Properties. Comparing and Ordering Rational Numbers Using a Number Line
|
|
|
- Florence Josephine Ryan
- 6 years ago
- Views:
Transcription
1 Chapter 5 Summary Key Terms natural numbers (counting numbers) (5.1) whole numbers (5.1) integers (5.1) closed (5.1) rational numbers (5.1) irrational number (5.2) terminating decimal (5.2) repeating decimal (5.2) bar notation (5.2) real number (5.3) Venn diagram (5.3) closure (5.3) Properties Additive Identity (5.3) Multiplicative Identity (5.3) Additive Inverse (5.3) Multiplicative Inverse (5.3) Commutative Property of Addition (5.3) Commutative Property of Multiplication (5.3) Associative Property of Addition (5.3) Associative Property of Multiplication (5.3) Reflexive Property of Symmetric Property of Transitive Property of Comparing and Ordering Rational Numbers Using a Number Line Fractions and decimals can be compared and ordered by converting fractions to decimals and plotting on a number line. The number line is used to show The fraction 5 5 is equal to Chapter 5 Summary 305
2 Performing Operations with Rational Numbers A rational number is a number that can be written in the form a, where a and b are both b integers and b is not equal to 0. You can add, subtract, multiply, and divide rational numbers in much the same way that you do using integers Identifying Terminating and Repeating Decimals A terminating decimal is a decimal that has a last digit. A repeating decimal is a decimal with digits that repeat in sets of one or more. Two different notations are used to represent repeating decimals. One notation is to write the decimal, including one set of digits that repeat, and place a bar over the repeating digits. Another notation is to write the decimal, including two sets of the digits that repeat, and using dots to indicate repetition. s 8 is a terminating decimal: and 4 is a repeating decimal: ) ) Chapter 5 The Real Number System
3 Writing Repeating Decimals as Fractions Some repeating decimals represent common fractions, such as , and are 3 used often enough that we recognize the fraction by its decimal representation. However, there are decimals in which it is difficult to determine the fractional equivalent. To determine the fraction for the decimal, first, write an equation by setting the decimal equal to a variable that will represent the fraction. Next, write another equation by multiplying each side of the equation by a power of 10. The exponent on the power of 10 is equal to the number of decimal places until the decimal begins to repeat. Then, subtract the first equation from the second equation. Finally, solve the equation. The repeating decimal is equal to the fraction w w w w w 5 15 w Identifying Irrational Numbers Decimals that do not repeat and do not terminate are said to be irrational numbers. An irrational number is a number that cannot be written in the form a, where a and b are both b integers and b fi 0. An example of an irrational number is 11 because it is a square root that is not a perfect square and therefore has no repeating patterns of digits. Chapter 5 Summary 307
4 Classifying Numbers in the Real Number System Combining the set of rational numbers and the set of irrational numbers produces the set of real numbers. Within the set of rational numbers, a number can be or not be an integer, whole number, natural number, or some combination. s π is an irrational number. 28 is a rational number and an integer. 23 is a natural number, whole number, integer, and rational number. 1 is a rational number. 4 Understanding the Properties of Real Numbers The real numbers, together with their operations and properties, form the real number system. The properties of real numbers include: Closure: A set of numbers is said to be closed under an operation if the result of the operation on two numbers in the set is another member of the set. Additive Identity: An additive identity is a number such that when you add it to a second number, the sum is equal to the second number. Multiplicative Identity: A multiplicative identity is a number such that when you multiply it by a second number, the product is equal to the second number. Additive Inverse: Two numbers are additive inverses if their sum is the additive identity. Multiplicative Inverse: Two numbers are multiplicative inverses if their product is the multiplicative identity. Commutative Property of Addition: Changing the order of two or more addends in an addition problem does not change the sum. Commutative Property of Multiplication: Changing the order of two or more factors in a multiplication problem does not change the product. Associative Property of Addition: Changing the grouping of the addends in an addition problem does not change the sum. 308 Chapter 5 The Real Number System
5 Associative Property of Multiplication: Changing the grouping of the factors in a multiplication problem does not change the product. Reflexive Property of Equality: For any real number a, a 5 a. Symmetric Property of Equality: For any real numbers a and b, if a 5 b, then b 5 a. Transitive Property of Equality: For any real numbers a, b, and c, if a 5 b and b 5 c, then a 5 c. s (2128) 5 0 shows the additive inverse (27) shows the commutative property of multiplication shows the multiplicative identity. (31 3 x) 1 y (x 1 y) shows the associative property of addition. If x y and 7 1 y 5 21, then x 5 21 shows the transitive property of equality. Chapter 5 Summary 30
The word zero has had a long and interesting history so far. The word comes
Worth 1000 Words Real Numbers and Their Properties Learning Goals In this lesson, you will: Classify numbers in the real number system. Understand the properties of real numbers. Key Terms real number
The Real Number System
The Real Number System Pi is probably one of the most famous numbers in all of history. As a decimal, it goes on and on forever without repeating. Mathematicians have already calculated trillions of the
Decimal Binary Conversion Decimal Binary Place Value = 13 (Base 10) becomes = 1101 (Base 2).
