In this lesson, students refer to the table that they completed in Study the Shapes.
Return the Exploring Geometric Solids activity sheet to the students if you collected it in the previous lesson, as they will need it for today's lesson.
The table introduces the students informally to Euler's Formula,
faces + vertices = edges + 2,
which is often written as
F + V - E = 2.
Students are asked to refer to the table they completed in the previous lesson to answer the following questions.
Look at the first shape in the table you made.
- Find the sum of the number of faces and the number of
vertices. How does this sum compare with the number of edges?
- Do you think this may be a rule for the other shapes?
- Add the number of faces and the number of corners for the other shapes in the table. Compare the sum of faces and corners to the number of edges. What did you find out? Is there a rule for all of the
shapes?
Note that these questions appear on the activity sheet as questions 1, 2, and 3.
You may wish to mention that a famous mathematician discovered this formula a long time ago. His name is Leohnard Euler (pronounced 'Oiler'). This rule is called Euler's Formula:
faces + vertices = edges + 2
You could mention to your students that someday some of them might discover an important mathematical pattern and have a formula named after them!
