The types of triangles used in Montessori math are the mathematical triangles -- the right triangle, which has one right angle; the obtuse triangle, which has one angle greater than 90 degrees; and the acute triangle, in which all angles are less than 90 degrees. These are the mathematical triangle types that are accepted in all studies and practices. The difference with Montessori triangles is how they are used and what types of materials they're made of.
Triangles are used in Montessori math as manipulative items -- they can be picked up and held -- to teach pupils about math and shapes. Several sizes of triangles are cut out of plastic, cardboard or paper. Pupils can explore the way the triangles look and feel with their fingers. They can match triangles to create other shapes, such as squares.
Montessori triangles are often presented in different colors. Bold colors, one for each type of triangle, are used so that pupils have another way of recognizing which type of triangle they are looking at. In a particular classroom, all the acute triangles will be one color, all of the obtuse triangles and right triangles another.
Triangles are also used in different types of math instruction with the Montessori method, such as fractions and parts-of-a-whole instruction. Pupils learn that two right triangles, put together, make a square. Other pieces can be created from triangles, such as other geometric shapes. Pupils are allowed to explore these activities with minimal instruction.