Reasoning · Grade 6-1 Prisms and Pyramids
Problem
Sorting the faces separates pyramid from prism.
You do not have to imagine any folding yet — just sorting the drawn faces into rectangles and triangles already decides which solid you are looking at, because a pyramid and a prism have completely different face lists.
6.G.A.4Identify SubproblemsSorting the drawn faces into rectangles and triangles already names the solid, before any folding is imagined.
Each face is either a rectangle or a triangle and never both, so the two counts describe the net completely.
A pyramid and a prism have completely different face lists, so one list of counts points to one solid and no other.
Both need 5 faces, so each lacks one.
Counting faces is simple subtraction, and it turns 'complete the net' into the much smaller question 'where does one particular face go?'.
6.G.A.4Identify SubproblemsNet (1) is missing a triangle.
Once you know which side of the base is still bare, the missing face is not a guess — you copy the triangle already drawn on the opposite side.
2.G.A.1Draw A DiagramIt can attach in three places.
Listing the faces the missing one touches, rather than every edge of the right length, is what keeps the list complete and stops an impossible spot from sneaking in.
6.G.A.4Make A Systematic ListNet (2) is missing a rectangle.
Every side face of a prism has the same width — the prism's height — so the only thing left to read off the picture is which side of the triangle is not yet covered.
2.G.A.1Draw A DiagramIt can attach in four places.
Going round the loop of side faces in order tells you exactly which edges belong to the missing face, so you never attach it where the picture only looks right.
6.G.A.4Make A Systematic ListDrawing and folding shows each closes up.
Cutting the shape out and folding it is the honest test: if the faces meet with nothing overlapping and no hole left, the net is right.
6.G.A.4Create A Physical RepresentationCount the rectangles and triangles first — the face list alone tells you whether it is a pyramid or a prism, and then you only have to find the one face that is missing.