By the end of elementary school, students should have a strong grasp on numbers and the four arithmetic operations: addition, subtraction, multiplication and division. Students should be comfortable with multi-digit problems across all the operations. They should also be able to complete math problems with positive and negative numbers, and add and subtract decimals to the hundredths and fractions. Students should understand place values, estimations and rounding whole numbers and decimals. They should also be writing and reading whole numbers to the millions.
Basic geometry is typically introduced in elementary school and students learn about geometric solids and how to calculate volume and area. Students should feel comfortable drawing lines, points, right, acute and obtuse angles, and perpendicular and parallel lines. Students should also be able to graph points on the coordinate plane, or x-axis and y-axis, and classify two-dimensional figures based on their properties. For example, they should be able to differentiate between rectangles and trapezoids.
Prior to middle school, students should understand the basics of algebraic thinking and basic equations. They should be able to write and interpret numerical expressions and be using brackets, parentheses and braces in numerical expressions. Students should also begin to use math to solve real world problems, recognize that some solutions are more efficient than others are and learn to think of math as a process that leads to a solution. By the end of fifth grade, students should be comfortable analyzing patterns and relationships with numbers.
At the end of elementary school, students should be able to measure with accuracy using U.S. standard units and metric units and be comfortable collecting and recording data. They should understand concepts of volume and be able to relate volume to multiplication and addition. They should feel comfortable with unit cubes and using cubic centimeters, inches and feet to solve problems. Students should be able to convert from one measurement unit to another, such as inches to feet.