

### 0.8 Rational Expressions and Equations

96 Prerequisites 0.8 Rational Expressions and Equations We now turn our attention to rational expressions - that is, algebraic fractions - and equations which contain them. The reader is encouraged to

### Grade 9 Assessment of Mathematics 2013, Academic Released Item-Specific Rubrics and Sample Student Responses with Annotations

Grade 9 Assessment of Mathematics 2013, Academic Released Item-Specific Rubrics and Sample Student Responses with Annotations EQAO, 2 Carlton Street, Suite 1200, Toronto, ON M5B 2M9 1-888-327-7377 Web

### Algebra 1 If you are okay with that placement then you have no further action to take Algebra 1 Portion of the Math Placement Test

Dear Parents, Based on the results of the High School Placement Test (HSPT), your child should forecast to take Algebra 1 this fall. If you are okay with that placement then you have no further action

### GRADE 6 MATH: SHARE MY CANDY

GRADE 6 MATH: SHARE MY CANDY UNIT OVERVIEW The length of this unit is approximately 2-3 weeks. Students will develop an understanding of dividing fractions by fractions by building upon the conceptual

### Practice Test Answer and Alignment Document Mathematics: Algebra II Performance Based Assessment - Paper

The following pages include the answer key for all machine-scored items, followed by the rubrics for the hand-scored items. - The rubrics show sample student responses. Other valid methods for solving

### Overview. Essential Questions. Grade 4 Mathematics, Quarter 3, Unit 3.3 Multiplying Fractions by a Whole Number

Multiplying Fractions by a Whole Number Overview Number of instruction days: 8 10 (1 day = 90 minutes) Content to Be Learned Understand that a fraction can be written as a multiple of unit fractions with

### Grade 7 Red Math Weekly Schedule December 6 th December 10 th Mr. Murad

Lesson 1&2 6/12/2015 Lesson 3 7/12/2015 Lesson 4 8/12/2015 Lesson 5&6 9/12/2015 Grade 7 Red Math Weekly Schedule December 6 th December 10 th Mr. Murad Date Class Work Home Work 2-1 -find the absolute

### Sample Math Questions: Student- Produced Response

Chapter Sample Math Questions: Student- Produced Response In this chapter, you will see examples of student-produced response math questions This type of question appears in both the calculator and the

### Session 19 Fraction Basics

How would you answer this question? Session 19 Fraction Basics MSUM is hosting a six kilometer women s cross-country meet at Johnson Park on a course that is two kilometers long. Pat completed two laps.

### Number Factors. Number Factors Number of factors 1 1 1 16 1, 2, 4, 8, 16 5 2 1, 2 2 17 1, 17 2 3 1, 3 2 18 1, 2, 3, 6, 9, 18 6 4 1, 2, 4 3 19 1, 19 2

Factors This problem gives you the chance to: work with factors of numbers up to 30 A factor of a number divides into the number exactly. This table shows all the factors of most of the numbers up to 30.

### MATH 65 NOTEBOOK CERTIFICATIONS

MATH 65 NOTEBOOK CERTIFICATIONS Review Material from Math 60 2.5 4.3 4.4a Chapter #8: Systems of Linear Equations 8.1 8.2 8.3 Chapter #5: Exponents and Polynomials 5.1 5.2a 5.2b 5.3 5.4 5.5 5.6a 5.7a 1

### LESSON PLANS FOR PERCENTAGES, FRACTIONS, DECIMALS, AND ORDERING Lesson Purpose: The students will be able to:

LESSON PLANS FOR PERCENTAGES, FRACTIONS, DECIMALS, AND ORDERING Lesson Purpose: The students will be able to: 1. Change fractions to decimals. 2. Change decimals to fractions. 3. Change percents to decimals.

