Junk Drawer Geometry: 50 Awesome Activities That Don't Cost a Thing

Junk Drawer Geometry: 50 Awesome Activities That Don't Cost a Thing

by Bobby Mercer

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Overview


Geometry is a hands-on subject. What better way to explore the concepts of area, perimeter, and volume than actually measuring area, perimeter, and volume? With this helpful resource, you will build polygons out of pipe cleaners and flexible drinking straws, explore Mobius strips made from index cards, model the Pythagorean theorem using cheese crackers, and much more. Junk Drawer Geometry proves that you don't need high-tech equipment to comprehend math concepts—just what you can find around the house or in your recycling bin.

Each of this book’s 50 creative geometry projects includes a materials list and detailed, step-by-step instructions with illustrations. The projects also include ideas on how to modify the lessons for different age and skill levels, allowing anyone teaching children to use this to excite students. Educators and parents will find this title a handy guide to teach problem-solving skills and applied geometry, all while having a lot of fun.

Product Details

ISBN-13: 9780912777795
Publisher: Chicago Review Press, Incorporated
Publication date: 10/02/2018
Series: Junk Drawer Science Series
Pages: 192
Sales rank: 322,055
Product dimensions: 5.90(w) x 8.90(h) x 0.20(d)
Age Range: 9 - 18 Years

About the Author


Bobby Mercer has been sharing the fun of science for more than two decades as a high school physics teacher. He is the author of Junk Drawer Physics, Junk Drawer Chemistry, and Junk Drawer Engineering

Read an Excerpt

CHAPTER 1

Geometry Tools

Geometry naturally lends itself to fun tools. Compasses, protractors, and rulers, just to name a few, are staples in math classrooms. Traditional math tools are important, and there are easy, inexpensive ways for students to make some of their own tools. You can also create some new tools out of everyday objects.

Math is not a spectator sport; it should be experienced. People understand math better when they touch it. So let's make some tools to help us learn geometry.

Pencil Compass

Use two pencils, rubber bands, and scrap cardboard to create perfect small circles.

Geometry Concepts: Compasses, circles, radius, and diameter

From the Junk Drawer:

* 2 sharpened pencils
Step 1: Wrap a rubber band several times around the eraser end of two sharpened pencils that are the same length, binding the pencils together. You should be able to pull the sharpened ends of the pencils apart.

Step 2: Cut a piece of scrap corrugated cardboard approximately ½ inch wide by 1½ inches long. Cut a small v out of each short end of the scrap as shown.

Step 3: Slide the notched cardboard between the two pencils. The rubber band should be loose enough that you can move the cardboard up and down. Loosen or tighten the rubber band as needed.

Step 4: Wrap the second rubber band around the two pencils directly below the notched cardboard piece. This rubber band will keep the cardboard from sliding. Your compass is ready to use now.

Step 5: Place a sheet of paper on top of a larger scrap of corrugated cardboard. Use a pushpin or thumbtack to punch a small hole through the paper and cardboard. Put one pencil point in this hole — you want this pencil to remain in place. Hold the top of your Pencil Compass with one hand, then use your other hand to spin the second pencil 360 degrees to draw a circle.

Step 6: Move the notched cardboard piece up or down between the pencils to create different-sized circles. With practice, you can stop using the pushpin and the scrap cardboard under the paper and draw simple circles all day long with your Pencil Compass.

The Math Behind It

Compasses are one of the most useful tools around (pun intended). Compasses allow you to draw circles. Store-bought compasses are a staple in most math classes, but there are several ways to make your own. The distance between the two pencil points is the radius of your circle. The diameter is the complete width of your circle.

Math for the Ages

This activity is suitable for all ages. Younger students should use the scrap corrugated cardboard beneath the paper when drawing circles to help steady their hands.

World's Simplest Compass

A strip of paper, a pencil, and a thumbtack are all you need to draw circles.

Geometry Concepts: Concentric circles, radius, and diameter

From the Junk Drawer:

* Strip of heavy paper (like old holiday cards or recycled magazine covers)
Step 1: Cut a 1-by-6-inch strip of heavy paper. Use a thumbtack or pushpin to poke a hole through one end of the paper. The hole should be centered. Mark that point C for center with a pencil.

Step 2: Using a ruler, mark every inch from the hole to the other end of the paper, as shown. At each mark use the thumbtack to poke a hole big enough for the pencil's lead to go through.

