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Introduction to Algebra: 5th Grade Worksheet

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Part 1: Writing Algebraic Expressions

Write an algebraic expression for each of the following word phrases.

• Add $7$ to a number $n$.

• The product of $4$ and a number $x$.

• A number $y$ decreased by $12$.

• The quotient of a number $z$ and $3$.

• $10$ less than a number $k$.

Part 2: Evaluating Expressions

Evaluate each expression using the given value for the variable.

• Evaluate $x + 15$ when $x = 9$.

• Evaluate $8m$ when $m = 7$.

• Evaluate $25 - p$ when $p = 11$.

• Evaluate $\frac{w}{4}$ when $w = 32$.

• Evaluate $2n + 3$ when $n = 5$.

Part 3: Solving One-Step Equations

Find the value of the variable that makes the equation true.

• $a + 6 = 20$

• $b - 8 = 15$

• $4c = 36$

• $\frac{d}{3} = 9$

• $12 + x = 30$

Part 4: Geometry and Word Problems

Read the instructions or problems carefully and provide the algebraic answer.

• Draw a square on your paper. Label one side of the square with the variable $s$. Write an expression that represents the perimeter of the square (the distance around all four sides).

• A candy bar costs $c$ cents. If Jason buys $5$ candy bars, write an expression for the total cost.

• Maria has $24$ pencils. She shares them equally among $f$ friends. Write an expression to show how many pencils each friend receives.

• A mystery number $x$ is increased by $10$, and the result is $22$. Write an equation to represent this and solve for $x$.

• Think of a rectangle. The length is $l$ and the width is $5$. Write an expression for the area of the rectangle (length times width).

Introduction to Algebra: Teacher Answer Key

Part 1: Writing Algebraic Expressions

• $n + 7$

• $4x$ or $4 \cdot x$

• $y - 12$

• $\frac{z}{3}$ or $z \div 3$

• $k - 10$

Part 2: Evaluating Expressions

• $9 + 15 = 24$

• $8 \cdot 7 = 56$

• $25 - 11 = 14$

• $32 \div 4 = 8$

• $2(5) + 3 = 10 + 3 = 13$

Part 3: Solving One-Step Equations

• $a = 14$

• $b = 23$

• $c = 9$

• $d = 27$

• $x = 18$

Part 4: Geometry and Word Problems

• Expression: $4s$ or $s + s + s + s$

• Expression: $5c$

• Expression: $\frac{24}{f}$ or $24 \div f$

• Equation: $x + 10 = 22$; Solution: $x = 12$

• Expression: $5l$ or $l \cdot 5$