little background on Beast Academy

We started creating Beast Academy way back in the dark ages, in 2011. While we can hardly remember those days, we can still remember what was driving us like it was only yesterday.

With Beast Academy, we wanted to make a curriculum that could teach in-depth math concepts to elementary students. More than that, we wanted our students to discover the joys of strategic problem solving. And we wanted to help them become math beasts — so that, someday, they’d be ready and excited for the more abstract math of AoPS Online courses, starting with Prealgebra 1.

Well, that day finally arrived! In 2018, we finished publishing a full set of Beast Academy books, from Grade 2 through Grade 5, and introduced a full suite of Beast Academy Online materials that make it possible for students in the same grades to work through an even bigger collection of engaging problems and puzzles. In August 2022, we published Beast Academy Grade 1 as a full book set and online level. With this addition, students can begin building their problem solving foundation as early as age 6.

You might have noticed your child working on advanced concepts like equivalent fractions or negative numbers as early as Grades 3 and 4. Why’d we include those challenging and fun problems? Because we had a sneaking suspicion that, with the right support, young math students could do way more than most people had thought. And our students keep proving us right!

And maybe you also have questions about what comes next. Your child has learned a lot of math, but you’re not quite sure what’s the right next step for them. Have no fear — you’ve come to the right place. In this article, we’ll address questions like:

• How can I tell my child is ready to move on from Beast Academy?
• Why is AoPS Prealgebra 1 the next step?
• What should we expect in Prealgebra 1?

To get answers, I sat down with Anakaren Santana, Curriculum Lead for Beast Academy Online. Not only has Anakaren coordinated the development of the online lessons for Beast Academy, but as part of the AoPS Online School quality control team, she’s also read hundreds if not thousands of students’ homework assignments. That means she knows a whole lot about what skills students need to succeed at different levels in our math curriculum.

Anakaren, what's the difference between Beast Academy Grade 5 and Prealgebra 1?

To answer that question, I’m going to start by taking a step back. So, in Beast Academy, we’re teaching elementary math in depth. We offer students different models, examples, strategies, and challenging problems that help them truly understand and apply math concepts. Along the way, our students also get to develop strategic problem solving skills.

Students see a limited number of abstract algebraic representations in Beast Academy, but it’s still an elementary math curriculum. That means we rely more on the kinds of intuitive reasoning and tangible models that are most accessible to younger students.  

By the time students have worked their way through Beast Academy, they’re good critical thinkers and problem solvers. Their next step is to start extending and generalizing those math concepts — and that’s where Prealgebra 1 comes in. You could say that the difference between Beast Academy Grade 5 and Prealgebra 1 is really less about the content of what students learn — and more about the approach they’re taking.

Prealgebra 1 formalizes a lot of the principles that students learned in a more tangible context in Beast Academy. The overall focus is on putting all the old, familiar pieces together and developing a high degree of fluency using those tools. Prealgebra 1 students aren’t just going to use those tools with a particular set of numbers anymore—they’re going to use those tools with everything, in a way that’s more formal and mathematically mature.

Can you give me an example of that more formal approach?

Sure. So, just to set the stage, Beast Academy students are used to thinking about math concretely. For example, we introduce a clever strategy for approaching division that uses marbles and buckets. We tell students that we have 12 marbles that we want to put in three buckets, with an equal number of marbles in each bucket. Then, we say, we get another 18 marbles, and distribute those additional marbles evenly into the same three buckets. And we represent that procedure by telling students that (12+18)÷3=(12÷3)+(18÷3).

Beast Academy students then get to use the same strategy to divide much larger numbers, so they learn to recognize 63,042÷7 as (63,000÷7)+(42÷7). As you’ll see, Beast Academy students are definitely tackling difficult problems! But the way they approach those problems is much more concrete, and much less abstract, than what they’ll see in Prealgebra 1.

And how is the AoPS Prealgebra 1 approach to math different?

In Art of Problem Solving’s Pre Algebra 1 books (and class), students see a very similar problem. Except now, we formally define division as 𝑎÷𝑏=𝑎⋅1𝑏. And then we show them how to put that together with the distributive property of multiplication.

That’s an example of how, in Prealgebra 1, students start thinking about math on a more abstract level. In the Prealgebra textbook, Problem 1.41 asks

Using the definition of division, explain why

(12+18)÷3=12÷3+18÷3.

And as you’ll see, in the solution to that problem, we’re citing definitions and properties of arithmetic operations:  

Later, we go on to extend that example with an algebraic representation of that property—we tell students that (𝑎+𝑏)÷𝑐=(𝑎÷𝑐)+(𝑏÷𝑐). And they can use that in even more complex problems, like (𝑎+𝑏+𝑐+𝑑+⋯)÷𝑛.

