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Algebra

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By Nisha · Mathematics · Grade 7 · Published Nov 2, 2026 · New

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1. Algebra: Patterns, Expressions, and Equations

A way to represent relationships with numbers and symbols

Speaker notes: Algebra uses symbols to represent numbers and relationships. Students will connect expressions, equations, and real-world situations.

2. What Is a Variable?

  • A variable is a letter or symbol that represents a number.
  • The value of a variable can change or be unknown.
  • In 4 + n, n is the variable.
  • If n = 3, then 4 + n = 7.

Speaker notes: Explain that a variable is a number placeholder. Ask what 4 + n equals when n is 10.

3. Expressions and Equations

  • An expression combines numbers, variables, and operations.
  • An equation states that two expressions are equal.
  • Expression: 3x + 5
  • Equation: 3x + 5 = 20

Speaker notes: Point out that an equation includes an equals sign, while an expression does not. Ask students to identify which example can be solved for x.

4. Parts of an Expression

  • In 6x + 4, the terms are 6x and 4.
  • The coefficient is the number multiplying a variable: 6.
  • The constant is a number without a variable: 4.
  • The operation between terms is addition.

Speaker notes: Clarify that 6x means 6 multiplied by x. In the expression 2y − 9, ask students to identify the coefficient and constant.

5. Evaluate an Expression

  • Replace each variable with its given value.
  • Use the order of operations.
  • If a = 4, then 3a + 2 = 3(4) + 2.
  • 3(4) + 2 = 14

Speaker notes: Model substitution with parentheses to show that the coefficient multiplies the value. Ask students to evaluate 2a + 5 when a = 4.

6. Combine Like Terms

  • Like terms have the same variable raised to the same power.
  • Add or subtract their coefficients.
  • 3x + 5x = 8x
  • 3x + 5 cannot be combined.

Speaker notes: Emphasize that only like terms can be combined. Ask why 3x and 5 are unlike terms.

7. Use the Distributive Property

  • Multiply the factor outside parentheses by each term inside.
  • 4(x + 3) = 4x + 12
  • 2(3y − 5) = 6y − 10
  • Check that every term inside the parentheses is multiplied.

Speaker notes: Show how the outside factor applies to every term in the parentheses. Ask students to expand 3(x + 2).

8. Solve a One-Step Equation

  • Use an inverse operation to isolate the variable.
  • Keep both sides of the equation balanced.
  • x + 7 = 12
  • Subtract 7 from both sides: x = 5

Speaker notes: Describe an equation as balanced: doing the same operation to both sides preserves equality. Check the solution by substituting 5 for x.

9. Write an Equation from a Situation

  • Translate words into operations and symbols.
  • A number increased by 8 is 21.
  • Let n represent the number.
  • Equation: n + 8 = 21; so n = 13.

Speaker notes: Explain that choosing a variable helps represent the unknown. Ask students how they could check whether 13 fits the situation.

10. Algebra: Key Ideas to Remember

  • Variables represent numbers; expressions represent quantities.
  • Equations show that two quantities are equal.
  • Combine like terms and use the distributive property to simplify.
  • Solve equations by keeping both sides balanced.
  • Reflection: How can substitution help you check a solution?

Speaker notes: Review how expressions and equations are different. Invite students to explain one strategy they can use to solve or check an equation.

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