Nets & 3D Shapes in NVR

<p>Spatial reasoning questions test your ability to think in three dimensions. A very common type shows you a flat net and asks which 3D shape it folds into, or shows a 3D shape and asks which net it unfolds into.</p>

<h2>What Is a Net?</h2>

<p>A net is a flat pattern that folds up to make a 3D shape. Imagine cutting along the edges of a cardboard box and laying it flat — that flat shape is the net. Different shapes have different nets: a cube has 6 squares, a triangular prism has 2 triangles and 3 rectangles.</p>

<h2>Cube Nets</h2>

<p>A cube has exactly 11 different possible nets. They all contain 6 squares joined edge-to-edge. The most common one looks like a cross. Key rules:</p>

<ul>

<li>No square can overlap another when folded</li>

<li>Every face of the cube must be covered</li>

<li>All squares must be connected by at least one edge</li>

</ul>

<p>A useful trick: any arrangement of 6 squares that forms a line of more than 4 in a row is NOT a valid cube net (because the 5th and 6th squares would overlap).</p>

<h2>Identifying Opposite Faces</h2>

<p>In the 11+ exam, nets often have patterns, letters, or symbols on each face. You must work out which face is opposite which when folded.</p>

<p><strong>Rule for a cross-shaped net:</strong> the top and bottom of the cross become opposite faces. The two arms of the cross become opposite to the faces above and below them.</p>

<p><strong>Worked Example:</strong> A cross-shaped net has faces labelled A (top), B (second from top), C (left arm), D (right arm), E (third from top), F (bottom). When folded: A is opposite E, C is opposite D, and B is opposite F.</p>

<h2>"Which 3D Shape Does This Net Make?"</h2>

<p>Count the faces and identify their shapes:</p>

<ul>

<li>6 squares → cube</li>

<li>6 rectangles (3 pairs of identical size) → cuboid</li>

<li>2 triangles + 3 rectangles → triangular prism</li>

<li>1 square + 4 triangles → square-based pyramid</li>

<li>4 triangles → tetrahedron (triangular pyramid)</li>

</ul>

<h2>"Which Net Folds Into This Shape?"</h2>

<p>You are shown a 3D shape with patterns on visible faces and must choose which net, when folded, produces exactly that shape. Use these steps:</p>

<ol>

<li>Count the faces on the 3D shape and match with the net</li>

<li>Identify adjacent faces on the 3D shape — they must be connected on the net</li>

<li>Check the orientation of any patterns: when the net folds, a pattern may rotate</li>

<li>Check which faces are opposite — they must NOT be adjacent on the net</li>

</ol>

<h2>Tracking Pattern Orientation</h2>

<p>This is the hardest part. When a net folds, the direction a pattern faces can change. Imagine the letter "T" on one face. When that face folds up to become the top of a cube, which way does the T point?</p>

<p><strong>Tip:</strong> Mentally fold one face at a time and track where the top of the pattern ends up. Some students find it helpful to point their finger in the direction the pattern faces and then "fold" their hand to track the rotation.</p>

<h2>Cubes with Dots or Symbols</h2>

<p><strong>Worked Example:</strong> A cube shows 3 dots on top, 1 dot facing you, and 2 dots on the right. Which net matches?</p>

<p>You know: 3 dots is adjacent to both 1 dot and 2 dots. And 3 dots is opposite to some face you cannot see. Eliminate nets where 3 dots is opposite to 1 or 2 dots.</p>

<h2>Practice Tips</h2>

<ul>

<li>Print nets, draw patterns on them, and physically fold them — this builds 3D thinking faster than anything else</li>

<li>Learn the 11 valid cube nets by heart so you can quickly reject invalid ones</li>

<li>Always check opposite faces — the most common trick is to put two faces that should be opposite next to each other on the net</li>

<li>For pattern orientation, use a real cube (a dice works well) and mark faces with sticky notes</li>

</ul>