9th Grade algebra · Ages 14–15
Algebra 1
Algebra 1 feels like a hundred new rules. It is really three old moves — balance, undo, rewrite — used on bigger things.
The one idea
Every algebra move is one of three things: keep it balanced, undo in reverse, or rewrite it in a friendlier shape.
Ready?
9th Grade algebra · Algebra 1
Algebra 1 feels like a hundred new rules. It is really three old moves — balance, undo, rewrite — used on bigger things.
Full screen — no distractions
For grown-ups: 9th Grade algebra
If your teenager is stuck, ask which of the three moves they are trying to make. Factoring and expanding are both “rewrite” — the same thing said a different way — and the area rectangle from Grade 6 still works for both.
This page is the right one if they can already…
- Solves two-step equations with negatives
- Expands a(x + b)
- Finds slope and writes y = mx + b
Not yet? Start at 8th Grade: Lines and Slope — algebra only works one rung at a time.
🏠 Try it at home
Variables on both sides
Two savings plans: one starts with $15 and adds $2 a week, one starts with $3 and adds $5. When are they level?
Exponent rules come from counting
Fold a sheet of paper in half again and again. 1 fold = 2 layers, 2 folds = 4… layers = 2ⁿ. How many after 5 folds?
Multiply two brackets
Cut a paper rectangle into four pieces with lengths x + 2 and x + 3. Label each piece’s area.
Factor it back
Play “product and sum”: say “multiply to 18, add to 9” and race to find 3 and 6.
The words, in plain English
- Exponent
- How many times to multiply a number by itself.
- x³ = x · x · x
- Binomial
- An expression with two terms.
- x + 3
- Expand
- Multiply out the brackets.
- (x + 2)(x + 3) = x² + 5x + 6
- Factor
- Rewrite as brackets multiplied together.
- x² + 7x + 12 = (x + 3)(x + 4)
- Quadratic
- Has an x² term as its highest power.
- x² + 5x + 6
🌍 Algebra in an ordinary day
- Comparing two deals that start at different prices and grow at different rates
- Doubling: bacteria, folded paper, compound interest
- Area of a garden that grows by 2 m one way and 3 m the other
🏁 By the end of 9th Grade
- Solves equations with variables on both sides
- Uses exponent rules and can rebuild them by counting
- Expands two brackets with the area model
- Factors x² + bx + c
Where this fits
One idea, twelve rungs. The hiding spot just gets cleverer.
Frequently Asked Questions
What algebra should a 9th Grade child learn?
Every algebra move is one of three things: keep it balanced, undo in reverse, or rewrite it in a friendlier shape. By the end of the year they should be able to: solves equations with variables on both sides; uses exponent rules and can rebuild them by counting; expands two brackets with the area model; factors x² + bx + c.
Isn’t 9th Grade too early for algebra?
No — algebra 1 is standard 9th Grade maths in most curricula. This page breaks it into single moves so it never feels like a jump.
What is the most common 9th Grade algebra mistake?
Writes x² · x³ = x⁶. They multiply the exponents because the bases are being multiplied. The fix: Write the x’s out and count them. If you forget a rule, you can always rebuild it this way.
What if my child is stuck?
Go down one rung. Every lesson here builds on the 8th Grade page, and the “ready for this page if” list at the top tells you exactly what they need first. In practice, a wrong answer gives a hint, and a second wrong answer shows the full worked solution.
Is it free?
Yes. All 4 lessons, the pictures, the worked examples, the balance scale and the practice questions are free with no signup. The practice never runs out — every question is generated fresh and checked.