# DEVELOPING MATHEMATICAL THINKING IN FRACTIONS, DECIMALS, PERCENTS, AND ALGEBRA

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 DEVELOPING MATHEMATICAL THINKING IN FRACTIONS, DECIMALS, PERCENTS, AND ALGEBRA By Brad Fulton and Bill Lombard Teacher to Teacher Press PO Box 2, Millville, CA Phone: (50) Fax: (50)

2 2 All material in this manual not specifically identified as being reprinted from another source is copyright 2011 by Bill Lombard and Brad Fulton. This resource manual is dedicated to the students of Brad Fulton and Bill Lombard, who have been sources of inspiration to us as teachers. Without these students our lives would not be as rich and rewarding as they are. For consultant services contact: Brad Fulton PO Box 2 Millville, CA Phone: (50) Fax: (50) Bill Lombard 5885 Avery Way Redding, CA 9600 Phone: (50) Teacher to Teacher Press

4 4 Fraction Number Line Helps students understand the magnitude of fractions, decimals, and percents Demonstrates fractional, decimal, and percent equivalencies Develops fraction number sense Fosters mathematical communication in a fraction environment Can be used as a warm-up or whole class activity

5 ACTIVITY 2 Materials: fraction cards tape string activity master PROCEDURE Skills: Comparing fractions Ordering fractions Simplifying fractions Finding equivalent fractions Understanding reciprocals Fraction Number Line Overview: If you want to build number sense with fractions, if you want to help students see the connections between fractions, decimals, and percents, if you want to generate rich mathematical discussion then this quick and easy activity is for you. Use it as a planned activity, a warmup, or a quick filler. Vocabulary: numerator, denominator, greater than, less than, reciprocal 1 You will need to draw a number line on the board. It should run the length of the entire board. It should only include the numbers zero and one as shown: Give each student a card from the simplified fraction set. (You can copy these onto card stock to make them more durable.) Each student can come to the board and tape their fraction where it should go. You may wish to have them do this one at a time, in small groups, or as a whole class. Students should be able to explain their reasoning for the placement. Ask other students if they agree with a card s location and have them explain why. 5 For example, let s assume 1 / 4 and 1 / have been placed on the number line. The next student has to place 1 / 5 on the line. He or she might use common denominators to determine that 1 / 5 is the smallest of the three. On the other hand, the student could reason that larger denominators mean a whole has been cut into smaller parts, so the one fifth is smaller than the one fourth or the one third. The student might use division to convert the three fractions to decimals or use percent equivalents to tell that the fifth was the smallest. Encouraging students to look at these fractions in multiple ways will foster the conceptual fraction sense students need.

6 4 Once students have completed this task, they are ready for the equivalent fraction cards. There are two ways to present this activity. The first is to pass out the cards from this set as before. The second is to mix these cards with the simplified set. This will allow students to see the equivalency of the fractions as shown here: 0 1 / The third activity that can be done with the cards involves the decimal cards. Again these may be presented individually or mixed with the fraction cards to show equivalency. / 6 Both approaches are conceptually rich, and doing the activity one way does not preclude doing it the other. Good Tip! 6 You can play a variation of the card game, War by using the cards. Give pairs of students a set of cards and let them play against another pair. Each team lays a card face up and the team with the greater fraction wins both cards. In the event the cards are equal, an addition card is played. 6 Lastly, mix the percent cards with the decimal and fraction cards so students will become familiar with all three forms of fraction notation. 7 This activity is most powerful if presented over a period of days throughout the year. More learning and more retention will occur that way. If you would like to make it easier to use this activity on a regular basis, consider putting up a permanent number line. To do this, run a string from a nail or tack on one side of your chalkboard (A) to the other, over another nail, and down to the chalk tray (B) as shown. Fasten it there with a third nail. When you want to remove the number line, unhook it from the nail and run it under the chalk tray as shown by the dotted line. Each fraction card has a dashed line indicating where to fold it backward so it can be hung on such a string. A string chalkboard string in use string down 4 nail B 8 Two blank masters are included to make cards of your own. You can also use x 5 index cards or sticky notes.

