## Distributive Property of Multiplication: When Students Ask

• Why do I need to know about multiplication?
Multiplication is a faster way of adding the same number over and over. The operation is used in all levels of mathematics. Explain that multiplication is used outside of school when shopping, cooking, baking, scoring sports events, calculating an amount of carpeting, buying tickets, and many other activities.
• How can I estimate a product?
Round one or both factors to numbers that are more convenient to multiply mentally. For example, to find 7 x 96, round 96 to 100, then find 7 x 100. The estimated product of 700 is close to the exact product of 672.
• Why should I estimate a product?
Estimating a product tells you whether or not your answer is reasonable. You can check your answer by estimating the product mentally. Then compare your answer with the estimate. For example, to find 23 x 58, round 23 to 20 and 58 to 60. Find 20 x 60 by using mental math. Compare it to the product you found to determine if your product is reasonable.
• What are different ways of multiplying?
Emphasize that although there are several ways of multiplying, no one method is best all the time. First, demonstrate the use of base-ten blocks as a hands-on approach to multiplication. Second, use repeated addition of a factor to find a product. Third, stress that the multiplication algorithm can be extended to allow for any number of digits in the factors. Fourth, some problems lend themselves easily to counting on. Last, you can use mental math with the aid of the multiplication properties.
• Why do I need to know about the properties?
The Commutative, Associative, and Distributive Properties help make your multiplication accurate. The properties offer different ways to solve the same problem, often in an easier way. By allowing for different opportunities to solve the problem, it is easier to check your work and find a correct product.
• Why is mental math important?
Being able to find answers accurately in your head allows you to think about more complex and advanced problems. It gives you more freedom and extra time to spend on making other mathematical decisions.