⚖️ Grade 7 · equations · session 1 of 12 · 60 minutes · free

Like terms: combining and simplifying expressions

An expression is built from terms. Like terms have the same variable part, so they can be added together: 3x + 5x = 8x, but 3x + 5 stays as it is. Simplifying makes an expression shorter without changing its value.

🎯 Practice mode 🖨 Print a worksheet

A complete lesson · 60 minutes

Teach it, see it, practise it, all on this page.

Open this page with your learner and work down it, or press Teach this lesson to go through it one step at a time on a big screen. Every section has something to do.

See the teacher's plan

Warm-up4 min
Terms and coefficients9 min
Combining like terms9 min
Rational coefficients and checking9 min
Activity 17 min
Activity 27 min
Activity 35 min
Quiz6 min
Set the project4 min

By the end you can

Name the terms, coefficients and constants in an expression
Combine like terms, including negative and decimal coefficients
Check two expressions are equivalent by substituting a value
NJSLS-M 7.EE.A.1 (Common Core 7.EE.1)

Before you start

Adding and subtracting integers
Using a letter for an unknown number

Have ready

Algebra tiles (on screen) or paper squares and strips

Grade 7 · Unit 2 · NJSLS-M and Common Core 7.EE

Warm-up · think first

You buy 3 packs of pencils and later 5 more packs, plus 4 loose pencils. How would you write the total if a pack has p pencils?

Show the answer

3p + 5p + 4 = 8p + 4. The packs combine because they are the same kind of thing; the loose pencils stay separate.

Teacher tip: Ask: why can't 8p and 4 be added into 12?

More warm-ups for every class →

Part 1 of 3 · learn, see, practise

Terms, coefficients and constants

A term is a number, a variable, or a number times a variable: 7, x, 4y, −2.5x.

The coefficient is the number in front of the variable (in −2.5x it is −2.5). A term with no variable is a constant.

Terms are separated by + and − signs, and each sign belongs to the term after it.

Example 1

In 6x − 3 + x, name the terms and coefficients.

Split at the signs: 6x, −3, +x.
6x has coefficient 6; x has coefficient 1.
−3 is the constant.

Answer: Terms 6x, −3, x; coefficients 6 and 1; constant −3

Practise it

Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.

Warm-up1What is the coefficient of x in 9x + 2?

Warm-up2What is the constant in 4x − 7?

Core3What is the coefficient of x in −x + 5?

Core4How many terms are in 3x + 2y − 5 + x?

Stretch 🔥5What is the coefficient of x in 0.5x − 1.25x? (Combine first.)

Answers (for the teacher)

9
-7
-1
4
-0.75

Part 2 of 3 · learn, see, practise

Combining like terms with algebra tiles

Like terms have exactly the same variable part: 3x and −5x are like terms; 3x and 3 are not.

Add the coefficients of like terms and keep the variable: 3x + 5x = 8x.

A positive tile and a negative tile of the same kind make a zero pair: x + (−x) = 0.

Example 1

Simplify 4x + 3 − x − 5.

Group like terms: 4x − x and 3 − 5.
4x − x = 3x; 3 − 5 = −2.
Write it with the x-term first.

Answer: 3x - 2

Algebra tiles

Green strips are +x, yellow squares are +1, pink tiles are negative. Tap a tile to remove it; Simplify groups like terms and removes zero pairs.

Simplify the starting tiles: what do they show?
Build 3x − 2 (and simplify).
Build −x + 4.

Practise it

Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.

Warm-up1Simplify: 5x + 2x

Warm-up2Simplify: 7x - 3x + 4

Core3Simplify: 6x + 4 - 2x - 9

Core4Simplify: -3x + 8 + x - 2

Stretch 🔥5Simplify: 2.5x - 4 + 1.5x + 0.5

Answers (for the teacher)

7x
4x + 4
4x - 5
-2x + 6
4x - 3.5

Part 3 of 3 · learn, see, practise

Rational coefficients and checking by substitution

The same rules work for decimals and fractions: 0.4x + 1.1x = 1.5x and 1/2 x + 1/4 x = 3/4 x.

To check a simplification, put a number in for x in both expressions: equivalent expressions always give the same value.

Write answers with the x-term first, like 1.5x − 2.

Example 1

Simplify 1/2 x + 3 + 1/4 x − 1 and check with x = 4.

1/2 x + 1/4 x = 3/4 x; 3 − 1 = 2.
So 3/4 x + 2 (or 0.75x + 2).
Check x = 4: original 2 + 3 + 1 − 1 = 5; simplified 3 + 2 = 5. ✓

Answer: 0.75x + 2

Practise it

Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.

Warm-up1Simplify: 0.4x + 1.1x

Core2Simplify: 1/2x + 1/4x + 3

Core3Simplify: 1.2x - 3 - 0.2x + 5

Core4Put x = 3 into 4x − 1 + 2x. What is the value?

Stretch 🔥5Simplify: -0.6x + 2.4 - 1.4x - 0.4

Answers (for the teacher)

1.5x
0.75x + 3
x + 2
17
-2x + 2

Watch out

Common mistakes

Adding unlike terms

3x + 5 is already simplest; you cannot make 8x.

Losing the sign

The sign in front belongs to the term: in 4 − 2x the term is −2x.

Forgetting the hidden 1

x means 1x and −x means −1x.

Class activity 1 of 3

Simplify race

Simplify each expression. Write the x-term first.

Underline like terms in the same colour.
Add their coefficients.
Check with x = 2.

