Math-2A Lesson 2-1. Number Systems
|
|
- Barry Foster
- 5 years ago
- Views:
Transcription
1 Math-A Lesson -1 Number Systems
2 Natural Numbers Whole Numbers Lesson 1-1 Vocabulary Integers Rational Numbers Irrational Numbers Real Numbers Imaginary Numbers Complex Numbers Closure
3 Why do we need numbers? Lebombo Plain (Africa) Lebombo counting sticks appeared about 35,000 years ago! How can you write the number zero using a counting stick? How can you write a negative number using a counting stick?
4 A few horses? How do you count?
5 Vocabulary Natural numbers: the positive counting numbers that are usually shown on a number line Whole numbers: the natural numbers and the number zero Integers: the whole numbers and the negative counting numbers
6 Can anyone interpret what the following means? Rational numbers R : R a ; a,b integers b Vocabulary Rational numbers: can be written as a ratio of integers: ½, -⅔, etc.
7 When converting a rational number into its decimal form (using division) the decimal with either terminate (1/ = 0.5) or repeat (/3 = ). Write the integer -3 as a rational number Are these all the,,, same thing? Why is -3 not equal to?
8 If the triangle below is a right triangle, how can we find length c (the hypotenuse)? Pythagorean Theorem: If it s a right triangle, then side lengths can be related by: a b c 1 c 5 c 5 c What numbers system does this number belong to?
9 Property of Equality: if the same operation is applied to both sides of an equal sign, then the resulting equation is still true (has the same solution). x 4 x 4 Square both sides of the equation x 4 The same value of x makes both the 1 st and last equation true (x = ). x
10 Vocabulary Irrational numbers: cannot be written as a ratio of integers: ½, -⅔, etc. The decimal version of an irrational number never terminates and never repeats. (0 = ). If we see the radical symbol, the number is usually irrational (unless it is a perfect square). 3 4 (rational #)
11 3 Identifying the type of number. (1) () (3) (4) (5) Natural Whole Integer Rational Irrational
12 Exact vs. Approximate: Exact: 17 Approximate: Converting an irrational number into a decimal requires you to round off the decimal somewhere.
13 Irrational Numbers The square root of x really means, what number squared equals. x Why do these both refer to the same number (that makes both equations true)? Because of the Property of Equality.
14 1 The square root of -1: x 1 really means, what number squared equals -1. x 1 What real number when squared becomes a negative number? It doesn t exist so it must be an imaginary number 3 (1)* 3 (1) * 3 i 3
15 Vocabulary imaginary numbers: a number that includes the square root of a negative number. 1 i 3 3 real numbers: a number that can be found on the number line
16 Think of the complex numbers as the universe of numbers. Complex Numbers a b Real # s a b Imaginary # s
17 Complex Numbers Venn Diagram Imaginary Numbers 1 Integers Real Numbers Rational Numbers Irrational Numbers e i,-, -1, 0, 1,, 3, 4, i
18 Complex # s Real # s Imaginary # s Rational # s Irrational # s Integers Whole # s Natural # s 1 3 natural natural natural Is this always true? 3* 6 natural* natural natural Is this always true? 1 1 integer integer integer Is this always true? natural - natural natural Is this always true?
19 Which number system came first? Man probably invented the natural number system first. When the idea of zero was no longer scary, then it was probably added to form the whole number system. Then smart people started doing math with the numbers in the system. 1 What s wrong with this? 1? 3 duh! One subtract two is not in the whole number system!!! They needed a new number system!!!
20 Vocabulary Closure: a number system is closed for a particular operation (add, subtract, multiply, divide, etc.) when two numbers have an operation performed on them and the resulting number is still in the number system. We say that whole numbers and natural numbers are not closed under subtraction. Is there another operation for which the whole numbers or the natural numbers are not closed? 7 0? 1?
21 Associative Property of (multiplication) If there are 3 or more factors, you must pick two of them to combine first. *3*4 (*3)* 4 6* 4 4 Associative Property of (Addition) If there are 3 or more addends, you must pick two of them to combine with addition ( 3) 4 5 4
Math-2 Section 1-1. Number Systems
Math- Section 1-1 Number Systems Natural Numbers Whole Numbers Lesson 1-1 Vocabulary Integers Rational Numbers Irrational Numbers Real Numbers Imaginary Numbers Complex Numbers Closure Why do we need numbers?
