Elementary students must develop a firm mathematical foundation to ensure more advanced math development later in school. According to a research paper titled “Elementary School Mathematics Priorities” by Professor W. Stephen Wilson, numbers, place value system, whole number operations, fractions and decimals, and problem solving are the five math areas that elementary students must learn. Elementary math terms come from one (or more) of those sections. State standards and individual school requirements will vary.

### Kindergarten

Counting and numbers are the baseline for all kindergarten math. Students learn about patterns and the number line. Addition and subtraction are introduced, as well as the terms minus, plus, difference and equal. Concepts of time are taught, including the terms hour, minute, second and day. Calendar study introduces the terms week, month, year, today, yesterday and tomorrow. Students learn about money and the terms penny, dime, nickel, quarter and dollar. Shapes are covered in detail as well, including square, circle, rectangle, triangle, oval and hexagon. Three-dimensional shapes, such as pyramid, cube, cylinder and sphere, are also introduced. Weight-related activities introduce terms such as heavier, lighter, scale, ounce and pound. Beginning measurement terms of centimeter, inch and foot are taught in kindergarten. Relational terms such as shorter, longer, taller, above and below help children learn about comparison, and bar graphs and data are analyzed in kindergarten. Specific terms learned in kingergarten may vary by state or school.

### Early Elementary

First and second grades are critical times for children to expand upon the terms learned in kindergarten, such as sum, product, multiple and difference. Fractional terms are introduced, including denominator and numerator. Curriculum generally includes the terms before, after, less than, greater than, place value, estimation and comparison. Students learn even and odd numbers. Venn diagrams help students analyze data. Acute, obtuse and right angles are compared. Children learn the difference between the terms edge, face and perimeter. The shape of a pentagon is analyzed, and the terms vertex, meter, prism and plane are included. Other terms may be introduced, depending on state standards.

### Mid-Elementary

Multiplication and division are covered in detail. Decimal place and whole numbers are studied. The terms diameter, area, radius and center are introduced. Distance terms, such as kilometer, mile and yard, are studied, as well as measurement terms, such as gram and kilogram. Children learn about intersecting lines, grids, segments and vertex. Capacity, density and mass introduce students to concepts of volume. Other common math terms for third- and fourth-graders are grouping, factor, century, divisor, classification, capacity, variables and sequencing. Scalene, obsoletes, and equilateral triangles are also compared. Other terms may be covered depending on state math standards and individual school curriculum.

### Upper Elementary

Upper elementary students will learn the skills needed for middle and high school. Fifth and sixth graders work on terms such as benchmark, inverse operations, inverse fraction, surface area, absolute value, ray, base and exponent. The numeric terms billion and million are compared. Parallel and perpendicular lines are introduced, as well as the terms plane and hypotenuse. Students learn the difference between the words ascending and descending, as well as how to label an x-axis and a y-axis on a graph. Other math terms may be included in upper-elementary instruction, depending on school curriculum and state standards.

#### References

- Johns Hopkins University: Elementary School Mathematics Priorities
- PBS Parents: Preschool & Kindergarten Math Milestones
- North Carolina Department of Public Instruction: K Grade Mathematics
- Virginia Department of Education: Mathematics Standards of Learning
- Ohio Resource Center: Ohio's Academic Content Standards in Mathematics
- Scholastic: Parent Primer: Math

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