Helping Students Understand Pre-Algebra
|
|
|
- Elfreda Burns
- 5 years ago
- Views:
Transcription
1 Helping Students Understand Pre-Algebra By Barbara Sandall, Ed.D., & Mary Swarthout, Ph.D. COPYRIGHT 2005 Mark Twain Media, Inc. ISBN 10-digit: digit: Printing No. CD Mark Twain Media, Inc., Publishers Distributed by Carson-Dellosa Publishing Company, Inc. The purchase of this book entitles the buyer to reproduce the student pages for classroom use only. Other permissions may be obtained by writing Mark Twain Media, Inc., Publishers. All rights reserved. Printed in the United States of America.
2 Introduction to the Helping Students Understand Algebra Series...iv Principles and Standards for School Mathematics NCTM...1 NCTM Standards and Expectations Grades 6 8 Algebra NCTM...2 Common Mathematics Symbols and Terms Types of Numbers...8 Natural Numbers...8 Whole Numbers...9 Integers...9 Rational Numbers (Fractions)...10 Irrational Numbers...10 Real Numbers...11 Chapter 2: Operations of Numbers and Variables...16 Addition...17 Subtraction...18 Multiplication...20 Division...23 Zero...26 Order of Operations...28 Chapter 3: Working With Integers and Signed Numbers...33 Integers...34 Positive Integers...34 Negative Integers...34 Absolute Value...35 Additive Inverse Property of Addition...35 Addition of Integers...36 Subtraction of Integers...37 Multiplication of Integers...42 Division of Integers...43 Operating on Signed Numbers...45 Chapter 4: Properties of Numbers...49 Identity Property of Addition...49 Identity Property of Multiplication...50 Commutative Property of Addition...50 Mark Twain Media, Inc., Publishers iii
3 Commutative Property of Multiplication...50 Associative Property of Addition...51 Associative Property of Multiplication...52 Inverse Operations...53 Reciprocal or Multiplicative Inverse Operations...53 Distributive Property of Multiplication Over Addition...55 Chapter 5: Exponents and Exponential Expressions...60 Exponents or Powers...61 Scientific Notation...61 Exponential Expressions...61 Rules for Whole Number Exponents...62 Chapter 6: Square Roots...74 Square Roots and Perfect Squares...74 Rules for Simplifying Radical Expressions...76 Chapter 7: Using Algebra to Generalize Patterns...84 Patterns in Number Lists...84 Patterns in Tables...85 Algebraic Expressions and Equations...86 Solving Simple Linear Equations...87 Chapter 8: Problem-Solving Strategies...95 Problem Solving...95 Problem-Solving Strategies...97 Making Tables...97 Guess, Check, and Revise...97 Using Linear Equations to Solve Problems...98 Answer Keys References Mark Twain Media, Inc., Publishers iv
![Galileo said, [The universe] cannot be read until we have learned the language and](/docs-images/84/89115104/images/4-4.jpg "become familiar with the characters in which it is written.")
