Learning Multiplication

Multiplication is a major topic in fourth grade mathematics and we have been working hard to learn it.  Many parents wonder why we approach multiplication so differently now than when they were learning it.  Multiplicative reasoning is more than being able to multiply and divide.  It is learning to think in groups.  Multiplication and division strategies can be considered as falling within three levels.

Level 1 is making a picture and counting all of the quantities.  If we need to find the total number of wheels on 5 tricycles, we would draw the five tricycles, each having three wheels and count the wheels.  This level is generally used in second grade.  Level 2 is skip counting by a number such as for 3: 3; 6; 9; 12; 15; 18; 21; 24; 27; 30. The count-bys give the running total.  It can be hard to skip count by numbers that are high.  I know I can't count by 8's without already knowing multiplication facts.  At some point I would revert to counting by ones which is a level 1 strategy.  This level is generally used in the beginning of third grade. Between levels 1 and 3 you will find students repeatedly adding quantities to find an answer to a multiplication situation. These two levels have been left behind at this point in fourth grade.  By the end of third grade students are moving from skip counting to thinking of multiplication problems in an array.

Level 3 methods use the associative property or the distributive property to take numbers apart, multiply the parts and put them back together.  This strategy is what we work to solidify in fourth grade.  We do this by relating multiplication to finding the area of a rectangle.  See example below.

We move from using the diagrams like the one above to using partial products.  Our goal is for every fourth grade student to use partial products to multiply multi-digit numbers by the end of the year.  We will introduce the traditional algorithm before the end of the year and they are taught the traditional multiplication algorithm in fifth grade.

It is important that students have a deep understanding multiplication before they learn the traditional algorithm or they won’t learn to think in groups.  If students don’t fully develop multiplicative reasoning abilities they will have trouble understanding fractions and proportional reasoning in middle school, which will then impact their ability to understand algebra.  

For information go to -- http://commoncoretools.me/wp-content/uploads/2011/05/ccss_progression_cc_oa_k5_2011_05_302.pdf