A Montessori art studio or general Montessori environment using the MAM curriculum has many art form activities that are two- or three-dimensional that allow for a breadth of experiences. Also included are activities that demystify how art is made, how art reflects life in different periods of time, and how an idea can be expressed differently -- all of which allow for a depth of understanding. In Montessori art education, both breadth and depth are controlled by each child. Some children sample all art forms and go back to those that most interested them. Children also choose one or more special work activities which is part of their contract. In my studio they were asked to do special work every time they came to the studio.
This course is a continuation of the MAM Curriculum Section Art Forms I, presenting additional fundamental forms. Some art forms were brought to my attention by parents and became perennial favorites with the children and myself.
Georgie Story
The head of the art education department at my university said at the beginning of her series of classes that a complete curriculum was possible if all you had to work with was paint and clay. Children would develop a deep understanding of making both two- and three-dimensional art. Traditional Art Education at that time described the perfect curriculum as having both breadth and depth. Both of these characteristics were controlled by the teacher. Breadth means that children would have the opportunity to creatively express themselves using a wide range of art forms using a wide range of materials. Depth meant that children exposed to an art form again and again would increase their skill with that art form. Depth also meant the children’s complete exposure to the many factors that influence the understanding of how art is created (see Special Work, in Understanding Art — I and II). In the Montessori environment, both these characteristics are controlled by the child.
The word collage comes from the French word “coller” that means “to glue.” Found images were incorporated into paintings or drawings by Braque and Picasso around 1910. The word assemblage is also used to describe a composition made from scraps, junk, and odds and ends, such as paper, cloth, wood, stone, or metal. Such artworks are usually three-dimensional.
A Collage Center is quite different from a collage tray (see MAM Section Basic Skills). Usually the materials in a tray are meant to decorate another art form. The variety of materials is small. Materials may be added to origami, for instance, to help define what the idea of the piece is, e.g., eyes on an animal shape.
The Collage Center has an enormous variety of materials. These materials, by themselves, can motivate creative ideas in the minds of children and the adults that introduce the art form. It also can accommodate specialty materials such as rub-on letters and numbers, glitter, magazine pictures, larger pieces of cloth, natural materials such as pine cones, sticks, stones, shells, etc.
Prerequisite: Experience using the Basic Skills
Introduction to Traditional Ideas
Introduction to the Art Continuum
(See: The Art Chart and Generating Personal Ideas) Experience using a collage tray
Direct Aim: Creative expression
Indirect Aim: Preparation for photomontage
Point of Interest: “Did you create an idea for your collage by looking at all the materials you could use?”
Materials: 5-12
- A Collage Center: An entire shelf unit or any spaces or structures or cabinets able to house 16–25 containers of different collage materials (See: Resources)
- Heavy background paper – bristol board, railroad board (smooth and colored on both sides), or mat board, different sizes and colors in a container
- 5” x 7”, 7” x 7”, 8½” x 11”, 9” x 9”, 12” x 12”
- Half sheets of paper that have a printed design or texture
- Wire record holder to hold background boards and patterned paper
- Check antique stores, or search eBay with the phrase ‘wire record holder’ (See Photograph)
- Narrow individual add-on file-folder holders
- 2–4 pencils in a container
- A long donut tray to contain all the small items (See: Basic Skills for individual presentations of the following equipment and materials)
- 4 Scissors in a container
- 4 Glue sticks in a container
- 4 2oz. bottles of Elmer’s Glue – with labels removed – in a container (no school glue)
- Caps from individual containers of bottled water
- Or individual empty containers that once held dry watercolor paint
- Or butter dishes
- Plastic toothpicks in a container
- 2–4 Staplers
- 2–4 hole punches ⅛”, ¼” in a container
- 2 Punch tools, as used in Montessori to punch out the shapes of continents
- 2–4 small square rugs for punching
- Alternative punch tool: 4–6 roofing nails (1½” – 2”) in the same container
- 2 sizes of brads in containers
- 2 Punch tools, as used in Montessori to punch out the shapes of continents
- 16–25 different collage materials
- A tray for the presentation
- Envelopes in a container
- A damp sponge from the sink for the presentation
Preparation: All Levels
- Select shelving and containers for each separate collage material (See: Resources)
- Cut the background paperboards and place them in the display container. Include paper with printed designs.
- Fill the donut tray (optional) with all the equipment and materials listed above – line them up in containers
- Note: When presenting to 5s, display only materials and tools you have presented in isolation (See: Basic Skills for detailed plans).
- Put one kind of material in each collage container (Less rather than more).
- Label each container.
- Staple or glue an example on the front of each box or drawer.
- Use words to label the boxes or drawers, especially for 9-12 students.
- If the drawers or boxes are transparent, they may not need labeling.
- Decide on the idea you wish to present. If an idea doesn’t come to you easily, look through all the boxes and see if your idea could be inspired by one or more collage materials.
- Make envelopes to store a few collage materials yet to be used.
- Choose collage materials such as
- Plain and printed paper strips and shapes
- Colored feathers, exotic feathers (cut in half if very big)
- Large and small sequins, flat buttons, small pom-poms
- Precut felt and/or plastic foam shapes
- Strips of lace or ribbon, silver and/or gold rick-rack
- Silk flower parts (new), sprigs or petals of plastic flowers (cleaned if used)
- Strips of raffia, jumbo yarn
- Pieces of colored plastic or cellophane straws
- Strips of chenille pipe cleaners cut into various lengths
- White or silver/gold paper doilies cut into interesting pieces
- Wallpaper shapes or scraps
- Fancy origami paper, wrapping paper, designs printed on tissue boxes
- Small pictures of objects taken from magazines (optional)
- Materials collected by parents.
- The materials may come from their place of work
- I received empty paper bobbins that once held thread for sewing.
- Ask parents for art materials that are no longer needed.
- Ask for used plastic flowers. Clean them before using.
- The materials may come from their place of work
- Label each container.
Note: When giving this presentation to 6-12, I only made one collage for that level. I worked on it for each class. The finished work was displayed when the classes returned. The presentation that follows is a description of the making of a collage landscape I made for 6-9 children. There are other examples of collages made during presentations. Students 9-12 need a presentation only if it is their first experience with this art form.
Presentation:
- See my collage designed for 6-12 students described in this presentation (see photo). Design a simple idea for 5-year-olds (a flower garden, an animal, a kite or airplane in the sky).
- Start your lesson at the Collage Center. Take a tray with you to collect what you need. Use the time to introduce the art form.
- Stop by the sink and get a damp sponge.
- A bowl of damp sponges can be placed where children will be working.
- “This is the Collage Center. Each box contains a different material that you can use to create an idea. On the shelf above the boxes, are glue and the rest of the equipment you will need to make a collage. The word collage comes from the French word “coller” that means “to glue”. Found images were incorporated into paintings or drawings by Braque and Picasso around 1910.”
- Very briefly, open and close a couple of boxes to see what is in them. “Look at all the materials available until you get an idea you want to make.”
- “Choose a color of heavy paper as the background for your idea. Put your name (and room number) on the paper.”
- “I am putting everything I need to start my collage on the tray.”
- Name everything as you put it on the tray: scissors, bottle of glue, a small container, a toothpick, a glue stick, a nail, a couple of brads, a hole punch, and stapler.
- “Don’t forget to get a damp sponge from the sink.”
- "Open and close boxes (drawers) and choose three pieces of collage materials. Get more pieces as you work.”
- “I’m ready to start. I like the dark blue board because I want to make an autumn landscape.”
- “I have a piece of printed paper I like, but I do not know what I am going to do with it yet. I found thin plastic sticks that could make a tall bush that had already lost its leaves. The yellow straw will look like a field of dried corn stalks after they have been cut down.”
- “The printed paper I like has a strip with circles in a row. I will cut the strip out and glue it to the bottom of my collage.”
- Use the glue stick to attach the strip to the bottom of the board.
Uncap the stick. Show how to wind the glue up. Spread the glue on the paper and place on the bottom of the board. Press down. Turn the board over and trim any extra paper that might be sticking out beyond the board.
- “Wind the glue back into the tube and put the cap back on it. Turn the stick over then push down on it until you hear the cap click closed.”
- Make a hole with a ⅛” hole punch in the center of the first circle (left side) on the strip. “I am using the smaller hole punch to make a hole in the center of the circle so I can decorate it with a paper fastener.
- “Sometimes you may wish to put a rug under the work, I can use a nail or punch tool to make a hole in the center of the next circle. Now I can add another paper fastener.”
