Dealing with Word Problems: Comparing Entities

It has always been a challenge for us parents when it comes to math word problems, how to let our kids grasp the concept and approach to let them understanding the problem.

Take for example the following math word problem phrases:

Paul’s age is 5 more than Peter’s age.

On the second day, he planted 125 seeds less than the first day.

I have devised an approach when dealing with comparing entities on a math word problem.

Approach to Comparing Entities. The comparative phrase of the math word problem is being broken down to parts.

1. Compare – the entity being compared
2. Compare to – the entity being compared to
3. Operator – the keywords indicating the math operation to be used (e.g., more than, less than, older, taller, etc.)
4. By how much – the incremental value indicated in the comparative phrase of the math word problem

To better illustrate things, let’s take our first example:

Paul’s age is 5 more than Peter’s age.

The entities being compared here are Paul’s age and Peter’s age. Breaking the comparative math phrase:

Compare	Compare to	Operator	By How much
Paul’s age	Peter’s age	more than	5

Note that the operator is indicative of what mathematical operation is going to be used.

• Operators such as ‘more than’, ‘older’, ‘taller’  and other positive comparative form adjectives denotes addition as the mathematical operation.
• Operators such as ‘less than’, ‘lesser’, ‘fewer’ and other negative comparative form adjectives denotes subtraction as the mathematical operation.
• Operators such as ‘twice’, ‘doubles’ are some words that denotes multiplication.
• Operators such as ‘half’,’a third of’ are some words that denotes division.

Now, in the example above, we can establish the number sentence:

Paul’s age = Peter’s age + 5

Taking the second example:

On the second day, he planted 125 seeds less than the first day.

The entities being compared here are first and second day, so splitting up the comparative math phrase:

Compare	Compare to	Operator	By how much
second day	first day	less than	125 seed

Based on the operator, the mathematical operation to be used is subtraction. We can, then, derive the number sentence as:

Second day = First day – 125 seeds