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- 1. Grades 2–3BY KAREN BAICKERNew York • Toronto • London • Auckland • SydneyMexico City • New Delhi • Hong Kong • Buenos AiresOrigami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 2. ᨺScholastic Inc. grants teachers permission to photocopy the reproducibles from this book for classroom use. No other part of this publica-tion 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 permission of the publisher. For information regarding permission, write toScholastic Teaching Resources, 557 Broadway, New York, NY 10012-3999.Cover and interior design by Maria LiljaInterior illustrations by Jason RobinsonCopyright © 2004 by Karen Baicker. All rights reserved.ISBN 0-439-53991-9Printed in the U.S.A.1 2 3 4 5 6 7 8 9 10 40 11 10 09 08 07 06 05 04For Joseph Baicker with thanks for all thehelp with math, even though he wouldn’tlet me do it the teacher’s way.Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 3. 3ᨺ3Introduction . . . . . . . . . . . . . . . . . . . . . . 4How to Use This Book . . . . . . . . . . . . . . . . . . . . . . . . . 5Tips for Teaching With Origami . . . . . . . . . . . . . . . 6The Language and Symbols of Origami . . . . . . . . 7Basic Geometric Shapes Reference Sheet. . . . . . . 8ActivitiesTurn a Rectangle into a Square . . . . 9Math Concepts: shapes, patterns, symmetry,spatial relationsNCTM Standard 3What a Card! . . . . . . . . . . . . . . . . . . . . . . . 11Math Concepts: shapes, patterns, size,symmetry, spatial relationsNCTM Standards 2 and 3Whale of Triangles . . . . . . . . . . . . . . . . . 13Math Concepts: size, symmetry, shapes,patterns, spatial relationsNCTM Standards 2 and 3Instant Cup . . . . . . . . . . . . . . . . . . . . . . . . . 16Math Concepts: spatial reasoning, shapes, volumeNCTM Standards 3 and 4Playful Pinwheel . . . . . . . . . . . . . . . . . . . 19Math Concepts: spatial relations, pattern,symmetry, motionNCTM Standards 2 and 3Handy Hat. . . . . . . . . . . . . . . . . . . . . . . . . . 21Math Concepts: spatial reasoning, sequence,symmetry, scaleNCTM Standards 2 and 3Box It Up! . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Math Concepts: multiplication, division, dimensionNCTM Standard 3Noise Popper . . . . . . . . . . . . . . . . . . . . . . . 27Math Concepts: measurement, shape,spatial reasoning, symmetryNCTM Standard 3Itty-Bitty Book. . . . . . . . . . . . . . . . . . . . . 30Math Concepts: spatial reasoning, shapes, symme-try, fractions, multiplication, divisionNCTM Standards 1 and 3Jumping Frog . . . . . . . . . . . . . . . . . . . . . . . 33Math Concepts: shape, measurement,distance, heightNCTM Standards 3 and 4Kitty Cat . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Math Concepts: angles, symmetryNCTM Standard 3Floating Boat . . . . . . . . . . . . . . . . . . . . . . . 39Math Concepts: shape, fractions, areaNCTM Standards 2 and 3Page-Hugger Bookmark . . . . . . . . . . 42Math Concepts: shape, spatial reasoning,symmetry, congruenceNCTM Standards 3Paper Airplane Express . . . . . . . . . . . 45Math Concepts: symmetry, balance,spatial reasoningNCTM Standards 3 and 4Glossary of Math Terms. . . . . . . . . . . . . . . . . . 48Contents1234567109811131214Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 4. 4ᨺ4IntroductionWhy fold? The learning behind the funThe first and most obvious benefit of teaching with origami is that it’s fun and motivating for students.But the opportunities for learning through paper folding go much further. Many mathematical principles“unfold” and basic measurement and computation skills are reinforced as each model takes shape.The activities in this book are all correlated with NCTM (National Council of Teachers of Mathematics)standards, which are highlighted in each lesson.In addition, origami teaches the value of working precisely and following directions. Students will experiencethis with immediacy when a figure does not line up properly or does not match the diagram. Also, becausemath skills are integrated with paper folding, a physical activity, students absorb the learning on a deeperlevel. Origami helps develop fine motor skills, which in turn enhances other areas of cognitive development.Best of all, origami offers a sense of discovery and possibility. Make a fold, flip it over, open it up——and youhave created a new shape or structure!Tactile Learning Suppose youwant to see if two shapes are thesame size. You can measure the sidesto get the information you needabout area. But the easiest way to seeif two objects are the same size is toplace one on top of the other. That’sessentially what you are doing whenyou fold a piece of paper in half.Spatial Reasoning Origami activi-ties challenge students to look at adiagram and anticipate what it willlook like when folded. Often, twodiagrams are shown and the readermust imagine the fold that wasnecessary to take the first imageand produce the second. These arecomplex spatial relations problems——but ever so rewarding when the endresult is a cat or an airplane!Symmetry Origami patterns oftencall for symmetrical folds, whichcreate congruent shapes on eitherside of the fold, and clearly mark theline of symmetry.Fractions Folding a piece of paperis a very concrete way to demonstratefractions. Fold a piece of paper in halfto show halves, and in half again toshow quarters. For younger students,you can shade in sections to showparts of a whole. For older students,you can explore fractions. You caneven show fraction equivalencies.Is of the same as of ?Through paper folding, you can seethat it is!Sequence With origami, it iscritical to follow directions in aprecise sequence. The consequencesof skipping a step are immediateand obvious.Geometry Most of the basicprinciples of geometry——point, line,plane, shape——can be illustratedthrough paper folding. One exampleis Euclid’s first principle, that there isone straight line that connects anytwo points. This postulate becomesobvious when you make a fold thatconnects two points on the paper.For another example, older studentsare told that the angles of a triangleadd up to 180º. Folding a triangle canprove this geometric fact, as you seein the diagrams below. You can alsodemonstrate the concepts ofhypothesis and proof. Predict whatwill happen, and then fold the paperto test the hypothesis.2__31__21__22__3Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 5. Lesson 25ᨺ5How to Use This BookThe lessons in this book are organized from very simple to challenging; all are geared toward theinterests, abilities, and math skills of second and third graders. Both the math concepts and the origamimodels are layered to reinforce and build on earlier lessons. Nonetheless, the lessons also standindependently and you may select them according to the interests and needs of your class, in any order.In each lesson, you will find a list of Math Concepts, Math Vocabulary, and NCTM Standards thathighlight the math skills addressed. At the heart of each lesson is Math Wise!, a script of teaching pointsand questions designed to help you incorporate math concepts with every step on the student activitypage. Look for related activities to help students further explore these concepts at the end of the lessonin Beyond the Folds!Step-by-step illustrations showing exactly how to do each step in the origami activity appear on areproducible activity page following the lesson. Encourage students to keep these diagrams and bringthem home so that the skills and sequence can be reinforced through practice. A reproducible patternfor creating the activity is also included for each lesson. The pattern is provided for your convenience,though you may use your own paper to create the activities. The pattern pages feature decorativedesigns that enhance the final product and provide students with visual support, including folding guidelines and ★s that help them position the paper correctly. To further support students’ work withorigami and math, you may also want to distribute copies of reference pages 7 and 8, The Languageand Symbols of Origami and Basic Geometric Shapes Reference Sheet.Origami on the WebThere are many great websites for teaching origami to children. Here are somerecommended resources:www.origami.com This comprehensive site also sells an instructional video for origami inthe classroom.www.origami.net This site is a clearinghouse for information and resources related to origami.www.paperfolding.com/math This excellent site explores the mathematics behind paperfolding. Although geared for older students, it provides a useful overview for teachers.www.mathsyear2000.org Click on “Explorer” to find some math-related origami projectswith step-by-step illustrations, suitable for elementary students.Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 6. Lesson 26ᨺ6Prepare for the lessonᨺ Try the activity ahead of time ifpossible. Moving through the stepshelps you anticipate any areas ofdifficulty students may encounterand your completed activity pro-vides a model for them to consult.ᨺ Review the Math Wise! section andthink through the mathematicalconcepts you want to highlight.You can find helpful definitions forthe lesson’s vocabulary list in theglossary on page 48.ᨺ Photocopy the step-by-stepinstructions found in the lessonand the activity patterns (or haveother paper ready for studentsto use).Teach the lessonᨺ Familiarize students with the basicfolding symbols on page 7.ᨺ Introduce or review the origamiterminology students will use in thelesson. Note that communication isenhanced when you can describe aspecific edge, corner, or fold withprecision.ᨺ When possible, use the language ofmath as well as the language oforigami when creating these proj-ects. By saying, “Here I am dividingthe square with a valley fold,” youreinforce geometry concepts aswell as the folding sequence. Someof the ideas expressed in the MathWise! notes in the lesson plan maysound sophisticated. Yet, by usingthe proper language as you makethe folds, you will begin to teachstudents concepts that become thefoundation for success with mathin later grades. You’ll be surprisedat how much they grasp in thecontext of creating the origami.ᨺ Demonstrate the folds with a largerpiece of paper. Make sure thepaper faces the way the students’paper is facing them.ᨺ Support students who need morehelp with following directionsor with manipulating spatialrelationships by marking landmarkson the paper with a pencil as yougo around the classroom. You canmake a dot at the point where twocorners should meet, for example.ᨺ Arrange the class in clusters, and letstudents who have completed onefold assist other students. This willfoster cooperative learning andhelp you address all students’questions.Fold accuratelyᨺ Make sure students fold on asmooth, hard, clean surface.ᨺ Encourage students to make a softfold and check that the edges lineup properly to avoid overlapping.They can also refer to the diagramand make sure that the foldedshape looks correct. After theymake adjustments, they can makea sharper crease using theirfingernails.Choose your paperᨺ You can reproduce the patternsin this book onto copy paper.However, you can also use packsof origami paper, or cut your ownsquares. Keep in mind that thinnerpaper is easier to fold. Gift wrap,catalogues, magazines, menus,calendars, and other scrap papercan make wonderful paper for theseprojects. It is best to work withpaper where the two sides, frontand back, are easily distinguished.Encourage students toexplore geometryᨺ Unfold an origami project just tolook at the interesting pattern andthe geometric figures you havecreated through your series ofcreases. Challenge students tocreate their own variations—andmake their own diagrams showinghow they did it.Jumping frog unfoldedTips for Teaching With OrigamiOrigami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 7. Lesson 27ᨺ7The Language and Symbols of Origamiwhite side or back of papercolored side or front of paperfold toward the front(valley fold)fold toward the back(mountain fold)fold, then unfold turn overfoldcreasecutfolded edgeraw edgeOrigami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 8. Lesson 28ᨺ8Squarea quadrilateralthat has fourright angles andfour congruentsides. All squaresare rectanglesRectanglea quadrilateralthat has fourright angles (90°).All rectangles areparallelogramsQUADRILATERALSA quadrilateral is any figure that has four sidesIsosceles trianglea triangle withtwo congruentsides and twocongruent anglesRight trianglea triangle witha right angleIsosceles righttrianglea triangle withtwo congruentsides and oneright angleTRIANGLESA triangle is any figure that has three sidesScalene trianglea triangle withno congruentsides and nocongruent anglesEquilateraltrianglea triangle withthree congruentsides and threecongruent anglesCIRCLEa round shapemeasuring 360ºOVALan egg-shapewith a smoothcontinuous edgePENTAGONa shape withfive sidesHEXAGONa shape withsix sidesOCTAGONa shape witheight sidesParallelograma quadrilateralthat has twopairs of parallelsides andtwo pairs ofcongruent sidesBasic Geometric Shapes Reference SheetCONGRUENTequal in measurementcongruent linesegmentscongruent anglescongruent figures60° 60°Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 9. 9ᨺ9Knowing how to turn a rectangleinto a square is an invaluableorigami technique! It’s also agreat way to teach some basicgeometry. Use rectangular paperof any size. Then invite studentsto use the reproducible tangramspuzzle and geometric shapesreference sheet to furtherexplore basic shapes.Materials Neededpage 10 (steps and pattern), rectangularsheet of paper, page 7 (The Language andSymbols of Origami), page 8 (BasicGeometric Shapes Reference Sheet)Math Conceptsshapes, patterns, symmetry, spatialrelationsNCTM Standardsᨺ analyze characteristics and properties oftwo- and three-dimensional geometricshapes and develop mathematicalarguments about geometricrelationships (Geometry Standard 3.1)ᨺ use visualization, spatial reasoning, andgeometric modeling to solve problems(Geometry Standard 3.4)Math Vocabularyrectanglesquareright angleisosceles right triangletrianglecongruentBeyond the Folds!ᨺ Help students become familiar with the step-by-step directions they’ll read ineach lesson. Distribute copies of The Language and Symbols of Origami, page 7,and review the word and picture cues presented.ᨺ Explore shapes further by distributing the Basic Geometric Shapes ReferenceSheet, page 8.ᨺ Show how you can take a piece of paper with a square corner—any size—anduse it to test various corners in the classroom. If the edges line up with theirpaper, they have found a right angle. Note that if their right angle fits insidethe other angle with extra room, the other angle is bigger. It has a widermouth. If their right angle covers up the other angle, then the other angle issmaller. Find bigger angles and smaller angles around the classroom.ᨺ Distribute How to Make a Square, page 10. After students have madea square from any rectangular sheet of paper, you can try the tangrams activityat the bottom of the page. (For best results, photocopy onto heavier paperor glue onto cardstock.) Give students a little background on the history oftangrams. The tangram is a seven-piece puzzle that has been played in Chinafor over 200 years. Explain that squares, triangles, and rectangles can be usedtogether to make a wide variety of shapes. Challenge students to match thepictures shown and to create their own tangrams activities.Lesson 1Turn a Rectangleinto a SquareWhen we start, the corners of this rectangle are perfectsquare corners. Another word for a square corner is a rightangle. Let’s look around the room and find some right angles.(Point out the corners of the room, tables, books, and so on.) When wemake our fold, we’ve cut this angle exactly in half. And nowwe have two isosceles right triangles, which means that thetwo sides of the triangle that form the right angle are thesame length, or congruent.Now we have an extra shape we have to cut (or tear)away. What shape is this? (rectangle)Let’s open up this triangle. Now we have a perfectsquare. All four sides are the same length. We also have tworight angles. What is the word that describes lines, angles,or shapes that are equal in measure? (congruent)123Math Wise! Distribute copies of page 10. Use thesetips to highlight math concepts and vocabulary for each step.Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 10. 10ᨺ10Lesson 1Tangram Puzzle PiecesYou just made a rectangle into a square. Now you can take a square and make it into a whole lot more! These seven basictangrams shapes can be used to make hundreds of designs. Cut out the shapes below. Then try to make the shapes shownbelow. Or make up your own figures for others to solve. When you’re done, see if you can put them back into a square again.Cut off the extra rectangle, as shown.Or fold the extra paper at the top, using thetop of the triangle as a guide. Crease it well. Tearalong the crease.How to Make a SquareTake a rectangular sheet ofpaper. Bring the bottom rightcorner up, so that the bottomedge and the left side line up.Now open upyour square. Find thetwo triangles!2 31Tip: To tear, fold the creaseback and forth, scoring iteach time with your finger orfingernail. Then hold the paperdown firmly with one hand,and use the other hand to tearthe rectangle away. Keep yourhands close to the fold forbetter control.or creaseand tearOrigami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 11. 