4 Introduction to the Concepts of Numbers This section is a review of the basic mathematical concepts needed prior to learning algebra. According to the NCTM Standards, students need to be able to: Understand numbers, ways of representing numbers, relationships among numbers, and number systems. NCTM. Galileo said, [The universe] cannot be read until we have learned the language and become familiar with the characters in which it is written. In order to understand algebra, you need to understand the language of algebra. Algebra uses numbers, symbols, and letters. The numbers used in algebra include the types of numbers described in this section. Different symbols, shown in the chart on the previous pages, mean different things. All of the symbols used in mathematics help describe the numbers or the operations to be done. The letters (variables) used in mathematics represent unknown numbers. This chapter examines types of numbers used in algebra. More detail will be provided as you work your way through this worktext. Concepts 1 Types of Numbers A B C D E F Natural Numbers Whole Numbers Integers Rational Numbers (Fractions) Irrational Numbers Real Numbers Mark Twain Media, Inc., Publishers 7
5 (cont.) Explanations of Concepts 1 Types of Numbers The major types of numbers described in this worktext include natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers. A Natural Numbers Natural numbers are sometimes called counting numbers because they are the numbers you use to count how many items you have. Zero is not included in the set of natural numbers. TIP: One way to remember this is if you did not have any items, you could not count them. Example: Counting the oranges below you would count 1, 2, 3, so you have 3 oranges = 3 oranges Examples of other natural numbers: ,723 5 Examples of numbers that are not natural numbers: $j Mark Twain Media, Inc., Publishers 8
6 (cont.) B Whole Numbers Whole numbers include the natural numbers and zero. Examples of whole numbers: ,005 Examples of numbers that are not whole numbers: $g Look at the number line below. The numbers represented by the equally spaced marks to the right of zero are whole numbers. The arrow on the number line indicates that the line goes on forever or to infinity. Any number that is between the marks would not be a whole number C Integers Integers are natural numbers, their opposites or negative numbers, and zero. All whole numbers are integers and all natural numbers can be called integers. Examples of integers: , Examples of numbers that are not integers:!s 3!f Look at the number line below. The negative numbers have been added to the previous number line. The numbers represented by the equally spaced marks to the left or right of zero are integers. Any number represented between the marks is not an integer. For example, 1.5 is not an integer Mark Twain Media, Inc., Publishers 9
7 (cont.) D Rational Numbers (Fractions) A rational number is a number that can be expressed as the ratio of two integers. This ratio is sometimes called a fraction. The set of rational numbers includes the integers, whole numbers, and natural numbers that were discussed earlier. Decimals are rational numbers if the decimal has a finite number of places in it or it repeats a block of digits infinitely. To find the decimal form of!s, divide the numerator (in this case it is 1) by the denominator (in this case it is 2). The decimal form of!s = 0.5. Examples of rational numbers: 3 is a rational number because it can be written as or it can be written as 0.27, is a repeating decimal. It is a rational number because it repeats the same finite block of numbers forever or to infinity. Example of a decimal that is not a rational number: π is the symbol for pi. The decimal form of pi is and it continues. This pattern never ends, but it does not repeat the same finite block of digits, so it is not a rational number. E Irrational Numbers Irrational numbers are numbers that cannot be expressed as a ratio of two integers. The square root of two is an example of an irrational number. An irrational number can be defined as a decimal that never repeats and never ends. The square root of any number that is not a perfect square will be irrational. The square root of 16 ( 16 ) is 4, and 4 is a rational number. 3 = This is a decimal that never repeats the same finite block of digits and never ends, so it is an irrational number. Mark Twain Media, Inc., Publishers 10
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
Chapter 1: Review of Number Systems
Introduction to Number Systems This section is a review of the basic mathematical concepts needed prior to learning algebra. According to the NCTM Standards, students need to be able to: Understand numbers,
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
PRE-ALGEBRA BY MYRL SHIREMAN
PRE-ALGEBRA BY MYRL SHIREMAN COPYRIGHT 1994 Mark Twain Media, Inc. ISBN 10-digit: 1-58037-064-0 13-digit: 978-1-58037-064-6 Printing No. CD-1876 Mark Twain Media, Inc., Publishers Distributed by Carson-Dellosa
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
Properties. Comparing and Ordering Rational Numbers Using a Number Line
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
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,...},
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:,
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
ISBN Copyright 2015 The Continental Press, Inc.
TABLE OF CONTENTS Introduction 3 Format of Books Suggestions for Use Annotated Answer Key and Extension Activities 9 Reproducible Tool Set 183 ISBN 98-0-8-81-6 Copyright 01 The Continental Press, Inc.
