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

The Basic Framework ◆ 17

Figure 2.2 Taking From Problems

Problem Types Result Unknown Change Unknown Start Unknown

Separate/

Taking From

Marco had 10

marbles. He gave

his brother 4.

How many does

he have left?

Marco had 10

marbles. He gave

some away. Now

he has 5 left. How

many did he give

away?

Marco had some

marbles. He gave

2 away and now

he has 5 left. How

many did he have

to start with?

Bar Diagram

Modeling

Problem

10 10?

4?? 5 2 5

What are we

looking for?

Where is X?

In this story

we know the

beginning and

what happened in

the middle. The

mystery is what

happened at the

end. The result is

unknown.

In this story

we know the

beginning and the

end. The mystery

is what happened

in the middle.

The change is

unknown.

In this story

we know what

happened in

the middle and

what happened

at the end. The

mystery is how

did it start? The

beginning is

unknown.

Algebraic

Sentence

10 − 4^ =^? 10 −?^ =^5

5 + x = 10

? − 2 = 5

2 + 5 =?

Strategies to

Solve

Subtract Subtract until you

have the result

left/

Count up

Count up/

Subtract

Answer 10 − 4 = 6

He had 6 marbles

left.

10 − 5 = 5

5 + 5 = 10

He gave away 5

marbles.

7 − 2 = 5

2 + 5 = 7

He had 7 marbles

in the beginning.

Part-Part-Whole Problems

A Part-Part-Whole problem is a problem that discusses the two parts and
the whole. There are three types of Part-Part-Whole problems (see Fig-
ure 2.3). The first is a problem where the whole is unknown. For example,
The toy store had 467 big marbles and 598 small marbles. How many marbles
do they have altogether? Another example, John had $597.09 in his bank account
and $28.34 in his piggy bank. How much money does he have altogether? We
know both parts, and the task is to figure out the whole.