More informationSkills Practice Skills Practice for Lesson 4.1
Skills Practice Skills Practice for Lesson.1 Name Date Thinking About Numbers Counting Numbers, Whole Numbers, Integers, Rational and Irrational Numbers Vocabulary Define each term in your own words. 1.
More informationNAME DATE PERIOD. A negative exponent is the result of repeated division. Extending the pattern below shows that 4 1 = 1 4 or 1. Example: 6 4 = 1 6 4
Lesson 4.1 Reteach Powers and Exponents A number that is expressed using an exponent is called a power. The base is the number that is multiplied. The exponent tells how many times the base is used as
More informationMath-2 Lesson 2-4. Radicals
Math- Lesson - Radicals = What number is equivalent to the square root of? Square both sides of the equation ( ) ( ) = = = is an equivalent statement to = 1.7 1.71 1.70 1.701 1.7008... There is no equivalent
More informationNOTES: Chapter 11. Radicals & Radical Equations. Algebra 1B COLYER Fall Student Name:
NOTES: Chapter 11 Radicals & Radical Equations Algebra 1B COLYER Fall 2016 Student Name: Page 2 Section 3.8 ~ Finding and Estimating Square Roots Radical: A symbol use to represent a. Radicand: The number
More informationSECTION Types of Real Numbers The natural numbers, positive integers, or counting numbers, are
SECTION.-.3. Types of Real Numbers The natural numbers, positive integers, or counting numbers, are The negative integers are N = {, 2, 3,...}. {..., 4, 3, 2, } The integers are the positive integers,
More informationAssociative property
Addition Associative property Closure property Commutative property Composite number Natural numbers (counting numbers) Distributive property for multiplication over addition Divisibility Divisor Factor
More informationHow can you find decimal approximations of square roots that are not rational? ACTIVITY: Approximating Square Roots
. Approximating Square Roots How can you find decimal approximations of square roots that are not rational? ACTIVITY: Approximating Square Roots Work with a partner. Archimedes was a Greek mathematician,
More informationMath 8 Curriculum Map and I Can Statements Diane Hamilton
Math 8 Curriculum Map and I Can Statements 203 204 Diane Hamilton Unit : Numbers Review A Whole Numbers Place Value 2 Identify the place value of a whole number 2 Decimals Place Value 2 Identify the place
More informationSection 9.2 Objective: Students will be able to define and work with irrational numbers.
Lincoln Public Schools Math 8 McDougall Littell Middle School Math Course 3 Chapter 9 Items marked A, B, C are increasing in difficulty. Group A questions are the most basic while Group C are the most
More informationPre-Algebra Unit 2. Rational & Irrational Numbers. Name
Pre-Algebra Unit 2 Rational & Irrational Numbers Name Core Table 2 Pre-Algebra Name: Unit 2 Rational & Irrational Numbers Core: Table: 2.1.1 Define Rational Numbers Vocabulary: Real Numbers the set of
More informationIrrational Numbers Study Guide
Square Roots and Cube Roots Positive Square Roots A positive number whose square is equal to a positive number b is denoted by the symbol b. The symbol b is automatically denotes a positive number. The
More informationPre-Algebra Curriculum Map Unit 1: The Number System M08.A-N Essential Questions Standards Content Skills Vocabulary
Unit 1: The Number System M08.A-N Essential Questions Standards Content Skills Vocabulary Why is it helpful to write numbers in different ways? M08.A-N.1.1.1 Determine whether a number is rational or irrational.
