What is an algebraic expression?

Numbers and variables joined by operations, with no equals sign, like 4x + 7.

What is a coefficient?

The number multiplying a variable. In 4x, the coefficient is 4.

A term with no variable. In 4x + 7, the constant is 7.

Terms with exactly the same variable part, like 3x and 5x. They can be combined into 8x.

What grade learns algebraic expressions?

Grade 6 under Common Core 6.EE.A.2. In India, class 7.

Algebraic expressions

An algebraic expression is numbers and letters joined by operations, like 4x + 7. It has no equals sign. A quiz for kids, parent help below.

🧒 Kids: name the parts!

Look at 4x + 7. The 4 is the coefficient, x is the variable and 7 is the constant. Can you name them all? Then try the quiz!

▶ Quiz 🔢 More practice

💡 Trick: 4x + 7 splits into two terms: 4x and 7. The + sign is the cut!

More equations: What is an equation · Variables · Algebraic expressions · Evaluating expressions · Writing expressions · Inverse operations

For parents and teachers ↓

This part is for grown-ups: the key idea, pictures to draw, what to say, common mistakes, questions with answers and a free worksheet.

The trick: split at the + and − signs

Terms are the pieces of an expression between the + and − signs. A term with a variable has a coefficient in front. A term with no variable is a constant.

3x + 5: 2 terms: 3x and 5
2a − 4b + 9: 3 terms: 2a, −4b and 9
x: coefficient 1
6 − y: coefficient of y is −1

Patterns to spot

The sign in front of a term belongs to that term: 8 − 3x has the term −3x.
A variable on its own has a coefficient of 1.
Like terms have exactly the same variable, so 3x and 5x are like, but 3x and 3y are not.
Constants are always like terms with each other.
Changing the order of terms doesn’t change an expression: 7 + 4x = 4x + 7.
Combining like terms makes an expression shorter but keeps its value.

Key words

Expression: numbers, variables and operations with no equals sign, like 4x + 7.
Term: each part joined by + or −: 4x and 7 in 4x + 7.
Coefficient: the number multiplying a variable: 4 in 4x.
Constant: a term with no variable: 7 in 4x + 7.
Like terms: terms with the same variable part, like 3x and 5x.

Why it matters: Expressions are the building blocks of equations and formulas. Knowing the names of the parts lets children follow instructions like “combine like terms” or “find the coefficient”, which come up in every algebra lesson from grade 6 on.

See it: pictures to draw with your child

Draw these on paper or a whiteboard. A quick sketch makes the idea concrete before any rules.

The parts of 4x + 7.

Algebra tiles for 3x + 2 and 2x + 3. Together they make 5x + 5.

2x − 3: red tiles stand for negative amounts.

What your child already knows

Children already know the four operations and the order of operations. They have met variables like x and n. An expression puts these together without an equals sign.

In real life: A phone plan that costs $20 plus $5 per gigabyte is the expression 20 + 5g. Shop prices, recipes and scores in games can all be written as expressions.

Expression or equation?

An expression is like a phrase: 4x + 7 names an amount but says nothing about it. An equation is like a sentence: 4x + 7 = 19 says that amount equals 19.

You simplify or evaluate an expression. You solve an equation. Checking for an equals sign tells you which one you have.

Two expressions are equivalent when they have the same value for every number. 3(x + 2) and 3x + 6 are equivalent: try x = 1, 2 or 10 and both always match.

Worked examples

Example 1: Name the parts

In 6y − 2, there are 2 terms: 6y and −2.
The coefficient is 6 and the constant is −2.

Example 2: Count terms

How many terms are in 3a + 2b + 5?
Split at the + signs: 3a, 2b and 5.
There are 3 terms.

Example 3: Combine like terms

Simplify 3x + 2 + 2x + 3.
The x terms make 5x and the numbers make 5.
So the answer is 5x + 5.

Example 4: Two variables

In 4a − 2b + 6, the terms are 4a, −2b and 6.
The coefficient of a is 4, the coefficient of b is −2, and the constant is 6.

Common mistakes

Losing the minus signSays the terms of 8 − 3x are 8 and 3x.Fix: the minus belongs to the term: 8 and −3x.

Combining unlike termsWrites 3x + 4 = 7x.Fix: x terms and numbers are different kinds, so 3x + 4 stays as it is.

Forgetting the hidden 1Says x has no coefficient.Fix: x means 1x, so its coefficient is 1.

What to say to your child

A short script for your first session. Pause after each line and let your child answer.

“How many terms in 4x + 7?” (2.)
“Which number is with the x?” (4, the coefficient.)
“Which number is on its own?” (7, the constant.)
“Is 4x + 7 an equation?” (No, there is no equals sign.)
“Can 3x and 2x be combined?” (Yes, into 5x.)

Questions to try (answers below)

Ask these out loud or write them down. The last one is a stretch.

Terms in 5x + 9
Coefficient in 7m
Constant in 2y − 6
How many terms in a + b + c + 4?
Simplify 2x + 3x
Simplify 4 + x + 6
Are 5a and 5b like terms?
Coefficient of x in 9 − x
Stretch: simplify 3x + 2y − x + 5y

Show the answers

5x and 9
7
−6
4
5x
x + 10
No
−1
2x + 7y

Games to play at home

Tile sort

Cut out long and short paper strips for x and 1, build expressions and read them back.

Term hunt

Write expressions on paper. Your child circles each term in a different colour.

Price tags

Make price expressions for a pretend shop, like 3a + 2b for 3 apples and 2 bananas.

A 5-day plan for algebraic expressions

Ten minutes a day is enough. Short, regular practice works far better than one long session.

Day 1: Learn it with real things: a kitchen scale, cups and counters, or the pictures above.
Day 2: Read the script together, then ask the first four questions.
Day 3: Do the quiz at the top of the page and read the hints for anything missed.
Day 4: Play one of the games at home for ten minutes.
Day 5: Ask the rest of the questions, then do a round of the matching equation practice skill.

By grade

Grade 6 (Common Core 6.EE.A.2b and 6.EE.A.3) names the parts of an expression and generates equivalent expressions. Grade 7 (7.EE.A.1) adds, subtracts, factors and expands expressions. In India, algebraic expressions are part of class 7 and class 8.

More for each grade: Grade 6 math and the CBSE class 6 maths guide.