Mega-Fun Fractions
MEGA-FUN FRACTIONSMega-Fun Fractions Miller & Lee, Scholastic Teaching Resourcesby Marcia Miller and Martin LeeSCHOLASTICPROFESSIONALBOOKSN E WY O R KM E X I C O C I T YT O R O N T O N E W L O N D O ND E L H I H O N G A U C K L A N DKO N G S Y D N E YB U E N O SA I R E S
Mega-Fun Fractions Miller & Lee, Scholastic Teaching ResourcesWith love to Daniel and Joshua BrandesScholastic Inc. grants teachers permission to photocopy the reproducible pages from this book for classroom use. No other partof this publication may be reproduced in whole or in part, or stored in a retrieval system, or transmitted in any form or by any means,electronic, mechanical, photocopying, recording, or otherwise, without written permission of the publisher. For information regardingpermission, write to Scholastic Inc., 557 Broadway, New York, NY 10012.Cover design by Maria LiljaInterior design by Solutions by Design, Inc.Cover and interior illustrations by Michael MoranISBN: 0-439-28844-4Copyright 2002 by Marcia Miller and Martin Lee.All rights reserved. Printed in the U.S.A.1 2 3 4 5 6 7 8 9 104008 07 06 05 04 03 02
CONTENTSAbout This Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5C L A S S F R AC T I O N W A L LTeacher Tips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Using fraction concepts in an ongoing,interactive bulletin board . . . . . . . . . . . . . . . . . . . . . 26FRACTION ACTIVITIESMega-Fun Fractions Miller & Lee, Scholastic Teaching ResourcesHALFNESSP I C T U R E T H E S E F R AC T I O N SUsing visual estimation to determine half . . . . . . . . 7Applying fraction concepts to describe groupsshown in photos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27FILL ALL FOURM I X I N G S N AC K M I XPlaying a spatial reasoning game usingpattern blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Using hands-on fractions to create“snack mixes” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28W HAT ’ SF R AC T I O N M E S SAG EINP E TA L , M I S S I S S I P P I ?Identifying fractions of regions to solvea riddle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Finding fractions of words to solve a riddle . . . . 28W HAT ’ S L E F T ?Completing sentences with fraction terms . . . . . . 28Using visual estimation to identify fractions . . . . . 10F R AC T I O N SUP ATREEUsing visual and spatial estimation to drawfractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10C O LO R F U L R E G I O N ST H E L A N G UAG EOFF R AC T I O N SF R AC T I O N D I C TAT I O NWriting fractions and mixed numberssaid aloud . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32F R AC T I O N SANDE G G C A RTO N SDrawing dot-paper regions for given fractions . . 15Using empty egg cartons to modelequivalent fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . 33F R AC T I O N C HA RT P U Z Z L EBA D G E B U D D I E SAssembling a schematic chart to representfractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Identifying equivalent fractionsin a class game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34PA RT A RTE Q U I VA L E N T F R AC T I O NC O N C E N T R AT I O NApplying fractions to geometric designs ongrid paper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18C O L L A B O R AT I V E Q U I LTSApplying fraction concepts to create aclass quilt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19PAT T E R N B LO C K P RO O F SMatching equivalent fractions in a cardgame format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35F R AC T I O N S B I N G O —T I M E S T W OPlaying Bingo games with equivalentfractions and mixed numbers . . . . . . . . . . . . . . . . . . 36Exploring equivalent fractions withpattern blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20F R AC T I O N P O E M SS HA D E D S HA P E SS HA R I N G F R AC T I O N P I EShading equivalent fractions on grid paper . . . . 23S TA N D U PFORF R AC T I O N SApplying fraction concepts to describeparts of the class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Reinforcing fraction concepts through poems . . . 39Cutting clay “pies” to compare fractions . . . . . . . 41F R AC T I O N F I L L ’E M U PExploring hands-on fractions to compare unlikedenominators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
P RO V E I T !F R AC T I O N A D D -U PPresenting a “legal argument” to prove fractionrelationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Applying logical reasoning to find fractionsums and differences . . . . . . . . . . . . . . . . . . . . . . . . . 63F R AC T I O N W A RSUMSPlaying a card game to compare fractions . . . . . 44Playing a game involving adding, comparing,and ordering fractions . . . . . . . . . . . . . . . . . . . . . . . . 65Mega-Fun Fractions Miller & Lee, Scholastic Teaching ResourcesF R AC T I O N R O L L E RS , PA RT 1ON ARO L LPlaying a logic game to form the greatest andleast fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45F R AC T I O N PAT H P U Z Z L E ST HAT ’ SF R AC T I O N M AG I C F I G U R E SANORDER!Using logic to add and subtract fractions . . . . . . 66Playing a game that involves comparing andordering fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46Using logical reasoning to solvefraction puzzles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68F R AC T I O N SPA RTSOF AD AYOFPA RTSMaking a circle graph based onfractions of a day . