Balance on Every Side: The Expanded Square: Grades 3 to 5, teacher version

Overview

Students in grades 3 to 5 can plan before they make, compare artworks, and defend a choice with a reason. The expanded square asks for all three. Every shape cut from the edge of a dark square and flipped outward is one outline used twice: a light hole, which is negative space, and a dark piece, which is positive space. Where the pieces land decides how the whole design balances, so balance stops being a word on a poster and becomes a decision each student makes on every side of the square.

Students choose a motif from their own lives and plan it three ways in thumbnails: symmetrical, asymmetrical and radial. They test the plans in Studio Notan, where a piece can be copied, reflected, resized and refolded until a partner agrees the design holds still, then cut the chosen plan with scissors from black paper and glue it on a ground they painted in tempera. Along the way they meet Edgar Rubin’s vase and faces (1915), Arthur Wesley Dow’s Composition (1899), Japanese family crests and Hokusai’s Great Wave, with M. C. Escher’s Sky and Water I (1938) for fifth graders. They give feedback with sentence stems and finish with a short artist statement.

Learning outcomes

By the end of the unit, learners can do each of these. The middle column is what you will see or hear that shows it; the last column links to the standards it meets, quoted in full at the end of the page.

#	By the end, learners can	What you will see	Standards
1	Identify the positive and negative shapes along each side of an expanded square, and explain how a hole and its piece are one outline in opposite values.	Pointing to one side of their own or a classmate’s notan, the learner names the light hole as negative space and the dark piece as positive space and says the two outlines mirror each other across the edge; shown Rubin’s vase, the learner describes both the vase and the two faces.	§117.111(b)(1)(B) §117.114(b)(1)(B) §117.117(b)(1)(B)
2	Classify notans as symmetrical, asymmetrical or radial, and justify each label with evidence visible in the cuts.	Sorting six printed notans, the learner labels at least five correctly and names the evidence for each kind: matching cuts on opposite sides, unlike pieces that still feel even when squinted at, or similar cuts on all four sides turning around the center.	§117.111(b)(1)(C) §117.114(b)(1)(C) §117.117(b)(1)(C)
3	Develop three thumbnail plans for one motif drawn from their own life, one for each kind of balance, and choose one for the final with a written reason.	The planning sheet shows three small squares labeled symmetrical, asymmetrical and radial, each with holes drawn in the square and shaded pieces on the matching sides, a motif from the learner’s life, and a sentence beginning “I chose this plan because” that gives a reason about balance.	§117.111(b)(1)(A) §117.114(b)(1)(A) §117.117(b)(1)(A)
4	Build two balanced versions of the plan in the studio by copying, reflecting, resizing and refolding cuts, and export each one.	Two exported images of the same motif: one symmetrical across the center of the sheet, and one asymmetrical or radial that a partner agrees does not lean when squinted at; the teacher sees at least one piece refolded with the arrows beside its selection box.	§117.111(b)(2)(B) §117.114(b)(2)(B) §117.117(b)(2)(B)
5	Cut the chosen expanded square from black paper with scissors, test the arrangement loose on a painted ground, and glue it in the planned balance.	The collage has at least five cuts, including the personal motif, with no corner cut away and no piece lost; each piece meets the side beside its hole as its mirror, the balance matches the chosen thumbnail, and the teacher saw a dry fit before any glue.	§117.111(b)(2)(C) §117.114(b)(2)(C) §117.117(b)(2)(C)
6	Compare the purpose and the balance of a Japanese family crest and Hokusai’s Great Wave, and explain how Arthur Wesley Dow brought the word notan into American art teaching.	In discussion or on the planning sheet, the learner gives a purpose for each work, such as marking a family or showing Mount Fuji in a series of prints, names each one’s balance, radial or symmetrical for the crest and asymmetrical for the wave, and says that Dow taught notan in Composition (1899) after studying Japanese art.	§117.111(b)(3)(A) §117.114(b)(3)(A) §117.117(b)(3)(A)
7	Give a classmate specific feedback with sentence stems that names a kind of balance and one cut that helps or hurts it.	During the studio check, the learner completes at least two stems aloud or on a sticky note, such as “Your design feels ___ because the piece on the ___ side ___,” naming a real side and a real cut that the partner can then point to.	§117.111(b)(4)(A) §117.114(b)(4)(A) §117.117(b)(4)(A)
8	Present a three- to five-sentence artist statement, written or spoken, that names the motif, the kind of balance, the feeling it gives and one change made after testing or feedback.	The statement, displayed beside the work or recorded, names the motif and why it was chosen, the kind of balance, a feeling word such as calm or lively, and one specific change made after the squint test or a classmate’s comment.	§117.111(b)(4)(B) §117.114(b)(4)(B) §117.117(b)(4)(B)

