Embedded Assessment 1: The Art and Math of Folding Paper

Embedded Assessment 1: The Art and Math of Folding Paper
Extra Problems
Origami is the art of paper folding. In traditional origami, a single sheet of paper is folded to create a threedimensional design, such as a crane, a dragon, or a flower. Origami also has practical applications. For example,
origami has been used to fold car airbags efficiently so that they will inflate correctly in an accident.
Origami designs make use of geometric figures such as points, lines, rays, segments, and angles.
1. The diagrams at the below show how you can use origami to construct a regular hexagon from a square sheet
of paper. Describe each step in words as precisely as possible, using correct geometric notation. To do this,
you will have to add points to the diagrams. For example, you could add points A, B, C, and D to the vertices
of the original square in Step 1.
2. The diagram below show trapezoid ABCD from Step 12. You know that
.
C
B
D
60°
A
Complete the Prove statement and write a two-column proof for the equation.
Given:
Prove:
3. Consider this statement: “A hexagon is regular only if all of its sides have the same length.”
a) Write the statement in if-then form. Identify the hypothesis and conclusion.
b) Write the converse, inverse, and contrapositive of the conditional statement. Which are true?
c) Can the conditional statement be written as a biconditional statement? Explain.
4. Based on your earlier experience of folding paper, you think that you could fold a piece of paper
more times if the paper was large enough and thin enough. Thus, you find a piece of large banner
paper that is 0.01 inches thick. You make the following measurements.
Number of
folds
Thickness of
paper (in.)
0
1
2
3
4
0.01
0.02
0.04
0.08
0.16
a) Make a conjecture about the thickness of the stack after folding the paper in half six times.
Explain the pattern you used to determine your answer.
b) Did you use inductive or deductive reasoning to make your conjecture? Explain.
c) While constructing your table of thicknesses, you want to test your claim that you could fold a
single sheet of banner 30 times. Is your claim reasonable? Support your answer.