Comparison word problems in elementary schools

Students may start solving comparison word problems as early as first grade. Then, these problems get more and more challenging in 4th or 5th grade.  There are two types of comparison in math: additive and multiplicative.

Next we show some examples commonly used in elementary schools.

Additive comparison

In additive comparison, the problem may have the following expressions where x can be a whole number.

• How much more?  
• How much less?
• x more
• x less

Example #1

Darline has 6 candies. Sylvia has 5 more. How many candies does Sylvia have? Here is the model for this problem.

Sylvia has 6 + 5 candies or 11 candies.

Example #2

John has 15 books. Peter has 6 less. How many books does Peter have? Here is the model for this problem.

Peter has 15 - 6 or 9 books

Multiplicative comparison

In multiplicative comparison, the problem may have the following expressions where x can be a whole number.

• x times as many
• x times more ... than

Example #3

Noemy has 3 times as many dolls as Tatiana. Tatiana has 2 dolls. How many dolls does Noemy have?

Step 1

Draw a model for this situation.

Step 2

Use the model to write an equation. Let n be the number of dolls Noemy has.

n = 3 x 2

Step 3 

Solve the equation. n = 3. so Noemy has 6 dolls.

A challenging comparing word problem in elementary school.

Example #4

Kirk has 3 times as many baseball cards as Nancy. Together, they have 20 baseball cards. How many cards does Kirk have?

Step 1

Draw a box with the letter n in it to show that Nancy has an unknown number of cards. Kirk has 3 times as many cards as Nancy, so draw three identical boxes to represent Kirk’s cards.

Step 2

Use a model to write an equation. There are 4 equal boxes and each box has n cards.

To get the total numbers of cards, you need to do 4 x n. This amount must equal to 20 cards. So 4 x n = 20

Step 3

Solve the equation to find n.

4 times what number is equal to 20? Since 4 x 5 = 20, n = 5.

Nancy has 5 baseball cards.

Step 4

Find how many cards Kirk has. Kirk has 3 times as many as Nancy or 3 x 5.

Kirk has 15 cards.

Example #5

Kirk has 3 times as many baseball cards as Nancy. Together, they have 20 baseball cards. How many cards does Kirk have?