Explore Multiplication by Multidigit Numbers

Use this Sample Dialog to guide the discussion of strategies for solving 49 × 20 and 24 × 15.

Students may demonstrate a range of methods to solve the problem that include everything from informal counting and repeated addition to more formal algorithms. It is important that students are allowed to begin with a strategy that makes sense to them, rather than having everyone solve the problem with a standardized algorithm. It may take a few minutes for students to construct their own methods. Some may need time to get “unstuck”; others may try several methods until they find one that works.

A wide variety of strategies are possible for these problems, and many of them highlight different important aspects of multiplication. Figure 1 and the sample dialog demonstrate how students might approach the multiplication with these informal strategies. As students progress through the unit, they will continue to develop increasingly efficient methods.

An expression such as: 50 × 20 − 1 × 20 can be written using parentheses as: (50 × 20) − (1 × 20) to help make the expression more readable and easier to calculate. The parentheses also direct us to do the operation(s) inside of them first. So, parentheses used this way are helpful in mathematics for two reasons. First, they help organize the expression visually. Second, they tell us clearly in which order operations should be done without having to consider formal rules for the order of operations (i.e., exponents first, then multiplication or division, then addition or subtraction). Another way to approach this problem is to rewrite 49 × 20 as 20 × (50 − 1). Then using the distributive property, the expression again becomes 20 × 50 − 20 × 1, which may be a simpler mental calculation than the original 49 × 20.