11ᨺ11This activity is a simple butimportant introduction to basicmath and origami concepts—please don’t skip it! You mightteach how to make origamicards before a class party orholiday, and tailor the cardsaccordingly.Materials Neededpage 12 (steps and pattern), rectangularpaper or square paper (optional),crayons or markersMath Conceptsfractions, spatial relations, size, symmetryNCTM Standardsᨺ understand numbers, ways ofrepresenting numbers, relationshipsamong numbers, and number systems(Number and Operations, Standard 1.1)ᨺ represent and analyze mathematicalsituations and structures usingalgebraic symbols(Algebra Standard 2.2)ᨺ analyze characteristics and propertiesof two- and three-dimensionalgeometric shapes and developmathematical arguments aboutgeometric relationships(Geometry Standard 3.1)ᨺ apply transformations and usesymmetry to analyze mathematicalsituations (Geometry Standard 3.3)Math Vocabularyhalfquarterfractionline of symmetryBeyond the Folds!ᨺ Ask students to find different ways to express and . Folded paper isone way. Coins and dollars are another. Bar graphs, pie charts, and measuringcups are some others.ᨺ To further explore the “line of symmetry,” let students paint with watercolorson one half of a piece of paper. Then have them fold the page in half, press itfirmly, and open up again. They will have a symmetrical design.ᨺ Make a chart that shows “Folds” in one column and “Sections” in a secondcolumn. If you fold a piece of paper once, you have two sections; fill in the firstrow with 1 (fold) and 2 (sections). Have students fold the paper again (whileit is still folded) in the other direction. Then fill in the chart. Repeat again in theopposite direction again. Have students continue to fill in the chart. Have themtry to determine a pattern. (The number of sections doubles with each fold.)What a Card!1__21__4Lesson 2This fold is called a valley fold. That’s because we’remaking a little valley here. We started with a square, andnow we have two rectangles. The middle line is called the“line of symmetry.” That’s because the line divides therectangle into two halves that are exactly the same. We alsohave an inside and an outside now. Look what else hashappened. The short side is now the long side.& This fold is sometimes called a book fold. Why doyou think it has that name? Let’s unfold it for a minute justto see what’s happened. Look, we have four equal squares.Let’s say the whole card cost $1.00. How much would oneof these squares be worth? (25¢) So that’s a hundred centsdivided into 4 parts.Let’s fold it back up again, following the same steps. Noticehow one side now forms both the inside and the outside ofthe card? The other side is all folded up inside, you see.(Let students discuss and then decorate and fill in their cards. Encouragethem to use a square sheet of colored paper and follow these directions tomake a card of their own.)12 3Math Wise! Distribute copies of page 12. Use thesetips to highlight math concepts and vocabulary for each step.Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 12. 12ᨺ12Lesson 2Cut out the card pattern below.Place the paper facedown, with the ★in the bottom right corner. Fold in half,bringing the top down to meet the bottom.Fold in half again, bringing theleft side over to meet the right.Crease well again.How to a Make Card and Card PatternMake adesign on theback of this pageand fold itbackwards for areversible card!21★____________________________________________________________________________________This card was designed bydate:_______________________where:______________________time:_______________________RSVP:_______________________Decorate and fill in your card!3Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 13. 13ᨺ13Lesson 3Our Whale Pattern page hassome features drawn in. But youmay also want to distribute blueor gray paper and have studentsmake their own.Materials Neededpage 14 (steps), page 15 (pattern)or 6-inch square paperMath Conceptsshapes, patterns, symmetry, spatial relationsNCTM Standardsᨺ analyze change in various contexts(Algebra Standard 2.4)ᨺ analyze characteristics and properties oftwo- and three-dimensional geometricshapes and develop mathematicalarguments about geometricrelationships (Geometry Standard 3.1)ᨺ apply transformations and use symmetryto analyze mathematical situations(Geometry Standard 3.3)ᨺ use visualization, spatial reasoning, andgeometric modeling to solve problems(Geometry Standard 3.4)Math Vocabularysquarediamondtrianglerightleftpointcenterline of symmetryquadrilateralisosceles trianglescalene trianglemultiplydivideBeyond the Folds!ᨺ Make a whole school of whales and put the school on a bulletin board.Make them form an array, with rows and columns. You can teach basicmultiplication from your array.ᨺ Have students use bigger and smaller squares to see how the whales turn outdifferent sizes, depending on the initial square. Show how you can measurethe size by putting the squares, and the whales, on top of each other.1Math Wise! Distribute copies of pages 14 and 15. Use thesetips to highlight math concepts and vocabulary for each step.What shape are we starting with? (A square. You may wish topoint out that the shape is a quadrilateral—a shape that has four sides.)Notice how I turn or rotate the square like a diamond, so thepoint is at the top. Let’s make sure everyone’s paper is facingthe same way. (Encourage the class to look around the room to check forthe correct positioning. Looking from different angles will strengthen theirspatial relations skills.) Sometimes in origami we make folds, onlyto unfold them again! What’s the point? Well, as you’ll see,these folds always come in handy later on! Now we have twonew shapes. What are they called? (They are triangles; you may wishto point out that they are isosceles right triangles, each having a right angleand two sides of the same length.) Find the centerline we just folded.That’s called “the line of symmetry.” That means that theline divides two halves that match.This time we don’t have to unfold it! But look at whatshapes we’ve made. That’s right, two new triangles.(You may wish to note that these are scalene triangles, triangles that haveno sides that are the same length.)Now look how many triangles we have! Let’s count them.(Show students that some triangles are within larger triangles. There are eighttriangles showing, not counting the ones hidden underneath the folds.)Ah-hah! We’re using that line of symmetry again.Now you see why we folded it in the first place!& We just made our last triangle! When we slit the tail,we divided it in two. But it looks like we multiplied it, doesn’tit? That’s because we started with two layers. Go aheadand add some details to your whale—don’t forget to adda blowhole! What shape is that? (a circle)Whale ofTriangles2345 6Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 14. 14ᨺ14Lesson 3Fold the two lower sides to meetthe center fold, or line of symmetry.How to Make the WhaleCut out the whale pattern on page15. Position the square so that it lookslike a diamond with the ★ at the topfacedown. Fold the left point over tomeet the right point. Open it up again.Fold the top point down to meetthe folded triangles.2 31Rotate the shapes so that the longflat line is at the bottom.Fold the right side over to meetthe left side.Fold the left point up along thedotted line to form a tail. Slit the tailalong the cut line. Fold the trianglesout to form the flukes.5 64Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 15. 15ᨺ15Lesson 3Whale PatternFollow the steps on page 14 to create a whale.★✂Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 16. 