We provide a free interactive online textbook for Algebra 1. The interactive lessons use dynamic graphing and guided discovery to strengthen and connect both symbolic and visual reasoning. They give the student a hands-on visual introduction to all important Algebra 1 topics, reinforced by standards based adaptive exercises and randomly generated tests. All exercises and tests are checked and graded automatically.

We recommend our approach for all students, but especially for visual learners or students who struggle with traditional Algebra 1 textbooks or courses. As in all approaches, the teacher plays a key role for most students. By removing the need for hand grading and all but the occasional lecture, we free teachers up to answer questions and help students. We hope to put the fun back in teaching.

Students should have scratch paper available. Hover the mouse over or tap a link below to see an example from that lesson (“lab assignment”). Click or tap the link again to go to that lesson. Please send us your comments, questions and suggestions.

- Arithmetic on a Grid: Counting unit squares. Sum, difference, product, quotient.
- Two-Digit Addition: Two-digit numbers shown as
$a(10)+b$ on the grid. Addition with regrouping, carrying.

Exercises - Two-Digit Subtraction and Multiplication:
Subtraction with borrowing, multiplication with regrouping.

Exercises A B C - Negative Numbers: Green squares have value
$+1$, pink squares have value $-1$. Sums and differences. Word problems involving debt.

Exercises A B - Multiplication and Division with Negative
Numbers: Products and quotients with negative numbers on the grid, introduced
through analogy and pattern-matching.

Exercises A B - Fraction Addition and Subtraction:
Visualizing fractions using pie slices. Reducing to lowest terms. Finding common
denominators.

Exercises A B - Fraction Multiplication and Division:
Using an expanded grid to visualize fractions.

Exercises A B - Arithmetic Test

- Variables and Expressions: Expressions as
quantities. Simple linear expressions. Sliders.

Exercises - Word Problems: Cost of $n$ items. Multi-variable
expressions.

Exercises - More Complicated Expressions:
Examples involving negative numbers, division, fractions.

Exercises A B - Equations as Sentences: Solving equations
by trial and error, or by sliding a slider. Inverse problems as word problems.

Exercises - Grouping in Addition and Subtraction Problems:
Parentheses, associative law of addition, order of operations for addition and
subtraction. Simplifying expressions using the associativity of addition to regroup,
including for subtraction.

Exercises A B - Solving $x+b=c$: Adding a constant to both sides.

Exercises - Grouping in Multiplication Problems: Order of
operations including multiplication. Multiplying three numbers, associative law of
multiplication and its use in simplifying expressions.

Exercises A B C D - Solving $ax+b=c$: Adding $-b$ and then multiplying by
$$1/a$$, or dividing by $a$.

Exercises A B - Applications of Linear Equations:
Balanced scale, budgeting, temperature conversion.

Exercises - Variables, Expressions, and Simple Equations Test 1
- The Distributive Law and Combining Like
Terms: Expanding $a(x+c)$, $a(bx+c)$, $-(bx+c)$. Simplifying $ax+bx$ to $[a+b]x$.

Exercises A B C - Manipulating Linear Expressions:
Adding, subtracting, scaling, simplifying. Commutativity of addition and multiplication.
Zero and one laws.

Exercises A B - Solving $ax+b=cx+d$: Adding $-cx-b$ to both sides.

Exercises - Variables, Expressions, and Simple Equations Test 2

- Points and Coordinates:
Connecting the ordered pair $(x, y)$ with the coordinate plane. Quadrants.

Exercises A B - Investigating $y=x+b$:
Finding the $y$-intercept $(0, b)$ of a line.

Exercises - Investigating $y=mx$: Lines with slope $m$, positive or
negative.

Exercises - Investigating $y=mx+b$: Slope and $y$-intercept.

Exercises A B C D E - Solving Equations Graphically: Graphing each side and
finding the intersection, e.g. for $ax+b=cx+d$.

Exercises - Finding Formulas for Approximately Linear Data: Simple statistics application. Uses root-mean-square error.
- Finding Equations for Lines: Point-slope form.

Exercises - Parallel and Perpendicular Lines: Slopes $m$ and
$$-1/m$$.

Exercises A B - Equations for Lines in Standard Form:
$Ax + By = C$.

Exercises - Linear Graphs Test

- Linear Inequalities: Half-plane solution graphs, with
or without boundary line.

Exercises A B - Equivalent Inequalities: Adding a constant to both
sides of an inequality. Multiplying both sides by a positive or negative number.

Exercises A B - Solving Inequalities Algebraically: Finding algebraic
solutions to $ax+b < c$ and similar inequalities.

Exercises - Absolute Value: Definition of absolute value. Graphing
and solving equations which include absolute values.

Exercises - Inequalities and Absolute Value Test

You can also download our jqMath JavaScript module for web page authors.