Multiplication and Division as Inverse Operations

Students have been growing in their ability to multiply multi-digit numbers!  So far, we've been focusing on 2-digits X 1-digit situations, using unmarked arrays to model breaking apart one of the factors, multiplying each part, and combining the products (partial products strategy).

 

Equation: 3 x 45 = (40 x 3) + (5 x 3) = 120 + 15 = 135

 

On the division front, we're making progress in dividing larger 2-digit dividends by a 1-digit divisor using multiplication facts we know to get us there faster.  Last week, students were introduced to division with remainders and began learning how to interpret remainders, or decide what to do with the "extras" or "leftovers".  For example, leftover crackers can be divided into smaller fractional parts and shared; people cannot be divided this way, such as when arranging transportation to a destination.  Sometimes we just need to round up and get another vehicle, even though it won't be full.

This week, we'll continue investigating the inverse relationship between multiplication and division.  Here's a sneak preview!