Expressions
- Write expressions from words
- Recognize terms, coefficients, and variables
- Evaluate expressions using substitution
- Use parentheses correctly
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Grade 6 Expressions and Equations Practice Guide
Review the key Grade 6 algebra foundations with clear explanations, worked examples, common mistakes, and independent practice.
This guide supports the Grade 6 expressions and equations strand, including writing expressions, using variables, solving one-step equations and inequalities, and understanding relationships between dependent and independent variables. See the official mathematics standards.
Core skills
What students should know in Grade 6 expressions and equations
This topic is often a student’s first formal bridge from arithmetic to algebra.
Equivalent expressions
- Apply the distributive property
- Factor out a common factor
- Compare two forms of the same expression
- Check equivalence using values
Equations and inequalities
- Solve one-step equations
- Solve one-step inequalities
- Write equations from word problems
- Graph solutions on a number line
Key idea
Expressions and equations are not the same
Students make fewer algebra errors when they can clearly distinguish between the two.
Expression
An expression represents a quantity. It may contain numbers, variables, and operations, but it does not include an equals sign.
- Examples: 4x + 7
- 18 ÷ 3 + 2
- 5(a − 1)
Equation
An equation says that two expressions are equal. It includes an equals sign and can often be solved to find an unknown value.
- Examples: x + 5 = 14
- 3n = 21
- y/4 > 6 is an inequality
Helpful reminder
If there is no equals sign, it is not an equation. If there is an equals sign or inequality symbol, the goal may be to solve or compare values.
Step by step
Worked examples
Use the examples as a model for setting out clear algebraic reasoning.
1. Write an expression from words
Write an expression for “7 more than 3 times a number n.”
- 3n means 3 times n.
- 7 more than that gives 3n + 7.
Answer: 3n + 7
2. Evaluate an expression
Evaluate 5x − 2 when x = 4.
- Substitute 4 for x: 5(4) − 2.
- Compute: 20 − 2 = 18.
Answer: 18
3. Use the distributive property
Rewrite 4(y + 6) as an equivalent expression.
- Multiply 4 by each term inside the parentheses.
- 4(y + 6) = 4y + 24.
Answer: 4y + 24
4. Factor a common factor
Rewrite 18a + 30 as a product.
- The greatest common factor of 18 and 30 is 6.
- Factor out 6: 18a + 30 = 6(3a + 5).
Answer: 6(3a + 5)
5. Solve an equation
Solve x + 9 = 23.
- Undo +9 by subtracting 9 from both sides.
- x = 14.
Answer: x = 14
6. Solve an inequality
Solve n/3 < 5.
- Multiply both sides by 3.
- n < 15.
Answer: n < 15
Common errors
Six mistakes to watch for
Students improve faster when the error pattern is named and corrected directly.
- Writing 7 + 3n as 7n or 10n when the phrase is “7 more than 3 times n.”
- Substituting a value incorrectly, such as replacing x in only one place but not another.
- Forgetting to distribute to every term inside parentheses.
- Combining unlike terms such as 3x + 4 becoming 7x.
- Solving only one side of an equation without maintaining equality.
- Treating inequalities exactly like equations without thinking about the meaning of the solution set.
Independent work
Practice questions
Complete these without looking at the answers first.
A. Writing and evaluating expressions
- Write an expression for “5 less than twice a number m.”
- Write an expression for “the sum of p and 9.”
- Evaluate 6a + 3 when a = 5.
- Evaluate 2(b − 4) when b = 11.
- Evaluate 3x + 2y when x = 4 and y = 7.
B. Equivalent expressions
- Use the distributive property to rewrite 7(n + 2).
- Rewrite 24x + 16 as a product using the greatest common factor.
- Are 3(a + 4) and 3a + 12 equivalent? Explain briefly.
- Rewrite 5(y − 3) as an equivalent expression.
- Factor 12m + 18.
C. Equations and inequalities
- Solve x − 8 = 19.
- Solve 4n = 28.
- Solve y/5 = 9.
- Solve p + 6 > 14.
- Solve q − 3 ≤ 10.
D. Word problems
- A movie ticket costs d dollars. Write an expression for the total cost of 3 tickets and a $4 snack.
- Write an equation for: A number increased by 7 equals 20.
- Sam has 5 more stickers than Lina. If Lina has s stickers, write an expression for Sam’s stickers.
- A number divided by 6 is 8. Write and solve an equation.
- A rectangle has length x and width 5. Write an expression for its perimeter.
Try all 20 questions before opening the answer key.
Go to Answer KeyCheck your work
Answer key
Use the answers to locate the exact skill that still needs review.
Question 12m − 5
Twice a number m is 2m, then 5 less gives 2m − 5.
Question 2p + 9
The sum of p and 9 is p + 9.
Question 333
6(5) + 3 = 30 + 3.
Question 414
2(11 − 4) = 2(7) = 14.
Question 526
3(4) + 2(7) = 12 + 14.
Question 67n + 14
Distribute 7 to both terms.
Question 78(3x + 2)
The greatest common factor is 8.
Question 8Yes
Distributing 3 gives 3a + 12.
Question 95y − 15
Distribute 5 to each term.
Question 106(2m + 3)
The greatest common factor is 6.
Question 11x = 27
Add 8 to both sides.
Question 12n = 7
Divide both sides by 4.
Question 13y = 45
Multiply both sides by 5.
Question 14p > 8
Subtract 6 from both sides.
Question 15q ≤ 13
Add 3 to both sides.
Question 163d + 4
Three tickets plus the snack cost.
Question 17n + 7 = 20; n = 13
Translate the words and solve.
Question 18s + 5
Five more than Lina’s amount.
Question 19n/6 = 8; n = 48
Multiply both sides by 6.
Question 202x + 10
Perimeter = 2(length + width) = 2(x + 5).
Short revision plan
How to study expressions and equations in five sessions
Expressions only
- Translate words into symbols
- Identify variables and operations
- Evaluate simple expressions
Equivalent expressions
- Distributive property
- Common factors
- Check equivalence using substitution
Equations
- Solve one-step equations
- Write equations from words
- Check solutions
Inequalities
- Write and solve one-step inequalities
- Read solution statements
- Graph on a number line
Mixed review
- Complete a mixed set
- Correct errors
- Redo the weakest question type
Frequently asked questions
Grade 6 expressions and equations FAQ
What are expressions and equations in Grade 6 math?
An expression is a mathematical phrase that can include numbers, variables, and operations, but it does not contain an equals sign. An equation states that two expressions are equal.
What Grade 6 skills are most important in this topic?
Students should be able to write expressions from words, evaluate expressions by substitution, use the distributive property, identify equivalent expressions, and solve simple one-step equations and inequalities.
Do Grade 6 students solve equations with variables?
Yes. Grade 6 students typically solve one-step equations and inequalities involving a variable, such as x plus 5 equals 12 or y divided by 4 is greater than 3.
Why do students confuse expressions and equations?
Students often focus only on the numbers or operations and overlook the equals sign. A helpful reminder is that equations compare two equal quantities, while expressions simply represent a quantity.
How can I help a child improve in expressions and equations?
Use short practice sets, ask the child to translate words into symbols, require them to explain each step, and connect algebra to arithmetic patterns they already know.
Is this guide aligned to school standards?
It is based on commonly taught Grade 6 expectations, including the official Common Core mathematics standards, but state and district pacing may differ.
Need full Grade 6 practice in one place?
Use the complete revision pack for structured Grade 6 practice across expressions, equations, number systems, geometry, and statistics.