DOMAIN I. NUMBER CONCEPTS Competency 00 The teacher understands the structure of number systems, the development of a sense of quantity, and the relationship between quantity and symbolic representations.
or 5.00 or 5.000, and so on You can expand the decimal places of a number that already has digits to the right of the decimal point.
1 LESSON Understanding Rational and Irrational Numbers UNDERSTAND All numbers can be written with a For example, you can rewrite 22 and 5 with decimal points without changing their values. 22 5 22.0 or
NAME UNIT 4 ALGEBRA II. NOTES PACKET ON RADICALS, RATIONALS d COMPLEX NUMBERS
NAME UNIT 4 ALGEBRA II NOTES PACKET ON RADICALS, RATIONALS d COMPLEX NUMBERS Properties for Algebra II Name: PROPERTIES OF EQUALITY EXAMPLE/MEANING Reflexive a - a Any quantity is equal to itself. Symmetric
7th Grade Accelerated Math Unit 1 Number Sense Learning Targets. 7th Grade Number Sense (Operations with Fractions and Integers)
7th Grade Accelerated Math Unit 1 Number Sense Learning Targets 7th Grade Number Sense (Operations with Fractions and Integers) Integer Learning Targets (Positive and Negative Whole Numbers) 1. I can describe
CHAPTER 1B: : Foundations for Algebra
CHAPTER B: : Foundations for Algebra 0-: Rounding and Estimating Objective: Round numbers. Rounding: To round to a given place value, do the following Rounding Numbers Round each number to the given place
Algebraic Expressions
P.1 Algebraic Expressions, Mathematical Models, and Real Numbers P.2 Exponents and Scientific Notation Objectives: Evaluate algebraic expressions, find intersection and unions of sets, simplify algebraic
TABLE OF CONTENTS. About Finish Line PA Core Math 5. UNIT 1: Big Ideas from Grade 7 7 UNIT 1 REVIEW 38. UNIT 2: The Number System 43 UNIT 2 REVIEW 58
TABLE OF CONTENTS About Finish Line PA Core Math 5 UNIT 1: Big Ideas from Grade 7 7 LESSON 1 CC..1.7.D.1 Understanding Proportional Relationships [connects to CC...8.B.] 8 LESSON CC..1.7.E.1 Operations
Unit Maps: Grade 6 Math
Rational Numbers 6.4 Number and operations. The student represents addition, subtraction, multiplication, and division of rational numbers while solving problems and justifying the solutions. Comparison
Problem. Prove that the square of any whole number n is a multiple of 4 or one more than a multiple of 4.
CHAPTER 8 Integers Problem. Prove that the square of any whole number n is a multiple of 4 or one more than a multiple of 4. Strategy 13 Use cases. This strategy may be appropriate when A problem can be
Algebra 1 Review. Properties of Real Numbers. Algebraic Expressions
Algebra 1 Review Properties of Real Numbers Algebraic Expressions Real Numbers Natural Numbers: 1, 2, 3, 4,.. Numbers used for counting Whole Numbers: 0, 1, 2, 3, 4,.. Natural Numbers and 0 Integers:,
Chapter 1: Number and Operations
Chapter 1: Number and Operations 1.1 Order of operations When simplifying algebraic expressions we use the following order: 1. Perform operations within a parenthesis. 2. Evaluate exponents. 3. Multiply
Helping Students Understand Pre-Algebra
Helping Students Understand Pre-Algebra By Barbara Sandall, Ed.D., & Mary Swarthout, Ph.D. COPYRIGHT 2005 Mark Twain Media, Inc. ISBN 10-digit: 1-58037-294-5 13-digit: 978-1-58037-294-7 Printing No. CD-404021
Prentice Hall Mathematics: Course Correlated to: Massachusetts State Learning Standards Curriculum Frameworks (Grades 7-8)
Massachusetts State Learning Standards Curriculum Frameworks (Grades 7-8) NUMBER SENSE AND OPERATIONS 8.N.1 8.N.2 8.N.3 8.N.4 8.N.5 8.N.6 8.N.7 8.N.8 Compare, order, estimate, and translate among integers,