- Staple the plastic sticks together so they appear to be a tree near the left edge of the board. “I am using two or three staples to create a bushy tree with no leaves near the edge of the board about half way up my board. The tree marks the beginning of a forest of trees and creates enough space for the harvested corn field.”
- Twist a bottle of glue open and put a little in a bottle cap. “Apply the glue with a toothpick or your finger.” Alternate a piece of yellow yarn with a straw placed diagonally across the board to create the corn field. Experiment putting tiny drops of glue on ridged materials like straw, sticks, heavy paper, or buttons. “Gently squeeze the glue bottle to make the glue dots.”
- Demonstrate the following procedure. “My favorite way to clean glue off my fingers is to rub my fingers and thumb over each other until the glue dries and falls off.”
- “I am going to stop the lesson now. Watch where I go to put my work to dry.”
- “Put any materials you need to continue the lesson in an envelope.”
- “Put your name on the envelope and put it with your work in the unfinished work box.”
- “Twist the glue bottle closed and wipe off the end with your damp sponge.”
- When resuming the lesson for another class, present to them how everything was done, then continue creating your collage.
Below are examples of future steps taken in the presentation to continue the making of the collage landscape—however, it was never finished.
- A marker was used to color 10 big toothpicks that represent tree trunks
- Pieces from the paper used to make the bottom strip were used to make the fall leaves on 3 trees
- During each lesson more yarn and straw strips were added to make the corn field.
- Dark green leaves were glued and/or stapled on to represent pine trees. They could have been added all the way across the board.
- Paper fasteners were added one or two at each lesson to make the golden fall tree and finish the decorating the circles at the bottom of the collage.
- Glue was used to create tree leaves with bits and pieces of orange handmade paper. One tree was created with 5 pieces of pasta and another with a strip of crepe paper.
- Enjoy the process of creating your idea while giving your collage presentation(s).
Extensions:
- The idea boxes have the word “collage” in them, so it is possible that collage is selected by itself or in combination with any other art form (See: Generating Personal Ideas).
- See “The Tree” in the introduction to Large Projects. It is a movie made using collage materials to create this stop-motion animation.
- Use the college center as a practical life activity. You will know when each container needs to be sorted, with all pieces of materials that do not belong removed to their original container.
- Choose a container (basket) for any unrelated pieces. Place in your work space.
- Choose one of the drawers or boxes from the collage center and dump out the contents.
- Sort the materials. Place the good pieces back into it container.
- Place non-related pieces into the basket.
- The basket is sorted into trash or placed back into their proper drawer or box.
Resources:
- CollageCenter
- My collage center was one shelving unit 3’ high and 4’ wide that had a top and bottom and 5 interior shelves that held 24 boxes. Later in my teaching career I attached a 2’ high shelf to the Center. It provided a top shelf and had only two interior shelves that held large AkroBins bins for materials that were used to make 3 dimensional art forms. Until Collage Sculpture or Papier Mache was introduced the bins were filled with straw construction activities or different kinds of building blocks.
- Other possible storage containers for a Collage Center
- Target: Sterilite 3 Drawer Small Countertop Unit White with Clear Drawers (model 23758003) - $7.99
- Amazon: Sterilite 20738006 Small 3 Drawer Unit, White Frame with Clear Drawers, 6-Pack - $27.96
- Sources for collage materials
- Railroad board: https://www.dickblick.com/products/pacon-railroad-board/
- com
- Michael’s
- C. Moore (Eastern U.S.)
- Oriental Trading Company
- Fabric stores
- Discount stores
- School supply stores
To prepare for presentation of this art form, become very familiar with every aspect of the Photomontage lesson, from the Georgie Story through Resources, because it incorporates many different basic skills and design principles. The information given here will allow you and your students to experience the fun and pleasure of this unique form.
The object of making a photomontage is to create a new image that looks like a photograph but is made from parts of other photographs. Without a computer this requires advanced cutting and pasting skills to create the illusion of a new photograph. It takes time to master this art form so it is not unusual for some children to create a collage before understanding and producing photomontage.
The first difficult concept to grasp when making a photomontage is to work from the background image to the foreground when pasting down the pieces of the montage with the glue stick. We tend to see the foreground as most important, and beginning students will tend to work on finding the foreground pieces first. Review Understanding Art I – Parts of a Picture Plane (foreground, middle ground, background) as you teach making photomontages. All parts of the picture plane need to be consciously selected. The montage pieces must be saved until they can be pasted down in reverse order from how they usually appear: background first, then middle ground if any, and last the foreground object(s). Students must have large enough envelopes to safely protect their montage pieces until they are ready to use them.
The second difficult concept is the importance of negative shapes and how to cut them out without destroying the positive ones. For clean edges, negative shapes are always cut out, not punched out. The child might need to cut into a positive shape in order reach the negative shape to be eliminated. The cut will disappear when the positive shapes are carefully pasted down. Cutting out the negative spaces can, at times, create fragile pieces of paper that require the skillful use of a glue stick so as not to tear them. I suggest you individually instruct students who need individual attention. It is as simple as knowing where to hold the paper down to support it as the paste is stroked on.”
Georgie Story
A parent asked me if he could present photomontage to his child’s class. I agreed, and afterwards I asked his permission to reproduce his lesson for the rest of my 9-12 students. To start his presentation, the gentleman explained to our students that he made photomontages in his study whenever he needed to relax and forget his stressful work. He searched through magazines for pictures to add to his photo collection until he found an image that sparked an idea. Most of his montages were made from parts of at least 3 or more photographs. His presentation was so well organized that it was easy to understand and use to create my own example for teaching. The following lessons evolved from that.
My 9-12 students were so creative and skilled that a fellow Montessorian asked why I would allow students to display “a magazine photograph” and claim it as their own. I asked him to choose his favorite photomontage and gently run his finger down the image. When he turned around, the look on his face was one of wonder, as he discovered the student’s skillful illusion.
One year, the music teacher and I decided to do a project together for the winter holiday program. He would teach the choir holiday songs which would be illustrated by photomontages made by my 9-12 children. The children in each class were asked to find a working partner.
There were a few three-person groups and a few individuals who chose to work alone. Each group illustrated a portion of the lyrics of a song.
The montages were photographed and then projected onto the stage screen as the choir sang. This process became a school tradition. Once in a while a good idea needs to be changed and in this case it wasn’t. In hindsight it would have been more fun if all the illustrated songs were sung by all the children and special music was sung only by the choir with no images.
Two years after I retired the music teacher invited me to the Holiday Program. The choir was a large group of children who were able to sing music in complicated parts. There were no projected images; the emphasis of the program was on their excellent musical performance.
For the holiday programs, my 9-12 students never had to think of an idea because they were given song lyrics to interpret. They were creating more like graphic designers than like fine artists. One year, several nine year olds chose to make photomontages using their own ideas. The most successful montage was called “Fish Farm.” The foreground was a large hay stack with a fish swimming in the hay. The background was an Amish couple standing in their harvested field. It was done with 3 different photographs.
Every year I asked parents for old magazines (Compulsive, Home and Garden, National Geographic, Scientific American, Sheen, Smithsonian, Travel, Up Scale). They filled an entire closet from the floor to the hat shelf.
Late in my teaching career I began including magazine pictures in a separate box in the collage center box for 6-9 year old children to use. They were creative in integrating a picture of an object or two into their ideas, though they sometimes did not yet have the skill to precisely cut out the object from its surrounding visual material.
Prerequisite: Collage making 6-12 Parts of a Picture Plane: Foreground, Middle Ground, Background Negative shapes (See: Sensorial Materials)
Direct Aim: Creative expression
Indirect Aim: Preparation for advanced media work
Point of Interest: “What inspired your idea for your photomontage?”
Materials: 6-12
- Heavy paper (paperboard, mat board or bristol board)
- You choose the size. Keep in mind the size of the magazines your children will be using.
- They can use a vertical or horizontal format (portrait or landscape) for the work.
- All montages made for the holiday programs were done on a vertical format a bit smaller than the size of the National Geographic magazine.
- Paper trimmer (optional)
- 4-6 scissors in a container
- 4-6 glue sticks in a container (see Resources for recommendations)
- Damp sponges in a container
- A large collection of magazines
- (6-9 only) A collage box with selected small images cut from magazines and a small stack of magazines were provided.
- 1 tray or container for magazines
- Change the magazines often
- 9-12 students were given permission to choose magazines from the closet.
- Large envelopes for keeping all the pieces of the montage
- 9-12: A black and white image of a stool for cutting practice
- Print the stool graphic from the PDF image provided here
- 6-9: if cutting practice is needed for the student’s idea
- Change the magazines often
Preparation: 6-9: This is an optional addition to a regular collage lesson.