Step 3: Put your sheet of paper on top of the corrugated cardboard. Push the thumbtack through the C point and leave the tack in, but loose enough so the paper spins. This is your compass! Place your pencil lead through one of the holes and simply spin it (and the paper with it) around to draw a circle.

Step 4: Try drawing a bigger or smaller circle by putting your pencil in a new hole. The circles you draw are called concentric circles.

The Math Behind It

Concentric circles are circles with a common center and different radii. The distance from the center hole to the hole with the pencil lead is the radius of the circle. The diameter is the entire distance across the circle, or twice the radius.

Math for the Ages

This is a safe activity for all ages, especially if you use pushpins. Another option is to have elementary and middle school students draw six different-sized circles and then calculate the area of each. Middle and high school students could graph area on the y-axis and radius on the x-axis for each circle they drew. The shape of the graph will be a parabola, which reinforces that area equals pi times the radius of a circle squared (A = π × r2).

Magnetic Triangle Flash Cards

Create large triangles of all the different types — equilateral, isosceles, scalene, acute, obtuse, and right — for Triangle Flash Cards.

Geometry Concepts: Different types of triangles

From the Junk Drawer:

* Scissors
Step 1: Use scissors to cut out different types of triangles from old cereal boxes, file folders, or construction paper. Write the type of triangle on one side with a marker. The common types of triangles are:

Equilateral: each side equal length (and all angles equal)

Isosceles: two sides equal length (and two angles equal)

Scalene: all sides of different lengths

Right: one 90-degree angle

Acute: all angles less than 90 degrees

Obtuse: one angle greater than 90 degrees

Step 2: Use glue to affix a magnet to the back of each triangle. (To hide the magnets, you can cut a small square of the triangle material and cover the magnet with another dab of glue.) You can use almost any old magnet piece, or you can buy magnetic tape in the craft section at most big-box and dollar stores. You only need a small piece, so a roll will go a long way.

Step 3: Place the triangles with the writing side down on any magnetic surface, such as a refrigerator, filing cabinet, or whiteboard. Quiz yourself or friends on the definition and name of each triangle, then flip them over to see if you're right.

The Math Behind It

All triangles have three sides, but they are classified based on their angles and side lengths. Equilateral triangles have three equal sides and three equal angles. Isosceles triangles have two equal sides and two equal angles. Isosceles triangles can also be acute, obtuse, or right triangles, depending on their angles (see below). Scalene triangles have three different angles and three different side lengths.

Right triangles have one angle that is equal to 90 degrees. A right triangle is also classified as an isosceles triangle if the other two angles are 45 degrees each. Acute triangles have three different angles, all less than 90 degrees. Acute triangles can be right, isosceles, or scalene. Obtuse triangles have three different angles, but one angle is greater than 90 degrees. They can be isosceles or scalene, depending on the length of their sides.

This table summarizes the overlap of different types of triangles:

Math for the Ages

Triangles are taught to young children, so this activity is appropriate for almost all ages. And if children learn this at home, they will have a head start when they see it in school. In a classroom setting, you could have groups of students make sets of these magnetized triangles and then place them wherever they'll stick in the classroom. The students can quiz themselves or one another on the different types. This interactive activity gets students out of their seats for a few minutes. Research shows that students perform better when learning is interspersed with physical activity.

For older children, you could label two angle measurements on one side of each triangle with the actual number of degrees. Have the students calculate the missing angle. The interior angles of any triangle add up to 180 degrees. This activity extension would be a great way to practice and apply this fact.

Straw Polygon

Make a convertible polygon.

Geometry Concepts: Quadrilaterals, squares, rectangles, rhombuses, trapezoids, and parallelograms

From the Junk Drawer:

* Scissors
Step 1: Use your scissors to cut your two pipe cleaners in half, making four pieces. These pieces will be the corners of your Straw Polygons. Slide one pipe cleaner piece halfway inside one of your straws. Slide another straw onto the other end of the same pipe cleaner. Leave a small piece of the pipe cleaner exposed to be able to bend into a corner. Repeat for the remaining two straws.

Step 2: Bend one of the straw-pipe cleaner combinations to a 90-degree angle at the joint where the two straws meet. Repeat for the other straw-pipe cleaner combination.

Step 3: Slide a cut piece of pipe cleaner into the open end of one of the already bent straws. Make sure to leave half of the pipe cleaner sticking out of the straw. Now bend the pipe cleaner at 90 degrees. Slide the other combination on the other end of the pipe cleaner. Three of your four straws should now be connected.