Before you teach

What learners should already know

Cut a shape from an edge of a square and flip it over that edge so the piece mirrors its hole, as in the grades 1 and 2 unit.
Tell geometric shapes from organic shapes.
Use a mouse or trackpad to draw, select and drag on screen.

Vocabulary

notan: A Japanese word for the arrangement of dark and light in a design. Arthur Wesley Dow brought it into American art teaching; his book Composition appeared in 1899.
positive space: The shapes that read as the subject, or figure. In an expanded square, the dark square and the dark pieces.
negative space: The space around and between the subjects. In an expanded square, the light holes and the ground.
figure and ground: The figure is what we look at; the ground is behind it. In a notan the two can trade places.
expanded square: A notan exercise in which shapes are cut from the edges of a square and flipped outward, so the design grows beyond the square.
symmetrical balance: Both halves match, like mirror images across a center line.
asymmetrical balance: Different shapes on each side that still feel even, like a heavy box near the middle of a seesaw and a light box at the far end.
radial balance: Parts repeat around a center, like spokes on a wheel or petals on a flower.
thumbnail sketch: A small, quick drawing used to plan and compare ideas before making the final work.
artist statement: A few sentences in which an artist explains what they made, how they made it and why.

Materials

Computers or tablets with Studio Notan open at /studio, one per student or pair
A planning sheet with three 2-inch squares for each student, pencils and erasers
Squares of black construction paper, 6 inches, one per student, plus spares
Sheets of white sulphite or drawing paper, 12 by 18 inches, for the painted ground
Washable, nontoxic tempera with the AP seal in two or three light colors, such as yellow, sky blue and pale green
Sponges, cardboard combs or plastic forks for texture, 1-inch flat brushes, paper plates for palettes, water cups, paper towels, smocks and newspaper
Student scissors, plus loop or spring-open adaptive scissors for students who need them
Glue sticks, and a white colored pencil or chalk for drawing on black paper
Sticky notes and a printed card of feedback sentence stems for each table
Index cards for artist statements, and a tablet for recording spoken ones
Images to project: Edgar Rubin’s vase and faces (1915), a page of Arthur Wesley Dow’s Composition (1899), several Japanese family crests, Katsushika Hokusai’s Under the Wave off Kanagawa (about 1830 to 1832) and M. C. Escher’s Sky and Water I (1938)
Six printed notans for the balance sort: two symmetrical, two asymmetrical and two radial
A drying rack, and a heavy book for pressing glued work

Read first in the guide

Hub activities to draw on

Balancing the Flip Balance · Foundation
Space That Changes Sides Space · Developing

