Mastery of arithmetic helps students develop logic and reasoning skills. According to the Math Rider website, arithmetic helps students learn to think logically and break down problems into distinct steps so they can be solved. It also tests their ability to solve basic math problems encountered in everyday situations. These problems require addition, subtraction, multiplication and division.
Math Activities for Thinking Logically
Math activities of any kind are a rudimentary form of logical thinking; consider 2+2. Understanding higher math such as algebra, then, is a critical step forward for a mind of any age to gain logical thinking skills. Although many students find math difficult, it helps prepare them for the future, to succeed in jobs that may or may not have anything to do with math or equations.

Basic Arithmetic
Algebra

Algebra enables students to think logically when solving equations. It helps students learn to reason symbolically and introduces abstract thinking. Students who take algebra class learn that symbols such as x and y stand for units that vary and can be used to solve the missing pieces of reallife mathematical puzzles. For example, in the equation 4 + x = 7, “x” is the unknown variable and “3” is the solution the equation.

Geometry

There are many geometry activities that will improve a person's ability to think logically. Elementary school children should be taught how to identify geometric shapes. For example, students should learn about parallel lines and how to use a ruler, compass and protractor so they can then draw squares, rectangles, parallelograms and circles. In middle school (grades 6 through 8), students should understand and form abstract definitions and understand relationships between different shapes. According to Homeschoolmath.net, teachers can help middle school students think logically by asking them to study geometric concepts and allow them to experiment, investigate and play with geometric figures.
Word Problems

Word problems require logical thinking and other skills a student has learned in class, such as reading comprehension, algebra, geometry or trigonometry. Solving word problems often requires a translation of the wording into an equation.
Venn Diagrams

Venn diagrams show relationships between sets or groups of objects that may or may not share something in common. A Venn diagram is a good tool for organizing, evaluating and representing complex relationships visually. Venn diagrams typically consist of two or more overlapping or nonoverlapping circles that show the relationship between groups of things. When the circles overlap, items share a specified something in common. For example, lets say that circle A contains all red fruits and circle B contains all green fruits. Then, the intersecting portions of the two circles contain fruit that come in red and green varieties, such as apples and grapes. Venn diagram activities help students to organize similarities and differences visually. They can help students compare and contrast topics of any subject. According to Scholastic.com, a good math activity may involve using Venn diagrams for comparing and contrasting story elements.

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