More informationP.1 Prerequisite skills Basic Algebra Skills
P.1 Prerequisite skills Basic Algebra Skills Topics: Evaluate an algebraic expression for given values of variables Combine like terms/simplify algebraic expressions Solve equations for a specified variable
More informationAlgebra I The Number System & Mathematical Operations
Slide 1 / 72 Slide 2 / 72 Algebra I The Number System & Mathematical Operations 2015-08-21 www.njctl.org Slide 3 / 72 Table of Contents Review of Natural Numbers, Whole Numbers & Integers Review of Rational
More informationUnit 4, Ongoing Activity, Little Black Book of Algebra II Properties
Unit 4, Ongoing Activity, Little Black Book of Algebra II Properties Little Black Book of Algebra II Properties Unit 4 - Radicals & the Complex Number System 4.1 Radical Terminology define radical sign,
More informationChapter 3: Factors, Roots, and Powers
Chapter 3: Factors, Roots, and Powers Section 3.1 Chapter 3: Factors, Roots, and Powers Section 3.1: Factors and Multiples of Whole Numbers Terminology: Prime Numbers: Any natural number that has exactly
More informationUNIT 5 QUADRATIC FUNCTIONS Lesson 2: Creating and Solving Quadratic Equations in One Variable Instruction
Prerequisite Skills This lesson requires the use of the following skills: simplifying radicals working with complex numbers Introduction You can determine how far a ladder will extend from the base of
More informationKey Learning: Students will demonstrate an understanding of expression and equations with respect to linear equations. Unit Essential Question
Student Learning Map for Unit Topic: PA Common Core: M08.B-E.1 Demonstrate an understanding of expressions and equations with radicals and integer exponents. M08.B-E.2 Understand the connections between
More informationClassify, graph, and compare real numbers. Find and estimate square roots Identify and apply properties of real numbers.
Real Numbers and The Number Line Properties of Real Numbers Classify, graph, and compare real numbers. Find and estimate square roots Identify and apply properties of real numbers. Square root, radicand,
More informationChapter 4: Radicals and Complex Numbers
Section 4.1: A Review of the Properties of Exponents #1-42: Simplify the expression. 1) x 2 x 3 2) z 4 z 2 3) a 3 a 4) b 2 b 5) 2 3 2 2 6) 3 2 3 7) x 2 x 3 x 8) y 4 y 2 y 9) 10) 11) 12) 13) 14) 15) 16)
More informationNatural Numbers Positive Integers. Rational Numbers
Chapter A - - Real Numbers Types of Real Numbers, 2,, 4, Name(s) for the set Natural Numbers Positive Integers Symbol(s) for the set, -, - 2, - Negative integers 0,, 2,, 4, Non- negative integers, -, -
More informationRon Paul Curriculum Mathematics 8 Lesson List
Ron Paul Curriculum Mathematics 8 Lesson List 1 Introduction 2 Algebraic Addition 3 Algebraic Subtraction 4 Algebraic Multiplication 5 Week 1 Review 6 Algebraic Division 7 Powers and Exponents 8 Order
More informationPerform the following operations. 1) (2x + 3) + (4x 5) 2) 2(x + 3) 3) 2x (x 4) 4) (2x + 3)(3x 5) 5) (x 4)(x 2 3x + 5)
2/24 week Add subtract polynomials 13.1 Multiplying Polynomials 13.2 Radicals 13.6 Completing the square 13.7 Real numbers 15.1 and 15.2 Complex numbers 15.3 and 15.4 Perform the following operations 1)
More informationStepping stones for Number systems. 1) Concept of a number line : Marking using sticks on the floor. (1 stick length = 1 unit)
Quality for Equality Stepping stones for Number systems 1) Concept of a number line : Marking using sticks on the floor. (1 stick length = 1 unit) 2) Counting numbers: 1,2,3,... Natural numbers Represent
More informationUNIT 4 NOTES: PROPERTIES & EXPRESSIONS
UNIT 4 NOTES: PROPERTIES & EXPRESSIONS Vocabulary Mathematics: (from Greek mathema, knowledge, study, learning ) Is the study of quantity, structure, space, and change. Algebra: Is the branch of mathematics
More informationUnit 1 Foundations of Algebra
1 Unit 1 Foundations of Algebra Real Number System 2 A. Real Number System 1. Counting Numbers (Natural Numbers) {1,2,3,4, } 2. Whole Numbers { 0,1,2,3,4, } 3. Integers - Negative and Positive Whole Numbers
More informationSEVENTH EDITION and EXPANDED SEVENTH EDITION
SEVENTH EDITION and EXPANDED SEVENTH EDITION Slide 5-1 Chapter 5 Number Theory and the Real Number System 5.1 Number Theory Number Theory The study of numbers and their properties. The numbers we use to
