Alpha School · Math

Math Study Guides

Five grade-level guides. Each one walks a skill at a time — a question you can already answer, one new move, the rule, the trap it sets, then a short ladder of practice. Between the sections are mixed checks where nothing tells you which skill to use. That is the part a test is really testing, so they are the ones not to skip.

Every question is new. None of them is from a real test, and the numbers and stories have all been changed.

How to use a guide

Answer, press Check, then read the answer even when you were right — it shows the method, and where each wrong option comes from.

Your work is saved in your own browser, so you can close a guide and pick it up where you left off.

Grade 3

8 sections · 50 questions

Place value to 100,000 · adding and subtracting within 1,000 · multiplication and division · fractions on a number line · comparing fractions · perimeter and area · pictographs, dot plots and bar graphs

Grade 4

9 sections · 53 questions

Place value and rounding · decimals and fractions · multiplying big numbers · dividing with remainders · multi-step equations · adding and comparing fractions · angles and shapes · perimeter and area · data and patterns

Grade 5

9 sections · 55 questions

Comparing, ordering and rounding decimals · decimal arithmetic · multiplying and dividing whole numbers · order of operations · equations from a story · fraction operations · volume, area and perimeter · the coordinate plane · classifying shapes, reading data

Grade 7

9 sections · 56 questions

Negatives, decimals and fractions · proportional relationships and rates · percent change, discounts and interest · two-step equations and inequalities · similar figures · circles · volume and surface area · probability · box plots and inferences

Grade 8

10 sections · 60 questions

Real numbers and scientific notation · slope and rate · y = mx + b · functions and systems · equations with variables on both sides · transformations · the Pythagorean theorem · volume of cylinders, cones and spheres · surface area · scatterplots, mean absolute deviation, interest