16ᨺ16Lesson 4This cup really works. It can holdliquid—until the water soaksthrough! You can adapt this modelto make a hanging pocket holder.Start with a bigger sheet ofpaper. At the last step, don’t tuckthe final flap in. Keep the back tri-angle up, punch a hole in it, andhang it up to collect Valentines.You can also punch holes and addstraps to make a little carryall.Materials Neededpage 17 (steps), page 18 (pattern) or6-inch square paper, water (optional)Math Conceptsspatial reasoning, shapes, volumeNCTM Standardsᨺ analyze characteristics and propertiesof two- and three-dimensional geometricshapes and develop mathematicalarguments about geometricrelationships (Geometry Standard 3.1)ᨺ apply transformations and usesymmetry to analyze mathematicalsituations (Geometry Standard 3.3)ᨺ use visualization, spatial reasoning,and geometric modeling to solveproblems (Geometry Standard 3.4)ᨺ understand measurable attributes ofobjects and the units, systems, andprocesses of measurement(Measurement Standard 4.1)Math Vocabularyquadrilateral squaretrapezoid isosceles right triangleparallel diagonalline of symmetryBeyond the Folds!ᨺ Ask students if they think that a square double the size of the original squarewill make a cup that holds double the volume. Then have them conduct anexperiment: Make two cups with different-sized paper and test the volume.Fill the larger cup and then pour it into the smaller cup once. Then dumpthat water (or grains of rice) out, and refill from the larger cup. See how manytimes the smaller cup fills to compare the capacity of the two cups.ᨺ Make a large cup out of a big square of newsprint. Turn it upside down and it’sa hat! Use this activity to discuss the fact that form and function are often amatter of perspective—just like turning the square into a diamond in the firststep. Let students make and decorate their own hats.Instant CupA diamond is just a different way of looking at a square!Let’s make two triangles. For each triangle, two sides are thesame length, and they have a right angle. That makes themisosceles right triangles.We’re making this point (the tip of the angle) meet the dot(a small circle). This bottom part of our cup is called the baseof the triangle. The top point is called the apex.Let’s fold this top triangle down and tuck it in. What kindof triangle is it? (Isosceles right triangle) What makes it so?(two sides the same length, one right angle)& In origami, you often do something to one side andthen repeat the exact sequence on the other side. That isone kind of symmetry. Our final shape is a trapezoid.A trapezoid is a quadrilateral with one set of parallel edges.Which sides are parallel? What would happen with a cup ifthe bottom and top were not parallel? (The liquid would spill out;it wouldn’t balance on a table!)1234Math Wise! Distribute copies of pages 17 and 18. Use thesetips to highlight math concepts and vocabulary for each step.5Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 17. 17ᨺ17Lesson 4Fold up the bottom right cornerto meet the opposite edge. Line upthe corner so that it meets the dot.Crease the fold.How to Make the CupCut out the cup pattern on page 18and place it like a diamond, with the ★in the top point, facedown. Or use asquare sheet, positioned facedown likea diamond. Fold in half, bringing thebottom corner up to meet the top.Fold down the top layer of the tri-angle above, tucking it into the pocketof the cup as far as it will go. Crease.2 31Turn over and repeat steps 2 and 3above tucking in the remaining triangle.4 Gently pinch the sides together toopen your cup.5Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 18. 18ᨺ18Lesson 4Cup PatternThis cup actually holds water. Once you learn this simple model, you’ll alwaysbe able to whip up a cup anytime you’re thirsty and you’ve got paper to fold!★Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 19. 19ᨺ19Lesson 5This classic paper-foldedpinwheel is fun to create andplay with, and it makes agreat model for exploringsymmetry and patterns.Materials Neededpage 20 (steps and pattern), square paper(optional), pencils with erasers, scissors,push pins, glue (optional), crayons ormarkersMath Conceptsspatial relations, pattern, symmetry,motionNCTM Standardsᨺ understand patterns, relations, andfunctions (Algebra Standard 2.1)ᨺ specify locations and describe spatialrelationships using coordinategeometry and other representationalsystems (Geometry Standard 3.2)ᨺ apply transformations and usesymmetry to analyze mathematicalsituations (Geometry Standard 3.3)Math Vocabularydiagonalintersectisosceles right trianglescenterBeyond the Folds!ᨺ Experiment with patterns and using the back and front of the paper:Have students decorate the backside of their pinwheel pattern before foldingit. (Or have them decorate both sides, if they are using different paper.)Ask them to make a design with a repeating pattern or image or to usecomplementary colors or patterns on the opposite sides. Then test what thedesigns look like in motion! Have them take their pinwheels apart and refoldthem from the opposite side. Encourage them to consider how the directionof the folds makes the backs and fronts interconnected and alternating.ᨺ Discuss the fact that motion, in a way, can have a shape. What shape doesthe motion of the pinwheel form? (a circle or a spiral)When we cut along these lines from the corner in, whatdirection are the lines? (diagonal) The cut lines stop beforethey reach the center of the square. Describe what wouldhappen if they continued. (They would come together or intersect inthe middle. If they were cut, you would have four equal triangles.)What are the four different shapes we’re folding?(triangles)Why do our folds allow the pinwheel to spin?(The pockets can catch the air, like a sail.)Tip: If students’ pinwheels do not spin freely, adjust thetension by pulling the thumbtack out slightly. Also adjust theangle of the blades so that they do not hit the pencil.123Math Wise! Distribute copies of page 20. Use thesetips to highlight math concepts and vocabulary for each step.PlayfulPinwheelOrigami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 20. 20ᨺ20Lesson 5The magic ofpinwheels is the waythey look when they’respinning. Make somemore with differentdesigns and givethem a whirl!Place the pattern facedown. Foldthe top right corner to just past thecenter of the square. Do not crease.Hold in place with your finger, or usea dab of glue stick. Repeat this fold withthe other three corners.How to Make a Pinwheel and Pinwheel PatternCut out the pinwheel patternbelow or start with a 6-inch square.Cut along the diagonal lines, makingsure to stop well before the center,as marked. Color in the design.Ask a grown-up to push a thumbtackthrough all layers into the side of the eras-er end of a pencil, so that the folded sidesface out and the flat side faces the eraser.Spin away! If your pinwheel gets stuck,ask a grown-up to help you adjust it.2 31✂Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 21. 21ᨺ21Lesson 6This is the traditional newspaperhat. It may help to do it firston a smaller scale using ourreproducible Hat Pattern,and then try it with big sheetsof newspaper. There is oneadditional step when using thenewspaper sheets (see MathWise! step 3).Materials Neededpage 22 (steps), page 23 (pattern)or newspaper sheetsMath Conceptsspatial reasoning, sequence, symmetry,scaleNCTM Standardsᨺ analyze change in various contexts(Algebra Standard 2.4)ᨺ specify locations and describe spatialrelationships using coordinategeometry and other representationalsystems (Geometry Standard 3.2)ᨺ apply transformations and usesymmetry to analyze mathematicalsituations (Geometry Standard 3.3)Math Vocabularyhorizontalverticalline of symmetryperpendicularisosceles right triangleright anglerectangleHandy HatBeyond the Folds!ᨺ Distribute copies of the tangrams puzzle on page 10, and ask students touse the shapes to make a design for their hats. They can color the shapesand make a design that reflects something about them.ᨺ Use strips of construction paper to make feathers to stick in the hat,Robin Hood-style. This presents another opportunity to explore symmetry.Students can fold a strip in half, length-wise, to make slits on both sides andopen to find a feather shape.We’re starting with a big rectangle. The bigger therectangle, the bigger the hat we’ll end up with. Open upthe page after these two folds, just to take a look at thelines. We have two lines of symmetry—one horizontal andone vertical. These lines are perpendicular—they form rightangles where they cross. How many rectangles do we have?(five: the big one plus the four smaller ones inside)What shapes are we folding down? (triangles) Notice that inorigami when we make a fold on one side, we often repeat iton the other and we get two halves that are exactly thesame. What is the word that means perfect balance orexactly the same on each side? (symmetry)& What is the shape we are folding up? (rectangle)Note: for a newspaper hat, fold the bottom up twice:Fold once to meet the base of the triangle. Then fold again,as described.123Math Wise! Distribute copies of pages 22 and 23. Use thesetips to highlight math concepts and vocabulary for each step.4Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 22. 