1Simplify: 3x + 4x + 1

2Simplify: 10 - 2x + 5x - 3

3Simplify: -x - x - x + 6

4Simplify: 0.25x + 0.75x - 2.5 + 1

Answers (for the teacher)

7x + 1
3x + 7
-3x + 6
x - 1.5

Class activity 2 of 3

Spot the equivalent

Which expression is equivalent? Type the letter.

Simplify both.
Compare.
Check with a number.

1Is 5x − 2 + x equivalent to (A) 6x − 2 or (B) 4x − 2?

2Is 7 − 3x − 2 equivalent to (A) 5 − 3x or (B) 4x?

3Is 2x + 2x + 2 equivalent to (A) 6x or (B) 4x + 2?

4Is −x + 4 − 3x equivalent to (A) −4x + 4 or (B) −2x + 4?

Answers (for the teacher)

Class activity 3 of 3

Perimeter puzzles

Write a simplified expression for each perimeter.

Add all the sides.
Combine like terms.
Write the x-term first.

1A triangle has three sides of x + 3. Perimeter: x + 3 + x + 3 + x + 3

2A rectangle has sides 2x + 1 and x. Perimeter: 2x + 1 + 2x + 1 + x + x

3Sides x, x, 2x + 5 and 3x − 1. Perimeter: x + x + 2x + 5 + 3x - 1

4Sides 0.5x, 0.5x, 1.5x, 1.5x. Perimeter: 0.5x + 0.5x + 1.5x + 1.5x

Answers (for the teacher)

3x + 9
6x + 2
7x + 4
4x

After class · project

Expression menu

Design a café menu where every price is an expression, then simplify the cost of three orders.

Choose 4 items with prices like x (a drink) and x + 1.5 (a snack).
Write three customer orders as long expressions.
Simplify each order.
Check one order with x = 2.

What to make: A menu and three simplified order totals.

Stretch: Add a discount term like −0.5x to one order.

How it is marked

Look for	Done well when
Expressions	Prices use a variable sensibly
Simplifying	Like terms combined correctly
Check	Substitution shows equivalence

Project template

Copy it onto paper or print the practice sheet.

Item 1: ______  price: ______
Item 2: ______  price: ______
Order A: __________________ = (simplified) ______
Order B: __________________ = ______
Check with x = 2: ______

Homework

Practise at home

Try each on paper, then tap to see the answer and working. Or print the practice sheet.

Simplify 8x − 3 + 2x + 10.
10x + 7
Simplify −4x + 6 − x − 6.
-5x
Simplify 1.5x + 2.25 − 0.5x.
x + 2.25
Explain why 5x + 3 is not 8x.
5x and 3 are not like terms: one has x, one does not.

🔥 Challenge round · finished early?

The hardest questions of the lesson, no notes

Cover the notes and try these from memory. They are meant to make you think hard: draw, try small cases, and check your answer.

Stretch 🔥1What is the coefficient of x in 0.5x − 1.25x? (Combine first.)

Stretch 🔥2Simplify: 2.5x - 4 + 1.5x + 0.5

Stretch 🔥3Simplify: -0.6x + 2.4 - 1.4x - 0.4

Answers (for the teacher)

-0.75
4x - 3.5
-2x + 2

🧠 Think-hard question

Simplify 3x + 2y − x + 4y − 7 + 2.

Talk it through or use the drawing board. There is more than one way to get there.

🎯 Practice mode: one question at a time 🧩 Brain warm-ups 🎮 Maths and logic games

Quiz · 8 questions

Final quiz: check what you learned

Pick an answer to see if it is right and why. Your best score is saved on this device.

1Which are like terms?

Show the answer

4x and −x. Same variable part: x.

2Simplify 6x + 2 − 4x.

Show the answer

2x + 2. 6x − 4x = 2x; the 2 stays.

3The coefficient of −x is …

Show the answer

−1. −x means −1 × x.

4Simplify 3 − 5x + 2x − 7.

Show the answer

−3x − 4. −5x + 2x = −3x; 3 − 7 = −4.

5Simplify 0.3x + 0.9x.

Show the answer

1.2x. 0.3 + 0.9 = 1.2.

6Which is equivalent to 2x + 2x + 2x?

Show the answer

6x. Three lots of 2x.

7A tile +x and a tile −x together make …

Show the answer

0. A zero pair.

8Check with x = 2: is 3x + 1 + x equal to 4x + 1?

Show the answer

Yes, both are 9. 3(2) + 1 + 2 = 9 and 4(2) + 1 = 9.

For parents and teachers

The 60-minute lesson plan

Use it as it is, or stretch any part over two sessions. Each row links to the part of the page you need.

Time	Part	The teacher	The learner
0–4 min	Warm-up	Put the warm-up on screen; take two or three answers before revealing.	Think, then share.
4–13 min	Terms and coefficients	Explain, show the example step by step, then the practice.	Practise up to the stretch question.
13–22 min	Combining like terms	Use the interactive tool together, then the practice.	Try the tool, then practise.
22–31 min	Rational coefficients and checking	Explain and show the example, then the practice.	Practise; the stretch can be homework.
31–38 min	Activity 1	Pairs or solo; hint only after a wrong check.	Solve and check.
38–45 min	Activity 2	Do the first item together.	Finish the activity.
45–50 min	Activity 3	Quick challenge; finish for homework if needed.	Solve the puzzles.
50–56 min	Quiz	Run it as an exit ticket.	Answer and read why.
56–60 min	Set the project	Show the template and agree a due date.	Start the project.

Questions to ask

How do you know two terms are like terms?
What is a zero pair?
How can you check a simplification?

If it feels hard

Use the tiles for every question; colour like terms the same before combining.

If it feels easy

Simplify 3x + 2y − x + 4y − 7 + 2.

FAQ