More information1-2 Study Guide and Intervention
1- Study Guide and Intervention Real Numbers All real numbers can be classified as either rational or irrational. The set of rational numbers includes several subsets: natural numbers, whole numbers, and
More informationMath-1010 Lesson 4-2. Add and Subtract Rational Expressions
Math-00 Lesson - Add and Subtract Rational Epressions What are like terms? Like variables: Like powers: y y Multiples of the same variable same base and same eponent. Like radicals: same radicand and same
More informationSolving Quadratic Equations by Formula
Algebra Unit: 05 Lesson: 0 Complex Numbers All the quadratic equations solved to this point have had two real solutions or roots. In some cases, solutions involved a double root, but there were always
More informationRational Numbers. a) 5 is a rational number TRUE FALSE. is a rational number TRUE FALSE
Fry Texas A&M University!! Math 150!! Chapter 1!! Fall 2014! 1 Chapter 1A - - Real Numbers Types of Real Numbers Name(s) for the set 1, 2,, 4, Natural Numbers Positive Integers Symbol(s) for the set, -,
More informationCh. 7.6 Squares, Squaring & Parabolas
Ch. 7.6 Squares, Squaring & Parabolas Learning Intentions: Learn about the squaring & square root function. Graph parabolas. Compare the squaring function with other functions. Relate the squaring function
More informationCHAPTER 1 REAL NUMBERS KEY POINTS
CHAPTER 1 REAL NUMBERS 1. Euclid s division lemma : KEY POINTS For given positive integers a and b there exist unique whole numbers q and r satisfying the relation a = bq + r, 0 r < b. 2. Euclid s division
More informationMath K-1 CCRS Level A Alignment College & Career Readiness Standards Version: April 2017
Math K-1 CCRS Level A Alignment Standard Math K Lessons Math 1 Lessons Number and Operations: Base Ten Understand place value 6 Compare 1, 26 Compare 50, 33 Skip Count 5s and 10s, 35 Group 10s, 36 Compare
More informationUnit Essential Questions. What are the different representations of exponents? Where do exponents fit into the real number system?
Unit Essential Questions What are the different representations of exponents? Where do exponents fit into the real number system? How can exponents be used to depict real-world situations? REAL NUMBERS
More informationcorrelated to the Utah 2007 Secondary Math Core Curriculum Algebra 1
correlated to the Utah 2007 Secondary Math Core Curriculum Algebra 1 McDougal Littell Algebra 1 2007 correlated to the Utah 2007 Secondary Math Core Curriculum Algebra 1 The main goal of Algebra is to
More informationNotice that we are switching from the subtraction to adding the negative of the following term
MTH95 Day 6 Sections 5.3 & 7.1 Section 5.3 Polynomials and Polynomial Functions Definitions: Term Constant Factor Coefficient Polynomial Monomial Binomial Trinomial Degree of a term Degree of a Polynomial
More informationAlg. 1 Radical Notes
Alg. 1 Radical Notes Evaluating Square Roots and Cube Roots (Day 1) Objective: SWBAT find the square root and cube roots of monomials Perfect Squares: Perfect Cubes: 1 =11 1 = 11 =1111 11 1 =111 1 1 =
More informationStandards of Learning Content Review Notes. Grade 8 Mathematics 1 st Nine Weeks,
Standards of Learning Content Review Notes Grade 8 Mathematics 1 st Nine Weeks, 2016-2017 Revised September 2015 2 Mathematics Content Review Notes Grade 8 Mathematics: First Nine Weeks 2015-2016 -This
More informationComplex Numbers. Essential Question What are the subsets of the set of complex numbers? Integers. Whole Numbers. Natural Numbers
3.4 Complex Numbers Essential Question What are the subsets of the set of complex numbers? In your study of mathematics, you have probably worked with only real numbers, which can be represented graphically
More informationCopy Material. Grade 8 Unit 7. Introduction to Irrational Numbers Using Geometry. Eureka Math. Eureka Math
Copy Material Grade 8 Unit 7 Introduction to Irrational Numbers Using Geometry Eureka Math Eureka Math Lesson 1 Name Date Lesson 1: The Pythagorean Theorem Exit Ticket 1. Determine the length of the unknown
More informationCommon Core Coach. Mathematics. First Edition
Common Core Coach Mathematics 8 First Edition Contents Domain 1 The Number System...4 Lesson 1 Understanding Rational and Irrational Numbers...6 Lesson 2 Estimating the Value of Irrational Expressions...