A. Incorrect! To simplify this expression you need to find the product of 7 and 4, not the sum.
Problem Solving Drill 05: Exponents and Radicals Question No. 1 of 10 Question 1. Simplify: 7u v 4u 3 v 6 Question #01 (A) 11u 5 v 7 (B) 8u 6 v 6 (C) 8u 5 v 7 (D) 8u 3 v 9 To simplify this expression you
Unit 7 Number System and Bases. 7.1 Number System. 7.2 Binary Numbers. 7.3 Adding and Subtracting Binary Numbers. 7.4 Multiplying Binary Numbers
Contents STRAND B: Number Theory Unit 7 Number System and Bases Student Text Contents Section 7. Number System 7.2 Binary Numbers 7.3 Adding and Subtracting Binary Numbers 7.4 Multiplying Binary Numbers
Unit 2: Accentuate the Negative Name:
Unit 2: Accentuate the Negative Name: 1.1 Using Positive & Negative Numbers Number Sentence A mathematical statement that gives the relationship between two expressions that are composed of numbers and
CGF Lecture 2 Numbers
CGF Lecture 2 Numbers Numbers A number is an abstract entity used originally to describe quantity. i.e. 80 Students etc The most familiar numbers are the natural numbers {0, 1, 2,...} or {1, 2, 3,...},
Math 10- Chapter 2 Review
Math 10- Chapter 2 Review [By Christy Chan, Irene Xu, and Henry Luan] Knowledge required for understanding this chapter: 1. Simple calculation skills: addition, subtraction, multiplication, and division
8 TH GRADE MATHEMATICS CHECKLIST Goals 6 10 Illinois Learning Standards A-D Assessment Frameworks Calculators Allowed on ISAT
8 TH GRADE MATHEMATICS CHECKLIST Goals 6 10 Illinois Learning Standards A-D Assessment Frameworks Calculators Allowed on ISAT ISAT test questions are derived from this checklist. Use as a curriculum guide.
Chapter 4 Section 2 Operations on Decimals
Chapter 4 Section 2 Operations on Decimals Addition and subtraction of decimals To add decimals, write the numbers so that the decimal points are on a vertical line. Add as you would with whole numbers.
Odd-Numbered Answers to Exercise Set 1.1: Numbers
Odd-Numbered Answers to Exercise Set.: Numbers. (a) Composite;,,, Prime Neither (d) Neither (e) Composite;,,,,,. (a) 0. 0. 0. (d) 0. (e) 0. (f) 0. (g) 0. (h) 0. (i) 0.9 = (j). (since = ) 9 9 (k). (since
Mastering California s 15 Most Challenging Skills
Mastering California s 15 Most Challenging Skills California Mathematics Golden Gate Bridge in San Francisco, California STUDENT NAME Table of Contents Irrational Numbers (NS.1.4)... 4 Squares and Square
Eighth Grade Math Assessment Framework Standard 6A Representations and Ordering
Eighth Grade Math Assessment Framework Standard 6A Representations and Ordering 6.8.01 Read, write, and recognize equivalent representations of integer powers of 10. Related Textbook pages Related Additional
Pre-Algebra Practice
By Dr. Barbara Sandall, Ed.D., Dr. Melfried Olson, Ed.D., and Travis Olson, M.S. COPYRIGHT 2006 Mark Twain Media, Inc. ISBN 978-1-58037-755-3 Printing No. 404041-EB Mark Twain Media, Inc., Publishers Distributed
Notes for Unit 1 Part A: Rational vs. Irrational
Notes for Unit 1 Part A: Rational vs. Irrational Natural Number: Whole Number: Integer: Rational Number: Irrational Number: Rational Numbers All are Real Numbers Integers Whole Numbers Irrational Numbers
GRADE 7 MATH LEARNING GUIDE
GRADE 7 MATH Lesson 9: Properties of the Operations on Rational Numbers Time:.5 hours Pre-requisite Concepts: Operations on rational numbers About the Lesson: The purpose of this lesson is to use properties
PITSCO Math Individualized Prescriptive Lessons (IPLs)
Orientation Integers 10-10 Orientation I 20-10 Speaking Math Define common math vocabulary. Explore the four basic operations and their solutions. Form equations and expressions. 20-20 Place Value Define
Algebra II Radical Equations
