The Broad Stair or Brown Stair




Ten, brown, wooden prisms all the same length but varying height and
width from 1 centimeter to 10 centimeters (or one decimeter squared).
The end faces represent the squares of the numbers one through ten.


This material provides for further refinement of the ability to
discriminate differences in size by providing a material which
varies in only two dimensions. This provides:
1) Visual and muscular perception of dimension
2) Understanding of dimensions
3) Awareness of dimension leading to observation
4) Preparation for the mathematical mind
a) Stress on 10 again
b) Demonstrates the relationship and difference between the
squares of the numbers 1 to 10:
Four of the first prism make the second (22).
Nine of the first prism make the third )32).
One hundred of the first prism make the tenth (102).


The teacher asks the child to spread a dark green mat on the floor and
has him or her help bring 2 or 3 prisms to the mat at a time. The teacher mixes
the prisms on the mat so they are parallel to one another, but not
touching. The child sits next to the teacher on the floor. Then,
beginning with the largest prism, the teacher places it towards the top
of the mat, grasping it across its thickness with one hand. This stretch
of the hand gives a muscular impression of thickness. Next, the teacher
looks around carefully choosing the next largest prism and brings it as
close as possible to the first prism. Then using both hands, one at each
end of the block, the teacher moves the second prism so the ends are
The teacher continues to arrange the prisms in a stair with the sequence
building towards the teacher keeping all the lengths exactly even. The
teacher pauses after placing each prism so the child may see that she is
choosing carefully. Finally, the teacher looks at the square ends of the
prisms with the child when finished. When the child understands, he or she may
continue. If the teacher has completed the entire stair, she would
rearrange the prisms in random order before inviting the child to do the


The child does the exercise as presented. (If he or she cannot grasp the
largest prism, it does not matter; the child can use two hands for this one. He or she
may grasp the others with one hand.) The child will make mistakes at


Later, the teacher shows the child how to hold the smallest prism with
one finger at each end and place it against each "step" of the stair,
sensorially reinforcing the difference between each successive prism.

FURTHER WORK (Possible discovery of relationships)

Sometimes children see the relationship between the pink tower and the
broad stair. They can take the pink tower and broad stair and do them
together. Some children match the largest pink cube to the largest prism
of the broad stair. Other children stand the prisms on end and place the
cubes on top. If they do this by themselves, the teacher should be
interested. However, allow them to discover this. Do not demonstrate it.


The child can usually see his or her mistakes, but if not, the teacher
should get the child to feel down the stair. The child can then feel any


When the child is familiar with the activity, and has grasped the concepts involved, the "Three Period Lesson" can be used to introduce the vocabulary below as appropriate.

Wide - Narrow
Wide - Wider - Widest
Narrow - Narrower - Narrowest


21/2 to 4 years


For developmentally delayed children, the teacher takes every other
prism to begin with, and works with five prisms presenting the lesson in
the same manner as if with the full ten prisms. The difference will then
be much greater and the child will have more chance of succeeding. The
child builds a stair. When he or she can work well, using every other prism, the child
can be given all ten to work with.


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