Common Core Standards: Math
5. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
Introducing negative numbers to students who haven't met them before is a little like being Morpheus in The Matrix: you get to obliterate a foundational misconception and help your students rescue mankind from deadly robots! Well, one of those things is true, anyway.
This standard introduces students to negative numbers with the help of our all-time favorite math widget: the trusty number line. We'll use it when we delve into 6.NS.6, too!
We use negative numbers everywhere (e.g., temperature, debt, work, altitude, etc.), so giving students real-world applications is crucial in helping them understand negative numbers. When working with negative numbers in real-world contexts, students should understand not only what negative and positive values mean, but also what 0 means in each situation.
Naturally, as students abandon one misconception, other misconceptions might worm their way in. Some students might think that the greater the magnitude of a negative number, the greater the number. Use the number line to reinforce the fact that this is most definitely not the case.
While you can ask students to perform solve problems with negative numbers, they do not need to perform any calculations with them. In other words, leave the whole subtracting-a-negative-is-actually-addition out of it. Let the seventh grade teacher deal with that. If a few of your more dutiful pupils want to start solving problems with negative numbers, make sure to supply them with number lines so that integer arithmetic isn't necessary.
So ultimately, it doesn't matter whether students choose the blue pill or the red pill; as long as they understand what negative numbers are and the types of real-world applications they have, they're fulfilling this standard just fine.
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