 # Achieving Math Standards by Grade

Updated: 4/17/18

Your state's Department of Education or other educational governing body sets the mathematics standards that all students must achieve throughout their years in elementary, middle and high school. Those curricular standards are then implemented by school districts. While standards may be worded differently from state to state, the idea is to teach every student to reason, communicate, problem-solve and make connections mathematically. For example, as stated in the New Jersey Core Curriculum Content Standards for Mathematics, the vision of the math standards is "to enable all of New Jersey's children to acquire the mathematical skills, understandings and attitudes that they will need to be successful in their careers and daily lives."

Standards typically fall into these general categories:

1. Numerical operations, analytical thinking
2. Patterns and algebra
3. Geometry and measurement
4. Data analysis and probability and statistics
5. Problem-solving, reasoning, connections and other mathematical processes

In 2010, Achieve, an independent, nonprofit education organization, coordinated a state-led effort to develop the Common Core State Standards for English and math. As examples, here are high-level summaries of what second- and fourth-grade students should be able to do:

• Operations/algebra: Represent and solve problems involving addition and subtraction, add and subtract within 20, and work with equal groups of objects to gain foundations for multiplication.
• Numbers: Understand place value and use place value understanding and properties to add/subtract.
• Measurements/data: Measure and estimate lengths in standard units, relate addition and subtraction to length, work with time and money, and represent and interpret data.
• Geometry: Reason with shapes and their attributes.

• Operations/algebra: Use the four operations with whole numbers to solve problems, gain familiarity with factors and multiples, and generate and analyze patterns.
• Numbers: Generalize place value understanding for multi-digit whole numbers, perform multi-digit arithmetic.
• Fractions: Extend understanding of fraction equivalence and ordering, build fractions from unit fractions, understand decimal notation for fractions, and compare decimal fractions.
• Measurements/data: Convert measurements from larger to smaller units, represent and interpret data, and understand concepts of angle and measure angles.
• Geometry: Draw lines and angles, and classify shapes by properties of their lines and angles.

Get detailed standards for all grades at www.corestandards.org.