1 Algebra II Radical Equations 2016-04-21 www.njctl.org 2 Table of Contents: Graphing Square Root Functions Working with Square Roots Irrational Roots Adding and Subtracting Radicals Multiplying Radicals
Section 1.8. Simplifying Expressions
Section 1.8 Simplifying Expressions But, first Commutative property: a + b = b + a; a * b = b * a Associative property: (a + b) + c = a + (b + c) (a * b) * c = a * (b * c) Distributive property: a * (b
Digits Interventions. Part 1/ Got It 1 (Journal Page) Part 2/ Got It 2 (Journal Page) Part 3/ Got It 3 (Journal Page) Lesson Check
Quarter 1 Core Content Process Skills/ Activities Unit A: Expressions & Interventions Equations Rocket Math Intervention Lessons: i1-1 Place Value i1-2 Comparing & Ordering Whole Numbers i2-1 Additional
Table of Contents. Introduction to the Math Practice Series...iv Common Mathematics Symbols and Terms...1
Table of Contents Table of Contents Introduction to the Math Practice Series...iv Common Mathematics Symbols and Terms...1 Chapter 1: Real Numbers...5 Real Numbers...5 Checking Progress: Real Numbers...8
1-3 Square Roots. Warm Up Lesson Presentation Lesson Quiz. Holt Algebra 2 2
1-3 Square Roots Warm Up Lesson Presentation Lesson Quiz 2 Warm Up Round to the nearest tenth. 1. 3.14 3.1 2. 1.97 2.0 Find each square root. 3. 4 4. 25 Write each fraction in simplest form. 5. 6. Simplify.
ALGEBRA I Summer Packet
ALGEBRA I Summer Packet 2018-2019 Name 7 th Grade Math Teacher: Objectives for Algebra I Summer Packet I. Variables and translating (Problems #1 5) Write Algebraic Expressions Writing Algebraic Equations
ACCELERATED MATH 6/7 Plans QUARTER
ACCELERATED MATH 6/7 Plans QUARTER 1 2017-2018 DATES (A & B) ASSESSMENT UNIT SOL LESSON 8/24 & 8/25 Class expectations; Getting-to-know-you activities 8/28 & 8/29 UNIT 1 - Integers 6.3, 7.3a, 7.1e Identify
A.4 Rationalizing the Denominator
A.4 Rationalizing the Denominator RATIONALIZING THE DENOMINATOR A.4 Rationalizing the Denominator If a radical expression contains an irrational denominator, such as,, or 0, then it is not considered to
Prentice Hall Mathematics: Course Correlated to: Ohio Academic Content Standards for Mathematics (Grade 7)
Ohio Academic Content Standards for Mathematics (Grade 7) NUMBER, NUMBER SENSE AND OPERATIONS STANDARD 1. Demonstrate an understanding of place value using powers of 10 and write large numbers in scientific
7 th GRADE PLANNER Mathematics. Lesson Plan # QTR. 3 QTR. 1 QTR. 2 QTR 4. Objective
Standard : Number and Computation Benchmark : Number Sense M7-..K The student knows, explains, and uses equivalent representations for rational numbers and simple algebraic expressions including integers,
8 th Grade Pre-Integrated Math
Use order of operations Evaluate expressions Use integers and absolute value Add integers Subtract integers Use inductive reasoning Multiply and divide integers Use properties of numbers Simplify variable
Rational and Irrational Numbers
LESSON. Rational and Irrational Numbers.NS. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion;... lso.ns.2,.ee.2? ESSENTIL QUESTION
Exponents and Real Numbers
Exponents and Real Numbers MODULE? ESSENTIAL QUESTION What sets of numbers are included in the real numbers? CALIFORNIA COMMON CORE LESSON.1 Radicals and Rational Exponents N.RN.1, N.RN. LESSON. Real Numbers
ACCELERATED MATH 6/7 Plans QUARTER
ACCELERATED MATH 6/7 Plans QUARTER 1 2017-2018 DATES (A & B) ASSESSMENT UNIT SOL LESSON 8/24 & 8/25 Class expectations; Getting-to-know-you activities 8/28 & 8/29 UNIT 1 - Integers 6.3, 7.3a, 7.1e Identify
6-8 Math Adding and Subtracting Polynomials Lesson Objective: Subobjective 1: Subobjective 2:
6-8 Math Adding and Subtracting Polynomials Lesson Objective: The student will add and subtract polynomials. Subobjective 1: The student will add polynomials. Subobjective 2: The student will subtract
Math Glossary Numbers and Arithmetic
Math Glossary Numbers and Arithmetic Version 0.1.1 September 1, 200 Next release: On or before September 0, 200. E-mail edu@ezlink.com for the latest version. Copyright 200 by Brad Jolly All Rights Reserved
ALGEBRA II A CURRICULUM OUTLINE
ALGEBRA II A CURRICULUM OUTLINE 2013-2014 OVERVIEW: 1. Linear Equations and Inequalities 2. Polynomial Expressions and Equations 3. Rational Expressions and Equations 4. Radical Expressions and Equations
5.1 to 5.3 P4.ink. Carnegie Unit 3 Examples & Class Notes
Carnegie Unit 3 Examples & Class Notes 1 2 3 This number is called the index. 1 Only multiply the numbers inside radical symbols, if and only if, they have the same index. 4 5 1 Use the times tables &
Introduction. Sets and the Real Number System
Sets: Basic Terms and Operations Introduction Sets and the Real Number System Definition (Set) A set is a well-defined collection of objects. The objects which form a set are called its members or Elements.
Middle School Math 3 and 8th GLEs
Middle School Math 3 and 8th GLEs Chapter. Lesson GLE's Description 1.1 1.2 1.3 1.4 1.5 3.1.1 Use Graphs to analyze data 1.1.6 Order of Operations 1.5.4, 1.5.5(7th) Write and Evalutate Variable Expressions
North Carolina Standard Course of Study, 2003, grade 8 [NC] PH Course 3 Lesson
![North Carolina Standard Course of Study, 2003, grade 8 [NC] PH Course 3 Lesson](/thumbs/96/126862347.jpg "North Carolina Standard Course of Study, 2003, grade 8 [NC] PH Course 3 Lesson")
[NC] North Carolina Standard Course of Study, 2003, grade 8 PH Course 3 Lesson COMPETENCY GOAL 1: The learner will understand and compute with real 1.01 Develop number sense for the real numbers. 1-2,
NFC ACADEMY MATH 600 COURSE OVERVIEW
NFC ACADEMY MATH 600 COURSE OVERVIEW Math 600 is a full-year elementary math course focusing on number skills and numerical literacy, with an introduction to rational numbers and the skills needed for
Mathematics. Grade 8 Curriculum Guide. Curriculum Guide Revised 2016
Mathematics Grade 8 Curriculum Guide Curriculum Guide Revised 2016 Intentionally Left Blank Introduction The Mathematics Curriculum Guide serves as a guide for teachers when planning instruction and assessment.
First Nine Weeks Grade: 8 Subject: Math Year: IN PROGRESS # Days SOL Student Essential Knowledge and Skills 1 Computation and
First Nine Weeks Grade: 8 Subject: Math Year: 2017-2018 IN PROGRESS # Days SOL Student Essential Knowledge and Skills 1 Computation and Identify the perfect squares from 0 Estimation to 400. determine
Final Exam MAT 100 JS 2018
Final Exam MAT 100 JS 2018 Miles College T Dabit MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Tell which set or sets the number belongs to: natural
Grade Level Expectations for the Sunshine State Standards
for the Sunshine State Standards FLORIDA DEPARTMENT OF EDUCATION http://www.myfloridaeducation.com/ The seventh grade student: Number Sense, Concepts, and Operations knows word names and standard numerals
Middle School Math Course 3 Correlation of the ALEKS course Middle School Math 3 to the Illinois Assessment Framework for Grade 8
Middle School Math Course 3 Correlation of the ALEKS course Middle School Math 3 to the Illinois Assessment Framework for Grade 8 State Goal 6: Number Sense 6.8.01: 6.8.02: 6.8.03: 6.8.04: 6.8.05: = ALEKS
Radical Expressions LESSON. 36 Unit 1: Relationships between Quantities and Expressions
LESSON 6 Radical Expressions UNDERSTAND You can use the following to simplify radical expressions. Product property of radicals: The square root of a product is equal to the square root of the factors.