More informationMath 1302 Notes 2. How many solutions? What type of solution in the real number system? What kind of equation is it?
Math 1302 Notes 2 We know that x 2 + 4 = 0 has How many solutions? What type of solution in the real number system? What kind of equation is it? What happens if we enlarge our current system? Remember
More informationGraphing Radicals Business 7
Graphing Radicals Business 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
More information1 of 7 8/11/2014 10:27 AM Units: Teacher: PacedAlgebraPartA, CORE Course: PacedAlgebraPartA Year: 2012-13 The Language of Algebra What is the difference between an algebraic expression and an algebraic
More informationBig Ideas: determine an approximate value of a radical expression using a variety of methods. REVIEW Radicals
Big Ideas: determine an approximate value of a radical expression using a variety of methods. REVIEW N.RN. Rewrite expressions involving radicals and rational exponents using the properties of exponents.
More informationExponents 4-1. Lesson Objectives. Vocabulary. Additional Examples. Evaluate expressions with exponents. exponential form (p. 162) exponent (p.
LESSON 4-1 Exponents Lesson Objectives Evaluate expressions with exponents Vocabulary exponential form (p. 16) exponent (p. 16) base (p. 16) power (p. 16) Additional Examples Example 1 Write in exponential
More informationMA094 Part 2 - Beginning Algebra Summary
MA094 Part - Beginning Algebra Summary Page of 8/8/0 Big Picture Algebra is Solving Equations with Variables* Variable Variables Linear Equations x 0 MA090 Solution: Point 0 Linear Inequalities x < 0 page
More informationPart 2 - Beginning Algebra Summary
Part - Beginning Algebra Summary Page 1 of 4 1/1/01 1. Numbers... 1.1. Number Lines... 1.. Interval Notation.... Inequalities... 4.1. Linear with 1 Variable... 4. Linear Equations... 5.1. The Cartesian
More informationChapter 1: Foundations for Algebra
Chapter 1: Foundations for Algebra 1 Unit 1: Vocabulary 1) Natural Numbers 2) Whole Numbers 3) Integers 4) Rational Numbers 5) Irrational Numbers 6) Real Numbers 7) Terminating Decimal 8) Repeating Decimal
More informationNumbers and Operations
Numbers and Operations George E. Hrabovsky MAST Mathematics as the study of objects, their relationships, and the structures created by their relationships Mathematics is the abstract study of objects
More informationGrade 8 Chapter 7: Rational and Irrational Numbers
Grade 8 Chapter 7: Rational and Irrational Numbers In this chapter we first review the real line model for numbers, as discussed in Chapter 2 of seventh grade, by recalling how the integers and then the
More informationAlgebra I The Number System & Mathematical Operations
Slide 1 / 178 Slide 2 / 178 Algebra I The Number System & Mathematical Operations 2015-11-02 www.njctl.org Slide 3 / 178 Table of Contents Review of Natural Numbers, Whole Numbers, Integers and Rational
More informationCK-12 Middle School Math Grade 8
CK-12 Middle School Math aligned with COMMON CORE MATH STATE STANDARDS INITIATIVE Middle School Standards for Math Content Common Core Math Standards for CK-12 Middle School Math The Number System (8.NS)
More informationCourse Learning Outcomes for Unit III. Reading Assignment. Unit Lesson. UNIT III STUDY GUIDE Number Theory and the Real Number System
UNIT III STUDY GUIDE Number Theory and the Real Number System Course Learning Outcomes for Unit III Upon completion of this unit, students should be able to: 3. Perform computations involving exponents,
More informationPre-Algebra Chapter 3 Exponents and Roots
Pre-Algebra Chapter 3 Exponents and Roots Name: Period: Common Core State Standards CC.8.EE.1 - Know and apply the properties of integer exponents to generate equivalent numerical expressions. CC.8.EE.2
More information1-1. Expressions and Formulas. Lesson 1-1. What You ll Learn. Active Vocabulary
1-1 Expressions and Formulas What You ll Learn Skim the lesson. Write two things you already know about expressions and formulas. 1. Active Vocabulary 2. Review Vocabulary Identify the four grouping symbols
More informationChapter Review. Connecting BIG ideas and Answering the Essential Questions. n+3 I n I 3 I r. 68 Chapter 1 Chapter Review
Chapter Review Connecting BIG ideas and Answering the Essential Questions 1 Variable You can use variables to represent quantities and to write algebraic expressions and equations. / Variables and Expressions
More informationMath 8A. Content Description Content Location U01-L01-A05. Learn: Text. Video U04-L18-A05. Learn: Text and. Video. Learn: Text and U04-L19-A03.