Why is the AoPS abstract approach to math so important?

Well, it helps students develop the skills they’ll need to solve more challenging kinds of problems. After all, as they keep learning math they’ll see problems that are more and more abstract—and mastering concepts and principles is essential to tackling math when it starts being presented formally. Eventually, they’ll start solving problems with step-by-step proofs, where each step relies on earlier proofs and definitions.

In fact, Prealgebra 1 students end up writing their own mathematical proofs as part of their weekly homework. We call these “writing problems,” and they help our students master math concepts on a more abstract level. After all, our goal is for students to be able to generalize their math knowledge so they can use it to solve lots of different kinds of problems.

That sounds like a big transition! How can a parent tell when their child is ready to move on from Beast Academy?

It’s a surprisingly tough question. After all, parents and teachers are using Beast Academy and Beast Academy Online with their students in all kinds of different ways. Ultimately, deciding when a child is done is always going to be up to the parent or teacher.

But you could say that a student is done with Beast Academy when they can pass the “Are You Ready?” placement test for Prealgebra 1. That’ll tell you if your child has the math skills they need to start learning more complex material.

Anything besides pure math skills that parents should keep in mind?

Yeah, students will also need a certain level of intellectual maturity. For example, Prealgebra 1 is an online class, which means that the format is totally different from working through the Beast Academy books or Beast Academy Online. If a student takes our Weekly Live Online Prealgebra 1, they’ll have a once-a-week session that’s an hour and fifteen minutes, where their instructor walks them and about 50 or 60 other students through a set of math problems.

Recently, we opened enrollment for a brand-new Self-Paced Prealgebra 1 course. It’s an automated learning experience that offers a more flexible schedule than our standard live courses. You’ll find it on the same page as our Live Prealgebra 1 class.

(Editor’s Note: keep an eye out for more information about Self-Paced classes being shared soon!)

Whether students take a Live class or a Self-Paced class, they’ll also have a Class Message Board where they discuss problems with their classmates and our expert teachers. Using resources like the Message Board really lets students advance their mathematical skills. If they want help, they have to communicate their question correctly, so it’s a great way to start learning the language of mathematics. Plus, it can be really fun to interact with peers who care about math! For those of us who love the subject, talking about math to other math-y folks is definitely one of the things we love most about AoPS.

What's a good way for parents to tell if their child is ready for the online classes?

I’d suggest that parents try sitting in on an introductory level AoPS Math Jam with their student. Math Jams are free online discussions we have periodically on AoPS Online, and the way you participate is exactly the same as one of our online math classes. They’re even about the same length. We’re having a Math Jam soon about graduating from Beast Academy and moving into Prealgebra 1. Parents can sit alongside their student and gauge whether their student is ready for the length of the class and the style of interaction. It’s also a great time for parents to get their questions asked and learn more about the supportive, math-focused community we’ve created at AoPS Online.

And what can you recommend for students who aren't quite ready?

That can happen sometimes — especially with younger students. Maybe they’ve been through all the material in Beast Academy, but they’re not comfortable yet with the more intense dynamic of the online classes. And that’s perfectly fine!

We want to make that transition to Prealgebra 1 as smooth and as comfortable as possible. No one should feel like they’re getting thrown out of the Beast Academy universe! Beast Academy Online is going to have tons of new material soon, including videos and the new Professor Grok’s Puzzle Lab. Plus, students can keep learning by tackling any harder problems they didn’t quite nail the first time, including those really tough Trophy Problems. The new Puzzle Lab, in particular, is going to be really exciting — it’ll help students build problem-solving muscles that they’ll use for years to come!  

Students can also branch out a little by looking at Alcumus, AoPS’s free online math practice tool. It’s a great way to start introducing some new material, even if students want to stay anchored in Beast Academy a little longer.

Any other options parents should keep in mind?

Another route that parents can explore, if their student isn’t quite ready for Prealgebra 1, is to get a copy of the Prealgebra textbook, and work through that, along with Alcumus and our Prealgebra videos, which cover stuff like How to Tell if a Number is Prime and Using the Pythagorean Theorem.

While older students often love that AoPS Online classes and textbooks feel ‘grown-up,’ that transition can be a little tricky for younger students. If your child finds the math and the problem solving of Prealgebra engaging, then they’re definitely ready for it.

But if you find that your child still needs the plot of the Beast Academy Guide Books and the charming monsters to stay interested in the math, then it’s totally fine to stay in the Beast Academy universe a little longer. Follow your child — they’ll let you know when it’s time to move on.

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