7 7 Journal Prompts: Put these three fractions in order from least to greatest. Explain your reasoning. / 7 5 / 6 10 / 11 The fractions 1 / 4 and 2 / 5 have been placed on the number line. What fraction might go in between them? How do you know? Homework: You can use the enclosed activity master for homework, or assign a page from a text or workbook. Taking a Closer Look: Include mixed numbers and improper fractions. Or ask students to place the reciprocals of their cards on the number line. Assessment: This activity can be checked as the students are putting up their cards. you can also check them by converting all the cards to decimals. If you assign the homework master, use the following key to check it. Answer Key: Set 1: 1 / 4 / 8 1 / 2 / 4 5 / 6 Set 2: 1 / 4 = 2 / 8 7 / 12 9 / 15 = / 5 2 / Set : 1 / 2 2 / / 4 4 / 5 5 / 6 Set 4: 1 / 5 =.2 1 / 4 0% 1 /.5 Set 5:.5%.05 1 / 10 1 / 4 50% 100%

8 8 Activity master Number Line Fractions Name Put the following fractions, decimals or percents on their number lines in the correct locations. Set 1: / 8 5 / 6 1 / 4 1 / 2 / Set 2: 2 / 8 2 / 9 / 15 7 / 12 1 / 4 / Set : / 4 2 / 1 / 2 5 / 6 4 / Set 4: 1 / 1 / / 4 0% Set 5: 100%.05 1 / 10 50%.5% 1 / 4 0 1

9

10

11

12

13

14

15

16

17 17 10% 1% 25% 50% 75% 1 / % 66 2 / % 11%

18 18 5% 9% 11% 72% 65% 70% 60% 80%

19 19 99%.5% 12 1 / % 9% 2 102% 150% 200% 1.1%

20 20 On a national test, only the most difficult items on division of decimals proved more difficult than ordering decimals. Research Ideas for the Classroom Early Childhood Mathematics Douglas Owens, Ed.

21 21 Visit the Teacher to Teacher Press website at... for many other great math activities. On our website you will find: A complete catalog of our materials Free sample chapters from our books Downloadable handouts from our workshops Quotes for motivating students Links to other valuable resource websites Order forms for our materials A bibliography of great mathematical reading Calendars showing where and when you can hear Brad and Bill present Happy surfing!

22 22 Books by Brad and Bill The Language of Math helps teachers create a classroom environment rich in mathematical thinking by showing them how to easily incorporate oral and written language into their math classes. Over 100 journal and discussion starters are included along with extensive instructions for making the most of your math time. Here are a dozen unique and conceptual activities that will help your students add, subtract, multiply and divide fractions as well as connect them to decimal and percent representations. Both you and your students will love the novel and creative approach. Teachers are raving about how effective these activities have been in their classrooms. Children as young as fourth grade and college students alike say that algebra is easy and makes sense because of this incredible approach. Students don t even think they are doing math sometimes because these activities are so fun and engaging, but they are developing rich and valuable number sense as they explore these eleven creative activities.

23 2 Our first book is still one of our most popular. Every teacher we talk to who has tried this approach to functions has been amazed at what their students have learned and accomplished. Over 150 pages of multiple representations of functions cover such concepts as slope, intercept, and function notation. Even elementary students have developed an understanding of functions with this book. Exponents will finally make sense to your students after they participate in the unique activities found in this book. Both positive and negative exponents are demonstrated conceptually. Your students will even be able to explain why n 0 = 1. Over one dozen geometry activities will excite your students as they discover the connections between geometry and fractions, decimals, percents, and even algebra. Area formulas, angle measurement, polygon attributes, vocabulary, and construction are covered. A dozen engaging and educational games await you and your students in this creative and highly adaptable book. You ll find games that reinforce basic operations with whole numbers, fractions, decimals, and integers as well as algebraic skills. Game masters will serve a spectrum of grade levels and skill levels. Your students will beg for more! Download free sample chapters at our website:

24 24 NEW PRODUCT! Simply Great Math Activities DVDs! You asked, and we listened! So many of you have wanted us to put our math workshops on DVDs, and now they are available. Each professional quality DVD is approximately 0 to 45 minutes in length and comes with all the files of the worksheets along with instructional demonstrations and teaching tips. Now you can attend your own Brad and Bill workshop anytime you want. We offer DVD versions of some of our most popular activities. Check our website to see the latest titles.