Know that there are numbers that are not rational, and approximate them by rational numbers. NS.A.1 Know that numbers that are not rational are called irrational. Understand informally that every number
More informationAlgebra I. Slide 1 / 178. Slide 2 / 178. Slide 3 / 178. The Number System & Mathematical Operations. Table of Contents
Slide 1 / 178 Slide 2 / 178 Algebra I The Number System & Mathematical Operations 2015-11-02 www.njctl.org Table of Contents Slide 3 / 178 Review of Natural Numbers, Whole Numbers, Integers and Rational
More informationA number that can be written as, where p and q are integers and q Number.
RATIONAL NUMBERS 1.1 Definition of Rational Numbers: What are rational numbers? A number that can be written as, where p and q are integers and q Number. 0, is known as Rational Example:, 12, -18 etc.
More informationSlide 1 / 178 Slide 2 / 178. Click on a topic to go to that section.
Slide / 78 Slide 2 / 78 Algebra I The Number System & Mathematical Operations 205--02 www.njctl.org Slide 3 / 78 Slide 4 / 78 Table of Contents Review of Natural Numbers, Whole Numbers, Integers and Rational
More informationAlgebra I. Slide 1 / 178. Slide 2 / 178. Slide 3 / 178. The Number System & Mathematical Operations. Table of Contents
Slide 1 / 178 Slide 2 / 178 Algebra I The Number System & Mathematical Operations 2015-11-02 www.njctl.org Table of Contents Slide 3 / 178 Review of Natural Numbers, Whole Numbers, Integers and Rational
More informationOBJECTIVES UNIT 1. Lesson 1.0
OBJECTIVES UNIT 1 Lesson 1.0 1. Define "set," "element," "finite set," and "infinite set," "empty set," and "null set" and give two examples of each term. 2. Define "subset," "universal set," and "disjoint
More informationLesson 9: Radicals and Conjugates
Lesson 9: Radicals and Conjugates Student Outcomes Students understand that the sum of two square roots (or two cube roots) is not equal to the square root (or cube root) of their sum. Students convert
More informationCHAPTER EIGHT: SOLVING QUADRATIC EQUATIONS Review April 9 Test April 17 The most important equations at this level of mathematics are quadratic
CHAPTER EIGHT: SOLVING QUADRATIC EQUATIONS Review April 9 Test April 17 The most important equations at this level of mathematics are quadratic equations. They can be solved using a graph, a perfect square,
More informationMath 9 Notes. Grade 6 8 Review. Multiplication and Division: Slide show and Table. M9 Intro Notes 2017.notebook. June 12, 2017.
Math 9 Notes Grade 6 8 Review Sep 11:32 AM Multiplication and Division: Slide show and Table Sep 11:34 AM 1 Long Division 11 Sept Sep 11:34 AM Find the first number that 6 divides into Divide 6 into 41
More informationDISCOVERY TEST A: AUGUST CCSS
8 th Grade Mathematics Quarter Curriculum Map 20-204 Unit : Real Numbers and the Coordinate Plane st Nine Weeks Suggested Instructional Days: 20-24 Unit Summary (Learning Target/Goal): Develop an understanding
More informationSkill: determine an approximate value of a radical expression using a variety of methods.