Math Interim Mini-Tests. 3rd Grade Mini-Tests
3rd Grade Mini-Tests Mini-Test Name Availability Area of Plane Figures-01 Gr 3_Model, Reason, & Solve Problems-04 Multiplicative Properties & Factors-01 Patterns & Using the Four Operations-01 Real-World
Illinois Math Assessment Framework, Grade 7. correlated to
Illinois Math Assessment Framework, Grade 7 correlated to Grade 7 correlated to Chapter 1 Variables, Expressions, and Integers (pp. 1 61) Lesson 1.1 (pp. 5 9) Expressions and Variables Evaluate and write
Alignment to Common Core State Standards Level 8 Unit Report Summary
Alignment to Common Core State Standards Level 8 Unit Report Summary No. Objective Code Common Core State Standards Objective Title Whole Number Addition and Subtraction - Level 8 - (Ascend Default Unit)
1.1. Real Number System Numbers, Numbers,... My Notes ACTIVITY
Real Number System Numbers, Numbers,... SUGGESTED LEARNING STRATEGIES: Activating Prior Knowledge, Graphic Organizer, Quickwrite, Think/Pair/Share Your teacher will use a Venn diagram to help you understand
Alabama State Standards correlated to Merit Software Math Programs
Alabama State Standards correlated to Merit Software Math Programs The Classroom Improvement Section is responsible for the development, implementation, and assessment of the minimum curriculum content
Houghton Mifflin MATHSTEPS Level 7 correlated to Chicago Academic Standards and Framework Grade 7
State Goal 6: Demonstrate and apply a knowledge and sense of numbers, including basic arithmetic operations, number patterns, ratios and proportions. CAS A. Describe and apply concepts of real numbers,
MATHia X: Grade 8 Table of Contents
Module 1 Linear Linear Exploring Two-Step Multi-Step Students use a balance tool to explore two-step equations. They use a general strategy to sole any two-step equation. Students practice solving equations
Seventh Grade Mathematics Content Standards and Objectives
Seventh Grade Mathematics Content Standards and Objectives Standard 1: Number and Operations beyond the field of mathematics, students will M.S.7.1 demonstrate understanding of numbers, ways of representing
Radical Expressions and Functions What is a square root of 25? How many square roots does 25 have? Do the following square roots exist?
Hartfield Intermediate Algebra (Version 2014-2D) Unit 4 Page 1 Topic 4 1 Radical Epressions and Functions What is a square root of 25? How many square roots does 25 have? Do the following square roots
Grade 7 Math Curriculum Map Erin Murphy
Topic 1 Algebraic Expressions and Integers 2 Weeks Summative Topic Test: SWBAT use rules to add and subtract integers, Evaluate algebraic expressions, use the order of operations, identify numerical and
Prentice Hall Mathematics: Course Correlated to: Colorado Model Content Standards and Grade Level Expectations (Grade 6)
Colorado Model Content Standards and Grade Level Expectations (Grade 6) Standard 1: Students develop number sense and use numbers and number relationships in problemsolving situations and communicate the
Grade 7 Math (Master) Essential Questions Content Skills
Wilmette Public Schools, District 39 Created 2006-2007 Fall Grade 7 Math (Master) Why is it important to differentiate between various multiplication methods? How can a procedure lead you to an accurate
Name: Date: Period: Mrs. K. Williams ID: A
Name: Date: Period: Mrs. K. Williams ID: A Review Assignment: Chapters 1-7 CHAPTER 1- solve each equation. 6. 1. 12x 7 67 x = 2. 6 m 12 18 m = 3. 5.4x 13 121 7. x = 4. 22.8 2p 44.4 5. p = CHAPTER 2- Determine
Ratios and Proportional Relationships (RP) 6 8 Analyze proportional relationships and use them to solve real-world and mathematical problems.
