📗 Class 7 maths · session 10 of 12 · 60 minutes · 🎁 free with an account

Algebraic expressions

Welcome to Team Calc hero training! Today we unlock the secrets of algebraic expressions to solve real world missions.

🤖 Written with Google's Gemini AI. A second AI solved all 55 questions without seeing the answers, and both agree. One of our teachers has not read it yet, so if something looks wrong, please tell us.

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.

🎁 Unlock free with an account Read part 1 free

Warm-up3 min
Warm-up games5 min
Variables, Constants, and Terms8 min
Like and Unlike Terms7 min
Adding and Subtracting Expressions7 min
Finding the Value of an Expression7 min
Captain Calc's Power Decoder6 min
Comic Store Inventory Mission5 min
Hero Budget Challenge6 min
Quiz5 min
Set the project1 min

By the end you can

Identify variables, constants, terms, and coefficients in algebraic expressions.
Distinguish between like terms and unlike terms.
Add and subtract algebraic expressions accurately.
Evaluate algebraic expressions for given values of variables.

Before you start

Understanding basic operations with positive and negative integers.
Familiarity with writing simple mathematical expressions.

Have ready

A notebook and pen for working out mission steps.
Two different colored pencils to highlight like terms.

Class 7 · CBSE, ICSE and state boards

Warm-up · think first

Captain Calc buys x notebooks at ₹20 each and pays ₹10 for a pen. Write an expression for the total cost in rupees.

Show the answer

20x + 10. Multiplying notebook cost ₹20 by quantity x gives 20x, then adding ₹10 for the pen gives 20x + 10.

Teacher tip: Ask students what changes if Captain Calc buys 3 notebooks.

More warm-ups for every class →

🎮 Warm-up games · 5 quick games

Play with Captain Calc

Six minutes with Captain Calc. Vote, say why, then show the answer.

Which expression does not belong with the others? (4x · -7x · 3x² · x)
Answer: 3x² does not belong because its variable has exponent 2, while the others are linear terms in x.
Would you rather simplify 10 terms with only x or 4 terms with x, y, and z? (Option A: 10 terms with only x · Option B: 4 terms with x, y, and z)
Answer: Both choices are great! Option A has only one variable type to combine, while Option B has fewer total terms.
The sum of two like terms is a like term. (Always · Sometimes · Never)
Answer: Always. When you add like terms, the variable part stays identical.
I am an expression. When you double me and add 4, you get 2x + 10. What am I?
Answer: x + 3. Subtracting 4 from 2x + 10 gives 2x + 6, and dividing by 2 gives x + 3.
Where in daily life in India might we use a variable like x instead of a fixed number?
Answer: When calculating total cost of auto rickshaw rides where distance x varies, or counting total runs scored in x matches.

Part 1 of 4 · learn, see, practise

Variables, Constants, and Terms

A variable is a letter like x or y that represents an unknown number.

A constant is a fixed number like 5 or -12.

Terms are created by multiplying variables and constants, separated by plus or minus signs.

Example 1

Identify the terms and coefficients in 5x - 3y + 8.

Separate the expression by its operations into terms: 5x, -3y, and 8.
Identify numerical coefficients for variable terms: coefficient of x is 5, coefficient of y is -3.
Identify the constant term: 8.

Answer: Terms are 5x, -3y, 8; coefficients are 5 and -3.

Example 2

Write an algebraic expression for: 7 taken away from 4 times a number p.

Multiply the number p by 4 to get 4p.
Take away 7 by subtracting 7 from 4p.

Answer: 4p - 7

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 7x?

Warm-up2How many terms are in the expression 2x + 3y - 5?

Core3What is the constant term in 4y - 9?

Core4What is the numerical coefficient of xy in -6xy?

Stretch 🔥5Write the expression for 8 added to product of 3 and m.

Stretch 🔥6Write terms of 5a² - 2b + 9 separated by commas.

Answers (for the teacher)

7
3
-9
-6
3m+8
5a²,-2b,9

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Unlocking the rest of this lesson gives you:

Part 2: Like and Unlike Terms, with practice at three levels
Part 3: Adding and Subtracting Expressions, with practice at three levels
Part 4: Finding the Value of an Expression, with practice at three levels
Class activity 1: Captain Calc's Power Decoder
Class activity 2: Comic Store Inventory Mission
Class activity 3: Hero Budget Challenge
A 10-question quiz
After-class project: Comic Hero Mission Cost Tracker
Homework and a printable practice sheet with answers
Teach mode and the minute-by-minute teacher's plan

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FAQ

Algebraic expressions: questions

Why are algebraic expressions important in Class 7?

Algebraic expressions build the groundwork for solving equations, understanding functions, and modeling real world situations.

What is the difference between an expression and an equation?

An expression has no equals sign, while an equation states that two expressions are equal.

Can we add x and x² together into one term?

No, x and x² are unlike terms because their exponents are different.

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