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    Alpha Omega Publications, Inc.Rock Rapids, IA

    Mathematics 6Teachers Guide

    Authors:

    Cindi Mitchell & Lori Fowler

    Editor:

    Alan Christopherson

    Graphic Design:

    Chris Burkholder JoAnn Cumming Lauren Durain

    Laura Miller Brian Ring

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    Horizons Mathematics 6 Teachers GuidePublished by Alpha Omega Publications, Inc.

    804 N. 2nd Ave. E., Rock Rapids, IA 51246-1759

    MCMXCIX by Alpha Omega Publications Inc., All rights reserved

    All rights reserved. No part of this publication may be reproduced, stored in an electronic retrievalsystem, or transmitted, in any form or by any means, electronic, mechanical, photocopying,recording, or otherwise, without the prior written permission of the publisher. Brief quotationsmay be used in literary review.

    Printed in the United States of AmericaISBN 978-0-7403-0012-7

    Scripture taken from the HOLY BIBLE, NEW INTERNATIONAL VERSION,Copyright 1973, 1978, 1984 by International Bible Society.

    Used by permission of Zondervan Publishing House.

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    ContentsSection OneIntroduction Page

    Before You Start. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Readiness Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Preparing a Lesson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Scope & Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Where to Use Mathematics Worksheets. . . . . . . . . . . . . . . . . . . . . . . . 20Appearance of Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

    Section TwoTeachers Lessons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

    Section ThreeAnswer Keys (Lessons 1160) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213Test Keys (Tests 116) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289

    Section FourWorksheets (180). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301Worksheet Answer Keys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385

    Section FiveUnit Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405Unit Test Keys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435

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    Introduction

    H o r i z o n s M a t h e m a t i c s 6

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  • Before You Start THE CHALLENGETodays average high school graduate will need to know more math than theircounterpart of ten, fifteen, or twenty years ago. Basic math skills must be strongif this country is to continue to be a leader in shaping the technology of thefuture. The general trend of modern education is to better prepare students forwhat lies ahead.

    THE GOALThe goal of this curriculum is to provide the parent and teacher with a tool thatwill help them effectively teach math skills and raise the level of studentperformance. Research of the content and methods of other existingcurriculums, the concepts evaluated by achievement tests, and typical courses ofstudy resulted in selection of the Scope and Sequence starting on page 17. Thiscurriculum was not planned around any particular group of students. Rather, itwas determined that the material in this curriculum constituted a reasonablelevel of performance for sixth grade students. The curriculum is designed sothat the teacher can adapt its use to student(s) of widely varying ability. Inother words, the curriculum is a tool that is capable of performing well over abroad range of student ability to help them achieve a higher minimum level ofproficiency. The two major components of the curriculum are the student text(in two volumes) and the Teachers Guide. These are the absolute minimumcomponents for accomplishing the objective of teaching the concepts in theScope and Sequence. Since this handbook was designed as an integral part of thecurriculum, it is absolutely necessary to use the handbook. The handbookcontains activities not found in the student texts that are essential to theaccomplishment of the curriculum objectives. As you will see in the followingsections, this Teachers Guide contains a significant number of suggestions andhelps for the teacher.

    THE DESIGNTake a moment to look at the sample chart entitled, Appearance of Concepts, onpage 22. Take note of how the curriculum concepts are developed. The firstpresentation is usually a brief familiarization. Then the basic teaching isaccomplished as part of three to five lessons. The thoroughness of apresentation depends on how new and how important the concept is to thestudents academic development.

    The DevelopmentEach concept will be reviewed for three to five lessons after the completepresentation. For the next two months the concept will be presented every twoweeks as a part of two or three lessons. After a break in presentation of a fewweeks, the concept will be thoroughly reviewed as part of the lesson for three tofive days. This will be followed by a period where the concept will be reviewedevery two weeks as part of two or three lessons. This progression continuesuntil the student(s) have had the opportunity to thoroughly master the concept.

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  • An ExampleSome mathematics curriculums might teach division for two months and not goback to it again. In this curriculum it will be introduced and practiced for twoweeks. For the next two months, division will be presented every two weeks asa part of two or three lessons to give the student(s) continual practice to developmastery of the concept. The third month will be considered a break frompresenting the concept. In the fourth month, division will first be thoroughlyreviewed and again practiced every two weeks as a part of two or three lessons.By having a series of practices every two weeks, the student(s) will retain whatthey have learned to a greater degree. Short periods of exposure repeated manytimes is much more effective than long periods with fewer exposures. Reviewthe chart on page 22 to see how the concepts are developed.

    Readiness EvaluationWHY EVALUATE READINESS?Teaching could be defined as the process of starting with what a student knowsand guiding him to added knowledge with new material. While this may not bea dictionary definition of teaching, it is descriptive of the processes involved.Determining a students readiness for sixth grade mathematics is the first step tosuccessful teaching.

    TYPES OF READINESSTrue readiness has little to do with chronological age. Emotional maturity andmental preparation are the main components of academic readiness. The teacherwho is dealing directly with the student is best able to determine a childsemotional maturity. All emotionally immature students may need special studenttraining in their problem areas. A childs mental preparation can be more easilydiscerned with a simple diagnostic evaluation. Observing the childs attitude ofconfidence or insecurity while taking the evaluation may help determineemotional readiness.

    DETERMINING READINESSThe sixth grade Readiness Evaluation on pages 812 helps the teacher to determineif student(s) are ready to begin studying math at the sixth grade level. Completethis evaluation the first or second day of school.

    The evaluation should take 45-60 minutes. It would be helpful to evaluate all ofthe students to determine what each student knows. However, you may want toevaluate only those student(s) who have not had a thorough third gradeprogram. It is especially important to evaluate any student who is using thiscurriculum for the first time. The student(s) should be able to complete the teston their own with the teacher making sure they understand the directions foreach individual activity.

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  • The answer key is on page 8. Count each individual answer as a separate point.The total for the test is 83 points. The student(s) should achieve a score of 59 ormore points to be ready to begin sixth grade. Be sure to note the areas of weak-ness of each student, even those who have scored over 59 points. If thestudent(s) scored under 59 points, they may need to repeat fifth grade math ordo some refresher work in their areas of weakness. For possible review of theidentified areas of weakness, refer to the chart Appearance of Concepts on page 22of the Horizons Math 5 Teachers Guide. It will locate lessons where the conceptswere taught.

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  • Preparing a LessonGENERAL INFORMATIONThere is some room on the teacher lessons for you to write your own notes. The moreyou personalize your teachers guide in this way, the more useful it will be to you.

    You will notice that there are 160 student lessons in the curriculum. This allows forthe inevitable interruptions to the sch

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