6th Grade algebra · Ages 11–12
Balance and Tip
Equations are balanced scales and inequalities are tipped ones. Grade 6 learns to handle both — and to tidy up messy expressions.
The one idea
An equation is a balance; an inequality is a tipped scale. Whatever you do to one side, do to the other.
Ready?
6th Grade algebra · Balance and Tip
Equations are balanced scales and inequalities are tipped ones. Grade 6 learns to handle both — and to tidy up messy expressions.
Full screen — no distractions
For grown-ups: 6th Grade algebra
The biggest Grade 6 trap is adding things that are not alike: 3x + 4 is not 7x. If your child says “apples and oranges” out loud while simplifying, they will make this mistake far less. Inequalities are new too — the answer is a whole range of numbers, not one.
This page is the right one if they can already…
- Solves x + 9 = 23 and 6x = 42
- Knows 2x means 2 × x
- Can plot points on a grid
Not yet? Start at 5th Grade: Undo It — algebra only works one rung at a time.
🏠 Try it at home
Combine like terms
Empty a pocket of mixed coins. “3 dimes + 4 pennies + 1 dime” — tidy it up. You can’t call it 8 dimes.
One-step equations, all four ways
“I cut a pizza into 4 slices and each slice cost $3. What did the pizza cost?” That is x ÷ 4 = 3.
Inequalities: a tipped scale
Find inequalities in the wild: “Must be over 120 cm to ride.” Write it: h > 120.
Share out the brackets
Packing lunches: 3 lunches, each with a sandwich and 2 apples. How many of each? 3(s + 2a) = 3s + 6a.
The words, in plain English
- Like terms
- Terms with the same letter part.
- 3x and x are like; 3x and 4 are not.
- Simplify
- Tidy an expression by combining like terms.
- 3x + 4 + x = 4x + 4
- Inequality
- Says one side is bigger or smaller.
- x > 4
- Expand
- Multiply out the brackets.
- 3(x + 2) = 3x + 6
- Term
- One piece of an expression, between + and − signs.
- 4x + 4 has two terms.
🌍 Algebra in an ordinary day
- “You need at least 60 points to pass” — that is p ≥ 60
- Tidying a shopping list: 2 milks + 3 eggs + 1 milk
- Buying 3 of a meal deal: 3(drink + snack)
🏁 By the end of 6th Grade
- Combines like terms and never adds x’s to numbers
- Solves one-step equations with all four operations
- Solves and graphs one-step inequalities
- Expands brackets with the distributive property
Where this fits
One idea, twelve rungs. The hiding spot just gets cleverer.
Frequently Asked Questions
What algebra should a 6th Grade child learn?
An equation is a balance; an inequality is a tipped scale. Whatever you do to one side, do to the other. By the end of the year they should be able to: combines like terms and never adds x’s to numbers; solves one-step equations with all four operations; solves and graphs one-step inequalities; expands brackets with the distributive property.
Isn’t 6th Grade too early for algebra?
No — balance and tip is standard 6th Grade maths in most curricula. This page breaks it into single moves so it never feels like a jump.
What is the most common 6th Grade algebra mistake?
Solves x ÷ 4 = 3 as x = 3 ÷ 4. They copy the operation they see instead of reversing it. The fix: Ask: is x bigger or smaller than 3? It got divided down to 3, so it started bigger.
What if my child is stuck?
Go down one rung. Every lesson here builds on the 5th 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.