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Exploring the concept of multiplyingfractions on grid paper . . . . . . . . . . . . . . . . . . . . . . . 70TIMERO L L , RO U N D,FORF R AC T I O N SUsing fractions to express lengths of time . . . . . . 50C O I N I N G F R AC T I O N SANDRECORDPlaying a game that involves multiplyingfractions and rounding products . . . . . . . . . . . . . . . 72Using fractions to express money amounts . . . . . 51F R AC T I O N SFUNNY MONEYUsing fraction concepts to interpret data incalorie and exercise charts . . . . . . . . . . . . . . . . . . . 74Solving problems that involve fractionsof a set of coins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52F R AC T I O N SANDAGESUsing fractions and mixed numbersto express ages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53F R AC T I O N R O L L E RS , PA RT 2Playing a logic game to form the greatestand least mixed numbers . . . . . . . . . . . . . . . . . . . . . 54N OT I N G F R AC T I O N SExpressing fractions in the form of standardmusical notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55A HEADFORF R AC T I O N SUsing mental math to add (or subtract)fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57F R AC T I O N SINANCIENT EGYPTExploring the fraction notation usedin ancient Egypt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58ANDC A LO R I E SF R AC T I O N S TO R I E SWriting original story problems to be solvedusing fraction concepts . . . . . . . . . . . . . . . . . . . . . . . 76F R AC T I O N S CAV E N G E R H U N TEstimating and measuring to find itemsin fractional lengths . . . . . . . . . . . . . . . . . . . . . . . . . . 77O N LY O N E -T H I R D A G R E E D T HAT Applying fraction concepts in order toanalyze a survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79F R AC T I O N S E V E RY D AYInvestigating everyday uses of fractions . . . . . . . . 80F R AC T I O N Q U I C K I E S . . . . . . . . . . . . . . . . . . . 81R E P RO D U C I B L E S . . . . . . . . . . . . . . . . . . . . . . . . 84A N S W E R K E Y . . . . . . . . . . . . . . . . . . . . . . . . . . . 93F L I C K E R F R AC T I O N S U M SPlaying a board game that involvesadding fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6050 Fabulous Measur
ABOUT THIS BOOKNCTM STANDARDSIn the 2000 edition of Principles and Standards for School Mathematics, theNational Council of Teachers of Mathematics (NCTM) states that students ingrades 3–5 should:Develop understanding of fractions as parts of unit wholes, as parts of acollection, as locations on number lines, and as divisions of whole numbersMega-Fun Fractions Miller & Lee, Scholastic Teaching ResourcesUse models, benchmarks, and equivalent forms to judge the size of fractionsDevelop and use strategies to estimate computations involving fractions insituations relevant to students’ experienceUse visual models, benchmarks, and equivalent forms to add and subtractcommonly used fractionsOUR GOALWe have written Mega-Fun Fractions to provide in one resource a variety ofways for you to immerse your students in fraction concepts. All activitiesaddress one or more of the NCTM fraction standards listed above. The rangeof fraction lessons includes hands-on explorations and activities that invokeproblem solving, reasoning and proving, communicating, connecting, andrepresenting fractions. Cross-curricular activities link fractions to language arts,music, science, art, and social studies.We hope that as you use the ideas in this book in your classroom, yourstudents will develop a deeper understanding of fractions and become morecomfortable with this strand of the mathematics curriculum. Our goal is to fostera strong conceptual understanding that, we believe, will lead to greater easein working with fractions and rational numbers at more advanced levels.THE FORMATMega-Fun Fractions offers activities written directly to the student as well asguided plans to help you present activities to your whole class, to smallgroups, or to individuals. Each lesson begins with a question you may pose tostudents, a learning objective, a list of necessary materials, sequenced steps tofollow (The Plan), and several follow-up ideas. The back of the book has threepages of Fraction Quickies—additional ideas presented in an abbreviatedmanner. You will also find helpful reproducibles and a Fraction Self-EvaluationForm that students complete. Answers appear at the end of the book.ement Activities Scholastic Professional Books5
