Is there a pattern in the areas obtained after 3 fold?
Answers
Step-by-step explanation:
it multiplies i think this is an activity for geometric sequence
Answer:
This whole-class lesson is adapted from the Math By All Means replacement unit Geometry, Grades 1–2, written by Chris Confer. By folding a square of paper in several predetermined ways, children investigate and record the different shapes they can make. This activity gives children valuable experience with learning about how shapes relate to one another.
To prepare for the lesson, Chris cut squares from copier paper for the children. (The squares were about 4 inches on a side.) Chris also had ready one 12-by-18-inch sheet of newsprint for every pair of children and a large sheet of chart paper to use for tracing shapes for a class record.
After giving each child a square, Chris said, “Watch closely and fold your paper just like I fold mine.”
Chris folded her square in half to make a rectangle. When the children had folded their papers, she had them count to verify that there were four sides and four corners. “What shape is it?” she asked. (See figure 1.)

Figure 1.
Most of the children answered, “Rectangle.”
Chris unfolded the rectangle, refolded it in the other direction, and had the children do the same.
“We want to be able to fold the paper easily back and forth, back and forth,” she explained, wiggling the fold to match her words. The children did likewise. Chris then asked the children to unfold the paper to its full square shape.
“Watch first as I fold two corners down the way we do when we make a paper airplane,” Chris said. (See figure 2.)

Figure 2.
After the class had folded their papers and counted the sides and corners, Chris explained, “When a shape has five sides and five corners, it’s called a pentagon.” She asked the children to say “pentagon” aloud softly. Then she told them to wiggle the new folds back and forth a few times.

Figure 3.
Chris then showed how to fold down the remaining two corners to make a square that was smaller than the original one, but the children had their own ideas. “It’s a kite!” “It’s a dia- mond.” (See figure 3.)
Chris rotated her folded square so one side was parallel to the floor. “What is this shape?” she asked.
“It’s a square,” the students responded. “But I know it’s a diamond,” Steve insisted.
“This shape may look like a kite or a diamond when I hold it like this,” Chris explained, rotat- ing the shape so a corner was up. “But it’s still a square no matter how it’s turned.”
Then Chris introduced the exploration. “Today we’re going to investigate the shapes you can make by folding your paper different ways. The rule is: You can fold your paper on one, two, or more folds, but only on the folds we’ve already made. You can’t make any new folds. Trace the different shapes you find. You’ll work with a partner, tracing your shapes on the same sheet of newsprint.”
As Chris distributed a sheet of 12-by-18-inch newsprint to each pair of students, she asked, “How many shapes do you think you’ll find?”
Children’s estimates ranged from two to ten. (There are actually nine different shapes, if you count the original square; see the diagram below, figure 4.)

Figure 4.
Observing the Children
Chris circulated as children began folding their papers and tracing the shapes they found.
Danny asked, “Can we write something in the middle?” He pointed to the pentagon he had traced.
“Like what?” Chris inquired.
“Superman,” he answered. The shape reminded Danny of the symbol on Superman’s shirt.
Step-by-step explanation:
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