Problem Solving Through POWER Model in Algebra

Description of the activity:

Activity Overview:

• Initiate the Activity (10 minutes):

Explain the POWER model for problem-solving to the students.

Clearly outline the steps of the adapted P.O.W.E.R. Model for Problem Solving in the context of algebra.

• Problem Analysis in Groups (25 minutes):

Divide students into small groups of three or four.

Distribute the following problem statements to each group and instruct them to apply the POWER model to solve the problem.

Sample Problems for Groups:

• Group 1:

Problem Statement:

You are running a concession stand at a basketball game. You are selling hot dogs and sodas. Each hot dog costs $1.50 and each soda costs $0.50. At the end of the night, you made a total of $78.50. You sold a total of 87 hot dogs and sodas combined. You must report the number of hot dogs sold and the number of sodas sold. How many hot dogs were sold and how many sodas were sold?

• Solution Steps:

P (Problem): Identify the problem: finding the number of hot dogs and sodas sold.

O (Options): Set up equations based on the given information.

W (Weigh): Compare methods like substitution or elimination to solve the system of equations.

E (Elect and Enact): Solve using the chosen method.

R (Review and Reflect): Reflect on the accuracy and efficiency of the method used.

• Group 2:

Problem Statement:

A theater sells tickets for a play at $8 for adults and $5 for children. If 250 tickets were sold and the total amount collected was $1700, how many adult tickets and how many children's tickets were sold?

• Solution Steps:

P (Problem): Identify the problem: finding the number of adult and children's tickets sold.

O (Options): Set up equations based on the given information.

W (Weigh): Compare methods like substitution or elimination to solve the system of equations.

E (Elect and Enact): Solve using the chosen method.

R (Review and Reflect): Reflect on the accuracy and efficiency of the method used.

• Group 3:

Problem Statement:

You have a budget of $100 to spend on pencils and notebooks for a school project. Pencils cost $1 each and notebooks cost $2.50 each. If you need to buy a total of 50 items, how many pencils and how many notebooks can you buy?

• Solution Steps:

P (Problem): Identify the problem: finding the number of pencils and notebooks to buy within the budget.

O (Options): Set up equations based on the given information.

W (Weigh): Compare methods like substitution or elimination to solve the system of equations.

E (Elect and Enact): Solve using the chosen method.

R (Review and Reflect): Reflect on the accuracy and efficiency of the method used.

• Group 4:

Problem Statement:

A farmer wants to plant two types of crops on his 120-acre farm. He plans to plant wheat on one part and corn on the other. He wants to plant twice as many acres of wheat as corn. If he plants the whole farm, how many acres of each crop will he plant?

• Solution Steps:

P (Problem): Identify the problem: determining the acres of wheat and corn to plant.

O (Options): Set up equations based on the given information.

W (Weigh): Compare methods like substitution or elimination to solve the system of equations.

E (Elect and Enact): Solve using the chosen method.

R (Review and Reflect): Reflect on the accuracy and efficiency of the method used.

Class Discussion (10 minutes):

Invite each group to present their problem, the options they considered, their chosen solution, and their reflections.

Encourage other groups to provide feedback and discuss alternative solutions.

Wrap-Up (5 minutes):

Summarize the key points discussed and emphasize the importance of structured problem-solving.

Encourage students to apply the POWER model to other areas of their academic and personal lives.