TEACHER TIPSThe activities in Mega-Fun Fractions are organized according to a very broadoutline, and they are presented in this order:fractions of a regionfractions of a setequivalent fractionscomparing, ordering, and rounding fractionsfractions and measurementadding, subtracting, and multiplying fractionsculminating activitiesMega-Fun Fractions Miller & Lee, Scholastic Teaching ResourcesFeel free to work through the book in any order that suits you. Revisit activities atany time during the year.You may find that some fraction activities are too advanced for your class,whereas others may be too basic. Revise, adapt, or extend tasks to suit yourstudents’ needs.You may choose to use the tasks in this book as full lessons, warm-ups, homeworkassignments, math corner activities, group projects, informal assessments, orportfolio assessments. It’s up to you!Determine the best grouping to suit your teaching style, as well as the learningstyles and levels of your students. Invite students to work individually, in pairs, insmall groups, or as an entire class. Be sure to allow time for sharing andcomparing.Encourage sharing, discussing, analyzing, and summarizing of students’ findings.Establish an atmosphere that promotes intellectual exploration and anappreciation of and respect for one another as mathematicians, thinkers, andproblem-solvers.You may wish to duplicate and distribute the fraction strips (page 84) to providestudents with a ready reference for comparing and ordering fractions. Havestudents color each strip a different color for visual ease.The Prepare to Share feature on many student pages stimulates students to planwhat they wish to say when you summarize the activity. You may wish to askstudents to record their responses and ideas in a math log.Whenever you make manipulatives, such as fraction cards or fraction numbercubes, keep them for use in subsequent activities. If space permits, set up aFractions Center in your classroom where you can store such materials.650 Fabulous Measur
HALFNESSCan you open a book to the halfway page?Can you pour half a glass of water?Can you walk halfway to the classroom doorfrom your seat?G OA L : Students use their visual estimation skills to identify half of a region.M AT E R I A L S : student page 8, various books, water glasses, dried beans or water, coins orMega-Fun Fractions Miller & Lee, Scholastic Teaching Resourcescounters, string, pencils, various measurement tools (rulers, tape measures, scales,and so on)TH E PLAN1Begin by brainstorming with students everyday situations in which people make a quick visualestimate of half. For example:I’ll take half a piece, please.211Fill it up about halfway.Hang it up about halfway between here and the door.The book goes in the middle of the top shelf.322Continue by having students suggest other examples that involve estimating about half of a space, adistance, or a quantity.433Divide the class into pairs or small groups. Give each group a set of materials. Then direct groups totackle the visual estimation activities on page 8. Have students try each task more than once, andnote whether their estimates of half improve or stay about the same.544As students work, guide them to figure out ways to use suitable measurement tools to verify howclose to half their estimates actually are.65 E AC H I N G T I P S5 THave students compare their estimates and strategies with those of other groups.76677Invite discussion of students’ strengths and weaknesses in visual estimation.Ask students to describe orally or write a description of how and why their estimates changed withsubsequent repetitions.Invite students to create other tasks in which they visually estimate half of something.Challenge students to visually estimate “half again” of a distance or quantity.ement Activities Scholastic Professional Books7
Name DateHALFNESSYour senses can help with fractions.It’s great if you can visually estimate half.Work in pairs or small groups. Try each task threetimes to sharpen your fraction estimating skills.Judge how close your estimates are. Do yourestimates get better the second and third time?Mega-Fun Fractions Miller & Lee, Scholastic Teaching ResourcesChoose a book of any thickness. Open it to itsmiddle page.Fill a glass halfway with beans or water.Place two coins or counters a distance aparton the floor or on a table. Then place anothercounter halfway between them.Have two classmates stand a reasonable distance apart. Stand halfwaybetween them.Choose something within the classroom, at a distance from you. Walk halfwaythere. Mark where you started and where you stopped.Use string to make a large, closed irregular shape on a desktop. Place a row ofpencils across it to divide the shape in half.Have a classmate stand tall. Show where half his or her height is.A R E TO SHA R EPREPHow did you check your visual estimates?Did your estimates get better as you went along? Explain.Which kind of visual estimation was the hardest for you? The easiest?8
FILL ALL FOURPlay a two-person game that involves filling regions of a hexagon.G OA L : Students use visual and spatial reasoning skills to fill hexagonal regions.M AT E R I A L S : student page 11, number cube (p. 85), pattern blocks (p. 86)T EACHING T IPSMega-Fun Fractions Miller & Lee, Scholastic Teaching ResourcesGo over the rules of the game with students. Have each student choose a partner. Provide eachstudent with student page 11 and enough pattern blocks to play. As an alternative, students mightplay in two-person teams.Give each student a blank number cube. Guide them as they fill in the cube according to thedirections on page 11.Challenge students to name the fractional amount of the hexagons that are filled at any given pointin the game.Invite students to play several times to sharpen their strategies for mastering the game.Have students compare their game-playing strategies.WHAT ’S IN PETAL, MISSISSIPPI?Identify fractions of regions to answer a riddle.G OA L : Students name fractional parts of a region.M AT E R I A L S : student page 12TEACHING T IPSDuplicate and distribute copies of page 12 toeach student. Explain that if students correctlyname the fractional part of each balloon and fill inthe correct number in the coded answer below,they will figure out the answer to the questionabout Petal, Mississippi.Invite students to develop variations of this puzzlefor classmates.ement Activities Scholastic Professional Books9