Worksheets

Worksheet 1: Foundations, the four gates

Unit plan

Session 1: Figure, Ground and the Word Notan

45 minutes · Paper and paint

Rubin’s vase, 5 minutes. Project the figure the Danish psychologist Edgar Rubin published in 1915 and ask: “What do you see first? Now what else?” When the vase is the figure, the faces are ground, and the other way round. Say: “The shape we look at is positive space. The space around it is negative space.”
Where the word comes from, 8 minutes. Show a page of Arthur Wesley Dow’s Composition (1899). Explain that Dow, an American artist and teacher, studied Japanese art in Boston with the scholar Ernest Fenollosa and used the Japanese word notan for the pattern of dark and light; his book was used by art teachers across the country. Add that in 1968 the American artist and teacher Dorr Bothwell and the educator Marlys Frey published a book of notan exercises, Notan: The Dark-Light Principle of Design, and that the expanded square is commonly adapted from it.
Read an expanded square, 7 minutes. Project one made in the studio. Point to one side and ask a volunteer to name the hole and the piece, then ask: “Which is positive and which is negative? What happens to that outline when it crosses the edge?” Draw out the answer: the same outline is light inside the square and dark outside it. Collect a quick exit ticket on this at the end of the session.
Paint the ground, 20 minutes. Students write their names on the back of a 12 by 18 inch sheet, cover the front with two or three light tempera colors, and pull texture through the wet paint with a sponge, a cardboard comb or a fork. Say: “Keep it light, so the dark pieces will stand out.” Lay the sheets on the drying rack.
Clean up, 5 minutes. Rinse brushes and sponges, wipe tables and wash hands.

Session 2: Three Kinds of Balance, in Thumbnails

45 minutes · Paper and paint

The seesaw, 5 minutes. Draw a seesaw on the board with a large box near the middle and a small box at the far end, and ask why it can still balance. Say that pictures balance the same way: large and dark shapes weigh more, and a shape far from the center pulls harder.
Sort the notans, 10 minutes. Name the three kinds of balance: symmetrical, matching cuts on opposite sides; asymmetrical, unlike pieces that still feel even; radial, similar cuts on all four sides turning around the center. Tables sort the six printed notans and give a reason for each. Balancing the Flip has more examples.
A crest and a wave, 10 minutes. Show several Japanese family crests, kamon, often one bold shape in a circle, which families have used for hundreds of years on kimono, banners and lanterns. Ask what each is for and which kind of balance it uses. Then show Katsushika Hokusai’s woodblock print Under the Wave off Kanagawa (about 1830 to 1832): a huge wave rises on the left over rowers in their boats, answered by the small, still Mount Fuji in the distance. It is one of a series of prints, Thirty-six Views of Mount Fuji, each showing the mountain from a different place. Ask: “What is this picture about, and why does it not tip over?”
Choose a motif, 5 minutes. Each student picks one motif from their own life: a leaf from the schoolyard, a paw, a star, a fish, a tool from a hobby. Model turning it into a simple outline with no inside details, the kind scissors can cut in one line starting and ending on an edge.
Three thumbnails, 15 minutes. In each of the three small squares on the planning sheet, students draw the motif as a cut against a side, add two to four simpler cuts, and shade each piece outside its own side. They label the squares symmetrical, asymmetrical and radial, circle one, and write: “I chose this plan because …”

Session 3: Test the Balance in the Studio

45 minutes · In the studio

Set up, 5 minutes. A new design in the studio starts on a sheet 4 inches wide and 5.5 inches tall, so students first open the Paper section on the Controls tab and set both the width and the height to 5 inches. Remind them that each arrow in the ‘Flip direction’ chooser folds the piece over that side of the sheet.
Build the chosen plan, 15 minutes. Students draw the motif with Draw or the Pen and the simpler cuts with Rectangle, Ellipse, Triangle or Hexagon. For a matching cut on the opposite side, select the cut with Move, Option-drag (Alt-drag) a copy across, turn on Reflect Y in Transform (Reflect X for a cut on the top or bottom) and press Apply, then click the arrow beside the far side of its box to fold it over that side. Export from the ‘File’ button as Artwork, PNG.
Make a second version, 10 minutes. Students turn the same design into another kind of balance without starting over: drag a handle to resize a piece, click a different arrow beside its box to refold it, or turn a copy a quarter turn by dragging just outside a corner handle with Shift held, which turns in 15-degree steps. Export this version too.
Squint and give feedback, 12 minutes. Partners trade seats. The visitor squints at the screen and completes two stems on a sticky note: “Your design feels ___ because the piece on the ___ side ___.” and “One thing I would try is ___.” The maker may make one change and export again.
Close, 3 minutes. Ask: “Which version held still best when you squinted? What moved the balance most: size, number or distance from the center?”