Step 4: Bend the last pipe cleaner piece at 90 degrees. Use this piece to make the fourth corner, so all of the straws are connected. With all four sides equal in length and all four angles at 90 degrees, you have a square. By changing angles, you can use the Straw Polygon to show almost all of the four-sided polygons.

Step 5 (optional): If the square is loose or you want a more permanent Straw Polygon, use any glue suitable for plastic. Pull one end of the pipe cleaner piece out of its straw and put glue onto it. Immediately slide it back into the straw. Repeat for all the other corners. Let the Straw Polygon dry completely before continuing to Step 6.

Step 6: Grab opposite corners of your Straw Polygon and gently tug. You now have a rhombus, which is just a lopsided square.

Step 7: Using two hands, stretch out the flexible part of one straw completely, then do the same for the straw on the opposite side. It is OK if the pipe cleaner comes out — just slide it back in. With the angles the same as your rhombus, you now have a parallelogram.

Step 8: Bend all four corners back to 90 degrees and you have a rectangle.

Step 9: Using two hands, slide only the top flexible straw pieces together. If the bottom angles are equal, you have a trapezoid.

Step 10: Though it's harder, by squeezing the flexible parts of the straws to different lengths and making the four inside angles different, you can make a quadrilateral, where no sides or angles are equal. You could also use the scissors to change the lengths of the straws if the Straw Polygon is not glued together.

The Math Behind It

Any four-sided shape is a quadrilateral, so all of the shapes you made are quadrilaterals. But quadrilaterals can be further divided into subtypes. A square is the first quadrilateral students learn about, containing four equal sides and four equal angles. A rhombus is a tilted square, with four equal-length sides and equal opposite angles. A stretched-out rhombus with two sets of equal length sides that are parallel is a parallelogram. A special parallelogram is the familiar rectangle — it has four right angles. One set of parallel sides means you have a trapezoid. Quadrilaterals come in many shapes and sizes.

Math for the Ages

The Straw Polygon is an activity for all ages. Younger children may need supervision while cutting, and help with the glue, if you choose to use it.

Parallel Lines

Draw perfect parallel lines using two books.

Geometry Concepts: Parallel lines, perpendicular lines

From the Junk Drawer:

* 2 books (or any objects with straight lines, like scrap cardboard)
Step 1: Lay one book down on a piece of paper. (You could also use a straight piece of cardboard, like a shoebox lid, or any very straight and hard piece of plastic. You can even use notebooks.) Place the second book with its edge firmly against the first at a 90-degree angle, as shown. The edge of the second book will be perpendicular to the first. Use a pencil to draw a line along the edge of the second book.

Step 2: Slide the second book down the edge of the first and draw another line. The line is perfectly parallel to the first. Slide and repeat as many times as you want.

The Math Behind It

This is actually an old drafting trick using plastic drafting triangles, but you can do it with stuff from your junk drawer.

Parallel lines will never cross. They would go one forever without crossing. The edges of wood flooring and floor tiles are a great place to see parallel lines. The walls of most rooms are also parallel. The lines on notebook paper are one of the best places to see parallel lines at home or school.

Two (or more) perpendicular lines drawn from a single other line will always be parallel to one another.

Math for the Ages

This activity is great for all ages and is a wonderful way to introduce the terms parallel and perpendicular to younger children. High school students would benefit from doing this, even if it only takes them two minutes. This is a great activity to fill the last few minutes of class before the bell rings. And high school students draw parallel lines in graphing functions, statistics, and geometric translations.

Paper Protractor

Learn the most common angles as you build a simple Paper Protractor.

Geometry Concept: Common angles

From the Junk Drawer:

* 8½-by-8½-inch piece of paper
Step 1: Fold your square piece of paper in half. (If you have trouble finding a perfectly square piece of paper, you can cut one yourself with scissors.) Crease the folded edge.

Step 2: Use your pen or marker to draw a dashed line along the fold. Turn the paper so that the center fold is vertical and unfold the paper. Then fold the bottom right-hand corner up until it reaches the creased fold line, with the new fold leading down directly to the lower left corner, as shown. Crease the folded edge down.

Step 3: This is the hardest step to visualize, so take your time. Rotate the paper clockwise until the lower left corner points up. Then fold the bottom up until it aligns with the bottom of your previous fold, as shown. Crease in place.

Step 4: Unfold the paper. The tri-folded angles are all exactly 60 degrees. You can mark the edges with a pen or a marker. If you want to verify the angles, check them with a protractor. This activity proves that a straight line is an angle of 180 degrees, since 3 × 60 = 180.