WHAT ’S LEFT?Use visual estimation to describe fractional parts.G OA L : Students apply visual and spatial reasoning toname fractional parts of foods.M AT E R I A L S : student page 13T EACHING T IPSDuplicate and distribute copies of page 13 to each student. Explain to students that they shoulduse visual and spatial reasoning to answer each food question.Mega-Fun Fractions Miller & Lee, Scholastic Teaching ResourcesInvite students to develop variations of this page for classmates.FRACTIONS UP A TREEUse visual and spatial estimation to follow fraction clues.G OA L : Students draw a hole that represents where a woodpecker pierced a tree.M AT E R I A L S : student page 14T EACHING T IPSDuplicate and distribute copies of page 14 to each student. Explain that students will use visual andspatial reasoning to draw the position of the woodpecker hole in each tree.Invite students to develop variations of this task for classmates.Translate this exercise into three dimensions by having students do similar tasks with drinking straws,cardboard tubes, interlocking blocks, or clay cylinders.1050 Fabulous Measur
Name DateFILL ALL FOURPlay a two-person game. Each player needs this game board, pattern blocks, and anumber cube labeled so that one face says 12 , two faces say 13, and three faces say 16 .The object of the game is to fill the four hexagons withfractional parts. Each hexagon 1 whole.RULESMega-Fun Fractions Miller & Lee, Scholastic Teaching Resources1 Before you play, find out which pattern block fills12the hexagon. Determine which pattern block1 fills 13 of the hexagon, and which fills 61 of it. Use21 these pattern blocks to play.121 Decide who goes first. That player rolls the fractionnumber cube and takes a pattern block for the32fraction shown. The player puts that block inside22 any hexagon where it will fit. Once a piece has3been placed, it may not be moved.433The next player rolls, takes the corresponding34 pattern block, and puts it anywhere it will fit.5444 In turn, players keep rolling and adding pattern5blocks to the hexagons to fill all four of them.6Any player who rolls a fraction that does not fit in an5556 available space may roll again. If the second rolldoes not fit either, that player’s turn ends.7666 The first player to fill all four hexagons wins.7777S T R AT E G Y H I N TIt’s okay to mix halves,thirds, and sixths in onehexagon as long as eachpiece clearly fits.11
Name DateWHAT ’S IN PETAL, MISSISSIPPI?Since 1976 the town of Petal, Mississippi, has hadsomething that no other town has. What is it?Mega-Fun Fractions Miller & Lee, Scholastic Teaching ResourcesTo find out, look at the balloons. Above each fraction, write the letter of the balloonwhose shaded area shows that fractional 355638A R E TO SHA R EPREPWhat would you expect to see at this unique place in Petal, Mississippi?1216
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assignments, math corner activities, group projects, informal assessments, or portfolio assessments. It’s up to you! Determine the best grouping to suit your teaching style, as well as the learning styles and levels of your students. Invite students to work individually, in pairs, in small groups, or as an entire class.
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Fractions Prerequisite Skill: 3, 4, 5 Prior Math-U-See levels Epsilon Adding Fractions (Lessons 5, 8) Subtracting Fractions (Lesson 5) Multiplying Fractions (Lesson 9) Dividing Fractions (Lesson 10) Simplifying Fractions (Lessons 12, 13) Recording Mixed Numbers as Improper Fractions (Lesson 15) Mixed Numbers (Lessons 17-25)
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Year 5 is the first time children explore improper fractions in depth so we have added a recap step from Year 4 where children add fractions to a total greater than one whole. What is a fraction? Equivalent fractions (1) Equivalent fractions Fractions greater than 1 Improper fractions to mix
Adding & Subtracting fractions 28-30 Multiplying Fractions 31-33 Dividing Fractions 34-37 Converting fractions to decimals 38-40 Using your calculator to add, subtract, multiply, divide, reduce fractions and to change fractions to decimals 41-42 DECIMALS 43 Comparing Decimals to fractions 44-46 Reading & Writing Decimals 47-49
fractions so they have the same denominator. You can use the least common multiple of the denominators of the fractions to rewrite the fractions. Add _8 15 1 _ 6. Write the sum in simplest form. Rewrite the fractions as equivalent fractions. Use the LCM as the denominator of both fractions
(a) Fractions (b) Proper, improper fractions and mixed numbers (c) Conversion of improper fractions to mixed numbers and vice versa (d) Comparing fractions (e) Operations on fractions (f) Order of operations on fractions (g) Word problems involving fractions in real life situations. 42