Session 4: Cut, Test and Glue the Expanded Square

45 minutes · Paper and paint

Demonstrate, 5 minutes. Review the scissor rules. On a black square, draw one cut in white pencil that starts and ends on the same side, cut it, and flip the piece out like a page in a book. Point to the three rules: never cut through a corner, keep every piece, and keep each piece beside its own hole.
Draw and cut, 15 minutes. Students copy their chosen thumbnail onto the black square in white pencil, motif first, and write a small matching number on each shape and beside its side, so no piece is lost; after the flip, the number is face down. Then they cut one shape at a time.
Dry fit, 10 minutes. Students lay the square on their dry painted ground and flip every piece out loose. They stand, step back and squint, compare the layout with the thumbnail and the studio export, and slide the whole square if the design leans. Check each dry fit before any glue comes out.
Glue, 12 minutes. Glue the square first, then each piece, lining up its straight edge with the side beside its hole. Press the finished work under a heavy book between sheets of newspaper.
Clean up, 3 minutes. Collect scissors closed with the points down, and check every scrap: if it is a lost piece, it goes back on.

Session 5: Critique, Artist Statements and a Gallery

45 minutes · Looking and talking

Gallery walk, 10 minutes. Lay the work on the tables with each student’s thumbnails and exports beside it. Students visit three works and leave a sticky note at each, using a stem: “I notice ___ balance because ___.” or “The positive shape I see first is ___.”
Figure and ground, the grand version, 8 minutes. Show M. C. Escher’s woodcut Sky and Water I (1938). In the middle band, dark birds and light fish fit together with no gaps; toward the top the fish melt into the sky, and toward the bottom the birds melt into the water. Ask fifth graders especially: “Where does figure turn into ground?” Connect it to the hole and the piece in their own work.
Write or record, 15 minutes. Post the frame: “My notan shows ___, which matters to me because ___. I used ___ balance. It feels ___. After testing, I changed ___.” Students write three to five sentences on an index card or record them. Circulate and ask each student to point to the change they named.
Share, 10 minutes. Volunteers read their statements beside their work. Before each reader points, the class guesses the kind of balance named in the statement.
Close, 2 minutes. Hang the work with its statement as a class exhibition, and file the thumbnails and studio prints in each student’s portfolio.

Differentiation

Support

For emergent bilingual students, give picture cards for positive space, negative space and the three kinds of balance with the word in the home language, post the feedback stems and statement frame with a model answer, pair students with a partner who shares their home language where possible, and accept a statement in the home language with one sentence in English.
For students with disabilities, offer loop or spring-open adaptive scissors, a 9-inch square, thicker cut lines and a card template of the motif to trace; allow the statement to be dictated or recorded, and give extra time.
In the studio, the flip chooser works from the keyboard: an arrow key chooses a side at once, and Tab and Enter move and confirm, keys that many switch interfaces can be set to send. Drawing a shape still needs a mouse, trackpad or touch, so a student who cannot use one works with a partner who draws. Set Interface size on the Controls tab to Large or Larger for bigger buttons.
For students who need a smaller task, plan two thumbnails, symmetrical and asymmetrical, and build one studio version.

Extension

In the studio, draw a small shape inside a hole and send it over a different side: it is cut from the piece that came from that hole. Decide whether this smaller piece helps or hurts the balance.
Fifth graders can design a cut whose piece reads as a second figure, in the spirit of Escher, so a viewer sees two things in one outline.
Build a radial version with Rotate and Copies in Transform, following the Copies chapter of the guide, and compare it with a Japanese family crest.
Connect to careers: graphic designers use negative space on purpose. The FedEx logo, designed in 1994 by Lindon Leader at Landor Associates, hides an arrow in the space between two letters. Students find another logo that uses negative space and redraw it as a notan.

