## 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.