Math Problem Statement

do the same

You start with a flat square of paper, fold it one or more times, then punch a hole through it while folded. You then unfold the square of paper. Where do the holes appear when the paper is unfolded?

Solution

The question involves folding a square sheet of paper, punching a hole, and then unfolding it to observe the pattern of holes. Based on the visual representation, it looks like the paper was folded into four layers (a simple fold along both horizontal and vertical axes). After punching a hole, unfolding the paper should create a symmetrical pattern with multiple holes.

To solve this:

  1. Initial fold: The diagram shows folding the square paper once along a diagonal line, resulting in four layers.
  2. Hole punch: A single hole is punched into one corner of the folded paper.
  3. Unfolding: When unfolded, the hole will be mirrored across the axes of symmetry created by the folds.

Based on the pattern shown in the answer choices, the correct answer should be the one where the holes appear symmetrically around the folded edges.

The correct answer appears to be option 4, which shows four symmetrical holes in the paper after unfolding.

Let me know if you would like more detailed reasoning or have any further questions!

Related questions:

  1. What happens if you fold the paper more times?
  2. How would the hole pattern change if the paper was folded into thirds?
  3. What is the maximum number of holes that could appear if folded multiple times?
  4. How does the symmetry of the fold influence the hole pattern?
  5. Can the hole pattern ever result in only two holes after multiple folds?

Tip: When folding paper to observe symmetry in holes, remember that each fold line acts like a mirror reflecting the punched holes.

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Math Problem Analysis

Mathematical Concepts

Symmetry
Geometric Transformations
Folding Techniques

Formulas

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Theorems

Symmetry Theorem
Reflection of Points

Suitable Grade Level

Grades 5-7