Before beginning this activity, you should know how to do the steps of both the partial products algorithm and the standard algorithm for multiplication.
Below we have a -by- array. Explain why this array can be used to model , and then
explain why the array could also be used to model . What are you seeing as one
group? One object?
Use the partial products method to calculate . Clearly label your steps.
Subdivide the -by- array to show the same multiplication steps that you took in the
partial products multiplication. For instance, you calculated or as part of the
algorithm. Where can we see this step in the array? What are you seeing as one
group? One object?
Why does adding together the subdivisions in the array give you the correct answer
to the multiplication problem ? How was the meaning of addition important, and
how did we use the meaning of multiplication?
Why have we now justified the partial products algorithm for the example of ?
How are the steps in the partial products algorithm related to the properties
of multiplication? Explain your thinking with equations and/or pictures.
Use the standard algorithm to calculate . How are these steps related to the steps in
the partial products algorithm?
If you have extra time, repeat the steps above to justify both the partial products
algorithm and the standard algorithm using the example of .
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