Skill: determine an approximate value of a radical expression using a variety of methods. N.RN.A. Extend the properties of exponents to rational exponents. Rewrite expressions involving radicals and rational
More informationNUMBERS( A group of digits, denoting a number, is called a numeral. Every digit in a numeral has two values:
NUMBERS( A number is a mathematical object used to count and measure. A notational symbol that represents a number is called a numeral but in common use, the word number can mean the abstract object, the
More informationCROSSWalk. for the Co on Core State Standards
Mathematics Grade 8 CROSSWalk for the Co on Core State Standards Table of Contents Common Core State Standards Correlation Chart... 6 Domain 1 The Number System.... Domain 1: Diagnostic Assessment for
More informationleg line of best fit line segment linear linear equation linear association linear extrapolation negative association nonlinear
adjacent angle(s) angle angle-angle criterion area base cluster coefficient cone constant coordinate grid coordinate plane complementary angles congruent cube root cylinder data decimal notation decreasing
More informationGive algebraic and numeric examples to support your answer. Which property is demonstrated when one combines like terms in an algebraic expression?
Big Idea(s): Algebra is distinguished from arithmetic by the systematic use of symbols for values. Writing and evaluating expressions with algebraic notation follows the same rules/properties as in arithmetic.
More informationProperties of Rational and Irrational Numbers
Properties of Rational and Irrational Numbers September 8, 2016 Definition: The natural numbers are the set of numbers N = {1, 2, 3,...}, and the integers are the set of numbers Z = {..., 2, 1, 0, 1, 2,...}.
More informationChapter 1: Foundations for Algebra
Chapter 1: Foundations for Algebra 1 Unit 1: Vocabulary 1) Natural Numbers 2) Whole Numbers 3) Integers 4) Rational Numbers 5) Irrational Numbers 6) Real Numbers 7) Terminating Decimal 8) Repeating Decimal
More informationLinear Equations & Inequalities Definitions
Linear Equations & Inequalities Definitions Constants - a term that is only a number Example: 3; -6; -10.5 Coefficients - the number in front of a term Example: -3x 2, -3 is the coefficient Variable -
More informationOrder of Operations. Real numbers
Order of Operations When simplifying algebraic expressions we use the following order: 1. Perform operations within a parenthesis. 2. Evaluate exponents. 3. Multiply and divide from left to right. 4. Add
More informationHighland Park Public School District
435 Mansfield Street Highland Park, New Jersey 08904 Curriculum Guide Mathematics 8 Version 1 Slated for Revision Final Review 6/30/2017 Mastery Skills Students will be able to understand, explain, and
More information10.1. Square Roots and Square- Root Functions 2/20/2018. Exponents and Radicals. Radical Expressions and Functions
10 Exponents and Radicals 10.1 Radical Expressions and Functions 10.2 Rational Numbers as Exponents 10.3 Multiplying Radical Expressions 10.4 Dividing Radical Expressions 10.5 Expressions Containing Several
More information( )( ) Algebra I / Technical Algebra. (This can be read: given n elements, choose r, 5! 5 4 3! ! ( 5 3 )! 3!(2) 2
470 Algebra I / Technical Algebra Absolute Value: A number s distance from zero on a number line. A number s absolute value is nonnegative. 4 = 4 = 4 Algebraic Expressions: A mathematical phrase that can
More informationWhat is proof? Lesson 1
What is proof? Lesson The topic for this Math Explorer Club is mathematical proof. In this post we will go over what was covered in the first session. The word proof is a normal English word that you might
More informationMATHLINKS: GRADE 8 CORRELATION OF STUDENT PACKETS TO THE RESOURCE GUIDE
MATHLINKS: GRADE 8 CORRELATION OF STUDENT PACKETS TO THE RESOURCE GUIDE Referenced here is the vocabulary, explanations, and examples from the Resource Guide that support the learning of the goals in each
More informationDay 6: 6.4 Solving Polynomial Equations Warm Up: Factor. 1. x 2-2x x 2-9x x 2 + 6x + 5
Day 6: 6.4 Solving Polynomial Equations Warm Up: Factor. 1. x 2-2x - 15 2. x 2-9x + 14 3. x 2 + 6x + 5 Solving Equations by Factoring Recall the factoring pattern: Difference of Squares:...... Note: There
More informationComplex Numbers: Definition: A complex number is a number of the form: z = a + bi where a, b are real numbers and i is a symbol with the property: i
