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Writing and Evaluating Expressions - Worksheet 10 - 6th Grade

Hard

Write and evaluate algebraic expressions with variables (Hard)

23 problems · 15-20 minutes · Skills: expressions, variables, operations

About This Worksheet

This hard-level worksheet contains 23 problems designed for 6th Grade students practicing writing and evaluating expressions. Hard worksheets feature challenging problems including multi-step questions, missing values, and real-world applications to push students further.

Writing and evaluating expressions is the entry point to algebra. The ability to represent an unknown quantity with a variable and manipulate expressions symbolically is foundational to all of high school mathematics.

  • Translate verbal phrases into algebraic expressions using variables
  • Evaluate algebraic expressions by substituting values
  • Identify and write expressions from real-world situations
  • Distinguish between an expression and an equation in algebraic notation
  • Use multiple variables to write expressions with more than one unknown

How to Solve: Worked Example

Example Problem: Solve the first problem on the worksheet.
Solution Steps:
  1. Read the problem carefully.
  2. Identify what is being asked.
  3. Use what you know to find the answer.
  4. Check your work.
Answer: See the answer key below
Tip: Take your time and read each problem carefully before answering!
1
Write: "3 times a number decreased by 1", then evaluate when x = 10
2
Write: "5 times a number decreased by 6", then evaluate when k = 9
3
Write: "4 times a number decreased by 7", then evaluate when k = 2
4
Write: "2 times a number decreased by 4", then evaluate when y = 2
5
Write: "8 times a number decreased by 6", then evaluate when x = 10
6
Evaluate 2y + 6 when y = 6
7
Write: "7 times a number decreased by 2", then evaluate when k = 5
8
Evaluate 7n + 5 when n = 3
9
Write: "4 times a number decreased by 4", then evaluate when y = 2
10
Write: "3 times a number decreased by 4", then evaluate when k = 4
11
Write: "6 times a number decreased by 2", then evaluate when x = 7
12
Write: "6 times a number decreased by 8", then evaluate when k = 3
13
Write: "7 times a number decreased by 8", then evaluate when n = 5
14
Write: "7 times a number decreased by 6", then evaluate when k = 10
15
Evaluate 6x + 7 when x = 8
16
Evaluate 6k + 6 when k = 8
17
Evaluate 2n + 3 when n = 2
18
Evaluate 5x + 4 when x = 10
19
Evaluate 3n + 2 when n = 8
20
Write: "7 times a number decreased by 6", then evaluate when y = 2
21
Evaluate 3x + 8 when x = 6
22
Evaluate 3n + 2 when n = 2
23
Write: "2 times a number decreased by 3", then evaluate when x = 6

Answer Key

1. 3x − 1 = 292. 5k − 6 = 393. 4k − 7 = 14. 2y − 4 = 05. 8x − 6 = 746. 187. 7k − 2 = 338. 269. 4y − 4 = 410. 3k − 4 = 811. 6x − 2 = 4012. 6k − 8 = 1013. 7n − 8 = 2714. 7k − 6 = 6415. 5516. 5417. 718. 5419. 2620. 7y − 6 = 821. 2622. 823. 2x − 3 = 9

Frequently Asked Questions

How do I download this writing and evaluating expressions - worksheet 10 worksheet?

Click the "Download PDF / Print" button at the top of the worksheet. You can save it as a PDF or print it directly. The answer key will be on a separate page.

How do I find worksheets at different difficulty levels?

Each subtopic has 10 worksheets: Worksheets 1-3 are Easy, 4-7 are Medium, and 8-10 are Hard. Start with Easy worksheets to build confidence, then progress to harder ones.

What skills does this expressions and equations worksheet cover?

This worksheet focuses on expressions, variables, operations. It is designed for 6th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

Can I use this worksheet in my classroom?

Yes. All worksheets on K12Worksheets are free for classroom use. You can print copies for your entire class. With 10 worksheets per subtopic at three difficulty levels, you have plenty of options for differentiated instruction and individualized practice.

How many problems are on this worksheet?

This worksheet contains 23 problems. It typically takes 15-20 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.