Grades 3-5 Math Problem Solving in Action_ Getting Students to Love Word Problems

Figure 2.8 Multiplicative Comparison Problems

Problem Types Bigger Part

Unknown

Smaller Part

Unknown

Difference

Unknown

(Number Times

as Many)

Compare Marco has 5

marbles. His

brother has 2

times as many

as he does. How

many more

marbles does his

brother have than

he does? How

many do they

have altogether?

Luke has 10

marbles. He has

2 times as many

as Marco. How

many does Marco

have?

Marco has 5

marbles. Luke

has 10 marbles.

How many times

as many marbles

does Luke have as

Marco?

Bar Diagram

Modeling

Problem 5

5 5

?

5 5

5

5

5 5

What are we

looking for?

Where is X?

In this type of

story, we are

comparing two

amounts. We

know the smaller

amount and we

have to find the

larger amount.

In this type of

story, we are

comparing two

amounts. We

are looking

for the smaller

part which is

unknown.

In this type of

story, we are

comparing

two amounts.

We know both

parts but we are

looking for how

many times as

many the larger

part is than the

smaller part.

Algebraic

Sentence

5 × 2 = 10

10 + 5 = 15

10 ÷ 2 = 5 5 ×? = 10 or

10 ÷ 5 = 2

Strategies to

Solve

Multiply

Addition

Divide Multiply or divide

Answer His brother

had 10 marbles.

Altogether they

had 15 marbles.

Marco had 5

marbles.

Luke had 2 times

as many marbles

as Marco.