### Adapted from SIMPLY GREAT MATH ACTIVITIES: ALGEBRA READINESS Teacher to Teacher Press by Brad Fulton and Bill Lombard

Adapted from SIMPLY GREAT MATH ACTIVITIES: ALGEBRA READINESS 2010 Teacher to Teacher Press by Brad Fulton and Bill Lombard www.tttpress.com Teacher to Teacher Press PO Box 233, Millville, CA 96062 Phone:

### This material is copyrighted and protected by U.S. anti- piracy laws.

This material is copyrighted and protected by U.S. anti- piracy laws. 2013 by Teacher to Teacher Press. All rights reserved. As a purchaser of this handout, you have a single- user license. You may duplicate

### 1 Computation Students will practice multiplication, division, addition, and subtraction. Order of operation will also be reviewed.

Fairfax Collegiate 703 481-3080 www.fairfaxcollegiate.com FCS FAIRFAX COLLEGIATE Intro to Pre-Algebra 6-8 Syllabus SUMMER PROGRAM Course Goals 1 Solidify Previous Knowledge Students will solidify previous

### Camp Kindergarten Summer, 2008

Camp Kindergarten Summer, 2008 You Are Invited to Camp Kindergarten! Camp Kindergarten 2007 in Atlanta was so AWESOME that we are going to offer even more seminars in 2008! Check out the dates and locations

### Numbers and Operations

Grade 7 MATH Unit Number 1 Numbers and Operations Title Big Ideas/Enduring Understandings Problems can be solved easier when using variety of equivalent forms. All numbers fall within the real number system.

### Sometimes it is easier to leave a number written as an exponent. For example, it is much easier to write

4.0 Exponent Property Review First let s start with a review of what exponents are. Recall that 3 means taking four 3 s and multiplying them together. So we know that 3 3 3 3 381. You might also recall

### Grade 7 Pre-AP Math Unit 1. Numbers and Operations *CISD Safety Net Standards: 7.3B. Suggested Time Frame. 1 st Six Weeks 15 Days

Numbers and Operations *CISD Safety Net Standards: 7.3B 7.3B Title Big Ideas/Enduring Understandings Problems can be solved easier when using variety of equivalent forms. All numbers fall within the real

### eday Lessons Mathematics Grade 8 Student Name:

eday Lessons Mathematics Grade 8 Student Name: Common Core State Standards- Expressions and Equations Work with radicals and integer exponents. 3. Use numbers expressed in the form of a single digit times

T68 Mathematics Success Grade 8 [OBJECTIVE] The student will determine the square roots of perfect squares, and categorize rational numbers in the real number system and apply this understanding to solve

### II. III Core Knowledge National Conference, Grade 2, Confucius Says = 2X3 1

Confucius Says 2+2+2 = 2X3 Introduction to Multiplication with a connection to the Study of Ancient China Grade level: Grade 2 Written by: Lottie Trudell, St. Mary s School, East Moline, Illinois Length

### First Six Weeks (29 Days)

Mathematics Scope & Sequence Grade 6 Revised: May 2010 Topic Title Unit 1: Compare and Order, Estimate, Exponents, and Order of Operations Lesson 1-1: Comparing and Ordering Whole Numbers Lesson 1-2: Estimating

### Improper Fractions and Mixed Numbers

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

### Algebra 1A and 1B Summer Packet

Algebra 1A and 1B Summer Packet Name: Calculators are not allowed on the summer math packet. This packet is due the first week of school and will be counted as a grade. You will also be tested over the

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

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

### Introduction to Fractions

Introduction to Fractions Fractions represent parts of a whole. The top part of a fraction is called the numerator, while the bottom part of a fraction is called the denominator. The denominator states

### Upon successful completion of this course you should be able to

University of Massachusetts, Amherst Math 113 Math for Elementary School Teachers I Fall 2011 Syllabus of Objectives and Learning Outcomes Overview of the Course This is a mathematics content course which

### Maths Area Approximate Learning objectives. Additive Reasoning 3 weeks Addition and subtraction. Number Sense 2 weeks Multiplication and division

