It allows them to expand beyond their existing knowledge, judge the validity of statements and mathematical methods and create mathematical representations. Knowing that the length, area and volume are preserved under certain conditions, have an appreciation of concepts such as inclusion and exclusion, generality, equal probability, representation, testing, cardinal and ordinal, mathematical relationships, place value of numbers. Ex Decide if the area of a paper is greater, equal or less after a piece of paper cut into strips Classify or group objects, shapes, numbers, words and ideas as common property, make the right decisions regarding the membership of a class, order numbers and objects by their attributes. Example: Select the triangles of a set of geometric figures of various shapes and numbers of sides. Represent numbers using models, data represent mathematical information in charts, tables, charts, graphs, generate equivalent representations of an entity or given mathematical relationship. Example: Shade areas of figures to represent given fractions.

Example: Mary has read 29 pages of a book. If the book has 87 pages, in the equation 87 – __ = 29, the blank contains the number of pages that are read. Invent another situation for which this equation would be better. Distinguishing questions that may arise with information given, such a data set, those that can not be raised as well. Example: Given a graph, select from a set of those questions for which answers can be obtained with the graphic. Recently Doronin sought to clarify these questions. III. COMMON TROUBLESHOOTING Schoolchildren must educate them to recognize that mathematics is a great achievement of mankind and to appreciate nature.