- Note: No formal photomontage lesson was given until children were 9-12 years old.
- Create the box of magazine pictures for the collage center that are objects, people etc. Leave some space around the object so the children have cutting practice.
- Provide a supply of additional magazines for children to browse and to find more images.
- The regular collage materials are already present in the collage center.
- Have ready a work of art you are using for the collage presentation. Browse with a child or small group of children and find something you can add to your collage.
- That is as much as I have done with this age group.
Preparation: 9-12
- Make your own photomontage for the presentation. It needs to be in pieces and not pasted down. Prepare a story about how you arrived at the idea. Or, you can use the suggested surrealistic idea below.
- Choose a great photo you like that depicts wide open space like the sky or landscape from far away. You may or may not want anything in the foreground in this background photo. Then collect lots of boats, one kind or many kinds. You will want some small, some medium and some large. Plan to glue them down like they would appear if they were on water. Small ones would be higher on the page, the medium lower, and the largest ones near to the bottom. They may overlap to give a greater sense of space. Have fun thinking of its title.
- If the image has something in the foreground, you can figure out how to make it look like the boats are behind it!
- The front part of a boat can appear to be entering the picture to the right or the very end of a boat leaving on the left.
- Hint: Cut around the positive shapes of the foreground if there are any and attach them after the boats are glued down.
Displayed here is a photomontage I made the last time I gave a photomontage lesson. The idea was about a Christmas tree with gifts placed in a public space. The ceiling was replaced with a “night sky” which was really a photograph of microscopic animals. The star was added. The negative shapes that represent the spaces between the posts (balusters) of the staircase had to be cut up each side so the tree would appear to be behind the staircase. I had to cut into the staircase in order to reach the negative shapes. The toys were placed on the steps so they could be seen; if I had placed them under the tree they would have been hidden by the staircase.
- Feel free to show my Christmas piece in your presentation, to illustrate how the bottom of the tree had to be threaded behind the balusters without glue and was then trapped in place when the stair case was glued down. This situation could occur in your students’ work if needed to create their idea.
- Download and print the stool image for practice cutting.
- With scissors, cut it out yourself to use in the presentation.
- Using the scissors, cut into the positive shapes of the stool along the dotted lines to get to the negative spaces.
- Print and/or project photomontage images found online (See Resources for examples)
- I suggest you preview them. The video has music and the images are shown in rapid succession. The ones you can download and print will allow your students more time to absorb and enjoy them.
- Cut heavy background board to desired size and put in container similar to the one used for collage paper, or use a desk tray
- The photomontage will cover the entire board
- My Christmas photomontage is 9¼” x 6⅜”.
- Place scissors in a container
- Place the glue sticks in a container
- Damp sponges and paper towels from the sink
- Place a collection of magazines in several (4) large AkroBins, on trays or in shallow pans (See: The Uniqueness of Montessori Art Education: Our Environment). Change the magazines when needed.
- My students could go to the cupboard and choose magazines and restore it at clean up time.
- Choose a great photo you like that depicts wide open space like the sky or landscape from far away. You may or may not want anything in the foreground in this background photo. Then collect lots of boats, one kind or many kinds. You will want some small, some medium and some large. Plan to glue them down like they would appear if they were on water. Small ones would be higher on the page, the medium lower, and the largest ones near to the bottom. They may overlap to give a greater sense of space. Have fun thinking of its title.
First Presentation: Choosing the idea
- “I am introducing an art form called Photomontage. The name describes what it is. Photo is short for photograph. Montage is when a new composition is artfully put together from different sources. The object of making a photomontage is to create a new image that looks like a photograph but is made from parts of other photographs. Without a computer, this requires advanced cutting and pasting skills to create the illusion of a new photograph.”
- “You will need an idea before you can start making the montage. I would like to show you several montages made by professional designers. Some are funny, some are a bit scary, but all are very clever and will help you think about ideas of your own.”
- Discuss some of the images. How did the designer make their idea interesting?
- “You can choose a working partner or do the work alone.”
- At this point in the presentation, display the pieces of your own prepared photomontage. Explain the elements of the photomontage to the children and tell them how you were inspired to create it. Keep it short.
Second Presentation: Practice cutting negative shapes, finding pictures for ideas
- “Before you start this work, I am asking you to practice cutting out negative shapes by cutting into positive ones. Watch how I do it.”
- “With scissors, the negative shapes in the stool are more easily cut out while you still can hold onto most of the paper that surrounds a negative shape.”
- “Cut into the positive shapes of the stool by following the dotted line and carefully cut out the negative shapes.”
- “Begin by removing the tiny D shape. Ask for help if you need it”
- Display the finished stool over a darker background surface or a large photograph, to illustrate the result of removing the negative shapes.
- “When you are finished cutting out the stool for practice, start looking for pictures you like. Let the pictures help you generate an idea.”
- “Put your name on a big envelope and store your cut-out stool and all pictures you selected.”
Third Presentation: Pasting the idea down after selected pictures are cut
- Bring your work in pieces for the presentation. Have the backing board for it, a glue stick, a damp sponge and paper towel from the sink.
- Show and explain in what sequence each piece of your montage is to be pasted down. What goes first, etc.
- “Most of you are ready to paste down your work.”
- “Choose a board that is the size of your montage background. Use the paper trimmer if needed to make the board the correct size.”
- “Bring a glue stick, and from the sink bring a damp sponge and paper towel.”
- “Lay out the pieces of your photomontage. You are ready to paste it down if it is exactly the image you want. You must know in what sequence each piece is to be pasted down. If you like, I will check your work before you start pasting.”
- “Start pasting down the background piece(s). Apply the paste and place the background piece that is at the top of the image.”
- “Flatten your hand and pat down the background. If you get paste on your fingers wipe it off with the sponge and dry your fingers again.”
- “Keep your fingers free of paste as you work.”
- “What goes next?”
- “There are two ways to paste down difficult pieces. You can start with the largest part of the piece and paste just that part down. Then the projections or fragile parts can be independently raised from the piece, backed with glue while it is supported by your hand, and then pressed down.”
Note: Display the children’s photomontages on a bulletin board or wall.
Extensions:
- Use photomontages to illustrate a story, a poem, a song, a piece of music done by the children.
- Print the stool on different colors and create a group image on a large sheet of paper. Ask the children to plan an idea. Allow each child to attach their stool so that it contributes to the composition of the idea. Make it into a small bulletin board, hang it in a hallway, put it in the office. Have fun giving it a title.
Resources:
- Paperboard, mat board, bristol board, etc.
- Railroad board: https://www.dickblick.com/products/pacon-railroad-board/
- “When graphic designers get bored” for presentation images
- Video: When Graphic Designers get bored
- Printable images: When graphic designers get bored…Abrasha
- Staples: Avery Glue Sticks – Permanent Acid-Free Photo Safe $3.79
- Highly recommended – large cap and transparent case!
- Amazon Basics All Purpose Washable Glue Sticks
- Old Magazines: Compulsive, Home and Garden, National Geographic, Scientific American, Sheen, Smithsonian, Travel, Up Scale and other interesting ones.
I first introduced drafting during the first year the Children’s House (later renamed Sands Montessori) was open. I had one room for children 5-9. I offered the presentation to any child that had made a drawing that could easily be translated using the drafting equipment. I asked if the child would like to remake the idea using only the drafting tools. Those who chose the work did an amazing job. Unfortunately I did not photograph the results.
Later I gave group lessons to 6-9 children using only the simplest tools. For the 5s, I set up a drafting board with paper already on it and only showed them how to use the straightedge and two different triangles, and a French curve. When we moved into the downtown Sands location, the room for the 9-12 environment came with four full-size drafting tables – 36” or wider. I kept the best two. It was then that I designed learning materials for the use of the equipment. The 9-12 children had every piece of equipment an adult would use. Eventually I decided they were bigger than necessary, and were taking up needed space, so I removed them and purchased drafting boards to use on tabletops.
The size of the drafting board is your choice. A board that is 18” wide with an attached straightedge is easier for the youngest children. For the older group, a 24” board seemed large enough. I started teaching drafting with a 24” board with an attached straightedge. Over time the straightedge failed and I replaced it with a T square for 9-12 students.
Note: This equipment can be used as a teaching tool for geometry lessons. Just add a protractor to this activity. You will enjoy creatively designing these lessons.
Prerequisite: Montessori Math materials
- Names of geometric shapes (5s)
- Beginning geometry lessons: horizontal, vertical, diagonal etc. (5-9)
- Concepts of convergence, divergence, and parallelism etc. (6-12)
Direct Aim: Creative expression
Indirect Aim: To understand the drafting method and its uses for architectural, industrial, and graphic design
Point of Interest: “Would you like to use drafting tools to express an idea that you did as a freehand drawing (painting, print, etc.)?”