### Solution Guide Chapter 14 Mixing Fractions, Decimals, and Percents Together

Solution Guide Chapter 4 Mixing Fractions, Decimals, and Percents Together Doing the Math from p. 80 2. 0.72 9 =? 0.08 To change it to decimal, we can tip it over and divide: 9 0.72 To make 0.72 into a

### Improper Fractions and Mixed Numbers

This assignment includes practice problems covering a variety of mathematical concepts. Do NOT use a calculator in this assignment. The assignment will be collected on the first full day of class. All

### Parallelogram. This problem gives you the chance to: use measurement to find the area and perimeter of shapes

Parallelogram This problem gives you the chance to: use measurement to find the area and perimeter of shapes 1. This parallelogram is drawn accurately. Make any measurements you need, in centimeters, and

### Grading: A1=90% and above; A=80% to 89%; B1=70% to 79%; B=60% to 69%; C=50% to 59%; D=34% to 49%; E=Repeated; 1 of 55 pages

100001 A1 100002 A1 100003 B 100004 B 100005 B 100006 A 100007 C 100008 C 100009 B1 100010 D 100011 A 100012 B 100013 B 100014 B1 100015 C 100016 B1 100017 A1 100018 A1 100019 A1 100020 B1 100021 A 100022

### Practice Test Answer and Alignment Document Mathematics - Grade 4 Performance Based Assessment - Paper

The following pages include the answer key for all machine-scored items, followed by the rubrics for the hand-scored items. - The rubrics show sample student responses. Other valid methods for solving

### 5.4 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

### GRADE 8 MATH: TALK AND TEXT PLANS

GRADE 8 MATH: TALK AND TEXT PLANS UNIT OVERVIEW This packet contains a curriculum-embedded Common Core standards aligned task and instructional supports. The task is embedded in a three week unit on systems

### APPLICATIONS OF THE ORDER FUNCTION

APPLICATIONS OF THE ORDER FUNCTION LECTURE NOTES: MATH 432, CSUSM, SPRING 2009. PROF. WAYNE AITKEN In this lecture we will explore several applications of order functions including formulas for GCDs and

### AP STATISTICS 2010 SCORING GUIDELINES (Form B)

AP STATISTICS 2010 SCORING GUIDELINES (Form B) Question 5 Intent of Question The primary goals of this question were to assess students ability to (1) calculate appropriate probabilities, including conditional

### Welcome to Math 19500 Video Lessons. Stanley Ocken. Department of Mathematics The City College of New York Fall 2013

Welcome to Math 19500 Video Lessons Prof. Department of Mathematics The City College of New York Fall 2013 An important feature of the following Beamer slide presentations is that you, the reader, move

### PETERS TOWNSHIP SCHOOL DISTRICT CORE BODY OF KNOWLEDGE MATH GRADE 5

PETERS TOWNSHIP SCHOOL DISTRICT CORE BODY OF KNOWLEDGE MATH GRADE 5 For each of the sections that follow, students may be required to understand, apply, analyze, evaluate or create the particular concepts

### How DIBELS Math Relates to the Common Core State Standards in Mathematics Dynamic Measurement Group, Inc. / May 7, 2014

How DIBELS Math Relates to the Common Core State Standards in Mathematics Dynamic Measurement Group, Inc. / May 7, 2014 DIBELS Math draws problem types from the Common Core State Standards for Mathematics.

### Singapore Math K st Grade

Singapore Math K- 5 Kindergarten There are 140 lessons in this Singapore Kindergarten Math Program. They will be covered 140, is noted below that. May: Lessons 117 131 June: Lessons 132-140 Textbook A

### Florida Math 0018. Correlation of the ALEKS course Florida Math 0018 to the Florida Mathematics Competencies - Lower

Florida Math 0018 Correlation of the ALEKS course Florida Math 0018 to the Florida Mathematics Competencies - Lower Whole Numbers MDECL1: Perform operations on whole numbers (with applications, including

### Welcome to Math 7 Accelerated Courses (Preparation for Algebra in 8 th grade)

Welcome to Math 7 Accelerated Courses (Preparation for Algebra in 8 th grade) Teacher: School Phone: Email: Kim Schnakenberg 402-443- 3101 kschnakenberg@esu2.org Course Descriptions: Both Concept and Application

### Math Foundations IIB Grade Levels 9-12

Math Foundations IIB Grade Levels 9-12 Math Foundations IIB introduces students to the following concepts: integers coordinate graphing ratio and proportion multi-step equations and inequalities points,

### Factoring - Greatest Common Factor

6.1 Factoring - Greatest Common Factor Objective: Find the greatest common factor of a polynomial and factor it out of the expression. The opposite of multiplying polynomials together is factoring polynomials.