Complex Numbers: Definition: A complex number is a number of the form: z = a + bi where a, b are real numbers and i is a symbol with the property: i 2 = 1 Sometimes we like to think of i = 1 We can treat
More informationLevel Unit Chapter Lesson ChapterTitle LessonTitle Introduction Introduction How to take the placement tests How to take the
Level Unit Chapter Lesson ChapterTitle LessonTitle 0 0 1 1 Introduction Introduction 0 0 2 1 How to take the placement tests How to take the placement tests 0 0 3 0 Placement Test I 0 0 4 0 Placement Test
More informationAlgebra II Chapter 5: Polynomials and Polynomial Functions Part 1
Algebra II Chapter 5: Polynomials and Polynomial Functions Part 1 Chapter 5 Lesson 1 Use Properties of Exponents Vocabulary Learn these! Love these! Know these! 1 Example 1: Evaluate Numerical Expressions
More informationProperties of Radicals
9. Properties of Radicals Essential Question How can you multiply and divide square roots? Operations with Square Roots Work with a partner. For each operation with square roots, compare the results obtained
More informationGrade 7/8 Math Circles Winter March 20/21/22 Types of Numbers
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 7/8 Math Circles Winter 2018 - March 20/21/22 Types of Numbers Introduction Today, we take our number
More informationNote-Taking Guides. How to use these documents for success
1 Note-Taking Guides How to use these documents for success Print all the pages for the module. Open the first lesson on the computer. Fill in the guide as you read. Do the practice problems on notebook
More informationAlgebra SEMESTER ONE. K12.com { Pg. 1 } Course Overview. Unit 1: Algebra Basics. Unit 2: Properties of Real Numbers
Algebra Course Overview Students develop algebraic fluency by learning the skills needed to solve equations and perform manipulations with numbers, variables, equations, and inequalities. They also learn
More informationLesson #33 Solving Incomplete Quadratics
Lesson # Solving Incomplete Quadratics A.A.4 Know and apply the technique of completing the square ~ 1 ~ We can also set up any quadratic to solve it in this way by completing the square, the technique
More informationCH 59 SQUARE ROOTS. Every positive number has two square roots. Ch 59 Square Roots. Introduction
59 CH 59 SQUARE ROOTS Introduction W e saw square roots when we studied the Pythagorean Theorem. They may have been hidden, but when the end of a right-triangle problem resulted in an equation like c =
More informationUse ordered pairs to locate points, to organize data,
Eighth Grade Math Scope and Sequence Lesson Title Lesson Objective(s) TEKS First Six Weeks Problem Solving Use problem solving strategies including making a plan and choosing an appropriate method of 8.1B;
More informationHow do I apply concepts of rational and irrational numbers? Concepts Competencies Resources Assessments CC E.1. number system properties.
M08.A-N The Number System M08.A-N.1 Demonstrate an understanding of rational and irrational numbers. M08.A-N.1.1 Apply concepts of rational and irrational numbers. How do I apply concepts of rational and
More informationNumber, Number Sense, and Operations Data Analysis and Probability
Algebra 1 Unit 1 Numbers 3 weeks Number, Number Sense, and Operations Data Analysis and Probability NC Apply properties of operations and the real number system, and justify when they hold for a set of
More informationSummer Solutions Common Core Mathematics 8. Common Core. Mathematics. Help Pages
8 Common Core Mathematics 6 6 Vocabulary absolute value additive inverse property adjacent angles the distance between a number and zero on a number line. Example: the absolute value of negative seven
More informationCommon Core Algebra Regents Review
Common Core Algebra Regents Review Real numbers, properties, and operations: 1) The set of natural numbers is the set of counting numbers. 1,2,3,... { } symbol 2) The set of whole numbers is the set of
More informationEureka Math. Grade 8, Module 7. Student File_B. Contains Exit Ticket and Assessment Materials
A Story of Ratios Eureka Math Grade 8, Module 7 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 informationTECHNICAL MATH Course Units of Study
TECHNICAL MATH Course Units of Study The Technical Math course features five units of instruction and a capstone project. This document clearly articulates the premise of each unit of study; the recommended
More information