Algebra Problem Solving Strategies

Students who are new to the abstract nature of algebraic thinking can struggle with finding an entry point into a problem. Writing an equation is not simple, and knowing what to do with an equation can also seem confusing. But often some carefully modeled questions can help them find their way into the problem, put them on more familiar footing, and recognize that they often know the answer.

Algebra Problem Solving Strategies:

Writing Simple Expressions

Here is a classic example of a problem that students new to algebra are puzzled by.

There are 100 cm in every meter. Write an expression that can be used to find the number of centimeters for any number of meters, m.

Asking “what if” helps to make the problem less abstract. 

• “What if you had 2 meters? How many centimeters would you have?” 
• “What if you had 3 meters? How many centimeters would you have?”

Have students record answers so that they can look for patterns.

Many students will say the pattern is to add 100 each time. This provides an opportunity to connect repeated addition to multiplication. Choosing a larger number motivates them to choose multiplication.

• What if you had 19 meters? How many centimeters would you have?

Help students recognize that they understand what steps to follow to fill in the pattern. Make a connection between what they are already doing for a specific value and how to turn that into an expression that can be used for any value.

• “What did you do to fill in the table?”

Multiplying the number of meters by 100 to find the number of centimeters is the same as the expression 100m.

Ask a “What if?” question again, but this time have students use the expression for the given value of m.

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More Complex Expressions

A pizza restaurant charges $12 for a small pizza and $2 for each topping. Write an expression to find the total cost of a pizza for any number of toppings, t.

• “What if you had one topping? What would the total cost be?”
• “What if you had two toppings? What would the total cost be?”

Students may notice the pattern that the cost of toppings and the total cost of the pizza increase by $2 each time a topping is added. 

• “What did you do to find the cost of the toppings?”
• “What did you do to find the total cost of the pizza?”

Multiplying the number of toppings by the cost of each topping and then adding that sum to the base cost of the pizza is the same as the expression 2t+12.

Ask a “What if?” question again, but this time have students use the expression for the given value of t.

Also read: How To Find Percents Using Double Number Line

Takeaway 

Modeling the “What if…” strategy out loud helps students recognize it as a tool for finding a way into a problem. It takes the abstract and makes it concrete. With enough practice,”What if…?” will become a strategy that students naturally use on their own.

Frequently Asked Questions on Algebra Problem Solving Strategies