Fourth Grade Math: Do we really add a zero?

We are diving deeper into multiplication concepts in 4th grade.  One thing we have been exploring is “the zero trick.”  When faced with a problem such as 6 x 30, students often solve it by saying, “I just did 6 x 3 is 18 and then I added a zero.”  Is that really what happened?  I know if I add zero to anything,  the value doesn’t change, so using the students’ reasoning, we would still have 18.

However, this “zero trick” does have mathematical reasoning behind it, but it doesn’t involve addition. What’s really happening is based on the associative property.  We can relate 6 x 3 and 6 x 30.  We know that 30 is equivalent to 3 x 10.  So, 6 x 30 = 6 x (3 x 10).  However, using the associative property, we can group our factors differently, making it (6 x 3) x 10.  Then, what we  have is 18 x 10.  So we’re not really “adding 0,” but multiplying the result by 10.

Here is an example of what it looks like using arrays to model the relationship between 3 x 2 and 3 x 20.  As you can see, ten 3 x 2 arrays can fit into the 3 x 20 array.

This week we will be continuing to explore multiplication properties, including the distributive property .

Have a great week!