Maths Area Approximate Learning objectives weeks Additive Reasoning 3 weeks Addition and subtraction add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar

### PROBLEM SOLVING, REASONING, FLUENCY. Year 6 Term 1 Term 2 Term 3 Term 4 Term 5 Term 6 Number and Place Value. Measurement Four operations

PROBLEM SOLVING, REASONING, FLUENCY Year 6 Term 1 Term 2 Term 3 Term 4 Term 5 Term 6 Number and Place Value Addition and subtraction Large numbers Fractions & decimals Mental and written Word problems,

### How do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.

The verbal answers to all of the following questions should be memorized before completion of pre-algebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics

### Hands-On Math Algebra

Hands-On Math Algebra by Pam Meader and Judy Storer illustrated by Julie Mazur Contents To the Teacher... v Topic: Ratio and Proportion 1. Candy Promotion... 1 2. Estimating Wildlife Populations... 6 3.

### Eureka Math Tips for Parents

Eureka Math Tips for Parents Place Value and Decimal Fractions In this first module of, we will extend 4 th grade place value work to multi-digit numbers with decimals to the thousandths place. Students

### MAT 096, ELEMENTARY ALGEBRA 6 PERIODS, 5 LECTURES, 1 LAB, 0 CREDITS

1 LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK MATHEMATICS, ENGINEERING and COMPUTER SCIENCE DEPARTMENT FALL 2015 MAT 096, ELEMENTARY ALGEBRA 6 PERIODS, 5 LECTURES, 1 LAB, 0 CREDITS Catalog

### Comparing and Plotting Rational Numbers on a Number Line

Comparing and Plotting Rational Numbers on a Number Line Student Probe Plot 4 on the number Lesson Description In this lesson students will plot rational numbers on a number This lesson is limited to positive

### SIXTH GRADE MATH. Quarter 1

Quarter 1 SIXTH GRADE MATH Numeration - Place value - Comparing and ordering whole numbers - Place value of exponents - place value of decimals - multiplication and division by 10, 100, 1,000 - comparing

### Year Five Maths Notes

Year Five Maths Notes NUMBER AND PLACE VALUE I can count forwards in steps of powers of 10 for any given number up to 1,000,000. I can count backwards insteps of powers of 10 for any given number up to

### LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK MATHEMATICS DEPARTMENT Fall 2014

1 LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK MATHEMATICS DEPARTMENT Fall 2014 MAT 097: Algebra 6 Lecture Hours, 2 Educo Lab Hours, 2 Tutoring Lab Hours, 0 Credits Catalog Description This

### Hitting ting the. WHAT DO PLOTTING POINTS, MAkING. A Dart Game Simulation Using Graphing Calculator Technology. Throwing Darts

k A T H L E E N C A G E M I T T A G A N D S H A R O N E. T A y L O R Hitting ting the Bull s A Dart Game Simulation Using Graphing Calculator Technology WHAT DO PLOTTING POINTS, MAkING decimal representations,

### CD 1 Real Numbers, Variables, and Algebraic Expressions

CD 1 Real Numbers, Variables, and Algebraic Expressions The Algebra I Interactive Series is designed to incorporate all modalities of learning into one easy to use learning tool; thereby reinforcing learning

### Contents. Block A Understanding numbers 7. Block C Geometry 53. Block B Numerical operations 30. Page 4 Introduction Page 5 Oral and mental starters

Contents Page 4 Introduction Page 5 Oral and mental starters Block A Understanding numbers 7 Unit 1 Integers and decimals 8 Integers Rounding and approximation Large numbers Decimal numbers Adding and

### Course Title: Math A Elementary Algebra

Course Title: Math A Elementary Algebra Unit 0: Course Introduction In this unit you will get familiar with important course documents, such as syllabus and communication policy. You will register on MyMathLab

### Overview. Opening 10 minutes. Closing 10 minutes. Work Time 25 minutes EXECUTIVE SUMMARY WORKSHOP MODEL

Overview EXECUTIVE SUMMARY onramp to Algebra is designed to ensure that at-risk students are successful in Algebra, a problem prominent in most of our country s larger school districts. onramp to Algebra