“Create an idea while you practice using the drafting tools.”
Note: Read the whole lesson for each age group. Although many features will be the same, reading all of them will make it easier to see how each level is structured to increase the level of difficulty.
Materials:
- The Basic Drawing Language Chart
- 1 Drafting Board 18” with straightedge attached
- The attached straightedge replaces a T-square for younger children (5-9)
- 1 Drafting Board 24” with an attached straightedge: (6-12)
- 1 Drafting Board: 24” 9-12, (optional)
- 1 24” T-square: 9-12 (optional)
- 1-2 Drafting tables with 24” T-square (9-12) (optional)
- 1 Drafting Board: 24” 9-12, (optional)
- Paper: 9” x 12”, 12” x 12”, 12” x 15”, 12” x 18”
- 4 pieces of removable tape for each board: 5-9
- Roll in a dispenser 6-12
- 2 Triangles:
- 1 right-angle scalene triangle: (8” for 5-9, 10” for 9-12)
- 1 right-angle isosceles triangle: (6” for 5-9, 8” for 9-12)
- 1 Set of French Curves for each level
- 1 Adjustable triangle: 9-12 (optional)
- 1 Small dusting brush: 5-12
- 1 Table brush: 9-12 which is larger (optional)
- 1 Drafting compass: 6-12
- Optional for 5s
- 1 Drafting divider: 9-12 (optional)
- 1 Pencil in a container
- 1 Pencil sharpener
- 1 Erase template: 6-12
- 1 Eraser
- 1 tray or container for all the small pieces of equipment
- 1 Dedicated table for drafting and an extra chair for an observer
Preparation: 5-12
- Copy the Basic Drawing Chart provided here on heavy paper and laminate it.
- Use a thin permanent ink pen or marker to make a short horizontal line 3” long in the center of the drawing board 2” down from the top to mark where the top of the paper needs to be placed, so the straightedge can be used to create lines all the way to the bottom of the paper. Instructions for how to make the paper parallel to the top of the drawing board are detailed in Preparation:
- Set up the drafting board on a desk or table, in front of a wall.
- Install the Basic Drawing Language chart directly on the wall behind the drafting board so it can be easily seen.
- Place the paper in a side loading letter tray or on a cafeteria tray near the drafting board.
- Place an observer chair next to the drafting table.
Preparation: 5
- Cut 4 pieces of removable tape and temporarily place them at the top edge of the board.
- Tape paper to the board. The paper is placed on the board (under the straightedge) parallel to the top edge of the board in landscape orientation.
- Line up the paper to follow the clear edge of the straight edge at the prepared line you drew on the board.
- Fold down the corner of each piece of tape and place it diagonally across each lower corner of the paper. (Folding a corner of the tape makes it easier to remove later.)
- Move the straightedge down and place a piece of tape diagonally across each upper corner of the paper.
- Put the 2 triangles and a French curve in a container (AkroBin). Place to the left of the board.
- Place the pencil in a tall container, the eraser in a shallow container.
Preparation: 6-9
- Set up the activity as suggested for the 5s and add more equipment.
- Add the erase template, pencil sharpener, and eraser in a shallow container or tray.
- Add all 3 French curves with the triangles in the Akrobin.
- Put the compass upright in a non-glass container with the pencil.
Note: The compass needs to be checked frequently to assure that the point of the pencil is sharp and aligns with the point of the needle. Every time the pencil is sharpened, the vertical position of the pencil will need to be adjusted in its holder, so the pencil point and needle point align again.
- Place the removable tape in its dispenser. Put it to the right of the board after teaching student how to attach the paper to the board as in Preparation: 5, above.
Preparation: 9-12
- Read the preparations for 5s and 6-9.
- Set up the activity using all the equipment. See the materials list above.
- Put related things together in containers and place them to the left of the drawing board (See 5-9 Preparation)
- Place the removable tape in its dispenser and place it to the right.
Note: In the following Presentations, the Lesson for each age group follows each part of The Basic Drawing Language chart.
Presentation: 5 – Individual Lesson (Group Lesson optional)
- To start the lesson, ask the child to sit at the drafting board. You sit in the observer’s chair. Once the demonstration is started other children may stand or sit to observe the lesson.
- “Drafting is done on a raised board. It is tilted towards you so you can more easily see what you are doing.”
- “Before we had computers, drafting was done using this equipment. It was the only way architects and designers had to draw plans for their buildings or machinery so other people could construct them. This is still an exciting way for you to draw an idea, or to plan a building, a bridge, a train or a car.”
- “Drafting is different from freehand drawing. Freehand drawing is done with only a pencil or a marker in your hand which is free to go anywhere on the paper you wish. Drafting is done with a pencil and drafting tools only. Both freehand drawing and drafting use the Basic Drawing Language that you see on the chart.
- “Your work today will be to have fun using each of the pieces of equipment you have and discover what you can do with them.”
- “This part of the board is called a straightedge because it is perfectly straight and can be moved up and down to make straight lines across the paper. Put both your hands on the straightedge and gently move the straightedge up then down the paper.” Assist the child. If needed, put your hands on theirs.
- “The Basic Drawing Language chart will help you learn to draw using the drafting tools.” Refer to the chart. “The chart shows you that a pencil mark called a ‘point’ might help you decide where on the paper you would like to start a straight line. Put a small dot there. Line up the straightedge with the dot. Now move the pencil point along the straightedge to make a straight line across the paper that looks good to you. It can be long or short.” Wait for the child to do their work.
- Refer to the chart. “There are two triangles that can be used to make lines that are straight up and down or lines that slant or lean over.”
- Give the child the scalene triangle: “This is a triangle that has 3 different sides and each side is a different length.”
- “Look at the chart to see how to place the triangle on the straightedge to make a straight line. Hold both of them steady as you make a straight line down the paper with your pencil.” Assist holding the triangle if needed. “Make the line as long or as short as you wish.”
- Wait for the child to do their work.
- “Place a different side of the triangle on the straightedge and discover what other kind of line you can draw. Remember to hold them together so they don’t move while you’re drawing, then make your new line.” Wait for them to do the work. Assist if needed.
- “Try turning the triangle over and see what happens.”
- “The next picture on the chart shows a second triangle on one of its sides. The two slanted sides look the same because they are the same length. Move the straightedge to a new place on the paper and make slanted lines.” (Suggest the child use the side closest to their dominant side).
- “Place a different side of the triangle on the straightedge and discover what other kinds of lines you can draw.”
- “The last picture is of a French curve. On the chart, the whole shape of the French curve tool was traced onto the board to show you what it looks like. The French curve has many different curves and is not meant to be traced completely as it is on the Chart. See if you can find and trace a special curve that is just one part of the French curve. You will have fun finding ways to use the different curves.”
- “Fill up the paper with lines and shapes you have created with your drafting equipment”
- Remember to ask the child if their work is finished.
- “I will help you remove your work when you are done drafting. You will need to put your name on the back of the work.”
- “Watch how I remove the tape and return it to the top of the drafting board.”
Presentation: 6-9
- Introduce the work as was done in the lesson for 5s.
- Demonstrate how to attach the paper to the board.
- “Cut 4 pieces of removable tape and place them at the top edge of the board.”
- “The paper is placed on the board parallel to the top edge of the board in landscape orientation (if rectangular).”
- “Move the straightedge up over the paper so it lines up with the paper guide near the top of the board.”
- “Line up the top edge of the paper so it follows the clear top edge of the straightedge.”
- “Fold down the corner of each piece of tape before you place it across a corner of the paper. This makes it easier to remove the tape later.”
- “Hold the paper down and tape down the two lower”
- “Move the straightedge down over the paper and tape the two top corners of the paper.”
- “All horizontal lines drawn on the paper with the straightedge will be parallel (going in the same direction as) to the top and bottom of the paper, and to each other.”
- Proceed as with the 5s presentation and introduce the pencil and the first triangle.
- “This is a scalene triangle. A triangle is a three-sided polygon. Tri means three. Each side of the scalene triangle is a different length. Where the sides meet they create three different sized angles.”
- Proceed to show how to place the triangle on the straightedge.
- “Drawing along the vertical edge of the triangle, lines that run up and down on the page will always be parallel (going in the same direction as) to the sides of your paper.”
- “Notice that the vertical line you draw with the triangle is not long enough to go from the top of the paper to the bottom.”
- “If you wish to continue the line, move the straightedge down the paper. Line up the triangle edge to match the first line and continue to draw the vertical line as long as you wish.”
