Using Small 2D Shapes to Build Large 2D Shapes: Lesson for Kids

Instructor: Bethany Calderwood

Bethany has taught special education in grades PK-5 and has a master's degree in special education.

Part of geometry is learning the properties of shapes. Large shapes can often be created using multiple smaller shapes. In this lesson, you will learn to use small shapes to construct larger shapes.

Making a Mosaic

Enzo makes mosaic tables - tables decorated using a pattern of small tiles. Each table is a large two-dimensional (or flat) shape, and the tiles are small two-dimensional shapes. In order to choose which tiles to use on his tabletops, Enzo must determine which small shapes can be used to build each larger shape.

Geometry is the study of points, lines and shapes. We can use geometry to figure out Enzo's mosaics. Let's look at some of Enzo's tables.

Building a Larger Shape From Smaller Shapes

We are going to use small two-dimensional shapes such as triangles, squares, diamonds and trapezoids to build our larger shapes. For some of the large shapes, there is more than one possible arrangement. Enzo wants to know what is the least number of shapes he can use, and what is the greatest number of shapes he can use for each table.


Enzo's first table is a square. Enzo tries out different tiles, and realizes that the square can be made using two smaller triangles, like this.

A square can be made using two small triangles.


Enzo's next table is a rectangle. First, Enzo tries to use triangles again. It takes four triangles to cover the rectangle. Next, he looks at the rectangle and realizes that if he wants to use fewer shapes, he can use two squares to make the rectangle. Look at the rectangular table.

A rectangle can be made using four triangles or two squares.


Now Enzo has a six-sided table - a hexagon. How many ways can he cover the hexagon table?

A hexagon can be made using two trapezoids, six triangles, or two triangles with two diamonds.

The least number of shapes Enzo can use is two trapezoids. The greatest number of shapes is six triangles. He can also use two triangles with two diamonds.

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