### Please see current textbook prices at EVALUATION AND ASSESSMENT

MAT051: ELEMENTARY ALGEBRA REVIEW SYLLABUS LECTURE HOURS/CREDITS: 1/1 CATALOG DESCRIPTION Prerequisite: Placement Score OR MAT050 Elementary Algebra with a grade of P or higher Prerequisite or Co-Requisite:

A Correlation of to the Minnesota Academic Standards Grades K-6 G/M-204 Introduction This document demonstrates the high degree of success students will achieve when using Scott Foresman Addison Wesley

### Math Foundations IIA Grade Levels 9-12

Math Foundations IIA Grade Levels 9-12 Math Foundations IIA introduces students to the following concepts: order of operations squares and square root multiplying decimals organizing and graphing data

### Grade 9 Mathematics Unit #1 Number Sense Sub-Unit #1 Rational Numbers. with Integers Divide Integers

Page1 Grade 9 Mathematics Unit #1 Number Sense Sub-Unit #1 Rational Numbers Lesson Topic I Can 1 Ordering & Adding Create a number line to order integers Integers Identify integers Add integers 2 Subtracting

### Junior Mathematical Processes, Problem Solving & Big Ideas by Strand

Junior Mathematical Processes, Problem Solving & Big Ideas by Strand Adapted from: The Ontario Curriculum Grades 1 8 Revised Mathematics 2005, Number Sense and Numeration Grades 4-6, Measurement Grades

FOURTH GRADE NUMBER SENSE Number sense is a way of thinking about number and quantity that is flexible, intuitive, and very individualistic. It grows as students are exposed to activities that cause them

### Unit 4: Exploring Math Patterns...106. Introduction...5. Unit 1: Visualizing Math...17. Unit 5: Exploring Probability...125

Introduction....................................5 WHAT IS MICROWORLDS EX, AND HOW CAN IT HELP ME IN THE MATH CLASSROOM?.................6 HOW TO USE THIS BOOK AND CD.....................10 CLASSROOM ENVIRONMENT..........................12

### Number Sense and Operations

Number Sense and Operations representing as they: 6.N.1 6.N.2 6.N.3 6.N.4 6.N.5 6.N.6 6.N.7 6.N.8 6.N.9 6.N.10 6.N.11 6.N.12 6.N.13. 6.N.14 6.N.15 Demonstrate an understanding of positive integer exponents

### MULTIPLICATION AND DIVISION OF REAL NUMBERS In this section we will complete the study of the four basic operations with real numbers.

1.4 Multiplication and (1-25) 25 In this section Multiplication of Real Numbers Division by Zero helpful hint The product of two numbers with like signs is positive, but the product of three numbers with

### Math Help and Additional Practice Websites

T92 Mathematics Success Grade 8 [OBJECTIVE] The student will create rational approximations of irrational numbers in order to compare and order them on a number line. [PREREQUISITE SKILLS] rational numbers,

### Over the forty years that I ve been

Using Games in Your Math Teaching by Marilyn Burns Over the forty years that I ve been teaching mathematics to children in classrooms and to teachers in workshops, games have played an important role.

### Unit 1 Number Sense. In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions.

Unit 1 Number Sense In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions. BLM Three Types of Percent Problems (p L-34) is a summary BLM for the material

### Basic Understandings. Recipes for Functions Guess My Rule!

Activity: TEKS: Recipes for Functions Guess My Rule! (a). (3) Function concepts. A function is a fundamental mathematical concept; it expresses a special kind of relationship between two quantities. Students

### Domain Essential Question Common Core Standards Resources

Middle School Math 2016-2017 Domain Essential Question Common Core Standards First Ratios and Proportional Relationships How can you use mathematics to describe change and model real world solutions? How

### Self-Directed Course: Transitional Math Module 2: Fractions

Lesson #1: Comparing Fractions Comparing fractions means finding out which fraction is larger or smaller than the other. To compare fractions, use the following inequality and equal signs: - greater than

### Math Foundations IIB Grade Levels 9-12

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

### Understanding Place Value of Whole Numbers and Decimals Including Rounding

Grade 5 Mathematics, Quarter 1, Unit 1.1 Understanding Place Value of Whole Numbers and Decimals Including Rounding Overview Number of instructional days: 14 (1 day = 45 60 minutes) Content to be learned