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
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
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
may be sent to:
B A S I C M A T H A Self-Tutorial by Luis Anthony Ast Professional Mathematics Tutor LESSON 1: NUMBERS Copyright 2005 All rights reserved. No part of this publication may be reproduced or transmitted in
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
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
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
MAT 003 Brian Killough s Instructor Notes Saint Leo University
MAT 003 Brian Killough s Instructor Notes Saint Leo University Success in online courses requires self-motivation and discipline. It is anticipated that students will read the textbook and complete sample
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
Working with Algebraic Expressions
2 Working with Algebraic Expressions This chapter contains 25 algebraic expressions; each can contain up to five variables. Remember that a variable is just a letter that represents a number in a mathematical
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
Math You ve Gotta Have This Book!
If You re Trying to Get Better Grades & Higher Test Scores in Math You ve Gotta Have This Book! Grades 4-6 By Imogene Forte & Marjorie Frank Incentive Publications, Inc. Nashville, Tennessee Illustrated
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.
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
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
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
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
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
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
2.Simplification & Approximation
2.Simplification & Approximation As we all know that simplification is most widely asked topic in almost every banking exam. So let us try to understand what is actually meant by word Simplification. Simplification
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
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
Rational Numbers: Multiply and Divide
Rational Numbers: Multiply and Divide Multiplying Positive and Negative Numbers You know that when you multiply a positive number by a positive number, the result is positive. Multiplication with negative
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
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
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
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)
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
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
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
Rational functions, like rational numbers, will involve a fraction. We will discuss rational functions in the form:
Name: Date: Period: Chapter 2: Polynomial and Rational Functions Topic 6: Rational Functions & Their Graphs Rational functions, like rational numbers, will involve a fraction. We will discuss rational
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
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
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
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
Kate Collins Middle School Pre-Algebra Grade 6
Kate Collins Middle School Pre-Algebra Grade 6 1 1 - Real Number System How are the real numbers related? *some numbers can appear in more than one subset *the attributes of one subset can be contained
Dr. Relja Vulanovic Professor of Mathematics Kent State University at Stark c 2008
MATH-LITERACY MANUAL Dr. Relja Vulanovic Professor of Mathematics Kent State University at Stark c 2008 1 Real Numbers 1.1 Sets 1 1.2 Constants and Variables; Real Numbers 7 1.3 Operations with Numbers
Section 1.2 Fractions
Objectives Section 1.2 Fractions Factor and prime factor natural numbers Recognize special fraction forms Multiply and divide fractions Build equivalent fractions Simplify fractions Add and subtract fractions
Examination Duration Date
Hillel Academy High School Grade 9 Mathematics End of Year Study Guide September2013- June 2014 Examination Duration Date The exam consists of 2 papers: Paper 1: Short Response Calculator Paper 2:Structured
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.
Watkins Mill High School. Algebra 2. Math Challenge
Watkins Mill High School Algebra 2 Math Challenge "This packet will help you prepare for Algebra 2 next fall. It will be collected the first week of school. It will count as a grade in the first marking
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
Rational and Irrational Numbers can be written as 1_ 2.
? L E S S O N 1.1 Rational and Irrational Numbers ESSENTIAL QUESTION 8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion;
This assignment is due the first day of school. Name:
This assignment will help you to prepare for Geometry A by reviewing some of the topics you learned in Algebra 1. This assignment is due the first day of school. You will receive homework grades for completion
1.1 The Real Number System
1.1 The Real Number System Contents: Number Lines Absolute Value Definition of a Number Real Numbers Natural Numbers Whole Numbers Integers Rational Numbers Decimals as Fractions Repeating Decimals Rewriting
Vocabulary: Looking For Pythagoras
Vocabulary: Looking For Pythagoras Concept Finding areas of squares and other figures by subdividing or enclosing: These strategies for finding areas were developed in Covering and Surrounding. Students
Summer Assignment Glossary
Algebra 1.1 Summer Assignment Name: Date: Hour: Directions: Show all work for full credit using a pencil. Circle your final answer. This assignment is due the first day of school. Use the summer assignment
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
Los Angeles Unified School District. Mathematics Grade 6
Mathematics Grade GRADE MATHEMATICS STANDARDS Number Sense 9.* Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line..* Interpret and use ratios
Algebra 2 Common Core Summer Skills Packet
Algebra 2 Common Core Summer Skills Packet Our Purpose: Completion of this packet over the summer before beginning Algebra 2 will be of great value to helping students successfully meet the academic challenges
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.
