The study of mathematics essentially involves learning a new language, one which contains both foreign words and words that are well-known but used in a different context or that have a different meaning entirely. That being the case, it is imperative that students learn not only the mathematical concepts and formulas, but the vocabulary as well. It is only then that students will be able to verbalize what they are doing when solving a problem and to expound on their mathematical knowledge. According to Dr. David Chard, the language and vocabulary consultant for Houghton Mifflin Math, “the language of math is critical to helping children develop the means to acquire new concepts.” Math vocabulary can be broken down by grade or into various categories of related topics.

### Algebraic Thinking

Algebraic thinking is the foundation of mathematics and helps students develop reasoning skills as they focus on concepts rather than processes. A vocabulary list for algebraic thinking could include the words "alike," "different," "size," "solution," "multiples," "match," and "range." Algebraic vocabulary terms make up a large part of lower elementary math vocabulary.

### Base Ten Operations

This category includes several subcategories, including, but not limited to, digits, counting, operations, place value, comparison and grouping. This is where students are introduced to number words, operational titles such as "add" and "multiply," processes such as skip counting, concepts like place value and the names of the various parts of a problem, for example, "addend" and "product." This category includes the majority of the mathematical vocabulary words and increases each year as new terms and concepts are taught.

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### Measurements and Data

As students learn to measure and record data, they will need the knowledge of the various instruments and terms that deal with this area of mathematics. Such language includes terms related to the calendar, the clock, graphing, measuring length, weight and volume, statistics, fractions, money and interpretation -- such as "mean" and "likelihood."

### Geometry

Geometry is the study of shapes and their properties. The initial introduction to geometry takes place in kindergarten where students are taught the names of basic shapes such as "circle," "triangle" and "square." As students progress, names of more elaborate shapes, such as "pentagon" and "octagon," are introduced, followed by the names of three-dimensional shapes, such as "sphere" and "pyramid." Geometry vocabulary branches off into the areas of classification (i.e. "rotate" and "angle"), description (i.e. "perimeter" and "corner"), lines (i.e. "perpendicular" and "right angle") and transformation (i.e. "symmetry" and "horizontal").

### The Number System, Expressions and Equations

Upper elementary students will be introduced to terms related to finding the greatest common factor, reducing, and recognizing cardinal numbers. They will also need to know terms like "coefficient," "real numbers," "variables" and "exponents." This group of vocabulary words readies students for algebra while introducing a variety of new concepts that will be built upon in upcoming years.

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