### Math Games Galore. For further information contact. Beth Hines

Math Games Galore ~ A Returning Developer ~ For further information contact Beth Hines Lewis Anna Woodbury Elem 610 S. Charleston Ave. Fort Meade, FL 33841 (863) 285-1133 beth.hines@polk-fl.net n PROGRAM

### Saxon Math Home School Edition. September 2008

Saxon Math Home School Edition September 2008 Saxon Math Home School Edition Lesson 4: Comparing Whole Lesson 5: Naming Whole Through Hundreds, Dollars and Cent Lesson 7: Writing and Comparing Through

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

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

### Math Games For Skills and Concepts

Math Games p.1 Math Games For Skills and Concepts Original material 2001-2006, John Golden, GVSU permission granted for educational use Other material copyright: Investigations in Number, Data and Space,

### Fractions and Linear Equations

Fractions and Linear Equations Fraction Operations While you can perform operations on fractions using the calculator, for this worksheet you must perform the operations by hand. You must show all steps

### 7 th Grade Integer Arithmetic 7-Day Unit Plan by Brian M. Fischer Lackawanna Middle/High School

7 th Grade Integer Arithmetic 7-Day Unit Plan by Brian M. Fischer Lackawanna Middle/High School Page 1 of 20 Table of Contents Unit Objectives........ 3 NCTM Standards.... 3 NYS Standards....3 Resources

### Intensive Intervention

Fit Your Framework. No matter how you frame it, it fits. focusmath provides the essential elements of Response to Intervention (RtI) in a validated instructional design for accelerating math achievement.

### NCTM Curriculum Focal Points for Grade 5. Everyday Mathematics, Grade 5

NCTM Curriculum Focal Points and, Grade 5 NCTM Curriculum Focal Points for Grade 5 Number and Operations and Algebra: Developing an understanding of and fluency with division of whole numbers Students

### Created specifically for the needs of early math learners in Grades K 2

For Grades K 2 Real learning, real math, really fun! Created specifically for the needs of early math learners in Grades K 2 Developed by a highly experienced team of teachers, educational writers, animators,

### Course Syllabus. MATH 1350-Mathematics for Teachers I. Revision Date: 8/15/2016

Course Syllabus MATH 1350-Mathematics for Teachers I Revision Date: 8/15/2016 Catalog Description: This course is intended to build or reinforce a foundation in fundamental mathematics concepts and skills.

### USING ALGEBRA TILES EFFECTIVELY

MATHEMATICS USING ALGEBRA TILES EFFECTIVELY TOOLS FOR UNDERSTANDING by Bettye C. Hall Reviewers James Gates, Ed.D. Yvonne S. Gentzler, Ph.D. AUTHOR Bettye C. Hall is the former Director of Mathematics

### AMSCO S Ann Xavier Gantert

AMSCO S Integrated ALGEBRA 1 Ann Xavier Gantert AMSCO SCHOOL PUBLICATIONS, INC. 315 HUDSON STREET, NEW YORK, N.Y. 10013 Dedication This book is dedicated to Edward Keenan who left a profound influence

### The notation above read as the nth root of the mth power of a, is a

Let s Reduce Radicals to Bare Bones! (Simplifying Radical Expressions) By Ana Marie R. Nobleza The notation above read as the nth root of the mth power of a, is a radical expression or simply radical.

### IEP Goals and Objectives. Los Angeles Unified School District Division of Special Education

IEP Goals and Objectives Los Angeles Unified School District Division of Special Education Objectives Learn the legal requirement for writing IEP goals Become familiar with goals written for the general

### SFUSD Mathematics Core Curriculum Development Project

1 SFUSD Mathematics Core Curriculum Development Project 2014 2015 Creating meaningful transformation in mathematics education Developing learners who are independent, assertive constructors of their own

### Objective. Materials. find a relationship between Greatest Common Factor (GCF) and Least Common Multiple (LCM) justify why Oliver s method works

. Objective To discover a relationship between the Greatest Common Factor (GCF) and the Least Common Multiple (LCM) of two numbers A c t i v i t y 4 Oliver s Method Materials TI-73 calculator Student Worksheet