22ᨺ22Lesson 6Fold in the top corners to meet thecenter line. Crease.How to Make a HatCut out the hat pattern on page23 and place the page facedown withthe ★ in the top left corner. Or use aplain rectangular sheet of paper, or asheet of newspaper opened up. Foldin half right to left. Crease and unfold.Then, fold in half top to bottom andcrease. This time, leave the paper folded.Fold up the top layer of thebottom edge. Turn over and repeaton the other side.2 31Pull out on the sides to open it.Try it on.4Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 23. 23ᨺ23Lesson 6Hat PatternThis page won’t make a hat big enough for you, but you might use it for a doll or anaction figure! Make these same folds on a sheet of newspaper and you’ll be covered!★Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 24. 24ᨺ24Lesson 7This is one of the simplest and mosttraditional origami box designs.With this box, the top and bottomare the same, so fitting themtogether may be a tightsqueeze—unless the lid is madewith a slightly larger rectangle.This activity works best withsturdy paper, so photocopy thepattern onto card stock ifpossible. Using the cover of amagazine also works well!Materials Neededpage 25 (steps), page 26 (pattern) or6-inch square of sturdy paperNote: For paper that’s just the rightweight and gives the box a glossy,colorful finish, use a magazine cover.Math Conceptsmultiplication, division, dimensionNCTM Standardsᨺ analyze characteristics and properties oftwo- and three-dimensional geometricshapes and develop mathematical argu-ments about geometric relationships(Geometry Standard 3.1)ᨺ specify locations and describe spatialrelationships using coordinate geometryand other representational systems(Geometry Standard 3.2)ᨺ use visualization, spatial reasoning, andgeometric modeling to solve problems(Geometry Standard 3.4)Math VocabularyheightvolumetrapezoidparallelBox It Up!Beyond the Folds!ᨺ Challenge students to figure out how to make the top slightly larger than thebottom. They can start with a slightly larger rectangle. But they can also“cheat” on the folding with the cabinet folds. They can make the edges notquite meet the center crease. They can imagine a closet door that can’t quiteclose! Ask them to think about why this will yield a larger box.ᨺ Ask students to explore different ways to make the box stronger. Then havethem list what properties add strength. Possible solutions include: usingheavier paper, making smaller boxes, using double layers, inserting cardboardon the inside.Let’s see if I can express this fold with an equation. WhenI fold it, it’s 1 ÷ 2 = . Now when I unfold it, I can say 1 x 2 = 2.This fold is sometimes called a cabinet fold. Can you seewhy? How would you express one of the “cabinet doors” asa fraction? ( )Now how many sections do we have? (8) So what is thefraction that represents each rectangle? ( ) We started outwith four sections for the “cabinet.” What equation could weuse to show what we now have? (4 x 2 = 8, or 4 + 4 = 8) Isn’tthat strange? When we fold it, we seem to be dividing it!But then when we open it, we’ve actually multiplied!We don’t need to open it up this time! But if we did, howmany sections do you think we would find? (16) You can takea peek and refold it to check your answer!When we fold our triangles, they don’t quite reach themiddle. You know what that tells me? These little sections arenot squares! If they were, the triangles would line up with thecrease, because all of the sides would be the same length.See how we have two trapezoids now! Trapezoids haveone set of parallel lines. But watch when we open it! Theseother sides will become parallel.& Voila! See how something that is two-dimensional,or flat, becomes three-dimensional! That’s why we had tomake all those creases. They formed the sides here, whichgive it the height, or third dimension.12345671__21__41__8Math Wise! Distribute copies of pages 25 and 26. Use thesetips to highlight math concepts and vocabulary for each step.8Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 25. 25ᨺ25Lesson 7Fold each side in half, folding inthe long edges to the center fold.Crease sharply. Unfold.How to Make a BoxCut out the box pattern on page26 and place it facedown with the ★in the upper left corner. Or use an8 by 11-inch rectangular sheet ofheavy paper and position the paperfacedown. Fold in half, right to left.Crease and unfold.Fold in half, top to bottom. Unfold.2 31Fold up the bottom right cornerup along the fold line so that the cor-ner meets the dot. Note that the topedge does not quite reach the centerfold. Crease firmly. Repeat this stepwith the other three corners.Fold in the short edges to meetthe center fold. Crease very sharply.This time, do not unfold.Fold back the edges, away fromthe center, to cover the top part ofthe triangles. Crease these bandssharply.5 64Now form the box by pullingopen the bands.71__2Help shape the corners of the boxby creasing the corners and bottomedges. Flex the sides inward.8Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 26. 26ᨺ26Lesson 7Box PatternMake two of these so your box will have a lid or attach a strip of paperto make a basket with a handle. Use it for paper clips, pennies, rubberbands, your favorite collector cards, hair clips, or any other favorite item!Create adesign on the back,which will showon the inside of yourfolded box. Colorthis side as well,if you wish.★Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 27. 27ᨺ27Lesson 8We know paper can fold, fly, spinand twirl. Add noise-making tothe list of paper’s possibilitieswith this snappy popper.Materials Neededpage 28 (steps), page 29 (pattern) or8 by 11-inch rectangle (loose-leafnotebook paper works best), crayonsor markersNote: The pattern on page 29 mustbe enlarged at least 125% to pop well.Math Conceptsmeasurement, shape, spatial reasoning,symmetryNCTM Standardsᨺ apply transformations and use symmetryto analyze mathematical situations(Geometry Standard 3.3)ᨺ use visualization, spatial reasoning, andgeometric modeling to solve problems(Geometry Standard 3.4)Vocabularyhorizontalparallelquadrilateralright angleNoise PopperBeyond the Folds!ᨺ Have students all snap their poppers in unison. Note how loud it sounds.Next divide the class into two groups. Have one half pop their poppers.Then have the other half snap. Does each group sound about half as loud?Then divide the group into quarters and let each group create the soundagain. Is it a quarter of the original volume? Point out that noise level canbe measured. What are some other things that can be measured?(Answers include: size, weight, volume, distance, speed, time.)Notice that we’re placing our paper horizontally.The longest side is going across. When people name themeasurements for something they usually give the widthfirst. A page of copy paper held this way (show vertically)is considered 8 by 11 inches. Turn it this way, and we’dsay 11 by 8 inches. But it’s the same piece of paper!The shape we end up with here looks a bit like a football.The shape of a football is made to spiral through the air.But this shape will be used to make sound.When we fold the shape in half, we have a shape withfour sides again—a quadrilateral. But there’s somethingspecial about this quadrilateral: two of its sides are parallel,equal distance apart at all points—like train tracks. Whichtwo sides are parallel? (The top and bottom. If students are ready foranother term, you may want to point out that a quadrilateral with two parallelsides is called a trapezoid.)Now we changed the shape again, but it’s still aquadrilateral. Are there any two angles that are the same?(Yes, there are two right angles.) Are there any two sides that arethe same length? (no)& Let’s take a look at it carefully before we use ournoise popper. How do you think we’ll make the noise? Whatkind of sound will be created? (Students may speculate that the trian-gular flap will pop out and make a popping or snapping sound. Show themhow to hold the popper straight down and snap with a flick of their wrists.)12345 61__21__21__2Math Wise! Distribute copies of pages 28 and 29. Use thesetips to highlight math concepts and vocabulary for each step.Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 28. 