We can write, for example, \(\text-(\text-\frac23)=\frac23\) to express that the opposite of the opposite of \(\frac23\) is itself and verify this fact using the number line. Point out that the opposite of the opposite of a number is always the number itself. For example, the opposite of -4 is 4, so \(\text-(\text-4) = 4\). Connect those sentence frames to equations. Do this for positive and negative numbers, including numbers written as fractions and decimals. Then ask them to find the opposite of the opposite. Display some examples of rational numbers like 4, -3.8, \(\text-\frac\) and their opposites on the number line. So rational numbers are all fractions and their opposites. The term “RATIOnal number” comes from the fact that ratios and fractions are closely related ideas.
Tell students that rational numbers are like fractions except they can also be negative. If not mentioned by students, connect this question to the warm-up by pointing out that the temperature is halfway between -1 and -2 on the number line, and so it must be -1.5 degrees. Select students to share their reasoning as to whether they agreed with Jada or Elena in question 2. The purpose of the discussion is to use temperature to explore the concept of negative numbers and introduce the vocabulary of rational numbers.
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