### Evaluating Statements about Rational and Irrational Numbers

CONCEPT DEVELOPMENT Mathematics Assessment Project CLASSROOM CHALLENGES A Formative Assessment Lesson Evaluating Statements about Rational and Irrational Numbers Mathematics Assessment Resource Service

### Variable. 1.1 Order of Operations. August 17, evaluating expressions ink.notebook. Standards. letter or symbol used to represent a number

1.1 evaluating expressions ink.notebook page 8 Unit 1 Basic Equations and Inequalities 1.1 Order of Operations page 9 Square Cube Variable Variable Expression Exponent page 10 page 11 1 Lesson Objectives

### Introduction to Signed Numbers

Worksheet 1.6 Signed Numbers Section 1 Introduction to Signed Numbers Signed numbers are positive and negative numbers. So far in the worksheets we have mainly talked about the counting numbers, which

### Integer Operations. Overview. Grade 7 Mathematics, Quarter 1, Unit 1.1. Number of Instructional Days: 15 (1 day = 45 minutes) Essential Questions

Grade 7 Mathematics, Quarter 1, Unit 1.1 Integer Operations Overview Number of Instructional Days: 15 (1 day = 45 minutes) Content to Be Learned Describe situations in which opposites combine to make zero.

### Simplifying 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.

### Chapter 4 -- Decimals

Chapter 4 -- Decimals \$34.99 decimal notation ex. The cost of an object. ex. The balance of your bank account ex The amount owed ex. The tax on a purchase. Just like Whole Numbers Place Value - 1.23456789

### *Converting Fractions to Decimals

*Converting Fractions to Decimals In this task, students will convert fractions to decimals. Back to task table STANDARDS FOR MATHEMATICAL CONTENT MGSE7.NS.2 Apply and extend previous understandings of

### Free Pre-Algebra Lesson 55! page 1

Free Pre-Algebra Lesson 55! page 1 Lesson 55 Perimeter Problems with Related Variables Take your skill at word problems to a new level in this section. All the problems are the same type, so that you can

### Solving Rational Equations

Lesson M Lesson : Student Outcomes Students solve rational equations, monitoring for the creation of extraneous solutions. Lesson Notes In the preceding lessons, students learned to add, subtract, multiply,

### Number Systems I. CIS008-2 Logic and Foundations of Mathematics. David Goodwin. 11:00, Tuesday 18 th October

Number Systems I CIS008-2 Logic and Foundations of Mathematics David Goodwin david.goodwin@perisic.com 11:00, Tuesday 18 th October 2011 Outline 1 Number systems Numbers Natural numbers Integers Rational

### This page must be completed and submitted with your Substantive Assignment. Incomplete or missing information WILL NOT be processed.

Welcome to Math 11 Pre- Calculus This page must be completed and submitted with your Substantive Assignment. Incomplete or missing information WILL NOT be processed. NOTE: Registration forms with attached,

### Vocabulary Words and Definitions for Algebra

Name: Period: Vocabulary Words and s for Algebra Absolute Value Additive Inverse Algebraic Expression Ascending Order Associative Property Axis of Symmetry Base Binomial Coefficient Combine Like Terms

### Math Help and Additional Practice Websites

Name: Math Help and Additional Practice Websites http://www.coolmath.com www.aplusmath.com/ http://www.mathplayground.com/games.html http://www.ixl.com/math/grade-7 http://www.softschools.com/grades/6th_and_7th.jsp

### Inequalities. Assessment Management. Dividing Decimals by Decimals: Part 1

Inequalities Objectives To find and represent all the values that make an inequality in one variable true; and to represent real-world situations with inequalities. www.everydaymathonline.com epresentations

### USING THE PROPERTIES TO SIMPLIFY EXPRESSIONS

5 (1 5) Chapter 1 Real Numbers and Their Properties 1.8 USING THE PROPERTIES TO SIMPLIFY EXPRESSIONS In this section The properties of the real numbers can be helpful when we are doing computations. In