K-12 Teaching and Learning From the UNC School of Education

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Learning outcomes

Students will;

  • learn how to bisect a segment
  • how to draw arcs
  • how to measure accurately (you can use metric measure or standard measurement)
  • have an opportunity to show their creative side in a math class

Teacher planning

Time required for lesson

90 minutes


Teacher materials:

  • a photocopy of the project for each student using the instructions in this lesson plan
  • practice papers
  • colored construction paper (red, pink, purple for Valentine’s Day)
  • glue, compasses and rulers for each student
  • items to decorate with such as markers, glitter glue, paper doilies, and colored tissue paper
  • pencils and erasers
  • Mira may be used for the lines in the drawing, so it would be a good chance to use a variety of construction tools.

Technology resources

Students may wish to construct using a software program, if accessible. Students may also wish to type their poem in a nice font for display. Use spell check, please.


Students need a solid knowledge of constructions in order to complete this project in ninety minutes. I recommend having taught them how to copy a segment, bisect a segment, and draw circles with their compass, measuring accurately with their ruler before you attempt this project.


  1. The teacher should have the materials for decorating the hearts at several stations.
  2. Distribute the handouts and ensure that each student has their own construction tools.
  3. Go through the instructions carefully with the students before they begin. Have them watch you do it on the board or an overhead. Labeling the points is crucial to the work.
  4. Then have students try a practice heart, following the instructions themselves, and asking questions as they work.
  5. When you have checked their practice copy, they repeat the exercise on a colored sheet of paper that will be their finished heart. Do not let them cut out their practice one and trace it.
  6. When their good copy is complete, they cut it out, and get to work on the art and poetry part of the project. They must beautify the work, and compose a math valentine poem. Be sure they write clearly on the side with no lines drawn.
  7. When the hearts are complete, I have a bulletin board prepared with a pink background and hearts border, with the message “Math=Happiness” or “We Love Math ” and the students display their work. Other students and teachers will gravitate to your room to read the poems.

Instructions for project and student handout: (convert to metric if you wish)

  1. Draw segment AB two inches long in the center of a sheet of paper.
  2. Construct a perpendicular bisector of AB intersecting at O. Call it XY.
  3. Measure OZ on line XY equal to three and one-half inches.
  4. With A and B as centers and a radius of one and one-fourth inches, construct arcs of circles intersecting XO at C and AB extended at points M and N.
  5. Construct a perpendicular bisector of a line drawn from M to Z and let it intersect arc CN at D.
  6. Using DZ as a radius and D as a center construct an arc from M to Z.
  7. Using DZ as the radius and Z as the center, locate point E on MC.
  8. Construct an arc from N to Z using DZ as the radius and point E as the center.
  9. Now that the figure is completed, write your poem and decorate your heart!!


I grade this exercise with a rubric, and I watch for the following categories: proper use of materials, ability to follow instructions, planning, and use of time, finished product. I also note other people’s comments about the finished products and sometimes include them as feedback for the students. The comments are always positive.

Supplemental information


I found the basic idea in a book called The Math Wizard published by J. Weston Walch. I decided to inspire my Grade 11 geometry students early in the semester. I originally used it for ten bonus marks and got exceptional results. Students took a great deal of time decorating and writing a poem that was suitable. The boys, in particular, seem to enjoy this. Some students make the valentines for a particular person. Lots of them were addressed to me. The teacher has to create one too!

  • Common Core State Standards
    • Mathematics (2010)
      • High School: Geometry

        • Congruence
          • GEO.C.12Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an...

North Carolina curriculum alignment

Mathematics (2004)

Grade 9–12 — Algebra 1

  • Goal 2: Geometry and Measurement - The learner will describe geometric figures in the coordinate plane algebraically.
    • Objective 2.01: Find the lengths and midpoints of segments to solve problems
    • Objective 2.02: Use the parallelism or perpendicularity of lines and segments to solve problems.

Grade 9–12 — Integrated Mathematics 2

  • Goal 2: Geometry and Measurement - The learner will describe geometric figures in the coordinate plane algebraically.
    • Objective 2.01: Find the lengths and midpoints of segments to solve problems.
    • Objective 2.02: Use the parallelism or perpendicularity of lines and segments to solve problems.