Ratios and Proportional Relationships (RP) 6 8 Analyze proportional relationships and use them to solve real-world and mathematical problems. 7.1 Compute unit rates associated with ratios of fractions,
Grades 7 & 8 Pre-Algebra/Course 3,
Grades 7 & 8 Pre-Algebra/Course 3, TERM 1 - AUGUST/SEPTEMBER/OCTOBER Algebra Tools Solving Equations Integers Solving Multi-Step Equations and Inequalities TERM 2 NOVEMBER/DECEMBER/JANUARY Functions &
8.NS.1 8.NS.2. 8.EE.7.a 8.EE.4 8.EE.5 8.EE.6
Standard 8.NS.1 8.NS.2 8.EE.1 8.EE.2 8.EE.3 8.EE.4 8.EE.5 8.EE.6 8.EE.7 8.EE.7.a Jackson County Core Curriculum Collaborative (JC4) 8th Grade Math Learning Targets in Student Friendly Language I can identify
APS Seventh Grade Math District Benchmark Assessment NM Math Standards Alignment
APS Seventh Grade Math District Benchmark NM Math Standards Alignment SEVENTH GRADE NM STANDARDS Strand: NUMBER AND OPERATIONS Standard: Students will understand numerical concepts and mathematical operations.
13. [Exploring Number]
![13. [Exploring Number]](/thumbs/89/98416032.jpg "13. [Exploring Number]")
1. [Exploring Number] Skill 1.1 Using order of operations involving a mix of ( ),,, + or MM. 11 44 MM6.1 11 44 Simplify inside the brackets. Multiply ( ) and/or divide ( ) in order from left to right.
Number and Operation Standard #1. Divide multi- digit numbers; solve real- world and mathematical problems using arithmetic.
Number and Operation Standard #1 MN Math Standards Vertical Alignment for Grade 5 Demonstrate mastery of multiplication and division basic facts; multiply multi- digit numbers; solve real- world and mathematical
Name Period Date. REAL NUMBER SYSTEM Student Pages for Packet 3: Operations with Real Numbers
Name Period Date REAL NUMBER SYSTEM Student Pages for Packet : Operations with Real Numbers RNS. Rational Numbers Review concepts of experimental and theoretical probability. a Understand why all quotients
Unit 3: Multiplication and Division Reference Guide pages x 7 = 392 factors: 56, 7 product 392
Lesson 1: Multiplying Integers and Decimals, part 1 factor: any two or more numbers multiplied to form a product 56 x 7 = 392 factors: 56, 7 product 392 Integers: all positive and negative whole numbers
8 th Grade Mathematics Unpacked Content For the new Common Core standards that will be effective in all North Carolina schools in the
8 th Grade Mathematics Unpacked Content For the new Common Core standards that will be effective in all North Carolina schools in the 2012-13. This document is designed to help North Carolina educators
Prentice Hall Mathematics: Pre-Algebra 2004 Correlated to: Colorado Model Content Standards and Grade Level Expectations (Grade 8)
Colorado Model Content Standards and Grade Level Expectations (Grade 8) Standard 1: Students develop number sense and use numbers and number relationships in problemsolving situations and communicate the
College Technical Mathematics 1
Lakeshore Technical College 10-804-115 College Technical Mathematics 1 Course Outcome Summary Course Information Alternate Title College Technical Math 1 Description Total Credits 5 Total Hours 108...prepares
Prentice Hall Mathematics: Course Correlated to: Colorado Model Content Standards and Grade Level Expectations (Grade 8)
Colorado Model Content Standards and Grade Level Expectations (Grade 8) Standard 1: Students develop number sense and use numbers and number relationships in problemsolving situations and communicate the
Written by Alaska Hults
Standards-Based Math Written by Alaska Hults Editor: Collene Dobelmann Illustrator: Corbin Hillam Designer/Production: Moonhee Pak/Rosa Gandara Cover Designer: Barbara Peterson Art Director: Tom Cochrane
PROGRESSION IS HIGHLIGHTED IN THE FOLLOWING DOCUMENT VIA BOLDED TEXT. MATHEMATICAL PROCESSES
Alberta's Program of Studies (Curriculum) - Mathematics - Number (Strand with Achievement Outcomes) Note: These strands are not intended to be discrete units of instruction. The integration of outcomes
1 Transforming Geometric Objects
1 Transforming Geometric Objects RIGID MOTION TRANSFORMA- TIONS Rigid Motions Transformations 1 Translating Plane Figures Reflecting Plane Figures Rotating Plane Figures Students will select translations
Page 1. Kobrin/Losquadro Math 8. Unit 10 - Types of Numbers Test Review. Questions 1 and 2 refer to the following:
9195-1 - Page 1 Name: Date: Kobrin/Losquadro Math 8 Unit 10 - Types of Numbers Test Review Questions 1 and 2 refer to the following: Use the number line below to answer the given question. 1) Which of
EXPLORE MATHEMATICS TEST
EXPLORE MATHEMATICS TEST Table 4: The College Readiness The describe what students who score in the specified score ranges are likely to know and to be able to do. The help teachers identify ways of enhancing
What Is A Relation? Example. is a relation from A to B.