28ᨺ28Lesson 8Fold the bottom right corner up sothat the right side lines up with thecenter crease. Repeat with the othercorners.How to Make a Noise PopperCut out the noise popper patternon page 29 and place it horizontally,facedown, with the ★ in the upperleft corner. Or use a sheet of loose-leafpaper. Fold in half, bottom to top, andcrease sharply. Unfold.Fold in half, top to bottomand crease.2 31Fold the front flap down, so that thetop edge lines up with the left edge.Turn over and repeat.Fold the top left corner over tomeet the top right corner.54 To snap the popper, pinch flapstogether firmly at the point, keepingyour fingers toward the bottom so theydo not block the action of the innerfolds. Snap your wrist forward andthe inner flap will pop out, making asnapping noise. If it doesn’t come out,loosen it a few times and try again.6pinchheresnap downand popOrigami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 29. 29ᨺ29Lesson 8Noise Popper PatternBang! Pop! See how loud you can snap this noise popper.Who knew paper could make such a racket?★Enlarge thispattern to 125%or larger to create apopper with a greatsound. Or use asheet of loose-leafpaper.Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 30. 30ᨺ30Lesson 9This is an elegant way to makean eight-page book out of a singlesheet of paper and one snip!The secret, of course, is in thefolds. There are dozens ofcross-curricular uses for thisproject—journals, poetry books,invitations, autobiographies,and more.Materials Neededpage 31 (steps), page 32 (pattern) orrectangular sheet of paper, scissors,crayons or markersMath Conceptsspatial reasoning, shapes, symmetry,fractions, multiplication, divisionNCTM Standardsᨺ understand numbers, ways of represent-ing numbers, relationships amongnumbers, and number systems(Number and Operations Standard 1.1)ᨺ understand meanings of operationsand how they relate to one another(Number and Operations Standard 1.2)ᨺ analyze characteristics and properties oftwo- and three-dimensional geometricshapes and develop mathematicalarguments about geometricrelationships (Geometry Standard 3.1)ᨺ specify locations and describe spatialrelationships using coordinate geometryand other representational systems(Geometry Standard 3.2)Math Vocabularyrectangle fractionsline of symmetry quarterseighths right angleItty-Bitty BookBeyond the Folds!ᨺ Students may use the Itty-Bitty Book pattern to create a “My ImportantNumbers Book.” Encourage students to list some of the many numbers thatare important in their lives. Numbers may include phone numbers, addresses,birthdates, grade level, number of classmates, and so on.ᨺ Have students make a blank book. Ask students to use their books to writeand illustrate a number story. For example, Jake had five books out from thelibrary (page 1). He went to the library and returned three books (page 2).But he checked out four more (page 3). How many did he have altogether?(page 4) Answer: Jake had six books (back of page 4).ᨺ Have students start with a blank page and plan a book. Ask them to figureout how the pages will fall when the book is folded. They can use the patternas an example, or open up a folded book and mark the page numbers.We’re going to make some folds and one snip, and turnthis piece of paper into a book. How many pages do youthink we can make?How would we show one of these sections as a fraction?( ) Now suppose we cut this section out. What fractionwould be left? ( )How many rectangles do we have? (five—the four smaller rectanglesplus the whole sheet as the fifth rectangle)Now we have one half of the page showing. The fold inthe middle divides that in half. Half of the half or xequals one quarter ( ). So each of these narrow rectangles isone quarter of our original sheet. Let’s fold it in half again.How many sections are there now? (8) So each section isone eighth ( ) of the whole page.We made our slit on an outer edge. But look now—it’s on theinside. And it’s twice as long! How did that happen? (The cutwas on a fold. When we unfolded, that fold became the middle. The slitwent through two layers. That’s why it’s double length.)Before we fold it in half, let’s count how many pages ourbook has. (8)& Watch what happens to the flat paper as we pushthe ends together. We’ve created a three-dimensional form.123451__21__21__41__81__43__4Math Wise! Distribute copies of pages 31 and 32. Use thesetips to highlight math concepts and vocabulary for each step.6 7Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 31. 31ᨺ31Lesson 9Fold in half, left to right. Crease itsharply, and leave it folded.How to Make an Itty-Bitty BookCut out the book pattern onpage 32 and place it facedown withthe ★ in the upper left corner. Oruse a rectangular sheet, and placeit horizontally, facedown. Fold thepaper in half, top to bottom.Crease and unfold.Fold again in the same direction.Unfold this last step.2 31Fold in half top to bottom, so thatthe two long edges meet.Cut in from the left side to thecenter, following the cut line. Makesure to stop at the middle crease.Open the whole sheet.Push the two outer edges in, sothat the slit opens and the inner pagesare formed. Crease the edges of allpages to make the book.5 64Design your book!7Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 32. 32ᨺ32Lesson 9Book PatternHow can you turn one page into an eight-page book with one little snip?Try this brilliant paper-folding project. Use it to make a mini-journal,or a long card for your best friend.★Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 33. 33ᨺ33Lesson 10This is a popular origami modelthat jumps! Introduce orreinforce measurement skillssuch as distance and height byholding an origami frog-jumpingcontest. You can measuredistance, height, and accuracy.Materials Neededpage 34 (steps), page 35 (pattern) ora 6-inch square of paper, crayons ormarkersMath Conceptsshape, measurement, distance, heightNCTM Standardsᨺ analyze characteristics and properties oftwo- and three-dimensional geometricshapes and develop mathematicalarguments about geometricrelationships (Geometry Standard 3.1)ᨺ specify locations and describe spatialrelationships using coordinate geometryand other representational systems(Geometry Standard 3.2)ᨺ understand measurable attributes ofobjects and the units, systems, andprocesses of measurement(Measurement Standard 4.1)ᨺ apply appropriate techniques, tools, andformulas to determine measurements(Measurement Standard 4.2)Math Vocabularyrectangle triangleintersection perpendicular linespentagon right angleBeyond the Folds!ᨺ In step 2, you can also introduce the concepts of line segmentsusing the top square with the intersecting folds. Label the cornersA (top left), C (top right), D (bottom left), and B (bottom right).Ask students to show you the fold that makes line segment AB. Point out thatthere are two ways that points A and B can be related through folding. One isto make a fold that forms the line segment. The other way is to make a foldin which A and B end up on top of each other. To make that fold, you end upmaking line segment CD! Line segments AB and CD are perpendicular.ᨺ Have a frog-jumping contest and measure the distances in both inchesand centimeters. You may also ask students to guess the distance beforemeasuring and record the accuracy of their estimates.We’re folding a square to make two rectangles. We couldjust start with a rectangle this size, but we make the paperthicker this way. That will help the frog keep its shape andjump better when we’re done.& Look, we’ve made an “X” here. The point where thetwo lines cross is called the intersection. See how we havefour perfect corners at the intersection? That means that thetwo lines are perpendicular to each other.When we’re starting this fold, we have three triangles,plus the bottom triangle that’s part of the house-shape(a pentagon). But we’re collapsing the two side triangles inhalf. That’s five triangles lining up over the bottom triangle.Now if we folded these triangles so that they line upperfectly with the top point, then we couldn’t see the feet.We’ll fold them so they stick out here. Did I just make theangle of the folded triangle bigger or smaller? (smaller/narrower)Take a look at how that changes the length of this edge.This looks a little like a house now. What is this five-sidedshape called? (a pentagon) When we fold these sides in, theshape looks more like a rocket.