Part 3
Understanding the Standard Algorithms for Multiplication and Division
Understanding the Standard Algorithms for Multiplication and Division
WATCH: The Standard Multiplication Algorithm
WATCH: The Standard Multiplication Algorithm
4.06_Standard Algorithm for Multiplication (#125).movDiscuss
Discuss
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 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.
WATCH: The Standard Division Algorithm(s)
WATCH: The Standard Division Algorithm(s)
4.07_Standard Algorithm for Division (#122)*.mp4Discuss
Discuss
What struck you as significant as you think about these two standard algorithms for division? Do you prefer one approach to the other? Why?
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?
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?
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?
Need a little help here...
Need a little help here...
In this classic video, Ma and Pa Kettle try their hand at the division algorithm! It doesn't go so well.
In this classic video, Ma and Pa Kettle try their hand at the division algorithm! It doesn't go so well.
Analyze their work. What are they doing wrong? What important idea do they not understand? How might this illustrate the dangers of using an algorithm without understanding?
Analyze their work. What are they doing wrong? What important idea do they not understand? How might this illustrate the dangers of using an algorithm without understanding?
If Ma and Pa Kettle were in your class, what would be your next instructional steps to help close this gap and build understanding?
If Ma and Pa Kettle were in your class, what would be your next instructional steps to help close this gap and build understanding?
TASK: Considering the Role of Teaching Standard Algorithms
TASK: Considering the Role of Teaching Standard Algorithms
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.
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.
Discuss
Discuss
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?
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?
If you think they do have a place, what tips would you give to educators who were preparing for this lesson?
Share
Share
Share your opinions and your suggestions around the teaching of the multiplication and division algorithms in this collaborative document.
Share your opinions and your suggestions around the teaching of the multiplication and division algorithms in this collaborative document.
