Standard Mathematics Primary 4 Geometry

Mei Ling cuts out four paper shapes for her Mathematics project. Each shape is made from 6 identical squares joined edge-to-edge. She wants to find the one shape that does NOT fold up into a closed cube. Which shape should she choose? A: A row of 4 squares; one extra square attached above the second square in the row, and one extra square attached below the second square. B: A 2-by-2 block of 4 squares; 2 more squares attached in a row to the right side of the top-right square of the block. C: A row of 3 squares; one square attached above the leftmost square; one square attached above the middle square; one square attached below the rightmost square. D: A row of 4 squares; one square attached above the second square; one square attached above the third square.

A A
B B
C C
D D
Show Worked Solution

Worked Solution

Step 1: Recall the rule. A valid net of a closed cube must have exactly 6 squares, AND when folded, no two squares may overlap (each face of the cube must be covered exactly once). Step 2: Test shape A. The 1-4-1 'cross' is the most familiar cube net — it folds into a closed cube. VALID. Step 3: Test shape B. A 2-by-2 block already covers 4 faces (top, front, bottom, back if we fold around it). Attaching 2 more squares in a straight line off one corner causes overlap: when folded, both extra squares try to land on the same face. INVALID. Step 4: Test shape C. The 1-3-1 staircase pattern is one of the 11 valid cube nets — every square folds onto a different face. VALID. Step 5: Test shape D. The 1-4-1 with two 'hats' on adjacent squares is also a valid cube net — the two hats become top and bottom. VALID. Final answer: B. Answer: B

Correct answer: B

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