### Prentice Hall. California Edition of Algebra 1 - Classics Edition (Smith/Charles) 2008. Grade 8

Prentice Hall Grade 8 California Edition of Algebra 1 - Classics Edition (Smith/Charles) 2008 C O R R E L A T E D T O California s Map for a Basic Grade Level Program Grade 8 PROGRAM DESCRIPTION Prentice

### SUMMER ASSIGNMENT FOR ALGEBRA 1 STUDENTS

SUMMER ASSIGNMENT FOR 2012-2013 ALGEBRA 1 STUDENTS This year, the summer math assignments are available online on the district homepage. To access the summer assignments, please go to the high school s

### Prentice Hall Mathematics, Algebra 1 2009

Prentice Hall Mathematics, Algebra 1 2009 Grades 9-12 C O R R E L A T E D T O Grades 9-12 Prentice Hall Mathematics, Algebra 1 Program Organization Prentice Hall Mathematics supports student comprehension

### Fun with Fractions: A Unit on Developing the Set Model: Unit Overview www.illuminations.nctm.org

Fun with Fractions: A Unit on Developing the Set Model: Unit Overview www.illuminations.nctm.org Number of Lessons: 7 Grades: 3-5 Number & Operations In this unit plan, students explore relationships among

### The authors wish to thank Mr. Bob Fine and especially all of our former students in Azusa, Inglewood, Los Angeles, and Santa Monica, California.

The authors... Janis Marcy and Steve Marcy San ta Monica -Malibu Unified School District Limited Reproduction Permission: Permission to duplicate these materials is limited to the teacher for whom they

### LAKE ELSINORE UNIFIED SCHOOL DISTRICT

LAKE ELSINORE UNIFIED SCHOOL DISTRICT Title: PLATO Algebra 1-Semester 2 Grade Level: 10-12 Department: Mathematics Credit: 5 Prerequisite: Letter grade of F and/or N/C in Algebra 1, Semester 2 Course Description:

### Middle School Math Assignment: How to Access IXL on a Computer or ipad

Middle School Math Assignment: How to Access IXL on a Computer or ipad Accessing IXL on a Computer: To log in to IXL you should go to the following site: www.ixl.com/signin/stmeshouston You will see this

### ARITHMETIC. Overview. Testing Tips

ARITHMETIC Overview The Arithmetic section of ACCUPLACER contains 17 multiple choice questions that measure your ability to complete basic arithmetic operations and to solve problems that test fundamental

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

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

### A Year-long Pathway to Complete MATH 1111: College Algebra

A Year-long Pathway to Complete MATH 1111: College Algebra A year-long path to complete MATH 1111 will consist of 1-2 Learning Support (LS) classes and MATH 1111. The first semester will consist of the

### Math Mammoth Fractions 2. Contents. Introduction Simplifying Fractions Simplifying Fractions

Math Mammoth Fractions 2 Contents Introduction... 4 Simplifying Fractions 1... 8 Simplifying Fractions 2... 12 Multiply Fractions By Whole Numbers... 16 Multiplying Fractions by Fractions... 20 Fraction

### HIBBING COMMUNITY COLLEGE COURSE OUTLINE

HIBBING COMMUNITY COLLEGE COURSE OUTLINE COURSE NUMBER & TITLE: - Beginning Algebra CREDITS: 4 (Lec 4 / Lab 0) PREREQUISITES: MATH 0920: Fundamental Mathematics with a grade of C or better, Placement Exam,

### LESSON 4 Missing Numbers in Multiplication Missing Numbers in Division LESSON 5 Order of Operations, Part 1 LESSON 6 Fractional Parts LESSON 7 Lines,

Saxon Math 7/6 Class Description: Saxon mathematics is based on the principle of developing math skills incrementally and reviewing past skills daily. It also incorporates regular and cumulative assessments.

