I hope everyone has a fun April vacation!  When we get back we will focus on making sure we understand the math content we will need for fifth grade.  Our first math unit following vacation focuses on building understanding and skills of multi-digit multiplication.  We will review and practice multiplying by 10, 100, and 1000.  We will review and practice multiplying by multiples of 10.  We will practice using what we know about area to sketch a multiplication problem, we will use partial products to solve multiplication problems and we will try out the standard algorithm (they method that you and I learned) for multiplication.

We will represent multiplication of two-digit by two-digit numbers using what we know about finding the area of rectangles.  For example:  27 x 23

When using this area model we draw a rectangle and label the length and width with our factors written in expanded form.  We find the area of smaller rectangles within the larger rectangle and add them together.  This method leads very nicely into partial products.

We will move from the visual representation above to the more efficient method of using partial products.  For example:

When using partial products we have to remember place value.  The 2 in 27 represents 20.  Just like in the area model above, when you have a two-digit number multiplied by another two-digit number you will end up with four equations.  In fact, the four equations are exactly the same as the four smaller rectangles in the visual model above.

Both of these initial methods help us to understand place value and magnitude.  We begin to really comprehend just how fast numbers grow when multiplying big numbers.  Adding 50 + 50 brings us to 100.  Multiplying 50 x 50 brings us to 2500.  That is a much greater increase.  The visual model helps us to see the difference.  Partial products help us to focus on the place value and thus the magnitude of the numbers we are multiplying.

We will introduce the standard algorithm (they method that you and I learned) and will show how it connects to the visual model as well as with partial products.  We will also discuss the fact that the standard algorithm is efficient but not always the most efficient method for finding an answer.

By the time we are finished students will have been exposed to the standard algorithm for two-digit by two-digit multiplication.  They will be experts in multiplying using partial products for three-digit by two –digit numbers.  And finally, students will be able to apply multiplication in problem solving situations.  These skills, as well as memorizing multiplication facts, are what we will need to be ready for fifth grade multiplication.