Understanding the Standard Algorithms for Multiplication and Division

What ideas do you consider important in thinking about the standard algorithm for multiplication? Describe any similarities or differences between the standard algorithm and some of your mental computations.

What struck you as significant as you think about these two standard algorithms for division? Do you prefer one approach to the other? Why?

Some people consider the "place value" algorithm to build on a Partitive model of division -- where you share the total among a given number of parts -- while the "Greenwood" method builds on a Quotative model of division -- where you split the total into groups of a known size. What do you think? How would this influence the model you use to represent the meaning of the algorithm?

If either of these algorithms are unfamiliar to you, take some time to explore it, perhaps using some of the division problems we solved mentally in part 2. What similarities and differences do you see when you compare your work with the standard algorithm(s) to your mental division strategies?

As we saw with addition and subtraction, standard algorithms are really just organizers to track a mental strategy -- based on place value and the properties of the operation . In fact, you may have noticed that some of the mental computation strategies you devised followed very similar thought processes, even though the organizer might have looked different.

So what do you think? How important is it to teach the standard algorithm for multiplication and/or division in today's classroom? It's not an easy question. What are the advantages and disadvantages?

If you think they do have a place, what tips would you give to educators who were preparing for this lesson?

Share your opinions and your suggestions around the teaching of the multiplication and division algorithms in Section 4.3 in your digital handout.