### Welcome to Basic Math Skills!

Basic Math Skills Welcome to Basic Math Skills! Most students find the math sections to be the most difficult. Basic Math Skills was designed to give you a refresher on the basics of math. There are lots

### Black GCF and Equivalent Factorization

Black GCF and Equivalent Factorization Here is a set of mysteries that will help you sharpen your thinking skills. In each exercise, use the clues to discover the identity of the mystery fraction. 1. My

### Maths Workshop for Parents 2. Fractions and Algebra

Maths Workshop for Parents 2 Fractions and Algebra What is a fraction? A fraction is a part of a whole. There are two numbers to every fraction: 2 7 Numerator Denominator 2 7 This is a proper (or common)

### Lesson List. Unit and Lesson Number Lesson Title Notes

Middle School Pre-Algebra Common Core Appendix Information K 12 has revised Middle School Pre-Algebra to align the course with Common Core State Standards (CCSS). To do this, we created an appendix of

### Comparing Fractions. The expectation that all students should use. The Roll Out Fractions Game: General Rules

The Roll Out Fractions Game: Comparing Fractions By Enrique Ortiz The expectation that all students should use models, benchmarks, and equivalent forms to judge the size of fractions is clearly stated

### Mathematics & the PSAT

Mathematics & the PSAT Mathematics 2 Sections 25 minutes each Section 2 20 multiple-choice questions Section 4 8 multiple-choice PLUS 10 grid-in questions Calculators are permitted - BUT You must think

### Text: Scott Foresman CA Mathematics

Grade 6 Mathematics 008-009 3 Course Introduction 7 Segment I: Algebra and Decimals -0 Variables and Expressions NS.0 AF. -9 Orders of Operation AF. 4- Powers and Exponents - Comparing and Ordering Decimals

### Everyday Mathematics Grade K-3. Parent Resource Guide

Everyday Mathematics Grade K-3 Parent Resource Guide . Dear Parents, In this booklet you will find information about the mathematics curriculum taught in our district for grades kindergarten through fourth

### Fourth Grade Math Curriculum Alignment

Fourth Grade Math Curriculum Alignment Timeline Strand/Concept Performance Objective Resources Lessons/Objectives Technology August Strand 1: Number Sense & Operations Concept 1: Number Sense PO 7. Compare

### Fraction Vocabulary. It is important that vocabulary terms are taught to students.

Rational Numbers Fractions Decimals Percents It is important for students to know how these 3 concepts relate to each other and how they can be interchanged. Fraction Vocabulary It is important that vocabulary

### Math 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.

Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used

### RATIONAL NUMBER ADDITION AND SUBTRACTION

21 RATIONAL NUMBER ADDITION AND SUBTRACTION INSTRUCTIONAL ACTIVITY Lesson 4 LEARNING GOAL Students will extend their understanding of integer addition and subtraction to addition and subtraction of rational

### Course: Math 7. engage in problem solving, communicating, reasoning, connecting, and representing

Course: Math 7 Decimals and Integers 1-1 Estimation Strategies. Estimate by rounding, front-end estimation, and compatible numbers. Prentice Hall Textbook - Course 2 7.M.0 ~ Measurement Strand ~ Students

### Overview. Essential Questions. Algebra I, Quarter 1, Unit 1.2 Interpreting and Applying Algebraic Expressions

Algebra I, Quarter 1, Unit 1.2 Interpreting and Applying Algebraic Expressions Overview Number of instruction days: 6 8 (1 day = 53 minutes) Content to Be Learned Write and interpret an expression from

### Estimating Square Roots with Square Tiles

Estimating Square Roots with Square Tiles By Ashley Clody The development of students understanding as the Georgia curriculum has become more conceptually based over the past 10 years. Students need to

### Number Talks. 1. Write an expression horizontally on the board (e.g., 16 x 25).

Number Talks Purposes: To develop computational fluency (accuracy, efficiency, flexibility) in order to focus students attention so they will move from: figuring out the answers any way they can to...

### Prentice Hall Mathematics: Course Correlated to: Alaska State Content Standards: Math (Grade 7)

Alaska State Content Standards: Math (Grade 7) A. A student should understand mathematical facts, concepts, principles, and theories. 1. understand and use numeration, including numbers, number systems,

### Click on the links below to jump directly to the relevant section

Click on the links below to jump directly to the relevant section Basic review Writing fractions in simplest form Comparing fractions Converting between Improper fractions and whole/mixed numbers Operations