Pre-Algebra | Index

Pre-Algebra covers the number skills you need before Algebra 1. You’ll work with negative numbers, fractions, ratios and percents. You’ll also learn exponents, area and simple data.

It’s for middle school students and high school students who want a refresher. It’s also for adults coming back to math.

What to know first: how to add, subtract, multiply and divide whole numbers.

Units in this course

Unit 1: Integers and the Coordinate Plane

  1. Negative Numbers — what negative numbers mean, the number line and comparing integers
  2. Absolute Value — a number’s distance from zero on the number line
  3. Adding and Subtracting Integers — add and subtract positive and negative numbers using a number line
  4. Multiplying and Dividing Integers — sign rules for multiplying and dividing negative numbers
  5. Coordinate Plane — plot points in all four quadrants and read ordered pairs

Unit 2: Factors, Fractions and Decimals

  1. Prime Factorization — break a number into prime factors with a factor tree
  2. Greatest Common Factor — find the largest factor two numbers share
  3. Least Common Multiple — find the smallest multiple two numbers share
  4. Fractions — what fractions mean, equivalent fractions and simplifying
  5. Adding and Subtracting Fractions — use a common denominator to add and subtract fractions
  6. Multiplying and Dividing Fractions — multiply straight across, and divide by multiplying by the reciprocal
  7. Mixed Numbers and Improper Fractions — convert between the two forms and compute with mixed numbers
  8. Operations with Decimals — add, subtract, multiply and divide decimals
  9. Converting Fractions and Decimals — change fractions to decimals and back, including repeating decimals
  10. Nested Fractions — simplify complex fractions, which have fractions inside a fraction

Unit 3: Ratios, Rates, Proportions and Percents

  1. Ratios — compare two quantities and write equivalent ratios
  2. Unit Rates — find the rate for one unit, such as price per ounce
  3. Proportions — write and solve proportions using cross multiplication
  4. Unit Conversions — convert units of length, time, weight and volume with conversion factors
  5. Percentages — convert fractions, decimals and percents, and find a percent of a number
  6. Percent Change — find percent increase and percent decrease
  7. Percent Word Problems — solve problems with discounts, sales tax, tips and markups
  8. Simple Interest — find interest earned or owed with the simple interest formula

Unit 4: Exponents, Roots and Real Numbers

  1. Exponents — what exponents mean and how to evaluate powers, including negative bases
  2. Square Root — perfect squares, square roots and estimating roots that aren’t whole numbers
  3. Cube Roots — find cube roots of perfect cubes, including negative numbers
  4. Scientific Notation — write very large and very small numbers in scientific notation and compute with them
  5. Rational and Irrational Numbers — sort real numbers into types and place them on the number line

Unit 5: Order of Operations and Number Properties

  1. Order of Operations — use PEMDAS to simplify expressions in the right order
  2. Properties of Numbers — the commutative, associative, identity and inverse properties

Unit 6: Perimeter, Area and Circles

  1. Perimeter — add side lengths to find the distance around a shape
  2. Area of Rectangles and Parallelograms — use base times height for rectangles, squares and parallelograms
  3. Area of Triangles — find the area of any triangle from its base and height
  4. Area of Trapezoids — average the two bases, then multiply by the height
  5. Circumference and Area of Circles — use pi with the radius or diameter to find circumference and area
  6. Area of Composite Figures — split a shape into simpler pieces to find its area

Unit 7: Data and Probability Basics

  1. Mean, Median, Mode and Range — find the center and spread of a small data set
  2. Dot Plots and Histograms — display data and describe its shape
  3. Box Plots — find the five-number summary and the interquartile range
  4. Probability — find the probability of simple events as a fraction, decimal or percent

For Teachers: Standards Alignment

Lessons follow the Common Core grade 6–8 standards for the number system, ratios, geometry, and statistics and probability. Some grade 6–8 topics are taught in later courses. Expressions, equations, functions and slope are in Algebra 1. Transformations, volume and the Pythagorean theorem are in Geometry.

Next course: Algebra 1 Index