Students analyze whether given statements are possible or impossible using their definitions of absolute value and the opposite of a number. If the statements are possible, students give an example of a pair of numbers that fit the statement. If the statements are impossible, students explain why.
- A number and the opposite of the number always have the same absolute value.
- In general, taking the opposite of n changes the sign of n. For example, the opposite of 3 is −3.
- In general, taking the absolute value of n gives a number |n|, which is always positive. For example, |3| = 3 and |−3| = 3.
- Since the opposite of 0 is 0 (which is neither positive nor negative), therefore −0 = 0. The number 0 is the only number which is its own opposite.
Goals and Learning Objectives
- Find pairs of numbers that satisfy different statements about absolute values and/or the opposites of numbers.
- State when it is impossible to find a pair of numbers that satisfies the statement and explain why.