Grade 7 Math Test Prep: Master Key Concepts
Jennifer Sellers
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9-29Mia: Okay, I think a lot of people just heard the words Grade 7 Math Test and felt a little shiver go down their spine. It feels like there are a million little rules to remember.
Mars: I get it. But honestly, most of it boils down to just a few core ideas. If you get those, the rest starts to click into place. It’s more like a toolkit than a giant rulebook.
Mia: A toolkit. I like that. So, let's open that toolkit. First up, two terms that sound similar but are opposites: factorization and expanded form. Factorization is about breaking a number down, like seeing 12 as 2 times 6. Expanded form is the reverse, like turning 3 times the quantity x plus 2 into 3x plus 6.
Mars: Exactly. A great way to think about it is that factorization is compressing, and expansion is stretching. You're taking a Lego structure apart to see the individual bricks versus snapping those bricks together to build something. It's just two different ways of looking at the same thing.
Mia: I see. Okay, next in the toolkit: powers. A square is a number multiplied by itself, so 5 squared is 25. A square root basically asks the opposite question: what number, when multiplied by itself, gives you this one? So, the square root of 25 is 5. Then you have exponents, which are just a shortcut. 2 to the power of 3 is just 2 times 2 times 2, which is 8.
Mars: Right. And here's a real pro-tip that saves so much time: memorize the perfect squares up to 12 squared, which is 144. It’s a total game-changer on a test. When you see a number like 81 or 121, your brain should immediately go Ah, that's 9 squared or That's 11 squared. It’s like having flashcards built into your brain.
Mia: That makes sense. It removes a whole step of calculation. Now for the one that trips everyone up: BEDMAS. It's the order of operations: Brackets, Exponents, Division, Multiplication, Addition, and Subtraction. It tells you the exact sequence to solve a problem.
Mars: It's the traffic light system for math. You can't ignore it. For example, if you see 3 plus 4 times 2 squared, you can’t just go left to right. That's the biggest mistake. You have to follow the rules: Exponents first, so 2 squared becomes 4. Then Multiplication, 4 times 4 is 16. Finally, Addition, 3 plus 16 gives you 19. Any other order gives you a wrong answer.
Mia: Got it. Okay, last set of tools: factors and multiples. Factors are the numbers that divide evenly into another number. The factors of 18 are 1, 2, 3, 6, 9, and 18. Multiples are what you get when you multiply up, like the multiples of 5 are 5, 10, 15, and so on.
Mars: You got it. And that directly leads to GCF and LCM. The Greatest Common Factor, or GCF, is the biggest factor two numbers share. So for 12 and 18, the GCF is 6. The Lowest Common Multiple, or LCM, is the smallest number that they both multiply into. For 6 and 8, the LCM is 24. A simple way to remember it is that factors fit inside a number, while multiples grow outside it. GCF is about breaking numbers down, and LCM is about building them up.
Mia: So if you had to boil all of this down into a final cheat sheet, what are the absolute must-knows?
Mars: Four things. First, factorization compresses, expanded form stretches—they're opposites. Second, memorize your perfect squares up to 144; it’s a superpower for square roots. Third, BEDMAS is non-negotiable; always follow the order. And finally, GCF is about finding the biggest shared piece you can break numbers down into, while LCM is about finding the first number they both build up to.
Mia: That actually makes it all sound way less intimidating. It's just about knowing which tool to use and when.