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

18 ◆ The Basic Framework

Figure 2.3 Part-Part-Whole Problems

Problem

Types

Quantity

Unknown

Part Unknown Both Addends

Unknown

Part-Part-

Whole/

Putting

together/

Taking

Apart

Marco has 5 red

marbles and 5

blue ones. How

many marbles

does Marco have?

5 + 5 = x

Marco has 10

marbles. Five are

red and the rest

are blue. How

many are blue?

10 − 5 = or

5 + x = 10

Marco has 10 marbles.

Some are red and some

are blue. How many

could be red and how

many could be blue?

Bar Diagram

Modeling

Problem

? 10 10

5 5 5???

*Often all of the

combinations are

represented in a table

What are we

looking for?

Where is X?

In this type of

story, we are

talking about

a group, set or

collection of

something. Here

we know both

parts and we are

looking for the

total.

In this type of

story, we are

talking about

a group, set or

collection of

something. Here

we know the

total and one of

the parts. We are

looking for the

amount of the

other part.

In this type of story,

we are talking about a

group, set or collection

of something. Here we

know the total but we

are to think about all

the possible ways to

make the group, set or

collection.

Algebraic

Sentence

5 + 5 =? 5 +? = 10

10 – 5 =?

x + y = 10

Strategies

to Solve

Add/

Count up

Count up/

Subtract

Count up/

Subtract

Answer 5 + 5^ =^10

He had ten

marbles.

5 + 5 = 10

10 − 5 =?

Five were blue.

1+9 4+6 9+1 6+4

2+8 5+5 8+2

3+7 10+0 0+10 7+3

These are the

possibilities.

The second kind of Part-Part-Whole problem is where one of the parts
is unknown. For example, The toy store had 1,000 marbles. There were 897
small marbles. The rest of the marbles were large. How many large marbles did
they have? Another example, Kelly had $500. She had $257 in her piggy bank
and the rest in her bank account. How much does she have in her bank account?