& First we make a valley fold and then a mountain fold.What letter are we making along the side edge? (Z) Let’smake a big “Z” on the board. Can you see why this shape isspringy? How will this Z-shape design help the frogs to hop?1245367 8Jumping FrogMath Wise! Distribute copies of pages 34 and 35. Use thesetips to highlight math concepts and vocabulary for each step.Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 34. 34ᨺ34Lesson 10Fold the top right corner over tomeet the dot on the left edge. Creaseand unfold. Repeat on other edge, andunfold so that you have an X at the top.How to Make a FrogCut out the frog pattern onpage 35 and place it facedown with the★ in the upper right corner. Or startwith a 6-inch square, facedown. Foldthe page in half, right to left.Fold the top points of the X downto meet the bottom points of the X.Crease and unfold.2 31Take the bottom two points of thetriangle and fold them up to create thefront legs.As you fold the top part downagain, collapse the side triangles inward.Use your fingers to poke the triangles inas you fold. The top becomes a triangle.Crease the sides of the triangle well.Fold the side edges in toward thecenter. Use the fold lines as a guide.5 64Fold in half, top to bottom. Do notcrease this fold sharply; simply bend it.7 Flip over. Fold the top layer in half,bottom to top, away from the legs andhead. Again, do not crease sharply.8 Your frog is ready to hop!Push down on the spot on the frog’sback and release to make him go.8Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 35. 35ᨺ35Lesson 10Frog PatternHop to it with this little jumping frog. Hold a frog-jumping contest withyour own frogs or challenge a friend to a hop-a-thon.★Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 36. 36ᨺ36Lesson 11Make these cat faces with blackpaper and use them as Halloweendecorations.Materials Neededpage 37 (steps), page 38 (pattern) ora 6-inch square of paper, crayons ormarkersMath Conceptsangles, symmetryNCTM Standardsᨺ analyze characteristics and propertiesof two- and three-dimensionalgeometric shapes and developmathematical arguments aboutgeometric relationships(Geometry Standard 3.1)ᨺ use visualization, spatial reasoning,and geometric modeling to solveproblems (Geometry Standard 3.4)Math Vocabularycongruentisosceles right trianglemidpointbaseanglescalene trianglehexagonBeyond the Folds!ᨺ You can display a litter of these cats by hanging a string across the room andthreading it through the top triangle fold of each origami cat. Tape the foldsdown over the string to make them stay in place. For a multiplicationconnection, ask students if cats have nine lives, how many lives are representedby this string of cats? Help them multiply by 9s. You can make this easier bycreating a story in which the cats have two lives each, and have them countby 2s. (Have students who need more support count two ears for each cat.)ᨺ Invite students to create an origami cat with a new piece of paper and drawtheir own cat faces that are exactly symmetrical. They might start by folding theshape gently in half to find the center line (line of symmetry). Have them workoff of this line, drawing eyes, whiskers, eyelashes, and so on in the same place,proportion, and number on each side.Kitty CatMake a valley fold to create two layers of congruent orequal-sized triangles. What special type of triangle is this?(isosceles right triangle)Before we make this fold, let’s find the midpoint, or middle,of the base of the triangle. How can we do that? (fold it in half)Let’s not crease it firmly here; just make enough of a fold tomark the midpoint. Now when we fold these corners up,notice that we are making three congruent or equal anglesat the base.Now that we’ve folded the top down, we can see wherethe ears will be, can’t we? What shape are the ears? (triangles)This kind of triangle has no congruent or equal sides orangles. It’s called a scalene triangle.& If we cover up the ears, what shape does the facebecome? (a hexagon)1234 5Math Wise! Distribute copies of pages 37 and 38. Use thesetips to highlight math concepts and vocabulary for each step.Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 37. 37ᨺ37Lesson 11Fold up the bottom right corneralong fold line. Repeat on the left side,so that the triangles cross.How to Make a CatCut out the cat pattern on page 38and place it like a diamond, with the ★at the top, facedown. Or start with a 6-inch square, facedown. Fold thebottom corner up to meet the top.Fold the top triangle down(both layers) along the fold line.2 31Fold the bottom point up to meetthe top point.4 Turn over and decorate the face ofyour cat.5Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 38. 38ᨺ38Lesson 11Cat PatternMake a bunch of black cats to hang up on Halloween. Or make one bigcat with a large square and a litter of kittens with smaller squares.★Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 39. 39ᨺ39Lesson 12This simple boat will actuallyfloat in water. Use a coin to helpbalance if the boat is too tippy.Materials Neededpage 40 (steps), page 41 (pattern) or6-inch square, crayons or markers,basin of water (optional)Math Conceptsshapes, fractions, areaNCTM Standardsᨺ understand patterns, relations, andfunctions (Algebra Standard 2.1)ᨺ analyze characteristics and propertiesof two- and three-dimensionalgeometric shapes and developmathematical arguments aboutgeometric relationships(Geometry Standard 3.1)ᨺ apply transformations and usesymmetry to analyze mathematicalsituations (Geometry Standard 3.3)Math VocabularyrectangletrianglehexagonareaBeyond the Folds!ᨺ Set up a basin of water and let students have a boat race. Measure speed,distance, and accuracy. Discuss and adjust balance as necessary. Experimentmaking boats from different weights and sizes of paper. Which floats better?Which moves faster?ᨺ This activity, like many, starts with a square. Show students how to determinethe area of a square by counting squares in a grid. Take a fresh 8-inch squareof paper and fold it in half, and then in half again two more times to create8 columns. Open it up and repeat these folds in the other direction to create 8rows. Open it again, and you should have 64 small squares. Tell students thateach square is 1 inch x 1 inch. Count the squares to determine that the areais 64 square inches. Show how you can multiply the width by the height(8 inches x 8 inches) to get the same answer. Explain that they can use thisformula to find the area of any rectangle.Let’s make a book fold. What two shapes do we havenow? (rectangles)How much of the page do we have with this strip here? ( )How much of the page do we have showing now? ( )What shape are these corners? (triangles) And what shapedo we have here when the corners are folded in? (hexagon)When we make this fold, all of the back side of the paperdisappears. It’s all tucked inside here.How do you think this shape helps keep the water out?Many boats have this shape, like a canoe. How does thisshape help it float through the water? (The pointed ends help theboat glide through the water smoothly. A flat front would slow down thespeed and make the boat hard to control.)123Floating Boat456Math Wise! Distribute copies of pages 40 and 41. Use thesetips to highlight math concepts and vocabulary for each step.1__41__2Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 40. 40ᨺ40Lesson 12Fold down the top edge, frontlayer only, to meet the bottom foldededge. Crease.How to Make a BoatCut out the boat pattern on page41 and place the ★ in the upper rightcorner, face up. Or start with a 6-inchsquare, face up. Fold in half, bottom totop. Crease and leave folded.Turn over and repeat step 2.This time, unfold that last fold.2 31Fold in half, top to bottom.Fold the top corners down to thecenter line and crease. Fold the bottomcorners up to the center line andcrease. Make sure to fold all the layers.Separate the top edges to openthe boat. Press down along thebottom and pull out the sides tocreate a flat bottom.5 64Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 41. 41ᨺ41Lesson 12Boat PatternThis simple boat actually floats. Try blowing it across a small tub of water with astraw. Have a boat race with a larger and smaller boat to see which moves faster.★Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 42. 42ᨺ42Lesson 13Students can use this friendlyfolded corner-hugger as abookmark.Materials Neededpage 43 (steps), page 44 (pattern) or6-inch square, crayons or markers,scissors, card stock, index cards, orheavy paper, glueMath Conceptsshape, spatial reasoning, symmetry,congruenceNCTM Standardsᨺ analyze characteristics and properties oftwo- and three-dimensional geometricshapes and develop mathematicalarguments about geometricrelationships (Geometry Standard 3.1)ᨺ use visualization, spatial reasoning, andgeometric modeling to solve problems(Geometry Standard 3.4)Math Vocabularydiamondsquaretriangleperpendicularpentagonline of symmetrycongruentPage-HuggerBookmarkBeyond the Folds!