16 ◆ The Basic Framework
Rubio ate ¾ of his candy bar in the morning and^1 ⁄ 8 in the evening. How much
of his candy bar did he eat altogether? In this problem the result is unknown.
Teachers tend to tell these types of problems. They are basic and straight-
forward. The teacher should start with concrete items, then proceed to
drawing out the story, then to diagramming the story and finally to using
equations to represent the story. This is the easiest type of story problem
to solve.
The second kind of adding to problem is the “change unknown” prob-
lem. For example, The toy store had 509 marbles. It got some more. Now the
toy store has 823 marbles. How many marbles did the toy store get? Another
example, Maria walked 2.45 of a mile in the morning. In the afternoon she
walked some more. By the end of the day, she had walked 5 miles. How far did
she walk in the afternoon? In this type of problem, the students are looking
for the change. They know the start and they know the end, but they
don’t know the change.
The third type of adding to problem is a “start unknown” problem. For
example, The toy store had some marbles. They got 345 more on Wednesday.
Now they have 1,000 marbles. How many did they have in the beginning? In
this type of problem, the students are looking for the start. This is the
hardest type of adding to problem to solve and it takes a great deal of
modeling.
Taking From Problems
Taking From problems are all about subtracting. There are three types (see
Figure 2.2). The first type is Taking From problems where the result is
unknown. For example, The bookstore had 1,997 magazines. Then they sold
1,768 more. How many do they have now? Another example, John had $20.
He spent $3.45. How much does he have left? In this problem, the result is
unknown. Teachers often tell these types of problems. They are basic and
straightforward.
The second kind of Taking From problem is the “change unknown”
problem. For example, The toy store had 507 toy cars. They sold some. They
have 199 left. How many did they sell? Another example, There was ½ a pan
of brownies left. The kids ate some. Now there is only ¼ a pan of brownies left.
How much of the brownies did the kids eat? In this type of problem, the stu-
dents are looking for the change. They know the start and they know the
end, but they don’t know the change.
The third type of Taking From problem is a “start unknown” problem.
For example, Jenny had some money. She gave John $3.75. Now she has $7.30
left. How much money did she have in the beginning? In this type of problem,
the students are looking for the start. This is the hardest type of Taking
From problem to solve and it takes a great deal of modeling.