Nature’s Numbers Educator’s Guide Nature’s Numbers Nature’s Numbers 1 Educator’s Guide Dear Educator, Welcome to the Educator’s Guide for the traveling exhibit “Nature’s Numbers”. We hope you and your class will enjoy your trip. Our goal is to generate enthusiasm and a love of math by helping your students see that math is everywhere, even in nature. To that end, the activites in this guide are arranged to support the following ideas: • Nature has some of the same patterns found in math • Mathematical Inquiry • Exploring early math principles The guide contains pre-trip and post-trip activities and a trip sheet for each grade level, but you can mix and match the activies to adapt the guide to your own classroom. We also have an annotated list of book and websites. Have fun at “Nature’s Numbers”! The Franklin Institute 2 Table of Contents 3 Description of exhibit..............................................3 3 K-4 Activities and trip sheet ..................................4 3 5-8 Activities and trip sheet ...................................7 3 9-12 Activities and trip sheet ...............................11 3 Additional resources ...........................................14 Math in Nature The pattern of spots on your dog, the delicate symmetry of butterfly wings, the angular shapes of crystals, and the rugged- ness of a coastline all involve math. “Nature’s Numbers” helps students understand the connections between math and nature with concrete, hands-on interactive exhibits. The exhibit focuses on three main themes: Symmetry and patterns, Sectioning, and Mathematical Inquiry. Many things in nature are symmetrical, such as plants or snow-flakes, and follow a regular pattern. Other natural objects can be sectioned, or divided into different parts, much like a corncob into kernels. Mathematical inquiry forms the basis for our explorations, whether it’s investigating random patterns of chaos or finding different ways to solve a puzzle. 3 K-4 Activities Pre-Trip Activity: Shape Claymation Objective: To discover how 2D and 3D shapes fit and relate to each other. Materials: Clay, plastic knives, pictures of shapes Discuss Before the Activity: Have students name different shapes, both 2D and 3D, around the classroom. Things to Do: 1. Try to find the pictured 3D solids around your classroom. 2. Have your students make solids out of clay. 3. Slice solids. What new 3D shapes do you create? What 2D shapes do you see in the face of the sliced parts? 4. Have students draw the new shapes. 5. Put the solids back together and try slicing in a different way. sphere cylinder cube rectangular solid pyramid cone tetrahedron Extensions: 3 Cut out pictures from magazines and make a collage of natural things and unnatural things. 3 Cut various two-dimensional shapes from construction paper and have students use the shapes to make all the winter objects they can think of, such as trees from triangles, snowmen from circles, and houses from rectangles and triangles. After the Activity: Ask students what they discovered. What can they say about the way different shapes fit together to make a 3D shape? During-Trip Activity to Nature’s Numbers: (see attached trip sheet to guide your visit) Post-Trip Activity: Making Patterns Objective: Create patterns using squares and triangles. Materials: squares, triangles Discuss: Draw a pattern on the chalkboard and ask the children to describe the pattern using the names of the shapes. Repeat with another pattern. Things to do: 1. Distribute the triangle and square blocks. Have the students create a pattern using the triangles and squares, and draw and color their patterns on paper. Repeat the activity using different shapes. 2. Students can write about a pattern that they use every day. Extensions: 3 Grow rock candy crystals and examine the resulting shapes. http://www.exploratorium.edu/cooking/candy/recipe-rockcandy.html 3 Examine patterns on objects in nature, by creating a pattern booklet. 4 K-4 Activities Pre-Trip Activity: Nature Walk Objective: Discover the many ways math is present in nature. Materials: Optional: magnifying glass Things to Discuss After the Activity: What can students say about math in nature? Do they recognize anything in nature seen in the exhibit? Things to Do: 1. Pick a nature spot. It can be anywhere—the schoolyard, a neighborhood park, or the beach. 2. Look carefully at plants and animals. Examine their shapes, count the leaves, flower petals, and legs present. Look for symmetry. During-Trip Activity to Nature’s Numbers: (see attached trip sheet to guide your visit) Post-Trip Activity: Snowflake Symmetry Objective: Cut snowflakes with varying numbers of line of symmetry. Materials: Paper, scissors, pencils Things to Discuss: Review the definition of symmetry. State that symmetry is when you have some-thing that is the same on both sides. Then ask how can we create line symmetry. Demonstrate by drawing a shape with line down the middle of it on the board. This shows that each half is a mirror image of the other. Things to Do: 1. Fold a square piece of paper in half lengthwise, widthwise or diagonally. 