Common misconceptions

Symmetrical means balanced, so an asymmetrical design must be unbalanced.: Return to the seesaw: unlike weights balance when the heavier one sits nearer the middle. Show Hokusai’s wave and an asymmetrical notan that the class agrees holds still.
Negative space is empty, leftover space.: Point to a hole and its piece: the same outline, one light and one dark. In a notan the negative shapes are designed as carefully as the positive ones, and Rubin’s vase shows that either one can become the figure.
Radial balance needs a circle.: Radial balance means parts repeat around a center. On a square, similar cuts on all four sides, each a quarter turn from the last, make it radial, just as leaves or petals repeat around the center of a crest.
A piece can slide anywhere along the edge to fix the balance.: A piece belongs beside its own hole, as its mirror. To move a piece, move its cut: in the studio, drag the shape and its piece follows; in paper, change the plan before cutting.

Assessment

Checks along the way

Exit ticket after Session 1: a small printed notan with one side circled; students label the positive shape and the negative shape.
The balance sort in Session 2: listen for reasons that name matching sides, even weight or turning around a center.
Thumbnail check before Session 3: every planned piece sits outside the side of its own hole.
Dry-fit check in Session 4: approve each layout before any glue.

Rubric

Criterion	Beginning	Developing	Meeting	Exceeding
Positive and negative space	Names holes and pieces but not which space each is.	Labels positive and negative space with help.	Labels both independently and explains that a hole and its piece are one outline in opposite values.	Also finds figure and ground trading places in an artwork such as Rubin’s vase or Escher’s Sky and Water I.
Planning and balance	One thumbnail, or plans with pieces away from their holes.	Three thumbnails, but one kind of balance is unclear.	Three clear thumbnails, one for each kind of balance, and a choice with a reason.	Inventive plans and a choice that weighs size, number and distance from the center.
Studio versions	One version, not yet balanced.	Two versions, one of which leans.	Two exported versions of one design, each balanced as intended.	Three versions, or a smaller cut from a flipped piece that improves the balance.
Craft in paper	A corner cut or a piece lost; pieces not beside their holes.	Most pieces beside their holes, with some gaps, lifting or glue marks.	Clean scissor cuts, every piece beside its hole, glued flat on an evenly painted ground.	Crisp cuts on a detailed motif, and a ground whose texture adds to the design.
Feedback and artist statement	Feedback is general, such as “nice”; the statement is one sentence.	Feedback names balance or a cut, not both; the statement misses one required part.	Feedback names a kind of balance and a specific cut; the statement names the motif, balance, a feeling and a change.	Feedback and statement use unit vocabulary precisely and connect the work to an artist from the unit.

Safety

Students cut with student scissors only; no craft knives or other blades are used at this level. Review the scissor rules before Session 4: cut while seated, carry scissors closed with the points down, keep the free hand behind the blades, and pass scissors handle first. Use washable, nontoxic tempera with the AP seal, cover tables with newspaper, wear smocks, and wash hands and brushes afterward. Let painted sheets dry fully before cutting or gluing, and give short breaks from the screen during studio work.

Standards cited

TEKS §117.111 (Art, Grade 3), §117.114 (Art, Grade 4) and §117.117 (Art, Grade 5). Quoted word for word from the official text.

Art, Grade 3

Foundations: observation and perception

Foundations: observation and perception. The student develops and expands visual literacy skills using critical thinking, imagination, and the senses to observe and explore the world by learning about, understanding, and applying the elements of art, principles of design, and expressive qualities. The student uses what the student sees, knows, and has experienced as sources for examining, understanding, and creating artworks. The student is expected to:

§117.111(b)(1)(A): explore ideas from life experiences about self, peers, family, school, or community and from the imagination as sources for original works of art; Source
§117.111(b)(1)(B): use appropriate vocabulary when discussing the elements of art, including line, shape, color, texture, form, space, and value, and the principles of design, including emphasis, repetition/pattern, movement/rhythm, contrast/variety, balance, proportion, and unity; and Source
§117.111(b)(1)(C): discuss the elements of art as building blocks and the principles of design as organizers of works of art. Source

Creative expression

Creative expression. The student communicates ideas through original artworks using a variety of media with appropriate skills. The student expresses thoughts and ideas creatively while challenging the imagination, fostering reflective thinking, and developing disciplined effort and progressive problem solving skills. The student is expected to:

