## Operations With Integers: Tips and Tricks

- Like many ideas in mathematics that are abstract or symbolic, it often helps students to have a visual model to help them conceptualize the idea. A number line is a great choice for this topic.
- Students should investigate whether the properties for addition of whole numbers hold for the addition of negative numbers.
- Make use of ideas students already know, such as multiplication being repeated addition. This can help them realize that 3 x (
^{-}3) =^{-}9, since^{-}3 + (^{-}3) + (^{-}3) =^{-}9 - Connect the fact that multiplication is commutative to help you justify
^{-}3 x 4 =^{-}12, since they already know that 4 x (^{-}3) =^{-}12. - Give students a positive or negative number and ask them to give you two numbers whose sum, difference, product, or quotient is the given number. For example, given the number
^{-}8, it could be the product of^{-}4 and 2. - Don't let students say things like, “Two negatives give a positive.” They need to state, “The product of two negative numbers is positive.” Otherwise, they may misuse the above when doing addition of two negative numbers.