This problem solving activity has a geometry focus.
Simon has just discovered copycats. A square is a copycat because you can put four of them together to make another square.
Simon wonders if triangles and circles are copycats. What do you think?
This problem explores tessellation: covering a plane surface by the repeated use of a single shape, without gaps or overlapping. Students are challenged in the first instance to identify shapes that tessellate (squares and triangles) and those that do not (circles). To do this, students should have some knowledge of two-dimensional shapes, and their basic properties (e.g. edges, corners, equal interior angles).
The 'copycat' idea in this problem involves students using tessellating squares to make a larger square, which is a 'copycat' shape of the smaller shape (i.e. the square), and using tessellating triangles to make a larger triangle in the same manner. This prompts the investigation of square numbers, such as 1, 4, 9, 16, 25, and so on.
The extension challenges students to find other shapes that tessellate to form a larger 'copycat' shape.
Simon has just discovered copycats. A square is a copycat because you can put four of them together to make another square.
Simon wonders if triangles and circles are copycats. What do you think?
All triangles are copycats. This can be shown using four triangles as in the picture.
On the other hand, circles aren’t copycats. Clearly two or more circles don’t tessellate to make a circle because there are always gaps between the shapes.
Any square number of squares 4, 9, 16, 25 can be used. Why can’t a non-square number be used? Is this the same for triangles too or do you have to use triangle numbers there?
The L-shape in the drawing below is a copycat. To check this out, put one L-shape around each of the top-left, bottom-left and bottom-right corners.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/copycats at 8:56pm on the 26th February 2024