Montana City School GRADE 5
Montana City School GRADE 5 Montana Standard 1: Students engage in the mathematical processes of problem solving and reasoning, estimation, communication, connections and applications, and using appropriate
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
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,
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 &
Middle School Math Course 2
Middle School Math Course 2 Correlation of the ALEKS course Middle School Math Course 2 to the Indiana Academic Standards for Mathematics Grade 7 (2014) 1: NUMBER SENSE = ALEKS course topic that addresses
Dinwiddie County Public Schools Subject: Math 7 Scope and Sequence
Dinwiddie County Public Schools Subject: Math 7 Scope and Sequence GRADE: 7 Year - 2013-2014 9 WKS Topics Targeted SOLS Days Taught Essential Skills 1 ARI Testing 1 1 PreTest 1 1 Quadrilaterals 7.7 4 The
Get to Know Your Calculator!
Math BD Calculator Lab Name: Date: Get to Know Your Calculator! You are allowed to use a non-graphing, scientific calculator for this course. A scientific calculator is different from an ordinary hand-held
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.
Working with Rational Expressions
Working with Rational Expressions Return to Table of Contents 4 Goals and Objectives Students will simplify rational expressions, as well as be able to add, subtract, multiply, and divide rational expressions.
Learning Log Title: CHAPTER 3: ARITHMETIC PROPERTIES. Date: Lesson: Chapter 3: Arithmetic Properties
Chapter 3: Arithmetic Properties CHAPTER 3: ARITHMETIC PROPERTIES Date: Lesson: Learning Log Title: Date: Lesson: Learning Log Title: Chapter 3: Arithmetic Properties Date: Lesson: Learning Log Title:
Example: Which of the following expressions must be an even integer if x is an integer? a. x + 5
8th Grade Honors Basic Operations Part 1 1 NUMBER DEFINITIONS UNDEFINED On the ACT, when something is divided by zero, it is considered undefined. For example, the expression a bc is undefined if either
Integers & Absolute Value Properties of Addition Add Integers Subtract Integers. Add & Subtract Like Fractions Add & Subtract Unlike Fractions
Unit 1: Rational Numbers & Exponents M07.A-N & M08.A-N, M08.B-E Essential Questions Standards Content Skills Vocabulary What happens when you add, subtract, multiply and divide integers? What happens when
Lesson 4.02: Operations with Radicals
Lesson 4.02: Operations with Radicals Take a Hike! Sheldon is planning on taking a hike through a state park. He has mapped out his route carefully. He plans to hike 3 miles to the scenic overlook, and
SKILL: What we want students to DO. Students will be able to: (pp. 1 61)
TIME FRAME [By Date/Week/ Month] STANDARD OR BENCHMARK CURRICULUM End Product of Learning, What You Teach CONTENT: What we want students to KNOW. SKILL: What we want students to DO. INSTRUCTION Means to
Chinle USD CURRICULUM GUIDE. SUBJECT: MATH GRADE: 6th TIMELINE: 2 nd Quarter. Kid Friendly Learning Objective
Concept 1: Numerical PO 1. Convert between expressions for positive rational numbers, including fractions, decimals, percents, and ratios. M I will convert between expressions for rational numbers; e.g.,
Mini-Lectures by Section
Mini-Lectures by Section BEGINNING AND INTERMEDIATE ALGEBRA, Mini-Lecture 1.1 1. Learn the definition of factor.. Write fractions in lowest terms.. Multiply and divide fractions.. Add and subtract fractions..
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.
