This investigation is an opportunity for children to make a table
  to record and organise their results. It would be helpful to
  print a series of the triangles onto a sheet of paper and copy
  them for the children to draw on the pathways. Some of the
  inquiries you could encourage are:-<br />

  <ul>
    <li>Is there a pattern in the numbers of letters on each line?
    How many paths can be taken from each letter in the first
    triangle? Can a pattern be found to describe the number of ways
    the word ABACUS can be made? Is there a relationship between
    the number of letters, the number of pathways and the number of
    ways the word can be made?</li>
  </ul>

  <ul>
    <li>In the second triangle, is there a pattern in the numbers
    of letters on each line? Predict if there will be more or less
    paths from each letter in this triangle. What evidence is the
    prediction based on? Estimate and then discover how many ways
    the word ABACUS can be made? Can a pattern be found to describe
    the number of ways the word ABACUS can be made? Compare the
    results of the first and second triangle, how are they alike,
    how are they different?</li>
  </ul>

  <ul>
    <li>The children should be able to construct a right triangle
    using the word ABACUS. Ask them to predict if the result of
    their explorations will be like or different from the other two
    triangles. The results are the same as the first triangle. Why?
    Can the three types of triangles be named? What is known about
    the properties of each triangle? Does knowing about different
    shaped triangles help explain the results?</li>
  </ul>At this point, you might want to introduce Pascal's Triangle
  to the children. Information and links for Pascal's Triangle can
  be found in this month's <a href=
  "http://nrich.maths.org/prime/nov00/magazine.htm#mag8">Mouldy
  Maths</a> section. The children could try to find connections
  between patterns that occur in Pascal's Triangle and in these
  triangular arrangements of letters.<br />

  <ul>
    <li>The children could extend their investigation to
    rectangles. How many different ways do they think they could
    write ABACUS in a rectangle following the conditions given?
    Will the results from the triangle investigations help them
    predict the results for the rectangles? When they write out the
    possibilities they might be surprised. Why do they get the
    results they do?</li>
  </ul><br />