§117.111(b)(2)(B): create compositions using the elements of art and principles of design; and Source
§117.111(b)(2)(C): produce drawings; paintings; prints; sculpture, including modeled forms; and other art forms such as ceramics, fiber art, constructions, mixed media, installation art, digital art and media, and photographic imagery using a variety of materials. Source

Historical and cultural relevance

Historical and cultural relevance. The student demonstrates an understanding of art history and culture by analyzing artistic styles, historical periods, and a variety of cultures. The student develops global awareness and respect for the traditions and contributions of diverse cultures. The student is expected to:

§117.111(b)(3)(A): identify simple main ideas expressed in artworks from various times and places; Source

Critical evaluation and response

Critical evaluation and response. The student responds to and analyzes artworks of self and others, contributing to the development of lifelong skills of making informed judgments and reasoned evaluations. The student is expected to:

§117.111(b)(4)(A): evaluate the elements of art, principles of design, or expressive qualities in artworks of self, peers, and historical and contemporary artists; Source
§117.111(b)(4)(B): use methods such as oral response or artist statements to identify main ideas found in collections of artworks created by self, peers, and major historical or contemporary artists in real or virtual portfolios, galleries, or art museums; and Source

Art, Grade 4

Foundations: observation and perception

§117.114(b)(1)(A): explore and communicate ideas drawn from life experiences about self, peers, family, school, or community and from the imagination as sources for original works of art; Source
§117.114(b)(1)(B): use appropriate vocabulary when discussing the elements of art, including line, shape, color, texture, form, space, and value, and the principles of design, including emphasis, repetition/pattern, movement/rhythm, contrast/variety, balance, proportion, and unity; and Source
§117.114(b)(1)(C): discuss the elements of art as building blocks and the principles of design as organizers of works of art. Source

Creative expression

§117.114(b)(2)(B): create compositions using the elements of art and principles of design; and Source
§117.114(b)(2)(C): produce drawings; paintings; prints; sculpture, including modeled forms; and other art forms such as ceramics, fiber art, constructions, mixed media, installation art, digital art and media, and photographic imagery using a variety of art media and materials. Source

Historical and cultural relevance

§117.114(b)(3)(A): compare content in artworks for various purposes such as the role art plays in reflecting life, expressing emotions, telling stories, or documenting history and traditions; Source

Critical evaluation and response

§117.114(b)(4)(A): evaluate the elements of art, principles of design, intent, or expressive qualities in artworks of self, peers, and historical and contemporary artists; Source
§117.114(b)(4)(B): use methods such as written or oral response or artist statements to identify emotions found in collections of artworks created by self, peers, and major historical or contemporary artists in real or virtual portfolios, galleries, or art museums; and Source

Art, Grade 5

Foundations: observation and perception

§117.117(b)(1)(A): develop and communicate ideas drawn from life experiences about self, peers, family, school, or community and from the imagination as sources for original works of art; Source
§117.117(b)(1)(B): use appropriate vocabulary when discussing the elements of art, including line, shape, color, texture, form, space, and value, and the principles of design, including emphasis, repetition/pattern, movement/rhythm, contrast/variety, balance, proportion, and unity; and Source
§117.117(b)(1)(C): discuss the elements of art as building blocks and the principles of design as organizers of works of art. Source

Creative expression

§117.117(b)(2)(B): create compositions using the elements of art and principles of design; and Source
§117.117(b)(2)(C): produce drawings; paintings; prints; sculpture, including modeled forms; and other art forms such as ceramics, fiber art, constructions, digital art and media, and photographic imagery using a variety of materials. Source

Historical and cultural relevance

§117.117(b)(3)(A): compare the purpose and effectiveness of artworks from various times and places, evaluating the artist's use of media and techniques, expression of emotions, or use of symbols; Source

Critical evaluation and response

§117.117(b)(4)(A): evaluate the elements of art, principles of design, general intent, media and techniques, or expressive qualities in artworks of self, peers, or historical and contemporary artists; Source
§117.117(b)(4)(B): use methods such as written or oral response or artist statements to identify themes found in collections of artworks created by self, peers, and major historical or contemporary artists in real or virtual portfolios, galleries, or art museums; and Source