Engineers' Guide

Mathematics Skills and Knowledge By Grade Level

States and school districts generally follow The National Council of Teachers of Mathematics "Principles and Standards for School Mathematics" (http://standards-e.nctm.org/1.0/89ces/Table_of_Contents.html). In mathematics as in science, the standards are grouped into grades K-4, 5-8 and 9-12. With such a wide range of grades and math contend within each of the three groups, you may want to check with the teacher on their classes' specific knowledge and math skills. For example, in K-4 the standards discuss that all students should know how to multiply even though that skill is generally not taught until the 3rd grade. In high school, students following a college-bound curriculum may be exposed to more advanced math concepts which have been noted.

For grades 9-12 you can expect students to know or be learning the following:

Students use multiple mathematical solution techniques from different math topics they have studied to solve problems.

Students may be introduced to mathematical arguments, logic, theorems, proofs and the use of counterexamples.

Students advance their skills in algebra and are able to work with and formulate equations, inequalities and matrices. They are able to use tables and graphs to express algebraic solutions.

Students continue their study of 2 and 3D geometry. The concepts of similarity and congruency are introduced. Students may be taught to draw and understand 3D diagrams of objects. College-bound students may be introduced to the concept of a vector.

Students study trigonometry including sine and cosine functions. College-bound students may also study circular functions, polar coordinates and complex numbers.

As students continue their study of statistics and probability they learn about distributions, random numbers and are asked to use simulation to solve problems.

Students may be exposed to computer algorithms as part of math and technology classes.

Students are informally introduced to calculus concepts: minimum and maximum of a curve and the area under a curve. College-bound students may also study slopes of a tangent, rates of change and graphing of polynomial and other functions.

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