2-D and 3-D Paper Folding Activity
Teacher’s Note:
This activity can be used as a review of geometric shapes and formulas or as an introductory activity to determine the knowledge level of students. This activity is a means of getting students actively involved in a review process that also allows them opportunities to write about mathematics. Reference: Modified from Dr. Sandra Atkins’ demonstration lesson given in MAE 5318; Sobel, M. A. & Maletsky, E. M. (1999). Teaching mathematics: A sourcebook of aids, activities, and strategies (3rdEd.). Boston: Allyn and Bacon.
Materials:
30 Pieces of Different Colored Paper with 6” to 7” diameter circles
30 Scissors (Circles can be precut to save time)
30 Recording Worksheets
Procedures:
Cut the circle out of the paper as shown in Figure 1 (skip this step if precut circles are used).
Figure 1.
Teacher holds up circle and asks:
QQQWhat do we call this?
AAACircle
Fold the circle in half, open it up and then fold it in half again at a different place as shown in Figure 2.
Mark the intersection (where the two folds cross each other) of the two folds with a point (small sized dot).
Figure 2.
QQQWhat do we call the point in the middle of the circle?
AAACenter
QQQWhat do we call the distance from the center to the edge of the circle?
AAARadius
QQQWhat do we call the distance from one edge of the circle to the other throughthe center of the circle?
AAADiameter
QQQWhat is the name associated with the distance around the circle?
AAACircumference (not perimeter like used for polygons)
The students should record the circle information on their data sheets.
Have the students carefully fold the circle as shown in Figure 3. That is fold an outer edge onto touch the center, and crease the paper.
Figure 3.
Next make another fold in a similar manner, being careful to not compromise the previous fold line as shown in Figure 4.
Figure 4.
Finally make a last fold as shown in Figure 5.
Figure 5.
QQQWhat is the name of the figure created? Name and draw this figure onto the data sheet.
AAATriangle
QQQHow could the midpoint of each side of the figure be found?
AAAPlace corners together and pinch a short crease to mark the center for each side of the triangle as shown in Figure 6.
Figure 6.
Fold one of the vertices so that it is on top of the midpoint crease directly opposite the vertex. See Figure 7.
Figure 7.
QQQWhat is the name of the figure created? Name and draw this figure onto the data sheet.
AAATrapezoid
Next fold each of the smaller equilateral triangles on top of each other. See Figure 8.
Figure 8.
QQQWhat is the name of the figure created? Name and draw this figure onto the data sheet.
AAATriangle
QQQWhat observations can you make about this figure? Record and describe your findings on the worksheet.
AAASmaller than 1st triangle; similar to 1st triangle; 4 small triangles make up the large triangle; etc.
Unfold the last three folds and hold the top three vertices together. See Figure 9.
Figure 9.
QQQWhat is the name of the figure created? Name and draw this figure onto the data sheet.
AAATriangular pyramid; Teacher note – this is one of the Platonic solids, the tetrahedron if you would like to give the students an exposure to this idea.
QQQWhat observations can you make about this figure? Record and describe your findings on the worksheet.
AAAAll of the faces are congruent; the base is the same shape as each face; all of the edges are congruent; there are four faces, four vertices, and six edges; etc. Teacher note – students can be exposed to Euler’s formula here: V + F = E + 2 and Euler’s constant: V + F – E = 2
Open up the previous figure. Now fold each vertex onto the center as shown in Figure 10.
Figure 10.
QQQWhat is the name of the figure created? Name and draw this figure onto the data sheet.
AAAHexagon
QQQWhere do you see this figure in nature?
AAAHoney comb; largest regular tessellatable shape, having the largest area; bees therefore use the most economical shape in terms of the work they need to do in order to make a honey comb; Conclusion? – Bees are smart!
QQQWhat observations can you make about this figure? Record and describe your findings on the worksheet.
AAASix sides; six congruent similar triangles inside; etc.
Finally, pull up the three vertices that were just folded over and place them on top of each other. See Figure 11.
Figure 11.
QQQWhat is the name of the figure created? Name and draw this figure onto the data sheet.
AAAThis is called a truncated triangular pyramid
QQQWhat observations can you make about this figure? Record and describe your findings on the worksheet.
AAATwo triangular faces are similar; 3 trapezoid faces are congruent; etc.
DDDSo, let’s review. Unfold the figure to each object as they are named. During this exercise we discovered information about truncated triangular pyramids, hexagons, triangular pyramids, similar equilateral triangles, trapezoids, equilateral triangles, and circles. See Figure 12.
Figure 12.
At the end of the work sheet write a paragraph about what you learned from this activity. Remember a paragraph is 3-5 sentences. Sentences start with a capital and end with a period.
The worksheet and the answer sheet are on the next two pages. The answer sheet is much more detailed than required to provide a wide range of lesson plan adjustments for this activity and uses a circle with a radius of 3.5 inches.
Name: Period:Date:
Answer Key
1