ᨺ Give students book-reading word problems or let them generate their own.Example: Joe read five pages at bedtime. The next morning he got upand read three more. On what page would you find his bookmark?ᨺ Note that this bookmark actually marks two pages——the front and theback of the folio corner it covers. If the bookmark is set on page 11, aright-hand page, what page does it also mark? (12) Suppose you use aregular bookmark——a rectangular strip. If the bookmark is set on page 11,what page does it also mark? (10)As you might know, the diamond is not really a shape.It’s just a square that we’ve rotated so that we see itdifferently. These two lines that we’ve folded areperpendicular to each other. See how the corners wherethey intersect, or cross, are perfect square corners?What fraction of the corners have we folded? ( )Before we make our fold, let’s look at this shape here.How many sides does it have? (5) What do we call a shapewith five sides? (a pentagon)How many sides does our shape have now? (4) We’retaking this big triangle and bisecting it, or cutting it in half,to form two equal, or congruent triangles. Actually, it’s threecongruent triangles, with this other flap here!& We’ve formed a pocket here that can fit on thecorner of our page. There’s another pocket in our bookmarktoo. Can you find it? Could we use this pocket as a bookmarkas well? (no) Why not? (because it’s not shaped like a corner, or right angle)123453__4Math Wise! Distribute copies of pages 43 and 44. Use thesetips to highlight math concepts and vocabulary for each step.6Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 43. 43ᨺ43Lesson 13Fold up the bottom point to meetthe center point. Crease. Repeat withthe left and top corners. Leave theright corner unfolded.How to Make a BookmarkCut out the bookmark pattern onpage 44 and place the square like adiamond with the ★ at the top, face-down. Or start with a 6-inch square,facedown. Fold in half left to right, sothe corners meet. Crease and unfold.Fold in half top to bottom so that thecorners meet. Crease and unfold.Fold down the top left corner tomeet the bottom right corner. Leavethat part folded.2 31Tuck the right hand point insidethe pocket formed by the left-handtriangle.Fold up the bottom left corner tomeet the top point. Crease well.54 Fill in your name on the back.Decorate your page-hugger bookmark.6Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 44. 44ᨺ44Lesson 13Bookmark PatternKeep this bookmark buddy handy and you’ll never lose your place.Thisbookbelongsto____________________________★Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 45. 45ᨺ45Lesson 14There are hundreds of ways tomake paper airplanes. This modelhas good gliding action. Use theairplane pattern on page 47, orany 8 by 11-inch sheet ofcopy paper!Materials Neededpage 46 (steps), page 47 (pattern)or 8 x 11-inch rectangle, paper clipMath Conceptssymmetry, balance, spatial reasoningNCTM Standardsᨺ apply transformations and use symmetryto analyze mathematical situations(Geometry Standard 3.3)ᨺ understand measurable attributes ofobjects and the units, systems, andprocesses of measurement(Measurement Standard 4.1)ᨺ apply appropriate techniques, tools, andformulas to determine measurements(Measurement Standard 4.2)Math Vocabularyhalfcenterweightcornerbisectanglesurface areaPaper AirplaneExpressBeyond the Folds!ᨺ Stage an airplane gliding contest and measure distance and accuracy.For distance, measure the distance between the launch and landing points.For accuracy, measure the distance between a target point and the actuallanding point. Calculate the average distance by compiling the flight recordsof all students.ᨺ Have students decorate their own planes, each wing with a different design.If we take a plain piece of paper and try to throw it, itdoesn’t travel very far! But if we crumple it up, look! We canthrow it much better. Why do different forms of the samepage fly better than others? (The crumpled-up ball has a smallersurface area—most of it is tucked into the center of the ball. Less of the paperhits the air, so it doesn’t slow down the way the open sheet does.) Whenwe fold an airplane, we want to make a design that has notmuch surface area and little wind resistance.Many paper airplanes have a sharp point at the front.Later, we’ll fold this point and make a blunt nose. How mightthe shape at the front affect the way a plane flies? (The shapeof the plane’s nose affects the flight pattern.)We’re folding these angles in half, or bisecting them.In this model you might notice that whatever we do onone side, we do on the other. That’s because planes dependon symmetry for smooth flying. What would happenif the two sides were different? (It would fly crooked.)& What happens to the plane when we fold the noseback? (The nose gets heavier.)& What does the paper clip do to the nose of theplane? (It adds more weight and keeps the sides together tightly, so there’sless surface area and wind resistance.)123475 6Math Wise! Distribute copies of pages 46 and 47. Use thesetips to highlight math concepts and vocabulary for each step.1__21__28Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 46. 46ᨺ46Lesson 14Fold down the top corners to thecenter line.How to Make a Paper AirplaneStart with the paper airplanepattern, page 47, and place the patternfacedown with the ★ in the upperright-hand corner. Fold in half left toright. Make a light crease. Unfold.Fold in each side from the point,to meet the center line. Crease alongthe fold lines.2 31Fold in half, left to right. Crease well.Fold down the tip of the plane’snose toward the middle, along the foldline.Fold down the top layer of the rearwing, along the short fold line. Turnover and repeat on other side.5 64Fold down the wings to the base,starting from the nose. Use the longfold line as a guide. Repeat on theother side.7 Spread the wings. Add a paper clipto the nose for balance and weight.8Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 47. 47ᨺ47Lesson 14Paper Airplane PatternWhat’s the longest distance your plane can fly?★Origami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources
- 48. 48ᨺ48angle the space formed by two linesstemming from a common pointarea the measurement of a space formedby edgesbase the bottom edge of a shapebisect to divide in halfcircle a round shape measuring 360ºcongruent having the same measurementdiagonal a slanted line that joins twoopposite cornersdiamond a square positioned so that onecorner is at the top (A diamond is not adistinct geometric shape.)equilateral triangle a triangle with threecongruent sides and three congruent anglesfraction a number that is not a wholenumber, such as 1/2, formed by dividingone quantity into multiple partshexagon a shape with six sideshorizontal running across, or left to rightintersection the point where two lines crossisosceles triangle a triangle with twocongruent sides and two congruent anglesline of symmetry a line that divides two alikehalvesmidpoint a point that lies halfway alonga lineoctagon a shape with eight sidesoval an egg-shaped figure with a smooth,continuous edgeparallel two lines that are always the samedistance apart, and therefore never intersectparallelogram a quadrilateral that has twopairs of parallel sides and two pairs ofcongruent sidespentagon a shape with five sidesperpendicular at right angles to a linequadrilateral any four-sided figurerectangle a quadrilateral that has four rightangles (All rectangles are parallelograms.)right angle an angle of 90º, which forms asquare cornerright triangle a triangle with a right angle(90º)scalene triangle a triangle with no congruentsides and no congruent anglessquare a quadrilateral that has four rightangles and four congruent sides (All squaresare rectangles.)symmetry a balanced arrangement of partson either side of a central dividing line oraround a central pointtrapezoid a quadrilateral with one pair ofparallel sidestriangle a figure with three sidesvertical running from top to bottomvolume the space contained within athree-dimensional objectGlossary of Math TermsOrigami Math: Grades 2-3 © Karen Baicker, Scholastic Teaching Resources

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