Two Step Equations Worksheet for Real-Life Problems
- Grades
- Grades 6–8, Middle School
- Pages
- 9
- File type
- Answer key
- Included
- Subject
- Math, Algebra
- Topic
- algebra, two step equations
- Resource types
- Worksheets & Printables, Word Problems, Worksheets
- Answer key
- Included
- Standards
- 7.EE.B.4
About this resource
What's inside this resource
Students in grades 6–8 turn short real-life stories into two-step equations and solve them in this nine-page worksheet. Page 1 defines equation, variable and coefficient with one shared example, then walks through an arcade-card problem: draw a bar model, write 8x + 5 = 61, undo the addition, undo the multiplication and check the answer.
Six practice pages build from there. Students match four stories, such as a kayak rental and a box of books, to an equation bank that holds two extra equations, and solve two of them. They then write and solve four problems from scratch with a bar-model sketch box, find and fix the mistake in two pieces of student work, write their own word problem for a given bar model, and pick the equation that fits three stories while explaining why another choice does not.
- 16 word problems: every answer is a whole number
- Answers: equations, solutions, bar-model guide and a teacher tip
- Two print copies: hand out the color or the grayscale version
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In the classroom
Teaching tips & learning objectives
Learning objectives
Define a variable for the unknown amount in a word problem
Represent a two-step word problem with a bar model and an equation
Solve two-step equations by undoing addition or subtraction first, then multiplication or division
Teaching tips
Work through the arcade-card example together so students see how each part of the bar becomes part of the equation
Point out that two equations in the Match It bank are not used, so students cannot finish by elimination
Ask students to run the equation checklist on page 5 for every problem, not just the error hunt
Skills covered
Modeling with bar diagrams: students sketch equal parts and a fixed amount under a total before writing an equation.
Writing equations: each story asks students to name what x stands for and set up a two-step equation.
Inverse operations: students undo the added or subtracted amount first, then the coefficient.
Good to know
Questions teachers ask about this resource
Do the problems involve negative numbers or fractions?
No. Every problem has a whole-number answer, so students can focus on setting up and solving the equation.
Do students have to draw bar models?
The Write and Solve problems include a sketch box for a bar model, and page 1 shows a worked example. The key describes what a correct sketch for each story should show.
What kinds of tasks are included besides solving?
Students match stories to equations, find mistakes in student work, write their own word problem for a bar model and choose the equation that fits a story.
Is there an answer key?
Yes. Two teacher pages give the equation, solution and units for every problem, along with a bar-model guide and a teacher tip.
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Curriculum
Standards, concepts & topics
Standards
Standards
- 7.EE.B.4 — Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.
Core concepts
Core concepts
two-step equations
word problems
bar models
variables and coefficients
inverse operations
Topics
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