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
Math 085 Final Exam Review
Math 08 Final Exam Review Objective : Use the rules of signed number arithmetic to perform operations on integers. These operations include, but are not limited to, addition, subtraction, multiplication,
MATHLINKS: GRADE 6 CORRELATION OF STUDENT PACKETS TO THE RESOURCE GUIDE
MATHLINKS: GRADE 6 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
Gateway Regional School District VERTICAL ALIGNMENT OF MATHEMATICS STANDARDS Grades 3-6
NUMBER SENSE & OPERATIONS 3.N.1 Exhibit an understanding of the values of the digits in the base ten number system by reading, modeling, writing, comparing, and ordering whole numbers through 9,999. Our
MATH STUDENT BOOK. 9th Grade Unit 7
MATH STUDENT BOOK 9th Grade Unit 7 Unit 7 Radical Expressions Math 907 Radical Expressions INTRODUCTION. REAL NUMBERS RATIONAL NUMBERS IRRATIONAL NUMBERS 2 COMPLETENESS 29 SELF TEST 2. OPERATIONS SIMPLIFYING
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
Fraction to Percents Change the fraction to a decimal (see above) and then change the decimal to a percent (see above).
PEMDAS This is an acronym for the order of operations. Order of operations is the order in which you complete problems with more than one operation. o P parenthesis o E exponents o M multiplication OR
Integers and Rational Numbers
A A Family Letter: Integers Dear Family, The student will be learning about integers and how these numbers relate to the coordinate plane. The set of integers includes the set of whole numbers (0, 1,,,...)
( 3) ( 4 ) 1. Exponents and Radicals ( ) ( xy) 1. MATH 102 College Algebra. still holds when m = n, we are led to the result
Exponents and Radicals ZERO & NEGATIVE EXPONENTS If we assume that the relation still holds when m = n, we are led to the result m m a m n 0 a = a = a. Consequently, = 1, a 0 n n a a a 0 = 1, a 0. Then
Algebraically Speaking Chalkdust Algebra 1 Fall Semester
Algebraically Speaking Chalkdust Algebra 1 Fall Semester Homework Assignments: Chapter 1 The Real Number System: Lesson 1.1 - Real Numbers: Order and Absolute Value Do the following problems: # 1 9 Odd,
MATHEMATICS 907 RADICAL EXPRESSIONS
MATHEMATICS 907 RADICAL EXPRESSIONS CONTENTS I. REAL NUMBERS...................... 2 Rational Numbers..................... 2 Irrational Numbers.................... 20 Completeness.......................
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
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.
ANNUAL NATIONAL ASSESSMENT 2014 ASSESSMENT GUIDELINES MATHEMATICS GRADE 8
ANNUAL NATIONAL ASSESSMENT 2014 ASSESSMENT GUIDELINES MATHEMATICS GRADE 8 INTRODUCTION The 2014 cycle of Annual National Assessment (ANA 2014) will be administered in all public and designated 1 independent
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
MDE-MEAP RELEASED ITEMS
RELEASED ITEMS MATHEMATICS GRADE 7 Fall 2006 MDE-MEAP RELEASED ITEMS 1 Page 2 MDE/MEAP RELEASED ITEMS GO ON TO THE NEXT PAGE Page 3 MDE/MEAP RELEASED ITEMS GO ON TO THE NEXT PAGE 5 6 Page 4 MDE/MEAP RELEASED
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
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.
NUMBERS AND NUMBER RELATIONSHIPS
MODULE MODULE CHAPTERS Numbers and number patterns 2 Money matters KEY SKILLS writing rational numbers as terminating or recurring decimals identifying between which two integers any irrational number
6th Grade Report Card Mathematics Skills: Students Will Know/ Students Will Be Able To...
6th Grade Report Card Mathematics Skills: Students Will Know/ Students Will Be Able To... Report Card Skill: Use ratio reasoning to solve problems a ratio compares two related quantities ratios can be
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