Types of word problems
We distinguish between many divisions of tasks, depending on the adopted criterion, e.g.. structure - design correctness, context layer or content mobility, multiplicity of mathematical operations, which must be done when solving, e.t.c. Here we will look at a few selected criteria, considered important from the point of view of mathematics education in the youngest grades.
Chained tasks. They can be naturally broken down into a sequence of simple tasks, so that a number found as the value of the unknown of one simple task becomes given to the next task in the chain.
There was in the store 8 boxes, and in each of them 10 kg of apples. The school purchased 25 kg of apples. How many kilograms of apples are left in the store?
First you need to calculate the weight of apples in the store, and then subtract the weight of apples sold from the value obtained. The solution can be written as two actions:
8 •10 kg = 80 Kg
80 Kg – 25 kg = 55 Kg.
The solution to this problem can be presented in the form of one record:
8 • 10 Kg – 25 kg = 55 Kg.
Chained tasks can also be illustrated with a graph.
Proper complex tasks are characterized by this, that at least two of the task conditions define the relationship between the unknowns, e.g..
Apples and pears were brought to the store, together 27 kg of fruit. There were apples 2 times more than pears. How many kilograms of pears were brought to the store?
The quantities of apples and pears brought to the store are unknown in the task – g, though the command only applies to apples. Dependencies can be written in the form of two equations (system of equations):
j + g = 27 and 2 • g =j.
This system is a natural mathematical model, which, however, does not lead directly to simple tasks. The solution of the task requires the determination of simple dependencies, legible and understandable for the student, so a different interpretation of the task situation and a different mathematical model.