Brown Stairs is a third Montessori sensorial material and is introduced after Pink Tower at around 2 and-a-half years old. (Knobbed Cylinders are generally introduced first, followed by Pink Power, and then by Brown Stair.) Brown Stair however, is for teaching thickness. While the length of the stairs (prisms) remains constant, the square section of the broad stair varies: sides of the square sections vary according to the series of natural numbers, i.e., in the 1st stair, the square of the section has sides of 1 cm, in the 2nd of 2 cm, in the 3rd of 3 cm, etc.. The stairs therefore are in the same proportion to one another as the numbers of the series of squares (1, 4, 9, etc.), for it would take 4 stairs of the 1st size to make the 2nd, 9 to make the 3rd, etc. The pieces which make up the series for teaching thickness are therefore in the following proportion: 1 : 4 : 9 : 16 : 25 : 36 : 49 : 64 : 81 : 100.
By contrast, Pink Tower is comprised of multiple cubes, thus teaching length, width and height.
Similarly as in Pink Tower presentation, the "control of error" allows a child to check himself by placing the smallest stair on the next consecutive stair and feel with the index finger that the two adjoining stairs are the same height. Dr. Maria Montessori observed, that given the opportunity, children would rather self-correct themselves than depend on an adult to do it for them. She believed that by offering "prepared environment" which incorporates the "control of error" in a child's work, we will facilitate an advancement of reasoning and inference abilities and promote independence.
p.s. Once the child is comfortable with Brown Stairs, you may combine it with the Pink Tower and offer extensions of this activity.