- Introduce the isosceles triangle as in the 5s presentation
- “The right angle isosceles triangle has two sides that are the same length and contains only two different angles.”
- “You can make your diagonal line longer by moving the straight edge down, then line up the triangle with the first diagonal line and make it longer.”
- Introduce the French curves as in the 5s presentation
Note: You can stop the lesson for 6-12 students here to allow the child to use these three pieces of equipment. Continue the lesson another day. Have the child put their name on the back of the drawing, and store it for the next lesson. The compass, the erase template and brush can be introduced during a second presentation.
- “This is the erase template. It is a rectangle of metal with different sizes and shapes of holes in it. As you are working, you may find a mistake in your drawing that you want to erase.”
- “Let’s pick part of a line to erase. Lay the erase template over the line so that the part you want to erase shows through one of the holes.”
- “Choose a hole that shows just the part you want to erase, but covers the nearby parts that you want to keep.”
- “Now erase the part of the line that you can see through the hole.”
- Help the child choose the appropriate hole, and erase the line through the erase template if needed.
- “When you are done erasing, pick up the erase template and put it away.”
- “We will not use our hands to sweep away the eraser crumbs, because we might smear the drawing. Use the small brush to sweep the crumbs off the paper.”
- “The piece of equipment that will make a circle or parts of a circle is called a compass. The further apart the legs of the compass are, the larger the circle.” (This lesson presumes you will use the basic compass which is adjusted by pulling the legs apart. See Resources for Wescott Scholastic Compass.)
- “To use a compass to make a circle:”
- “Be certain that the pencil point and the needle point are the same length.”
- “Pull the compass legs apart a little bit.”
- “Put the needle on the paper where you want the center of the circle, and turn the top knob to make the pencil draw that circle.”
- Assist the child with the compass, if needed. Wait for the child to do their work.
- “I will help you remove your work when you are done drafting. You will need to put your name on the back of the work.”
- “I will show you how to remove the tape and return it to the top of the drafting board.”
Presentation: 9-12
- Introduce the work as was done in the lesson for 5s.
- Demonstrate how to attach the paper to the board.
- Proceed as with the presentation for 5-9 and introduce the pencil and the first triangle.
- Proceed to show how to place the triangle on the straightedge.
- “Notice that the line is not long enough to go from the top of the paper to the bottom.”
- “If you wish to continue the line, move the straightedge down the paper. Line up the triangle to match the first line and continue to draw the vertical line as long as you wish.”
- Introduce the isosceles triangle. “The next picture on the chart shows a second triangle on one of its sides. The two slanted sides are the same size which makes it an isosceles triangle.”
- Move the straightedge to a new place on the paper and hold the triangle and the straightedge to make diagonal (slanted) lines. (Suggest the child use the side closest to their dominant side).
- “You can make your diagonal line longer by moving the straight edge down then line up the triangle with the first diagonal line and make it longer.”
- Introduce the French curve, the erase template, the small brush, and the compass as in the 6-9 presentation.
- Open and close the triangle as you explain how to use it. “An adjustable triangle has a screw when loosened will open the triangle to a new angle. When the screw is retightened the triangle is ready to use. It is a delicate instrument and easily broken. It is not necessary to screw it down tightly. Just enough to hold it in place. It opens easily and tightens easily. Be gentle and it will last a long time.”
- “The divider is a straight legged instrument that has two sharp points.”
- “It allows you to measure and then reproduce the same size somewhere else on the drawing.”
- “I will help you remove your work when you are done drafting. You will need to put your name on the back of the work.”
- “I will show you how to remove the tape and return it to the top of the drafting board.”
- “I will show you how to remove the tape and return it to the top of the drafting board.”
Extensions:
- Suggest that a child
- Draft an idea that was done in another art form such as painting, freehand drawing, printmaking, collage, etc.
- Draft a plan of their bedroom.
- Draft an imaginary house, world, animal, etc.
- Add color using pencils, markers, Simple Watercolor Paint and oil pastels.
- Create a shape that looks 3-dimensional, using the chart called “Draft The Cube” pictured here. Use the drafting tools to follow each step on your own paper. Next, try to draw the same cube freehand!
- “Could you use both freehand drawing and drafting techniques together to make one work of art?”
Resources:
- Drawing paper (see Resources under Tempera Painting)
- Alvin PXB Series Portable Parallel Straightedge Board 18" x 24" (item #PXB24)
- Alvin 24" Transparent Edge T-Square (item #C24)
- Alvin Mini Dusting Brush (item #2340)
- Alvin 3-Piece Hot Pink French Curve Set (item #LX3PK)
- Alvin 8" French Curve (item #FC3391)
- Alvin Stainless Steel Erasing Shield (item #3298)
- A fine inexpensive compass! https://www.michaels.com/westcott-scholastic-compass/10064577.html
- Alvin Introductory 6" Bow Compass/Divider (item #201)
- Alvin 5 1/2" Economy Divider (item #560)
- Amazon: Adjustable triangle: Westcott Triangular Scale (AT-10)
- Amazon: Architectural Drafting: Procedures & Processes by Marcia G. Martin
As a beginning teacher I became enchanted by the Platonic or regular polyhedrons. These shapes were known and studied by ancient philosophers. Plato believed that they were so basic that he could relate the whole universe to them.
They are described as being regular since each side of the polyhedron is a regular polygon having equal sides, equal angles and equal edges. Each edge in a polyhedron is an edge of two polygons in that shape. Having regular sides the shapes are easily made with straws and string.
The shapes can be found as dice for games. They are made out of stone or crystal and sold at mineral shows. Small wooden ones can be bought online. They can be found in home decor stores. The tetrahedron can even be made into a small, medium, or large kite!
Note: Three-dimensional art forms will be fun and challenging for you and the children, because you will be thinking in ways different than those required by two-dimensional forms.
Georgie Story
One Friday, I had several students who could build a tetrahedron and who wanted to make an octahedron. Following the instructions I had for making the shape seemed difficult for me and the students (See: Laycock, Mary. Straw Polyhedra). That night before going to sleep, I thought there must be an easier way to make an octahedron. Saturday morning when I awoke I was being lazy and kept my eyes closed so I could enjoy my warm comfortable bed. The most amazing thing happened while I was resting. I experienced seeing a movie about how to easily make an octahedron. Four upright triangles were tied together at the bottom angles creating a straight line of triangles. The last triangle moved down and to the left and came up to hook onto the first triangle. Now they formed a square in the middle. Each side of the square was the base of a triangle. The two triangles which were horizontally across from each other came up to form four triangles. They were the top of the octahedron. The two triangles vertically across from each other went down together beneath the upper four to form the last four triangles that made the bottom of the octahedron. That weekend I created the book of easy steps for making an octahedron (see photo of the steps installed on cabinet doors). The book enables a child to make the shape with little adult help.
Is there an easy way to make an icosahedron? I failed to find a way. Give it a try.
Prerequisite: Introduction to the Five Platonic Polyhedrons Ability to tie knots: See Basic Skills
Ability to make simple straw triangles
Direct Aim: Simple introduction to creating three-dimensional shapes
Indirect Aim: Creative expression
Point of Interest: “Did you know that one of the polyhedrons can be made into a kite?”
To Introduce the Five Platonic Polyhedrons
Materials and Preparation: 5-12
- An example of each polyhedron made with straws or paper
- Tetrahedron (4 faces, 6 edges, 4 vertices)
- Hexahedron (6 faces, 12 edges, 8 vertices)
- Octahedron (8 faces, 12 edges, 6 vertices)
- Dodecahedron (12 faces, 30 edges, 20 vertices)
- Icosahedron (20 faces, 30 edges, 12 vertices)
- A set of labels with or without accent or syllabication marks
- Make vocabulary cards
- To make paper polyhedrons: https://www.polyhedrons.net/en/
- To make straw polyhedrons: Laycock, Mary. Straw Polyhedra
- Try searching Google for paper polyhedrons patterns to find more
- Tiny wooden set: https://www.mathartfun.com/WoodPoly.html
Modular Origami Dodecahedron: 9-12
Presentation:
- Introduce in the same manner as the Geometric Solids.
Straw Platonic Polyhedrons: 5-12
Materials:
- Straws in a container
- Paper or plastic straws – you choose
Note: Be aware there are many good environmental reasons not to use plastic straws. The subject would be an excellent research project for 6-12 children to pursue.
- String on a holder (See: Resources)
- 4 to 6 scissors in a container
- Models of each step presented using straws
- Written instructions for making each polyhedron (Optional)
- Name tags, strings and pencils in containers
- Envelopes to store flat pieces
- Large opened paper clips
- to hang polyhedrons in progress that are no longer flat
Preparation: 5-12
- Order of presentation: Tetrahedron, Octahedron, Dodecahedron (not rigid when made with straws, however a lesson is included here), Icosahedron.
