extend a pattern in two directions, vertically and horizontally
these are some efforts to further use such an array
(there is another post with quadratic expansions)
these tasks use an idea from John Mason with Alan Graham and Sue Johnston-Wilder in their book 'developing thinking in algebra' published by the Open University in 2005
['going with and across the grain', developed further by Anne Watson and John Mason]
with multiplication sums, continuing the patterns might focus attention on how to adjust one sum to obtain results for a related sum
students are asked to complete the array i.e. to replace the gaps in the boxes:
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