Saturday, October 8, 2011


I had a teacher ask me how to teach 2 digit x 2 digit subtraction with manipulatives.  I thought this would be a great time to share this and talk about the importance of the CPA model of instruction.  Jerome Bruner's research has shown us that when we teach using manipulatives first (concrete), then moving to a pictorial represention (pictorial), and finally to the traditional algorithm (abstract), our students learn to a greater degree of mastery and have greater retention...yay!  Here's an example.
Using base 10 blocks, I've set up 12 x 21.  (It's important students see that numbers outside the lines not get added back in to the final product.)  Now I can start setting up the array.
I'm not sure why this picture rotated but I think you can still see it.  Students can see 10 x 10 =100 here and 1 x 10 = 100.  My students understood they needed to make a complete rectangle.  They really like to push it together!  (By the way, while place value disks are my favorite, this works much better with base 10 blocks.)

To build the pictorial, we go to the array model.

It wouldn't let me insert a table.  Having major computer issues today (for a change!)
Draw a connection between each of these partial products and the pictures above.

Now students can take it to partial product or traditional algoritm.

                      2  It's all about language here.  2 x 1 = 2
                    40  2 x 20 = 40
                    10  10 x 1 = 10 (Can you find it in the pic and the array?)
                  200  10 x20 = 200  
Partial products are great to use if your kids "put down the wrong number and carry the wrong number." It means they aren't using place value and this will help them.

Looking for a practice game?  Me too!  Have students each deal out 4 cards and arrange them to make a 2 digit x 2 digit problem.  Record the product.  Play 5 rounds.  Total them.  Person with the highest sum wins.  Do you have a double digit multiplication game?

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