- [A hexahedron made with straws and string collapses, so no straw hexahedron lesson is included here.]
- Download, print and assemble The Tetrahedron Book and The Octahedron Book included here as pdf files.
- Make a display tetrahedron using instructions below.
- Place on a shelf to the left of the materials.
- Display the steps for making the tetrahedron anywhere they can be seen (see photo of steps on chalkboard).
- Prepare written instructions if using. Place in a container.
- Place the straws, string, scissors, and instructions if any on a shelf, to the right of the display tetrahedron.
- Place name tags and string near the finished work box or with the work.
My Technique for Threading String into the Straws
Example: triangle
- Use the string directly from its holder. It is not measured.
- Hold the straw somewhat horizontally in front of you with the end that receives the string higher than the other end.
- Feed the string into it a little at a time.
- Insert 1½- 2” sections of string into the straw. Release the string. Pick up the string again 2” or more from the straw and push it into the straw.
- Put three straws on the string.
- Slide the straws down further on the string.
- Fold them into a triangle and make sure you have ample string (3”-4”) to easily tie three knots. Cut the string.
- Tie three overhand knots.
- Three overhand knots (granny knot) are taught because young children often say 1, 2, 3, as they make the knots but in reality only make two.
- It is discouraging to children when a polyhedron falls apart because of knots falling open, so tie three at each closure.
A Display Tetrahedron to Introduce the Study of Polyhedrons
Introduction: Best done individually or in small groups.
This is shelf work that precedes the materials for making of straw polyhedrons. Children are curious about the work and eager for its presentation. Later, general information about the common characteristics of the polyhedrons can be introduced with this work in a large group i.e. number of faces, edges, angles, vertices.
Materials
- White paper straws 7-8” long
- String used in food preparation (A heavier string is needed.)
- Sharp scissors
- A wooden bead
- Tacky glue
- A flat basket
Preparation: Display Tetrahedron
Note: For visual reference, download and print The Tetrahedron Book in this section, refer to it while preparing and presenting this lesson, then display it on the shelf with the materials. It is also helpful to display enlargements of the steps on a wall or board (see photo). In these illustrations, each new step is highlighted in red.
- Make a tetrahedron. Use the instructions given below (Presentation: 5-12: Tetrahedron).
- The bead called for in Materials serves two functions when installed
- It keeps the last straw from falling off the end of the string
- It allows the model to be easily opened flat to reveal the structure of the tetrahedron
- For this display model, do not tie the last long string to the top triangle that forms the tetrahedron. Instead, wind it around the top string once to make the tetrahedron stand up. Make sure the string is long enough to hang down into the center of the model (12” – you can cut it shorter if needed)
- Put the bead onto the end of the string and make a knot to hold it on.
- Rub tacky glue on the knot and end of the bead to secure it.
- Place the tetrahedron in a shallow basket or on a tray.
- Display it in the environment with the materials for making straw polyhedrons.
Presentation: Display Tetrahedron 6-12
Note: For 5 year olds, consider presenting your straw model without the technical terms “faces”, “edges”, and “vertices”. Introduce these terms later in a second presentation, at your discretion.
- “This is a model of a tetrahedron. It has four sides called ‘faces’. Each face is a triangle.” Count the faces.
- “I can unwind the string and open this model of the tetrahedron and lay it out flat.”
- “It is made of 6 straws which are called the ‘edges’ of the tetrahedron.” Count the edges.
- “The point at which 2 or more straws meet is called a ‘vertex’.” Count the vertices. [Note: the single straw in the open (flat) position only meets at one point.]
- “When I connect the last straw to the other two triangles, the tetrahedron is complete.”
- “The one last straw adds two more triangles. Each straw is an edge of one triangle and the triangle next to it! This is true of the edges of all”
- Put it back together and place it in the environment after the presentation, to be investigated again.
- Add more information if you wish.
Presentation: 5-12: Make a Straw Tetrahedron
- “Put 3 straws on a string, make sure you have ample string on each end (3”--4”) to easily tie 2 or 3 knots.”
- “Fold the straws into a triangle, cut the string and tie the knots.”
- “To add another triangle put 2 straws on a string, again leaving enough string on the ends to tie knots.”
- “Tie the free end of the string holding the 2 straws to one of the bottom angles of the first triangle. Make 2-3 knots.”
- “Slide the two straws on the string to meet the first triangle. Make sure you have ample string on the loose end to easily tie 2-3 knots.”
- “Fold the 2 straws up to the next angle of the first triangle and make 2-3 knots. You now have 2 triangles.”
- “Notice, the straw between the two triangles is a part of the triangle above and the triangle below. When the tetrahedron is complete each straw is the edge of two triangles.”
- “Put 1 more straw on a string to complete the tetrahedron.
- “Tie the string between either of the points where 2 straws meet. Make the string long enough to make 2-3 knots.”
- “Pull the single straw and the opposite triangle up and tie them together with 2-3 knots.”
- “With this one straw attached, you have added two more triangles which completes the tetrahedron.”
- “Remember, the tetrahedron has four sides. Each triangular side is called a face. Each triangle shares an edge with 1 other triangle. Because they share edges only one straw was able to create two more faces.”
- “The sharing of edges is true of all Platonic Polyhedrons.”
- Trace its edges with your finger to reveal this characteristic of the tetrahedron.
- “In a tetrahedron, there are four points where three straws meet called a vertex. A tetrahedron has four vertices.”
Second Presentation: 6-12
Introduction:
Simple tetrahedrons (single cell) such as the one presented above can be combined to make larger tetrahedrons; it is the only polyhedron that has that multi-cell characteristic. This is ideal as a 6-9 activity, and for 9-12 if they have not yet made polyhedrons. It creates a flurry of activity as the children want to make a bigger and bigger multi-cell tetrahedron, until they are satisfied with its size. The biggest tetrahedron we ever made was a 64 cell tetrahedron which was given as a gift to the school secretary.
While on a teacher exchange program in China, I introduced this work to a group of elementary students. They too made a 64 cell tetrahedron. One way of making a bigger one is to interest 256 children into each making one tetrahedron. Think ahead as to where you can put a large sculpture. A 16 cell will go through a doorway, a 64 cell might, and a 265 cell will not! Enjoy!
Materials:
- 4 tetrahedrons
- String
- Scissors
Presentation: 6-12
- “The tetrahedron has 4 triangular sides.”
- “I am going to attach these 4 one-cell tetrahedrons together to form 1 larger multi-cell tetrahedron.”
- “Tie three cells together so they form a negative triangle on the floor.” Do this.
- “There are three top vertices to which the 4th tetrahedron is attached.” Show them.
- “To complete the 4 cell tetrahedron, tie each of the bottom three vertices of the 4th tetrahedron to one of these top vertices.” Do that.
Single Cell Tetrahedron Kite
Introduction:
A tetrahedron made with 6 straws is a single cell. A single cell tetrahedron can be made into a kite. It is called a city kite in Steven Caney’s Toy Book Reissued (See: Resources).
To make a kite, cover two sides of the tetrahedron to make a “sail” with thin paper such as tissue paper or tracing paper, newsprint paper, or Dippity Dye paper. Below is an example of a sail pattern to print and cut out of laminated heavy paper. (See photo, and downloadable PDF file to print pattern.) The pattern here is sized for standard paper straws 7.75” long; it can be enlarged for use with longer straws. Fold in and glue down extra paper on the sides (flaps) with glue stick to hold the paper onto the straws. Color the sails with watercolor paint if desired.
The kite is flown point-down, which is opposite to the way it is placed on a table. The bridle on a tetrahedron kite is a slack string tied on from the bottom straw up to the top of the straw which is covered by the fold in the sail. It needs to be long enough for a loop knot to be made ¾ of the way up the kite. The flying string is attached to the loop. Happy Sailing!
Make four complete single cell tetrahedrons, and they can be connected and stacked to make a large multi-cell kite. Tie three cells together so they form a negative triangle on the floor. The sails must all be facing the same direction. The last cell is tied to the bottom tetrahedron so that its sail is facing in the same direction as those beneath it. Any size tetrahedron can be made into a kite.
Note: There are many online sites that explain how to make a tetrahedron kite. Here’s one I like https://youtu.be/qZUKTyRtL0Y to use with the following suggestions:
- The video shows an interesting alternative way to make the basic tetrahedron for 9-12 children.
- My preference is to use glue stick rather than plastic tape to adhere the flaps of the sails.
