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

92 ◆ Reasoning About Problems

Mike had some beans. Three were white beans. There were twice as

many butter beans as white beans. There were 2 fewer black beans

than white beans. How many of each bean was there? How many

beans were there altogether?

Figure 6.4 2-Bean Salad Problem

There are 2 types of beans.

There are 3 times as many red

beans as white beans. There are

15 red beans. How many white

beans are there? How many

beans are there altogether?

1. Use the beans to solve.
   2. Draw a sketch of the
   beans.
   3. Make the sketch a bar
   diagram.

Figure 6.5 3-Bean Salad Problem

There are 10 beans. Half of

them are red beans;^1 ⁄ 5 of them

are white beans. The rest are

black-eyed peas. How many

beans of each are there?

1. Use the beans to solve.
   2. Draw a sketch of the
   beans.
   3. Make a bar diagram.

Step 1: Act out the bean problem.

Step 2: Draw out the beans.

Step 3: Put the beans in a rectangle.

engaging, hands-on and rigorous. Students start out with simple prob-
lems that get progressively more difficult. See Figures 6.4 and 6.5 for
examples.
The absolutely most fantastic thing about the 2- and 3-bean problems
is that they scaffold nicely into a bar diagram. So, the students solve with
the beans. Then they draw a picture of what they solved. Then they put
a rectangle around that picture. Then they take out the beans and just put
numbers and label the rectangles. Voila! A bar diagram. Of course, you
don’t teach all of this at once. But you scaffold into the bar diagram (see
Figures 6.6 and 6.7).