One-Step Algebraic Problem Solving

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SWBAT problem solve by translating real-word problems into simple one-step algebraic equations that can be solved using one of the properties of equality.

Big Idea

One-Step Solutions to Real-World Situations: Seeing the one-step algebraic equation in the multi-stepped word problem.

Curriculum Reinforcer

5 minutes

The curriculum reinforcer, is a daily practice piece that is incorporated into almost every lesson to help my students to retain skills and conceptual understanding from earlier lessons. My strategy is to use Spiraled Review to help my students retain what they learned during the earlier part of the year. This will help me to keep mathematical concepts fresh in the students mind so that the knowledge of these concepts become a part of students' long term memories.


5 minutes

During the opening activity, I will present my students with 4 word phrases that can be written as algebraic expressions. It will be the job of my students to translate those word phrases to algebraic expression. I will use this activity to help my students to see the algebra expression hidden in the word problems that they will be working on today.

Instruction & Teacher Modeling

10 minutes

Today, I will remind students of the previous unit where they had to translate phrases into algebraic expressions. I will do this to show how writing an equation for a word problem is very similar. During this instructional piece, I will break down a word problem step by step to demonstrate to my students the method of pulling out the hidden algebraic equation presented in the word problem so that the problem can be solved.

During this time, my students should be taking note of key words and phrases that give hints to the hidden equation. They should be taking note of positioning of wording versus the positioning of the operation when the equation is written. In fact, to ensure that they do take note of these elements, I will ask questions to prompt their thinking.

For Example, I might ask my students the following:

  • Why did I place this quantity after the subtraction sign and not before it even though the problem states here, "9 less than Sarah"... Why didn't I write 9 - S, why did I write S - 9 instead? What let me know that I needed to use a subtractions sign?


While the problems that will be presented in this lesson are more complex, the method of prompting remains the same. Looking at the example, it could have been a portion of a more complex problem. Only questioning that particular piece is a great way of showing students how to break the problem down into workable parts. You would then do the same to the other parts that create the entire problem.


Try It Out

10 minutes

To practice the technique of breaking down word problems into workable parts and pulling out the equation hidden with in a problems words, my students will complete the attached task with my assistance.

Independent Exploration

20 minutes

To practice independently, my students will complete a worksheet with 14 word problems. When completing this worksheet, I will add to the directions, in that I will also require the students to write the one-step equation that would represent the situation presented in each of the word problems. After they have written the one-step equation, then they will have to solve that equation.


The worksheet that is used in this section of this lesson was pulled from This is a great website that offers a database of free worksheets for those times when the resources you have don't quite meet your expectations or you have run out of resources and/or ideas for new problems.

Closing Summary

20 minutes

To close out the lesson, I will choose 6 of the 14 problems to be presented to the class. I will choose a student for each problem to be the presenter of their assigned problem. We will analyze each problem and how the student chose to solve that problem.

Afterward, I will have my students write a short one paragraph essay about what they learned today.