Common Core Standards: Math
4. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.
This standard and the one before it are often mixed up, and it's easy to see why. After all, they both deal with equivalent expressions, they both use the same y + y + y and 3y example, and they both require a profound understanding of the universe that can only be gained through a genetic or radioactive mutation followed by a Karate Kid-style training montage.
Wait. Maybe not that last one.
While both 6.EE.3 and 6.EE.4 deal with equivalent expressions, this one is about identifying them rather than producing them. In other words, given two expressions, students should be able to figure out if the two expressions are equivalent.
They can do this by applying the properties of operations (the commutative, distributive, and associative properties, for instance) to identify equivalent expressions. For instance, they should know that 2(x + 3) and 6 + 2x are equivalent because we can distribute the 2 in the first expression to wind up with 2x + 6 and then use the commutative property to switch the two terms around.
But students should know that equivalent expressions are equivalent for another reason: it's because they'll evaluate to give us the same value—every single time. If we plug in x = 0, we'll find that both expressions evaluate to give 6. If we plug in x = 1, they'll both give us 8. If we plug in x = 2,we'll get 10. Two equivalent expressions will simplify to the same value for all values of x.
Once they know those basic rules, all they've got to do is identify. And honestly, of all the tasks we could ask students to perform, "identify" is easily one of the least intensive. Seriously, identifying can be as easy as pointing a finger, clearing your throat, and saying, "That one." And unless they're fingerless chain smokers, this shouldn't be too much of an ask.
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- CAHSEE Math 5.4 Statistics, Data, and Probability II
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