- For better kite control, I suggest tying the bridle across the entire edge of the kite, from the outside point of the first cell to the outside point of the last cell (regardless how many cells make up the kite).
Presentation: 6-12: Octahedron
Note: For visual reference, download and print The Octahedron Book in this section, refer to it while preparing and presenting this lesson, then display it on the shelf with the materials. It is also helpful to display enlargements of the steps on a wall or board (see photo). In these illustrations, each new step is highlighted in red.
- “Make 4 straw triangles. Make the knot and strings the top of each triangle. The string will be used to finish the octahedron. Do not trim.”
- “Line the 4 triangles up in a row. Use a piece of string and attach them to each other where two bottom angles meet.”
- “Move the right bottom angle of triangle 4 around to the left bottom angle of triangle 1 (forms a square in the center) and tie 2-3 knots.”
- “Arrange the triangles so that the bottom of each triangle forms 1 side of a square.”
- “Tie together the tops of the two triangles which are vertically across from each other. The spaces between these form two more triangles to complete the top of the octahedron.”
- “Move down and tie together the two triangles across from each other horizontally beneath the upper four, to form the last four triangles that make the bottom of the octahedron. Trim the strings.”
Motivational Presentation of a Dodecahedron: 5-12
Introduction:
I found this activity in a math book in my husband’s library (See: Resources). It was a favorite with children and adults, and became shelf work after I presented it. I gave the motivational presentation of a dodecahedron to all levels. This version motivates children to make a dodecahedron, yet isn’t necessarily the version they make. For 5-9, an activity using half of the dodecahedron shapes to make a nest became popular, as outlined below. A more fulfilling activity for 9-12 is described later as a “modular” version.
Materials:
Note: This dodecahedron is made with heavy paper because a straw-and-string construction of this polygon is not very stable.
- 2 halves of a dodecahedron made of heavy paper
- 1 large rubber band in a container
- Label: Dodecahedron
- 1 tray for the work
Preparation:
- Download and print the PDF file furnished.
- Cut out two halves of the dodecahedron.
- I had paper that was white on one side and green on the other.
- Score the dotted edges of the center pentagon and gently bend the attached pentagons down, with color on the outside if there is any.
- Use ordinary rubber bands out of a large collection of them.
- The rubber bands must be cut and knotted together into a circle to get the right size which is about 12” in circumference (6” when folded in half).
- If it is too little the dodecahedron will curl up in half
- Place the rubber band in its container.
- The rubber bands must be cut and knotted together into a circle to get the right size which is about 12” in circumference (6” when folded in half).
- Practice assembling the dodecahedron using the Presentation instructions below. Also refer to the photos of steps of assembly.
- Select the tray or basket for the work.
- Assemble the work on the tray.
Motivational Presentation: 5-12
Note: The presentation is given silently first using the directions below. It is given again using the spoken presentation. Practice.
- “Watch carefully while I demonstrate how to turn these two flat pieces of paper into a three dimensional shape called a dodecahedron.”
- Pick up each piece of the paper dodecahedron and describe them.
- “I have two pieces of paper that match. Each is made up of 6 pentagons (five-sided shapes). One pentagon is in the middle and there are 5 more pentagons connected to it.”
- “Each paper has been folded where one of the five pentagons is attached to the pentagon in the center.”
- “Notice I pick up the two pieces so that both have its 5 pentagons slightly drooping down from its center one.”
- “Watch what I do,” Turn the half that is in your left hand over so it cups up and slide it off your hand. Turn your hand over and press the paper flat.
- “Notice that there is space between each pentagon.”
- “I am going to place the top half down on the bottom half so the points of the top pentagons fill the spaces between the bottom ones.”
- “Notice that the bottom points fill the spaces between the ”
- “Now I am going to weave the top and the bottom half together using the rubber band.”
- “I use one hand to hold the centers of the two pieces down, while I thread the rubber bands around them.”
- Practice switching hands. “You might prefer to use the opposite hand half way through.”
- “Put the rubber band over the top points and under the bottom points.”
- Without talking, slowly lift your hand off the work and the dodecahedron stands up.
- “This is a dodecahedron. It has twelve sides. Each side is a pentagon.”
Dodecahedron Nests: 5-9
Introduction:
Children made nests using only half of a dodecahedron tied together with decorative string or yarn. Its function was to provide students practice using the basic skills such as cutting, punching holes, tying knots and lacing shoes. It is a higher level of difficulty to give the basket a handle. Grass can be made or purchased. I created a step-by-step to display for the children to follow.
Prerequisite: Introduction to the Platonic Polyhedrons Motivational Presentation of a Dodecahedron
Direct Aim: Practice using the basic skills tying knots, lacing shoes, and bow tying
Indirect Aim: Creative Expression
Point of interest: Can you think of another way to use the nest?
Materials:
- 1-6 halves of a dodecahedron printed on heavy paper
In a desk tray used for paper and file folders (Resupply as needed)
- 2-4 scissors
- 2-4 Paper punches ¼”
- 2 Burnishing tools (or round pencil, popsicle stick, ball point pen)
- Yarn, thin ribbon, or fancy string cut to 12” lengths (5-10 pieces for each nest)
- 4-6 wooden I form for yarn, string etc. Or
- Use large plastic foam hair rollers, remove hard plastic parts
- Burlap or other loosely-woven material, natural materials like straw, or commercial faux grass
- Colored markers for decorating
- Tray(s) and basket(s) for the equipment (see photos)
Preparation:
- Copy the dodecahedron pattern onto bristol board or two colored cover paper.
- Put scissors, paper punches, and burnishing tools in containers.
- Loosely wind yarn, thin ribbon and/or fancy string on an I form, or the materials will develop kinks.
- Foam hair roller will also hold the materials. If you press the beginning and end of the string directly on the foam cylinder it will usually stick to it.
- Cut out half of a dodecahedron for the presentation.
- Assemble the work.
Presentation:
- Quickly show the motivational dodecahedron again and remove the top half of the shape. “The bottom half can be turned into a basket or a container.”
- “Notice that the sides of each pentagon touch the others.”
- “Cut out half of the dodecahedron printed on the paper.” Demonstrate as you are cutting. I never cut the whole shape out because it makes the lesson too long.
- “If you wish you can color the outside of the basket using markers before you begin folding the shape together.”
- “Each side of the pentagon in the center has another pentagon attached to it.”
- “Use the line where the center pentagon meets one of the other pentagons to fold the attached pentagon down. Press along the line using a burnishing tool or both your pointer fingers (forefingers).”
- Demonstrate where to punch holes into the attached pentagons. “Punch two holes on each side of the attached pentagons. Punch one at the top, one at the bottom.”
- If you see that children have a hard time making two holes, suggest they make only one at the top of each side of each pentagon (see photo).
- The top hole of one pentagon is tied to the top hole of the pentagon next to it.
- “Each pair of holes can be strung together and tied into a bow. Thread (put) the string into the hole and then thread it out of the other hole. Make the ends equal.”
- “Tie a bow.”
- The sides can be laced like a shoe if that skill has been mastered or taught during the lesson.
- Add a handle that is 1” wide and 11”-12” long. Punch a hole on each end of the handle and attach it to holes punched on the basket.
Extensions:
- Make the nests (basket) to celebrate any holiday.
- Put treats in them
- Use as gift box
- How could a container like this made with laminated paper be used in the environment?
Resource:
- Burnishing and scoring tools: BronaGrand 2 Pieces Bone Folder Paper Creaser Set on Amazon
I did not develop directions for making a straw dodecahedron. Only one student ever made one. When it was finished it was too wobbly.
Instead, I found how to make a modular origami (paper) dodecahedron on a Web page (See Resources)
Prerequisite: Introduction to Platonic Polyhedrons Motivational Presentation of a Dodecahedron
Direct Aim: To make a modular origami dodecahedron
Indirect Aim: To use the shape to express an idea
Point of interest: Now that you know how to make an origami dodecahedron, can you imagine or create an idea using this skill? What paper would you use? Could it be a way to express an idea? Could it be a way to record learning?
Materials:
Note: This is an origami activity so each step taken can be pre-made and numbered. You will be making 12 pentagon shapes (modules) which will then be combined to create the dodecahedron.
- Use A4 size paper for larger shapes (easier for children to fold), or A6 size paper for smaller shapes (half a sheet of A4 size). [See Resources for A-size papers.] If A-size paper is unavailable, use 4” by 6” index cards.
- 2 Burnishing tools (or round pencil, popsicle stick, ball point pen)
- Envelopes or small bags to hold the pentagon modules
- Rub-on numerals and containers (for steps)
Preparation:
- Print an instruction page from the PDF file below: Instructions for making a “fauxdecahedron” (good enough!) [PDF]
- Make 2-4 copies of laminated instructions.
