How to Solve Word Problems with Keywords and Patterns

Have your students ever asked where to begin when solving a word problem? Do students ask questions such as, “Which goes first, the variable or the number?” If this question is familiar, keep reading. In this post, I will provide many examples of how to solve word problems with keywords and patterns.

#1 -The Left to Right Strategy: Word Problems with Keywords and Patterns

Your students are already nervous when they anticipate word problems. Due to this, begin with the easiest, most logical approach, the left to right strategy.

The algebraic expression is written in the same order as the phrase. This method allows students to begin to see the relationship between words, variables, and numbers.

You will discover that students quickly and confidently learn this orderly pattern.

See the examples of this strategy listed below. Color-coding has been added to provide visual emphasis on the parts: a literal number which is in blue, the operation which is in green, and the variable which is in pink.

word problems with keywords and patterns7 Algebraic Expressions written in word order

#2 – When the Keyword of the Operation Comes First

After your students are confident in the left to right strategy, explain that sometimes the operation is stated first. After the keyword for the operation is given, the literal number or variable follow. When this occurs, the operation is written between the literal number and the variable.

See the examples below.

4 algebraic expressions with the operation coming before the literal number and variable

#3 – Turn-Around Words and Phrases

“What does eight from a number, mean?”
“Ten less than a number?”

How many times have you heard these questions from students? No worries. You may already be familiar with the term, “turn around words,” or “turn around numbers” in reference to writing algebraic expressions.

Below is a great illustration to help students relate to those tricky “less than” and “from” phrases.

word problems with keywords and patterns:Candy in a jar illustrating the expression, "Subtract 3 from 10"

Using the same example from above, illustrate a math expression.

Arrows illustrating the turn around method for writing the algebraic expression, "Subtract 3 from 10"

Furthermore, share with students that there are only three operations that use turn-around words and phrases. These operations include addition, subtraction, and division, but NOT multiplication.

A. Turn-Around Key Words and Phrases for Addition: Word Problems with Keywords and Patterns

The commutative property for addition states that order does not matter. However, I highly recommend that students follow the turn around strategy with addition for two reasons.

a. provides students more opportunities to identify turn-around words and phrases.

b. helps prevent student confusion with problems such as:

word problems with keywords and patterns:Example of turn around words with the words, "more than" and "less than

Turn-around Keyword and a Phrase for Addition:
More than

Below are examples of turn-around keywords and phrases for addition.

word problems with keywords and patterns:4 keyphrase examples of turn around words used in addition

B. Turn-Around Keywords and Phrases for Subtraction: Word Problems with Keywords and Patterns

Turn-around Keywords and Phrases for Subtraction:
Subtract _____ from
Stubtracted from
Less than
Take ____ away from
Take ____ from
Fewer than

Below are examples.

4 keyphrase examples of turn around words used in subtraction

C. Turn Around Keywords and Phrases for Division: Word Problems with Keywords and Patterns

Furthermore, turn-around keywords for division, such as “divided into,” can be challenging for some students to understand. Include a number problem matching keywords used.

Turn-around Keywords and Phrases for Division:
Divided into
Divide ____ into

keyphrase examples of turn around words used in division

Conclusion

In conclusion, using these strategies will increase student confidence in word problems and writing algebraic expressions.

You may also be interested in the following posts:
1. How to Successfully Teach Algebra Expressions
2. Word Problem Activity: How to Engage Elementary-level Students

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