2. Trace a pattern on one half of the paper. Cut it out. Or, just start cutting. You can cut on the fold, but make sure you leave some of the fold left. 3. Open it up! How many lines of symmetry does your snowflake have (1)? 4. Can you make a snowflake with two lines of symmetry? Three? How can you make a six-sided snowflake. © 1994 Encyclopedia Britannica Extensions: 3 Cut sponges into different shapes, press into paint and make tessellation patterns. 3 Make a kaleidoscope. 3 Explore symmetry by manipulating pictures of students’ own faces. http://regentsprep.org/regents/math/symmetry/photos.htm 5 K-4 Activities “Nature’s Numbers” K-4 Trip Sheet 1. Find and draw something that reminds you of a butterfly. Why does it remind you of a butterfly? 2. Find one of the puzzles in the exhibit and try to solve it. Draw the solution. How did you figure out the answer? 6 5-8 Activities Pre-Trip Activity: Symmetry Objective: Explore the concept of bilateral symmetry and discover its relevance in nature. Materials: hand mirrors, objects from nature with symmetry (shells, flowers, fruits, honeycomb), geometrical shapes with 3,4,5, and 6 sides. If you divide a symmetrical object, the line Things to Discuss: down which you divide that object is called a 1. Pose the question, “What do you know about symmetry and how we can tell if line of symmetry an object has symmetry?” Discuss a definition. 2. Use a volunteer as a visual example on symmetries in the human body. Ask the students, “Which way could we divide him so that the two halves would be the same? Lead a discussion on how our bodies are not perfectly symmetrical due to uneven facial features, and asymmetrical haircuts. Things to Do: 1. Divide the class into teams. Distribute mirrors. Ask each group to investigate if the shape has a line of symmetry by using their mirrors. When the shape is (If don’t have natural objects use copies of placed in front of mirror, does its reflection complete the whole shape? Does it pictures. Pictures can be folded to test for symmetry) have more than one line of symmetry? Are there pattern from your findings? (The number of sides and number of lines of symmetry will be the same.) 2. Distribute natural objects and look for the lines of symmetry. Extensions: 3 While on a walk, have students find natural and man-made symmetry, like traffic signs. 3 Download SymmeToy, a Windows program for creating paint patterns, symmetry roses, tessellating art, and so forth: http://www.hufsoft.com/software/page4.html During-Trip Activity to Nature’s Numbers: (see attached trip sheet to guide your visit) Post-Trip Activity: Kaleidoscope Objective: See symmetry in the familiar form of a kaleidoscope. Materials: 35mm black plastic film canister, cardboard, overhead projector trans- parency black, construction paper, matte board, margarine tub lid, pin, markers Things to Do: 1. Cut three 7/8" x 1 7/8" rectangles out of the cardboard, transparency, and construction paper. Cut one rectangle of the same size out of the matte board. 2. Puncture a 1/4" diameter eyehole in the center bottom of the film canister. 3. Slide the three rectangles of cardboard into the canister so they form a triangle. Do the same with the construction paper, then the transparency. Set aside. 4. Use the markers to make a colorful design on the outside of the margarine lid. 5. Push the straight pin through the center of the margarine lid then stick it into the edge of the 7/8" side of one of the pieces of matte board. Slide the matte board into the film canister along side one of the cardboard pieces. 6. Hold the kaleidoscope up to the light and slowly turn the wheel. The three mirrors symmetrically reflect the pattern on the lid, which produces the kaleidoscope effect. Extensions: 3 Build a Butterfly Kaleidoscope. http://www.carolina.com/elementary/activities/kaleidoscope/kaleidoscope.asp 3 Have students' describe in a journal what they are seeing (lines of symmetry) in the kaleidoscope designs. 7 5-8 Activities Pre-Trip Activity: Generalized Fibonacci Sequences Objective: To understand Fibonacci sequence and how it is expressed in nature. Materials: pictures of flower petals, cauliflower florets, pinecones, and seed heads Things to Do: 1. Write this sequence 1 1 2 3 5 8 on the board. Ask the students to find the Good site for all things Fibonacci; good illustrations. pattern. (Add the previous two numbers to get the next number in the sequence).