7th Grade algebra · Ages 12–13
Two Steps Back
Two-step equations, negative numbers and real-world stories — the year algebra starts to look like algebra.
The one idea
Undo in reverse order: peel off the adding first, then the multiplying — like taking off shoes before socks.
Ready?
7th Grade algebra · Two Steps Back
Two-step equations, negative numbers and real-world stories — the year algebra starts to look like algebra.
Full screen — no distractions
For grown-ups: 7th Grade algebra
A two-step equation like 3x + 4 = 19 is just two one-step equations in a row. The order matters: undo the + 4 before the × 3, because the + 4 was the last thing done to x. Negative answers are normal now — x = −4 is a perfectly good answer.
This page is the right one if they can already…
- Solves one-step equations with all four operations
- Combines like terms
- Adds and subtracts negative numbers
Not yet? Start at 6th Grade: Balance and Tip — algebra only works one rung at a time.
🏠 Try it at home
Two-step equations
“Think of a number, triple it, add 4. Tell me the answer.” Work out their number in your head. Then swap.
Negative answers
Use a lift or a thermometer: “We’re on floor 3, we went up 7 to get here. Where did we start?” (Basement 4.)
Brackets in equations
“Two friends each buy a ticket and a $3 drink. They spend $16. What is a ticket?” That is 2(t + 3) = 16.
Write the equation from a story
Find a real price list with a fixed fee — delivery, a gym, a phone plan — and write it as an equation.
The words, in plain English
- Two-step equation
- Needs two undoing moves.
- 3x + 4 = 19
- Negative number
- A number less than zero.
- −4
- Distributive property
- a(b + c) = ab + ac.
- 2(x + 3) = 2x + 6
- Constant
- A number that doesn’t change.
- The $3 taxi fee.
- Rate
- How much per one of something.
- $2 per mile.
🌍 Algebra in an ordinary day
- Phone plans: $10 a month plus $5 per gigabyte
- Temperatures dropping below zero
- “Think of a number” tricks — every one is a two-step equation
🏁 By the end of 7th Grade
- Solves two-step equations in the right order
- Accepts and checks negative answers
- Solves equations with brackets two different ways
- Writes an equation from a real-world story
Where this fits
One idea, twelve rungs. The hiding spot just gets cleverer.
Frequently Asked Questions
What algebra should a 7th Grade child learn?
Undo in reverse order: peel off the adding first, then the multiplying — like taking off shoes before socks. By the end of the year they should be able to: solves two-step equations in the right order; accepts and checks negative answers; solves equations with brackets two different ways; writes an equation from a real-world story.
Isn’t 7th Grade too early for algebra?
No — two steps back is standard 7th Grade maths in most curricula. This page breaks it into single moves so it never feels like a jump.
What is the most common 7th Grade algebra mistake?
Writes x = 4. They calculate 7 − 3 because taking the bigger from the smaller “can’t be done”. The fix: Use a thermometer: 3° and the temperature drops 7°. Where is it? Below zero.
What if my child is stuck?
Go down one rung. Every lesson here builds on the 6th 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.