A question showing paper being folded and hole-punched. You must find what it looks like when unfolded.

1. Follow each fold carefully  2. Note where holes are punched  3. Unfold in REVERSE order  4. Remember holes appear on ALL layers the punch went through

How do you solve paper folding questions?

Usually 2 holes (one for each layer), unless the hole is on the fold line (then just 1).

When paper is folded once and punched, how many holes appear when unfolded?

If paper is folded twice and then punched once, how many holes maximum when unfolded?

If paper is folded 3 times and punched once, how many holes maximum?

Holes are symmetrical around the fold line.

What pattern do the holes make when paper is folded and unfolded?

On the left side, at the same height, mirrored across the fold line.

If paper is folded in half vertically and punched on the right, where is the other hole?

Holes are symmetrical around the diagonal fold line.

If paper is folded diagonally, what pattern do the holes make?

You must find a specific simple shape hidden within a more complex figure.

1. Know what shape you're looking for  2. Look for its distinctive features (corners, edges)  3. Try rotating the shape mentally  4. Trace the shape with your finger

1. The shape might be rotated  2. It uses existing lines (not new ones)  3. It must be complete (all sides present)  4. Extra lines may pass through it

What should you remember about hidden shapes?

Be systematic: count small shapes first, then combinations, then the whole figure if it's a shape too.

How many triangles are in a triangle divided by 1 line from vertex to opposite side?

A square is divided into 4 equal small squares. How many squares total?

A question where part of a symmetrical figure is shown, and you must identify the complete figure.

1. Find the line of symmetry  2. For each point on the given half, find its mirror point  3. Connect points to complete the shape

How do you complete a symmetrical figure?

Find where a simple shape fits exactly within a complex figure.

Embedded figures must fit EXACTLY - same size, same orientation. Hidden shapes might be rotated.

What's the difference between hidden shapes and embedded figures?

Identify each separate shape, then consider: what's in front, what's behind, where they intersect.

The intersection creates a new region that belongs to BOTH shapes.

When shapes overlap, what new regions are created?

Following a line or path through a complex figure to see where it leads.

1. Use your finger or pencil to trace  2. Go slowly at intersections  3. Don't jump lines  4. Check your path twice

1. Understanding perspective  2. Knowing how shapes look from different angles  3. Mental rotation ability  4. Recognizing hidden surfaces

What skills help with 2D to 3D visualization?

Find features that don't change (number of surfaces, relative sizes) and features that reveal the angle (which surfaces are visible).

How do you identify an object from a different viewpoint?

Shapes have codes (letters/numbers) based on their properties. You must decode the system and apply it.

1. Look at several coded shapes  2. Find what's similar/different  3. Match properties to code parts  4. Test your theory on all examples

1. Inside/outside  2. Above/below  3. Left/right  4. Touching/separate  5. Overlapping/adjacent  6. Relative size  7. Relative distance

What spatial relationships should you look for?

1. Practice with physical objects (folding paper, building blocks)  2. Draw shapes from different angles  3. Do jigsaw puzzles  4. Play spatial games

1. Forgetting about symmetry in paper folding  2. Missing rotated shapes  3. Miscounting layers  4. Rushing instead of visualizing carefully

What common mistakes happen in spatial reasoning?

Mental visualization - being able to picture shapes, rotations, and folds in your head.

What is the most important spatial reasoning skill?

Master paper folding, hidden shapes, and visualizing spatial relationships

Spatial Reasoning

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