- Create a pentagon in separate steps and number each step using the instruction page you printed. [For photo examples, see lesson Origami in MAM Section Art Forms]
- Place each step in a numbered container.
- Or, if each step is numbered, just place the steps in a basket.
- Assemble the pentagon module-making activity and place it in the environment along with the instructions.
- Make 23 origami pentagon modules
- 12 to display a finished dodecahedron
- 11 more to assemble a dodecahedron during the presentation
- Complete one dodecahedron using one set of 12 pentagon modules.
- Pay special attention to steps 7 and 8 in the fauxdecahedron instructions, and continue inserting module tabs into module pockets until the dodecahedron is complete.
Presentation:
- Show the instructions you have printed for making a pentagon module.
- Referencing the numbered steps you’ve prepared for pentagons, continue to fold the paper to produce the 12th pentagon module you need to assemble the dodecahedron
- Point out that the bottom of each pentagon is just a folded edge made in Step 4
- Optional: use the burnishing tool to sharpen the folds.
- Complete one dodecahedron using one set of 12 pentagon modules.
- Pay special attention to Steps 7 and 8 in the fauxdecahedron instructions, inserting the tabs of two modules into the pockets of a third, and bringing the bottoms of the first two together at the top point of the third.
- Continue inserting module tabs into module pockets until the dodecahedron is complete.
Extensions:
- Suggest using a fauxdecahedron to show evidence of learning.
- Use fancy paper to make a gift.
- Change scale and make a giant dodecahedron. Use heavy paper.
Resources
- Instructions for making a “fauxdecahedron” (good enough!) [PDF]
- Other instructions for making modular origami dodecahedron
- https://www.origami-resource-center.com/A6-dodecahedron.html
- https://www.youtube.com/watch?v=H6PvQb34AMo (video narration is in Spanish, but shows the complete construction of the dodecahedron from the 12 pentagons)
- The Amazon book: Brilliant Origami: A Collection of Original Designs (pages 80 and 81) also contains helpful illustrations.
- Amazon: Burnishing and scoring tools: BronaGrand 2 Pieces Bone Folder Paper Creaser Set
- Amazon: A-size paper: https://www.amazon.com/gp/product/B07FTXJCYF?pf_rd_p=183f5289-9dc0-416f-942e-e8f213ef368b&pf_rd_r=TKNCN77MDXXJRTRP8RHR
Straw Icosahedron: 6-12
Like the dodecahedron, I did not make my own book of instructions for making an Icosahedron. Students made them but only one person stellated it (see Extensions) and added strings of hanging beads (see photograph).
Use the following presentation, make the steps with straws end display them in the environment in preparation for the presentation.
Prerequisite: Introduction to Platonic Polyhedrons. Experience making a tetrahedron, octahedron, etc. Concept of Convex and Concave
Direct Aim: Higher level of construction difficulty
Indirect Aim: Creative Expression
Point of interest: Would you enjoy creating a dual of this platonic polyhedron? (see Extensions)
Materials:
- Straws in a container
- Paper or plastic straws – you choose
- The example in the photos here used standard-length drinking straws cut in half
Note: Be aware there are many good environmental reasons not to use plastic straws. The subject would be an excellent research project for 6-12 children to pursue.
- String on a holder (See: Resources)
- 4 to 6 scissors in a container
- Models of each step presented using straws
- Name tags, strings and pencil in containers
- Envelopes to store flat pieces
- Large opened paper clips
- to hang polyhedrons in progress that are no longer flat
Preparation:
- Create an example of each step in construction of an icosahedron.
- Attach each step to a wall or door with removable tape.
- See photos for step-by-step, and display options.
- Note that the examples are constructed with straws of a color which will show up well on the vertical surface you use for the display.
- Number each example in order.
- Construct a pentagon of 5 triangles for the presentation.
- Add four of the 5 hanging triangles to the pentagon. (The last one will be added during the presentation).
- Set out all materials for use.
Presentation:
- “The steps for making an icosahedron are displayed on the wall. It is a three dimensional shape that has 20 equilateral triangles for faces and 30 straw edges.”
- “I have made several steps ahead of time to speed up this presentation.”
- Make the icosahedron as you give the lesson.
- “Step one shows how to construct a pentagon of 5 triangles.”
- “Start by making 1 triangle and then adding 3 more.”
- “Put 3 straws on a string and tie 2-3 knots to make the first triangle.”
- “Put 2 straws on a string and tie the string to the bottom of the first triangle. Leave enough string to tie knots and cut the string. Attach the 2 straws to the first triangle to create the second triangle.”
- “Position the 2 triangles so that the first triangle points up and the second points down.”
- “Put 2 straws on a string and tie the string to the top of the top triangle. Leave enough string to tie knots and cut the string. Attach the 2 straws to the bottom of the top triangle, where it meets the bottom triangle, to form a third triangle.”
- “The third triangle points down.”
- “Put 2 straws on a string and tie the string to the top of the third triangle. Leave enough string to tie knots and cut the string. Attach the 2 straws to the bottom of the top triangle, where it meets the bottom triangle, to form a fourth triangle.”
- “There is a wide space between the 4 triangles.”
- “Put 1 straw on the string and tie it to the vertex of the bottom straw that points down.”
- “Leave enough string to tie knots and cut the string.”
- “Tie the straw to the bottom corner of the fourth triangle.”
- “This closes the gap and forms a pentagon of 5 triangles which I will I will put aside for now.”
- “Repeat this procedure to create a second pentagon of 5 triangles identical to the first in order to finish the icosahedron you will make.”
- “For this presentation, I have prepared a second pentagon of 5 triangles for the next step and I have added to it 4 additional hanging triangles.”
- “To finish this step, put 2 straws on a string to create the last hanging triangle and tie the string to the last vertex that is open. Leave enough string to tie knots and cut the string.”
- “Attach the other end to the next vertex and tie three knots.”
- “Now the second pentagon looks like a star.
- “With the second pentagon of triangles I just finished, the icosahedron now has 15 of its 20 triangular faces and all of its edges. No more straws are needed to complete the icosahedron.”
- [Point to each of the 5 spaces between the star points.]
- “The missing 5 triangular faces are present but do not have a third edge. Next we will do what needs to be done to complete the last 5 triangular faces.”
- “Attach a hanging vertex of an added triangle to an outside vertex on the first pentagon using 1 piece of string long enough to make knots. Then attach the next hanging vertex of the second pentagon to the other end of the same edge of the first pentagon.”
- Now the space between the 2 hanging triangles has formed another triangular face
- “Trim excess string.”
- “Continue to attach the hanging vertices to the next available outside edge of the first pentagon.”
- The first pentagon of 5 triangles will be positioned under the rest of the shape to complete the icosahedron. It will be turned up-side down from convex to concave. You made an icosahedron!
Extensions:
- Every Platonic Polyhedron has a dual. The dual is a multi-cell tetrahedron built out from the original single-cell.
- To create the dual, the original straw polyhedron is first stellated – made to look like a star.
- Build a pyramid on each face of any polyhedron. (A tetrahedron has four star points, a hexahedron six, an octahedron eight etc.)
- Connecting the points of the pyramids with new longer straws forms the dual, which is another polyhedron.
- The tetrahedron is its own dual because the resulting multi-cell shape is another tetrahedron. The hexahedron and octahedron are each other’s duals, as are the dodecahedron and the Icosahedron.
- Stellate each face of any polyhedron.
- Create its dual.
- To create the dual, the original straw polyhedron is first stellated – made to look like a star.
- Add beads on the string at each vertex while building the polyhedron.
- Add any decorations desired after it is made.
Resources:
- Paper straws – prices vary
- I used these straws to construct the examples in the photos.
- Platonic Solids in Douglas Fir - $44 per set
- Laycock, Mary. Straw Polyhedrons by Mary Laycock
- This book was published in 1970 and again in 1992, with two different covers. Prices may vary depending upon the source. It is a rich resource which includes illustrations of stellation and duals – the later edition cover (ISBN 0-918-932-99-8) has color photos of three of the duals.
- Steven Caney’s book - https://www.amazon.com/Steven-Caneys-Toy-Book-Reissue/dp/0911104178 See the City Kite
- Amazon: Steinhaus, H. Mathematical Snapshots. New York: Oxford University Press, 1969, Chapter 7, p 197. This chapter is filled with interesting photographs and information about the Platonic Polyhedrons. It is worth looking for online or in a library.
- Printable templates for constructing paper models of polyhedrons (scroll down each page to find downloadable PDF files)