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

The Basic Framework ◆ 19

In this type of problem, we are given the whole and one of the parts. The
task is to figure out the other part.
The third type of part-part-whole problem is a Both Addends Unknown
problem. In this type of problem both addends are not known; only the
total is given. For example, Jane has 25 cents. Name all the possible coin
combinations that she could have. The task is to figure out all of the pos-
sible combinations.

Compare Problems

Compare problems are the most difficult types of stories to tell. There are
three types of comparison stories (see Figure 2.4). The first type of com-
parison story is where two different things are being compared. For

Figure 2.4 Compare Problems

Problem

Types

Difference

Unknown

Bigger Part

Unknown

Smaller Part

Unknown

Compare Marco has 5

marbles. His

brother has 7.

How many more

marbles does his

brother have than

he does?

Marco has 5

marbles. His

brother has 2

more than he

does. How many

marbles does his

brother have?

Tom has 5 rocks.

Marco has 2 less

than Tom. How

many rocks does

Marco have?

Bar Diagram

Modeling

Problem

5 5

(^752)?
?
What are we
looking for?
Where is X?
In this type of
story, we are
comparing two
amounts. We
are looking for
the difference
between the two
numbers.
In this type of
story, we are
comparing two
amounts. We are
looking for the
bigger part which
is unknown.
In this type of
story, we are
comparing two
amounts. We
are looking
for the smaller
part which is
unknown.
Algebraic
Sentence
7 − 5 =? 5 + 2 =? 5 – 2 =?
Strategies to
Solve
Count up/
Count back
Count up Subtract
Answer His brother had
2 more marbles
than he did.
His brother had 7
marbles.
Marco had 3
marbles.
? 5
2