Math Skills Pyramid: Find Your Math Gaps and Where to Start

When a math skill feels impossible, the problem is often not that skill itself. It is a skill underneath it that never quite settled: a math gap. This pyramid shows every skill your problem is built on, from kindergarten up, and tells you exactly where to start.

It is free, it takes a few minutes, and it works whether you are a student falling behind in math, an adult re-learning math you forgot, or a parent or teacher trying to find the missing skills behind a struggle.

A three-row pyramid. The goal at the top is two-step equations. Underneath, one-step equations is marked got it and negative fractions and decimals is marked stuck. Under the stuck skill, multiply and divide integers and multi-digit decimals are marked got it, and divide fractions is highlighted as start here, your math gap.
An example: stuck on two-step equations. Only the stuck skill opens a new row, and the skill you have not mastered at the bottom is where to start.

On this page, you can

  • pick any math skill taught in school, from counting to calculus
  • find out why that skill feels hard, and test yourself with a quick question
  • see only the skills right underneath it, one row at a time
  • get one clear place to start, and a short path back up, with links to lessons

Interactive Math Skills Pyramid

Pick the skill you are stuck on. The pyramid shows the prerequisite skills right underneath it, and opens deeper rows only where you have a gap.

Or pick one:

How to Use the Math Skills Pyramid

  1. Pick the skill you are stuck on. Type a word, tap a popular skill, or browse by grade.
  2. Read why it can feel hard. Most struggles come from a few well-known traps, and the pyramid names the one for your skill.
  3. Look at the row underneath: only the skills your skill stands on directly. For each one, press "I've got it" or "I'm stuck". Not sure? Press "Try one" for a quick question.
  4. Each time you are stuck, a new row opens underneath with the skills that one needs. You only go as deep as you need.
  5. When every row is answered, the pyramid shows your deepest math gap, which is where to start, and the short path back up to your skill.
Remember

Be honest with "I've got it". Press it only when you can do that skill on your own, quickly and without mistakes. If you are not sure, press "Try one" first. A skill you only half know is often the hidden reason the skill above it feels hard.

Who the Pyramid Is For

Students who are behind in math

If you are falling behind in math class, more practice on this week's topic often does not help, because the trouble started earlier. Pick the topic from class, and the pyramid walks you down to the skill you missed. Fill that gap first, and the topic from class gets easier.

Adults re-learning math

If you forgot most of your school math and do not know where to start, you do not have to begin again from 1 + 1. Pick the skill you need now, for a course, an exam or a job, and press "I've got it" on everything you still know. The pyramid skips those skills and sends you straight to what you need to review.

Students getting ready for algebra

Many students struggle with algebra because of skills from earlier grades, such as fractions, negative numbers and the meaning of the equal sign. Pick an Algebra 1 skill, such as two-step equations, to check whether you have the prerequisite skills before algebra starts.

Parents and teachers

When a child is struggling with math, the pyramid helps you find the math gaps underneath the struggle. Sit down together, answer the rows, and you get a short list of skills to fill, in the right order, with a lesson for most of them. For more ideas on studying math well, see How to Learn Math.

How the Pyramid Is Built

Behind the pyramid is a map of 316 skills taught in school math, from counting in kindergarten to calculus. It covers the US Common Core standards from kindergarten to grade 12, grouped into the usual courses (Algebra 1, Geometry, Algebra 2, Precalculus), plus the topics of AP Statistics and AP Calculus AB and BC. Each skill is linked to the skills it directly needs.

Every skill also has a short note on why it can feel hard. These notes come from research on how students learn math, and from my own experience as a certified teacher who has taught math both in the classroom and online. Research shows which mistakes are common. Teaching shows me how they look in real students: the same few traps come up again and again, whatever the grade. Most struggles go back to these:

  • Treating fractions and decimals like whole numbers. Thinking 1/8 is bigger than 1/4, or 0.65 bigger than 0.7.
  • Reading the equal sign as "the answer comes next" instead of "the same amount as". This makes equations hard later.
  • Adding when you should multiply, as in thinking 2 : 3 is the same as 4 : 5. This is the most common error with ratios.
  • Slow basic facts. When 7 × 8 takes effort, there is little room left in your head for the rest of the problem.
  • Small algebra slips such as (a + b)² = a² + b², which cause most mistakes in calculus.

Every link between two skills comes with a short note that shows exactly where the lower skill is used inside the higher one. For example, adding 12 + 13 means rewriting both fractions as sixths, and that rewriting is equivalent fractions. When research shows that one skill is the most common cause of trouble, the pyramid marks it "Most common gap", so you can check it first.

When you finish, the pyramid shows your starting skill and the chain of links from it back up to your goal, so you can see why each step matters. Your answers are saved in this browser.

Common mistake

Practicing the same hard skill again and again without checking what is underneath. If a skill does not get easier with practice, step down the pyramid. The real math gap is often one or two rows below, and filling it is what makes the skill above it click.

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