For young children, this problem is best done as a physical pattern, built
with real blocks. The children should be asked to first make the up-and-down
staircase with one block, then with four blocks to make sure they understand
the essential characteristics of the pattern. Then invite them to build an
up-and-down staircase that has 3 steps up and 3 down, then the 4 step
staircase, then finally the 5 step staircase. <p>

Ask the children to explain how they built each staircase and about any
patterns they see. Some may recognise the horizontal layers as being the
sequence of odd numbers. Some may see the symmetry of the vertical
stacks. You may wish to introduce the concept of square numbers by simply
rearranging the blocks in an up-and-down staircase. <p>

<img src = "<!--#echo var = "directory"-->/fig3.gif">
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<img src = "<!--#echo var = "directory"-->/fig4.gif">

<p>

Some children may wish to continue to find larger numbers that make
up-and-down staircases (square numbers), in which case colouring squares on
grid paper might be helpful for recording. <p>