Reasoning and 11 Plus

Common mistakes in rotation and position

4 mistakes learners make with rotation and position, each one named and explained.

All common mistakes

Count the steps one at a time, and say where you are after each one.

Faces that touch mistaken for faces opposite

What it looks like

Two faces that share an edge on the net are called opposite on the cube.

Why it happens

On the flat net the two faces sit close together, and closeness feels like opposite once folded.

A worked example

Question. On a cross shaped net, which face ends up opposite the top square of the column?

A common answer. The square next to it, because they touch

The answer. The square two steps away along the column

Why. Faces that share an edge on the net still share an edge on the cube. Opposite faces sit two apart along a strip of the net.

Put the two side by side

Touching squares fold into neighbours.
Squares two apart in a line fold into opposite faces.

On a strip of the net, opposite faces are two apart, never next door.

Faces, edges and vertices mixed up

What it looks like

A count of vertices is given when edges were asked for.

Why it happens

The three counts live together in the same fact, and the question's exact word slips.

A worked example

Question. How many edges has a triangular prism?

A common answer. 6, which is its number of vertices

The answer. 9

Why. Edges are the lines where two faces meet: three around each triangle and three joining them. Vertices are the corners, and there are six of those.

Put the two side by side

6 counts the corners.
9 counts the edges.

Underline the word faces, edges or vertices in the question before counting.

The number of steps miscounted

What it looks like

A position after three moves is given as the position after two or four.

Why it happens

Counting moves and counting positions are easy to confuse when both are small numbers.

A worked example

Question. A dot starts top-left and moves one corner clockwise, three times

A common answer. top-right, after one move

The answer. bottom-left, after three

Why. Top-left goes to top-right, then bottom-right, then bottom-left.

Put the two side by side

One move: top-right.
Three moves: bottom-left.

Say each position out loud as you move. Counting under your breath loses a step.

The shape left exactly where it was

What it looks like

After a reflection or rotation, the untouched original is chosen.

Why it happens

The original arrangement is the picture already in your head, so it feels like the answer.

A worked example

Question. A flag with its pole on the left is reflected in a vertical mirror. What does it look like?

A common answer. Pole still on the left

The answer. Pole on the right, flag pointing left

Why. A mirror swaps left and right. If nothing moved, no reflection has happened.

Put the two side by side

The unchanged picture is the question, not the answer.
The reflected picture swaps left and right.

After any turn or flip, something must look different. Find what moved.

WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.

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