Follow one fold at a time and pause whenever you want. Ask me about any step: why each door is a quarter, where the 45° angles in the roof come from, or how many layers there are.

Paper House

Fold a square into a little house with a roof, and see the halves, quarters and 45° triangles inside

Start with a square, front side down. Fold the top half down onto the bottom half. The paper becomes a rectangle that is twice as wide as it is tall: each part is one half of the side.

Fold the right side to the middle, then the left side. Each side is one quarter of the width, so the two doors meet exactly in the middle. The folded paper is now a small square. Its side is half of the first side, so its area is a quarter of the first square, and it is covered by 4 layers of paper (4 × ¼ = 1: nothing is lost).

Now comes the best step, the squash fold. Open the top corner of one door and press it flat. The corner turns into a triangle with a right angle and two 45° angles: half of a small square, cut along its diagonal. Do the same on the other side. The two triangles and the rectangle between them make the roof, and the left slope and the right slope are mirror images of each other.

The finished house is as wide as the first square and has walls one quarter of the side tall; the roof is just as tall as the walls. Stand it on the table. Pause at any step and ask the tutor why the squashed corner is a 45° triangle, or how many layers there are.

Related Topics

Paper Garrison CapFractionsShapes
How do you fold a paper house?
Start with a square, front side down. Fold the top half down onto the bottom half, then fold the right side and the left side to the middle. Open the top corner of each door and squash it flat into a triangle: these are the two halves of the roof. Stand the house on the table.
What is a squash fold?
A squash fold opens a folded corner and presses it flat so that it becomes a new shape. Here each corner becomes a triangle with two 45° angles. In the 3D animation you can watch the paper open and flatten.
What math is in a paper house?
Halves and quarters (the first fold halves the paper, each door is a quarter of the width), squares (the folded paper is a square with half the side), mirror symmetry between the left and the right of the roof, and 45° right triangles for the roof slopes.
How is the house related to the paper soldier cap?
They begin with the same folds: in half, both sides to the middle, and two squash folds. The soldier cap goes on from the little house to make a brim.