Step 5: Refold the paper and tuck the bottom triangle underneath the left flap. With a pen or marker, write 30 degrees on both sides of the folded paper on the top. The left triangle is a 30-60-90 degree triangle, so mark the angles as shown in the picture. It is common to draw a rectangle to represent a 90-degree angle.

Step 6: Fold the right triangle flap in half. Crease this line down. The right triangle will be a 15-75-90 degree right triangle.

Step 7: Label the entire top angle 45 degrees. Label the smaller right triangle 15 degrees. This leftmost bottom angle of the skinnier triangle on the right is a right triangle, so label that angle 90 degrees. All triangles have three angles that add up to 180 degrees, so simple math tells us that the lower right angle must be 75 degrees because we already know one angle is 15 degrees and the other is 90 degrees. For a fun option, you can check all of the angles with a protractor. With practice, these angles will be perfect, although they might not be the first time.

Step 8: Unfold the right triangle. The bottom angle will be 150 degrees, and you can label it with a pen.

Step 9: Unfold the left triangle. The bottom angle will be 120 degrees (two 60 degree triangles together). Label it with a pen.

The Math Behind It

Protractors are designed to measure angles. The Paper Protractor will not allow you to measure angles directly; but it will cover most of the common angles that you encounter. The Paper Protractor is also a great way to reinforce that angles on a straight line must always add up to 180 degrees and all triangles have three angles that add up to 180 degrees.

Math for the Ages

This activity is appropriate for almost all ages. It is a great way to introduce angles and let the concept sink in. The more experience children get with angles, the better they can estimate angles; estimation will be a great way to check problems as they get older. If they understand what a 60-degree angle is, they will later solve complicated angle problems more easily. This is a short, fun activity that gives students a break from "doing math" — they will be doing math without even knowing it.

If you have older students who are familiar with geometry theorems, they could prove the angles by measuring the sides and using a few geometry facts.

Cubic Cardboard Boxes

Turn a rectangle cereal box into a cube. It will hold the same amount of cereal but use less cardboard.

Geometry Concepts: Volume, rectangular prisms, and cubes

From the Junk Drawer:

* Ruler
Step 1: Use your ruler to measure the length, width, and height of an empty cereal box in centimeters. (Measuring in centimeters is best since you can easily measure to the nearest tenth of a centimeter. If you measure in inches, you will have to convert the fractions of inches into decimals to multiply.) Then calculate the volume of the cereal box by multiplying the length (a), width (b), and height (c). V = a × b × c.

(Continues…)


Excerpted from "Junk Drawer Geometry"
by .
Copyright © 2019 Bobby Mercer.
Excerpted by permission of Chicago Review Press.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.

Table of Contents

Acknowledgments vii

Introduction ix

Student Whiteboards ix

1 Geometry Tools 1

Pencil Compass 1

World's Simplest Compass 5

Magnetic Triangle Flash Cards 7

Straw Polygon 11

Parallel Lines 16

Paper Protractor 17

Cubic Cardboard Boxes 22

Right Angle String 26

Soup Can Tangents 28

Cereal Box Caliper 32

Angle Machine 36

Yarn and Cardboard Graph Paper 39

Unit Circle Glove 43

X-Y-Z Box 46

2 Geometry Labs 51

A Voyage with Vectors 51

Area and Perimeter Flooring 54

Pipe Cleaner Translations 57

Cheese Cracker Pythagoras 59

Inscribed Angle Circles 61

Linear, Area, and Volume Markers 67

Marshmallow Volume 70

Midsegment Toilet Paper 72

Parallel Paper Plate Proof 75

Radians Are Fun 78

Smartphone Trig 82

Straw Components 85

Straw Triangles 88

Thumbs Up 91

Trig Function Coffee Filter 93

Wheat Cracker Area 98

Diameter of the Sun 101

How Tall Is Your House? 104

3 Fun Geometry Activities 109

Circle Art 109

Circle Art 2 112

Circles into Squares 115

Curved Yarn 119

Flip-Book Fun 123

Freehand Circles 125

Magnet Shapes 127

Math Triangles 130

Mobius Index Card 132

Mobius Strip 135

Paper Cones, Toilet Paper Tubes, and Flashlight Cones 138

Paper Folding 101 142

Recycled Lines of Symmetry 144

String Ellipses 147

T Puzzle 149

Tangrams 154

Tessellations Are Fun 159

Triangular Circle 163

Glossary 169

Solutions 175

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