Geometry Lesson Plan                                            

Toothpick Geometry           Level ___

Joyce Arafeh and Avi Barnes

from Geometry Teachers Activity Kit    by Muschla and Muschla

 

Objective:  Students will form squares and rectangles by removing and repositioning toothpicks.  Students should work individually or in pairs to complete this activity.

 

Special Materials:  12 toothpicks per student or pair, unlined paper to sketch their figures.

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Teaching Notes:  Toothpicks are an inexpensive manipulative that are perfect for forming squares and rectangles.  Toothpicks are straight and the same length – perfect for representing line segments.

 

  1. Introduce this activity by explaining that students will be asked to form squares and rectangles using toothpicks.  Review or introduce definitions of squares, rectangles, quadrilateral, congruent, right angles.  A rectangle is a quadrilateral with four right angles, and a square is a quadrilateral with four congruent sides.  Note that a square is always a rectangle, but a rectangle is only sometimes a square.  Ask the class to give examples of squares and rectangles they see in the classroom.  For this activity, when a rectangle is mentioned on the activity sheet it is a rectangle not a square.
  2. Distribute copies of the activity sheet and review the instructions with your students.  Emphasize the difference between “remove” and “reposition.”  Removing a toothpick means to take the toothpick away and not use it in the figure.  Repositioning the toothpick means to remove a toothpick from its place and to put it in another place to form the figure.  Note that students must start each problem with the arrangement on the top of the activity sheet.  After each problem the student should sketch their figure as their answer to the problem.
  3. The last question of the activity sheet is an opportunity for the students to create a toothpick problem of their own.  Use the student created problems to create another activity sheet or do the student problems with the class together.
  4. ANSWER KEY BELOW

Toothpick Problems

 

 

Constructing figures with toothpicks can be challenging.  Start each problem by arranging 12 toothpicks as pictured below.  Follow instructions for 1 to 10.  Be sure to make a sketch for each problem on the sketch paper, number your sketches.

 

                          ___  ___

              l___ l ___l

              l___ l ___l

                                   

 

 

 

When you finish a problem, sketch your figure on the sketch paper.  Then form the original toothpick arrangement with your toothpicks and start the next problem.

 

 

  1. Remove 2 toothpicks to form 2 rectangles.
  2. Remove 2 toothpicks to form 3 squares.
  3. Remove 4 toothpicks to for 2 squares.
  4. Remove 4 toothpicks to form 1 square.
  5. Reposition 3 toothpicks to form 2 squares and 1 rectangle.
  6. Reposition 4 toothpicks to form 1 square and 1 rectangle.
  7. Reposition 3 toothpicks to form 3 squares.
  8. Reposition 5 toothpicks to form 1 square and 1 rectangle.
  9. Reposition 7 toothpicks to form 1 rectangle.
  10.  Create a toothpick problem of your own.  Supply an answer key.