3.3 Relations What Is A Relation? Let A and B be nonempty sets. A relation R from A to B is a subset of the Cartesian product A B. If R A B and if (a, b) R, we say that a is related to b by R and we write
Integers are whole numbers; they include negative whole numbers and zero. For example -7, 0, 18 are integers, 1.5 is not.
What is an INTEGER/NONINTEGER? Integers are whole numbers; they include negative whole numbers and zero. For example -7, 0, 18 are integers, 1.5 is not. What is a REAL/IMAGINARY number? A real number is
Scope and Sequence: National Curriculum Mathematics from Haese Mathematics (4 7)
Scope and Sequence: National Curriculum Mathematics from Haese Mathematics (4 7) http://www.haesemathematics.com.au/ Last updated: 15/04/2016 Year Level Number and Algebra Number and place value Representation
Algebra II Chapter 6: Rational Exponents and Radical Functions
Algebra II Chapter 6: Rational Exponents and Radical Functions Chapter 6 Lesson 1 Evaluate nth Roots and Use Rational Exponents Vocabulary 1 Example 1: Find nth Roots Note: and Example 2: Evaluate Expressions
Carnegie Learning Math Series Course 1, A Florida Standards Program. Chapter 1: Factors, Multiples, Primes, and Composites
. Factors and Multiples Carnegie Learning Math Series Course, Chapter : Factors, Multiples, Primes, and Composites This chapter reviews factors, multiples, primes, composites, and divisibility rules. List
CASE21 North Carolina Pacing Guide: 8 TH GRADE MATH Updated August 10, 2010
Day Date Unit State Standards Core and Related Concepts 1 N/A Welcome Back Course expectations Math activity 2 Unit 1: 1.05 Integers Integers & (6 th Grade) Compare & order Rational 1.02 Absolute value
Prentice Hall. Connected Mathematics 2, 7th Grade Units Mississippi Mathematics Framework 2007 Revised, Grade 7
Prentice Hall Connected Mathematics 2, 7th Grade Units 2006 C O R R E L A T E D T O Mississippi Mathematics Framework 2007 Revised, Grade 7 NUMBER AND OPERATIONS 1. Apply concepts of rational numbers and
Slide 1 / 180. Radicals and Rational Exponents
Slide 1 / 180 Radicals and Rational Exponents Slide 2 / 180 Roots and Radicals Table of Contents: Square Roots Intro to Cube Roots n th Roots Irrational Roots Rational Exponents Operations with Radicals
6.1 Evaluate Roots and Rational Exponents
VOCABULARY:. Evaluate Roots and Rational Exponents Radical: We know radicals as square roots. But really, radicals can be used to express any root: 0 8, 8, Index: The index tells us exactly what type of
Central Valley School District Math Curriculum Map Grade 8. August - September
August - September Decimals Add, subtract, multiply and/or divide decimals without a calculator (straight computation or word problems) Convert between fractions and decimals ( terminating or repeating
CAMI KEYS. TOPIC 1.1 Whole numbers to to to to to
TOPIC 1.1 Whole numbers GRADE 9_CAPS Curriculum 1. Numbers, operations and relationships CONTENT Properties of numbers Describing the real number system by recognizing, defining and distinguishing properties
1 Transforming Geometric Objects
1 Transforming Geometric Objects Topic 1: Rigid Motion Transformations Rigid Motion Transformations Topic 2: Similarity Translating Plane Figures Reflecting Plane Figures Rotating Plane Figures Students
A.1 Numbers, Sets and Arithmetic
522 APPENDIX A. MATHEMATICS FOUNDATIONS A.1 Numbers, Sets and Arithmetic Numbers started as a conceptual way to quantify count objects. Later, numbers were used to measure quantities that were extensive,