Apples and Onions

By Catherine Mott, September 9, 2010

Grade Level

  • PreK-1


  • Architecture

Subject Area

  • Arts
  • Mathematics

Lesson Time

100 minutes for classroom activities


The purpose of this lesson plan is to combine mathematics and design elements for the students to understand the balance (design) of an object and symmetry vs. asymmetry (mathematics).

National Standards


Students will be able to:
  • recognize symmetrical and asymmetrical objects
  • recognize patterns/designs of nature
  • use directional vocabulary, “up,” “down,” “left,” “right,” etc.
  • recognize symmetry/asymmetry in the everyday objects that surround them (e.g. food, people, nature)
  • begin to recognize elements of design


"Let's Fly A Kite" by Stuart J. Murphy and Brian Floca


  • cut-out shapes - large shapes cut out from 9\" x 12” pieces of construction paper (circle, triangle, rectangle, square, diamond)
  • meter stick
  • rulers
  • crayons
  • pencils
  • 9” x 12” white construction paper
  • paint in four different colors (tempera or acrylic)
  • two of each of the following: apple, onion, garlic bulb, pear (Note: Fruit should be firm, not ripe.)
  • four paper plates
  • knife (for teacher\'s use only)


  • asymmetrical: not symmetrical
  • balance: an aesthetically pleasing integration of elements
  • diagonal: passing through two nonadjacent edges of a polyhedron
  • horizontal: parallel to, in the plane of, or operating in a plane parallel to the horizon
  • symmetry: the property of being symmetrical; especially correspondence in size, shape, and relative position of parts on opposite sides of a dividing line or median plane or about a center or axis
  • vertical: perpendicular to the plane of the horizon or to a primary axis


Day 1:

1.  Start by talking about lines. What lines do the students see in the room around them?  What types of lines are there?  What is the name of a line that goes “left” to “right” or along the horizon? (Horizontal) What is the name of a line that goes “top” to “bottom”? (Vertical) What do we call a line that crosses from corner to corner like a seatbelt does across our body? (Diagonal)

2.  Use a cut-out shape (Note: I find it most interesting to use a triangle) and ask what it would look like if you cut it in half, horizontally, vertically, diagonally?  Then identify the symmetry and asymmetry of that object when “cut” with a line.

3.  Talk about how an object can have symmetrical and asymmetrical lines depending on how you “cut” it.

4.  Have a student stand up and ask where a line would have to be to make him/her symmetrical?  Asymmetrical?  Use the meter stick to show these lines, or have students come up to show the lines to the class.  With each different line, talk about how that particular line would change the balance of each person.  Would our top half be heavier than our bottom if we were cut at the belly button?  What about if we were cut in half vertically?  Which cut appears to look more pleasing?  Why?

5.  Next have the students pair off and then randomly give them a cut-out shape (circle, triangle, rectangle, square, diamond).

6.  Using their rulers and crayons, have the student pairs draw a symmetrical line on one side of their shape and an asymmetrical line on the other side.

7.  Have all of the pairs with squares stand up and show one of their lines and discuss if is symmetrical or not. Then move on to the triangle groups, circles, diamonds, and rectangles.

8.  Finish the lesson by reading the book “Let’s Fly a Kite.”  This book emphasizes the ideas of symmetry and asymmetry.

Day 2:

(Note 1:  Cut a set of fruit and vegetables that you plan on printing with the day before to let them dry out some; this will allow the paint to adhere better and result in better prints for the students.)

(Note 2: If you can, arrange the tables or desks in a square so that you can be in the middle and students can move around the outside.  Make four stations, one for each fruit or vegetable.  Then when the students start to print they then can move around the outside of the square and you can assist from the middle.)

1. Review the vocabulary and concepts of symmetry. Pull out the set of cut-out shapes again and review.

2. Present the fruits and vegetables and have the class help you identify each.  Ask the students “Do you know what these look like when cut?  Do they have symmetry?  How could we cut them to make them symmetrical or asymmetrical?”

3. Using the apple, ask “Which way we would cut it to make it symmetrical?  And which way so it would be asymmetrical?  Which cut would look more appealing to you?  If you were sharing the apple which half would you want if it was asymmetrical?  Why?”

4. Cut the apple so it is symmetrical.  Ask “Will each half balance?  If we put them on a teeter-totter would they be even?  Which half would you want to eat of the apple if you were sharing it now that is symmetrical?”

5. Next ask “Which way you should cut the onion if we wanted it to be symmetrical?”  Cut the onion so that is symmetrical.  Note the rings in the onion and its layers.  Ask “Are the rings symmetrical?”

6. Ask the students what they think the inside of the garlic looks like.  “Do you think that this bulb could be symmetrical?”  Cut the bulb in half horizontally so that is asymmetrical.  Explain each clove is unique in shape and collectively they make the bulb, which is asymmetrical.

7.  Lastly look at the pear and ask “Which way would look the best to cut the pear?  How would we cut it so that one half would be heavier than the other?”  Cut the pear so that it is asymmetrical.

8. Give each student a piece of paper and have them write their names on their papers.  They should each then draw a line down the center and write “symmetrical” on one half and “asymmetrical” on the other.  As you are explaining illustrate the instructions on the board.

9. Ask the students to push up their sleeves up and put on their listening ears.

10. Place a paper plate next to each of the cut fruit/vegetables with a quarter-size amount of paint.  Have the students join you around the apple station and demonstrate. Talk about “lightly” touching the apple in the paint and spreading the paint over the surface of the side that is cut. (Note: More paint is not better in this situation.)  Then demonstrate how to print on your paper by placing the apple firmly on your sheet.  Ask “Which side of my paper does the apple go on?  Is it symmetrical or asymmetrical?  Since it is symmetrical you print it on that side.”  Now assign four or five students to each station and have them print and rotate until everyone has every print.

11. Place prints off to the side and let dry.


Draw shapes  (circle, triangle, rectangle, square, diamond) on the dry erase board.  Assign the symmetrical lines a color marker (green for example) and asymmetrical lines another color (red for example).  Ask students to come forward and draw either symmetrical or asymmetrical lines on the board.

Enrichment Extension Activities

From this lesson one could move on to talk about patterns in nature, leaves, shells, butterflies, etc., pulling in a science angle.
  1. I have taught middle school for the past 5 years and I can see how this could be a useful lesson for lots of students beyond PreK-1 grade. Your day 1 and day 2 could be combined for higher grades and the use of something a little less messy than fruits could suit any classroom.

    A lesson like this could easily be the opening to geometry units and could certainly be tied into a cross curricular unit with an art class. The ideas in your lessons are great and the structure is easily followed.

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