Common Core Standards: Math
1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
When a little tyke is first learning to speak, it's normal for him to just stick with single words and rough, unconjugated constructions like "Me want." And that's okay! But when that dude gets to seventh grade, he's probably not gonna tell his buddies, "Me want go mall," right? It's time for more complex phrases, with prepositions and subject-verb agreement and dependent clauses all up in this biz.
So why shouldn't math be the same way? Adding and subtracting numbers is so last year. Let's up the ante a bit.
Seventh grade is all about ch-ch-changes. We're slowly but surely edging from simple arithmetic into stuff that's starting to look downright algebraic. This time around, your students will be smashing entire linear expressions together, using their hard-won knowledge of addition, subtraction, factoring, and distributing to combine like terms and pop out a new expression.
Here's the good news: all the operations (addition, subtraction, multiplication) and properties (distributive, associative, commutative) work the same way they always have, so your students aren't technically having to learn any new concepts here. The key is that they'll now be treating an entire expression as an individual term, usually with one variable and a constant.
For example, a problem might ask them to subtract 5.6x – 3.45 from 8.99x + 22.1. From there, it's just a matter of combining like terms and keeping an eye on their signs. Just make sure they remember to distribute that negative sign if it's a subtraction problem.
One major thing to emphasize in this standard is that the order of operations is still the big cheese around these parts. With an expression like -19 + 5(0.2x + 3) – 12x, students should know that they've got to distribute the middle term before they can combine anything, since multiplication always comes before addition and subtraction. Haphazardly adding that -19 directly to the 5 or 3 will land 'em in hot water, and fast. And not the good kind of hot water, like a luxurious Jacuzzi. The bad kind.
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