6th grade equations and expressions
6th grade equations and expressions (class 6): a quiz for kids, then every skill in order with lessons, a checklist and a plan.
🧒 Kids: answer 10 grade 6 equation questions. Tap Check ✓ after each one!
🔢 Equation practice 🏆 Equation levels 🧮 Equation solver ⚖️ Balance scale
What 6th grader learn about equations
In grade 6 (class 6), children start algebra. They learn what a variable is, write expressions from words, and evaluate them by substitution. They combine like terms and use the distributive property. They then solve one-step equations with inverse operations and write simple inequalities.
- 6.EE.A.2: write, read and evaluate expressions in which letters stand for numbers.
- 6.EE.A.3: apply the properties of operations to make equivalent expressions.
- 6.EE.B.7: solve one-step equations like x + p = q and px = q.
- 6.EE.B.8: write inequalities like x > c and show their solutions on a number line.
The big idea in grade 6
Grade 6 is the year letters arrive in maths. Children learn that a letter, or variable, stands for a number, and they write, read and evaluate expressions like 3x + 5 (6.EE.A.1 to 6.EE.A.2).
They use the properties of operations to write equivalent expressions, such as 3(2 + x) = 6 + 3x and y + y + y = 3y (6.EE.A.3 and 6.EE.A.4).
Then they solve one-step equations like x + 7 = 15 and 4x = 28, and write simple inequalities like x > 3 (6.EE.B.5 to 6.EE.B.8). The balance scale is the key picture.
When your child gets stuck
Most grade 6 algebra trouble comes from the letter itself. If x feels scary, swap it for a box or a blank: □ + 7 = 15 is the same question, and most children can answer it.
Then put the letter back. Seeing that x is just a hiding number takes the fear away, and the inverse operations make sense after that.
6th grade equation skills, in order
Work down the list. Each lesson explains the idea for parents with pictures and has a quiz for your child.
By the end of grade 6, your child should be able to…
- Name the terms, coefficient and constant in 4x + 7.
- Write “5 less than twice a number” as an expression.
- Evaluate 3a + 2 when a = 6.
- Simplify 2x + 5 + 3x − 1.
- Expand 4(x + 3).
- Solve x + 9 = 23 and 6x = 42, and check each answer.
- Write and graph “at least 12 people”.
Unsure where your child is? The equation levels page has a short test for every step from expressions to systems.
A 4-week plan for 6th grade equations and expressions
| When | Focus |
|---|---|
| Week 1 | Variables, expressions and their parts |
| Week 2 | Writing and evaluating expressions |
| Week 3 | Like terms and the distributive property |
| Week 4 | Inverse operations, one-step equations and inequalities |
Add 5 minutes a day with the equation practice tool. Check answers with the equation solver, which shows every step, and use the balance scale to see why both sides change together.
More for grade 6
All 6th grade math · CBSE class 6: Patterns in Mathematics · 6th grade integers · Equations quiz for grades 6 to 8 · Equations for kids
What to say to your child
A short script for teaching it the first time. Pause after each line and let your child do the next step.
- “I think of a number and add 4. I get 10. What is my number?” (6.)
- “How could we write that with a letter?” (n + 4 = 10.)
- “What is 3n when n = 6?” (18.)
- “Is 2x + 3x the same as 5x?” (Yes, like terms.)
- “How do we undo × 5?” (Divide by 5.)
More worked examples
Example 1: write: 7 more than a number
n + 7.
Example 2: evaluate: 2x + 3 when x = 4
2 × 4 + 3 = 11.
Example 3: solve: x − 8 = 15
Add 8 to both sides: x = 23.
Practice questions (answers below)
Ask these out loud or write them down. Check each answer, and ask “how did you get that?” for one or two.
- The coefficient in 9y − 2
- Twice a number, plus 3
- 5k − 4 when k = 3
- 3x + 4x
- 2(x + 6)
- x + 14 = 30
- 7x = 56
- x ÷ 3 = 9
- “Fewer than 5 apples”
- Stretch: 3(2x + 1) + x
Show the answers
- 9
- 2n + 3
- 11
- 7x
- 2x + 12
- 16
- 8
- 27
- a < 5
- 7x + 3
Common mistakes
How to teach it at home
Five minutes a day
Short daily practice beats long weekend sessions.
Number riddles
“I think of a number, double it and add 3. I get 17.” Riddles like this are equations in disguise.
Real bills
Phone plans, taxi fares and gym fees are all fixed cost plus a rate, perfect for writing equations.
By grade
- Before: properties of multiplication and the order of operations
- After: 7th grade equations and inequalities
Not sure where to start?
The free 6th grade math check-up tests every grade 6 topic in 18–22 minutes. It shows which topics are solid and which lesson to start with.
Worksheets and practice
One-step equations worksheet: printable PDF with an answer key.
Last reviewed
Questions parents ask
What equations should a 6th grader know?
One-step equations like x + 7 = 15 and 4x = 28, plus writing and evaluating expressions, like terms, the distributive property and simple inequalities.
Do 6th graders solve two-step equations?
Not under Common Core. Grade 6 solves one-step equations; two-step equations like 3x + 5 = 20 are grade 7.
Is there a 6th grade equations quiz?
Yes. The quiz at the top of this page has 10 mixed grade 6 questions. Each one is marked straight away, with a hint for every mistake. Play again for a fresh set, or try the equations quiz for all three grades.
What is class 6 algebra?
Class 6 in India and grade 6 in the US cover similar algebra, though the order differs. This page lists the skills in order, starting with what is an equation, variables, algebraic expressions.
How much equation practice does a 6th grader need?
About 10 minutes a day: 5 minutes on the current skill with the practice tool and 5 minutes of mixed review. Short daily practice works better than long weekly sessions.