The Attached Square That Never Changes Fill
An analogy item pairs two figures on the left and starts a matching pair on the right. In the top pair, the left figure is a white square with a black outline and a small solid black triangle sitting on its top edge, point up and centred. The right figure is the same square, unchanged in size, outline and fill, but the small triangle now hangs from the bottom edge, points down, and is drawn white with a black outline.
The second pair starts with a white circle, black outline, with a small solid black square attached flat against its right side. The fourth figure is blank.
Five options are offered: a circle with a solid black square on its left; a circle with a white outlined square on its left; a circle with a white outlined square on its right; a circle with a half-size white square on its left; a white square with a small solid black circle on its left.
The instruction is to find one rule that turns the first figure into the second and apply it to the third.
1. Split the top pair into what changed and what did not, then derive the answer.
Read the worked answer
Changed:
- The small attached element moved to the opposite side of the main shape (top edge to bottom edge).
- Its fill reversed: solid black became white with a black outline.
Unchanged: the main shape's identity, size, outline and fill, and the small element's size and shape.
Apply both changes to the circle: it stays a white outlined circle, the small square moves from the right side to the left, and its solid black fill becomes white with an outline. Answer: a circle with a white, outlined square on its left.
Each other option breaks exactly one clause - black square on the left (fill not reversed), white square on the right (side not changed), half-size square (an invented size change), square as the main shape (roles of main and attached element swapped).
2. A student chooses the option with the solid black square on the left. Which half of the rule did they use, and what in the top pair contradicts them?
Read the worked answer
They applied the positional half and dropped the fill half. In the top pair the small triangle is solid black on the left and outlined white on the right; a change that visible is part of the transformation, not decoration.
The contradiction is internal to the item: if the second pair's square stayed black while the first pair's triangle turned white, the 'rule' would be different in each pair. An analogy item only works when the same operation runs in both halves. The student has matched the obvious change (movement, which is easy to see) and ignored the quieter one (fill, which requires comparing interiors).
A reliable check before committing: count the changes in the first pair - there are two - then confirm the chosen option shows two.
3. If the second pair's starting figure had shown a hollow square instead of a solid one, what would the fourth figure be? What does that reveal about how the rule should be worded?
Read the worked answer
It would be a circle with a solid black square on its left.
The reason: word the rule as an operation, not an outcome. 'Make the small element white' is an outcome; 'reverse the fill, black to white and white to black' is the operation the top pair actually demonstrates. Applied to an already-hollow square, the reversal makes it solid - the rule behaves differently from what a student who memorised 'the answer is white' would produce.
This is the safer general habit for analogy items: an operation can be applied to any starting figure, while an outcome only works when the starting figure happens to be the one you expected. Items that vary the starting figure's shading exist precisely to separate the two habits.