Articles / Curriculum finder

Placement guide, math

Which level of Art of Problem Solving should my child start?

How Art of Problem Solving levels line up with school grades, how its placement test works, what to do if your child lands between two levels, and the mistakes parents most often make.

Art of Problem Solving levels and the grades they usually suit

Grades are the publisher's own guide. Many children sit a level above or below, especially after switching programs.

How Art of Problem Solving placement works

• Each book page has two free PDF diagnostics.
• 'Are You Ready?' checks the prerequisites for the book.
• 'Do You Need This?' checks whether the child already knows the book's content.
• For Prealgebra, the child works the 26 problems with no calculator, no help and no time limit.
• The parent marks them, then gives a second chance on wrong answers except problems 4(a) to 4(d).
• A child who is ready answers at least 22 of the 26 correctly after the second chance.
• The Introduction to Algebra pretest has a Fundamentals part and a Problem Solving part: the child is ready if they solve nearly all of Fundamentals and at least half of Problem Solving.

Open the publisher's placement page

If your child lands between two levels

On the Introduction to Algebra pretest, a child who cannot solve more than 80 percent of Fundamentals should consider Prealgebra. A child who solves nearly all of Fundamentals but struggles with Problem Solving should consider reviewing Prealgebra first. On the Prealgebra 'Do You Need This?' test, nearly all of Fundamentals plus at least half of Problem Solving means Prealgebra would only be review. The publisher's general rule: a child who has finished elementary school but not a prealgebra course starts with Prealgebra, and a child who already handles square roots, simple variable expressions and simple linear equations may be ready for Introduction to Algebra.

Problems parents often run into

• Parents report that the 'Are You Ready?' tests check prerequisite skills but not the difficulty of the books, so a child who passes easily can still find the problems hard.
• Parents report that children used to worked examples followed by matching practice problems find the discover-it-yourself style frustrating at first.
• Parents report that reading a sample chapter (excerpts are on each book page) is a better guide to readiness than the test score.
• Parents report that younger starters often work through the book with a parent, take more than a year on it, and do better without a deadline.
• Parents report that children who dislike writing out their work struggle, because the problems need written reasoning.

Switching to Art of Problem Solving from another program

• The publisher recommends working through the core books in order: Prealgebra, Introduction to Algebra, Introduction to Counting & Probability, Introduction to Number Theory, Introduction to Geometry, then Intermediate Algebra.
• A student who has finished a typical school Algebra 1 course is ready for most of the Introduction series. The publisher suggests a break from algebra with Counting & Probability or Number Theory.
• Before Introduction to Geometry, the publisher suggests checking the Introduction to Algebra 'Do You Need This?' test, because that book goes well beyond a typical Algebra 1 course. The publisher calls Introduction to Geometry the most challenging Introduction-level book.
• Intermediate Algebra should come before Precalculus.
• Parents report that many children come to Prealgebra after finishing a grade 5 or grade 6 program from another publisher, and that some first cover negative numbers, because the book starts with them.

When you don't need a whole level

A placement test answers one question: which book. If your child is mostly on track but shaky in one area, say fractions or paragraph writing, a full lower level means months of review they do not need. Practising just the gaps is faster, and keeps them in the book that fits the rest of their skills.

Questions parents ask

Is it bad if my child places below their grade?

No. Programs pace topics differently, so a lower level often reflects the order things were taught, not how able a child is. What matters is starting where the work makes sense.

Do I need a placement test at all?

If you are switching programs or your child has had a hard year, yes. Starting too high is the most common reason a new curriculum stalls in the first month.

Keep reading

Sources

1. artofproblemsolving.com/store/recommendations
2. artofproblemsolving.com/store/book/prealgebra
3. artofproblemsolving.com/store/book/intro-algebra
4. artofproblemsolving.com/store/book/intro-counting
5. artofproblemsolving.com/store/book/intro-number-theory
6. artofproblemsolving.com/store/book/intro-geometry

This page is Point of Progress's own research, compiled in November 2026 from publishers' websites, placement materials and parent reviews. Publishers update their products, levels, placement tests and prices from time to time, so please verify all information with the provider before you buy. Point of Progress is independent and is not affiliated with any publisher named here.