1. Write and evaluate numerical expressions involving whole-number exponents.

Students are boppin' along, feelin' pretty good about their addition, subtraction, multiplication, and division chops—when suddenly, out of nowhere, something whacks them on the side of the head. They fall to the ground dazed, and after taking a few moments to recover from the blow, they spot the object that nearly gave them a concussion. It's a monkey wrench with a word scribbled on it, a word that worsens their headache a thousand times over.

Exponents.

That's right. Just as soon as students were feeling good about mastering the four basic operations with all types of numbers, we're throwing them for a loop and introducing exponents. Whatever doesn't kill 'em makes them stronger, and all that.

Students should start by understanding that exponents tell us how many times to multiply that base by itself—that 7³ just means three 7s multiplied together: 7 × 7 × 7. That's it. What's more, they should be comfortable going back and forth between these two forms.

Emphasize to them that exponents are just symbolic shorthand—a fast and easy way to write the exact same thing. And hey, fast and easy is what we're all about.

Remember two things. First, we're only dealing with whole-number exponents at this stage in the game, so leave negative and fractional exponents at the door. Leave them for the eighth grade and high school teachers to handle.

Second, we're talking about numerical expressions only. In other words, if you see a variable with an exponent on it, abort the mission. Students aren't ready for things of that caliber just yet.

What students should be able to do is write a numerical expression using exponents to model a real-world problem. A real-world problem using exponents could be, "A colony of Weebles doubles every day. If there are 5 Weebles on Monday, how many Weebles will there be in the colony on Saturday?" Students should know that'll end up being 5 × 2 × 2 × 2 × 2 × 2, or 5 × 2⁵ Weebles.

And don't forget that evaluating numerical expressions with exponents gives students the opportunity to revisit and practice the order of operations. Whether you're an avid PEMDAS supporter or not, students have to know which operations to complete in what sequence.