Engineers' Guide - Skills and Knowledge By Grade Level

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 5-8 you can expect students to know or be learning the following:

Students acquire solution techniques and strategies to solve problems dealing with math class and in other areas of life such as science, art, business, technology and music. Problems will have multiple steps. They also learn to use math to investigate math concepts.

Students are taught to express math concepts geometrically, graphically, algebraically as well as with oral and written language. Students are able to use logic to deduce solutions. They are able to use math to find alternative ways to validate solutions.

Students will have a working knowledge of integers, fractions, decimal, percentages, rational numbers (numbers which can be expressed as the quotient of two integers) exponents and scientific notation. They will be able to graph in 1 (line graphs) and 2 dimensions (X and Y axis plots). They will understand proportions and ratios, as well as prime numbers, factors, and multiples of a number.

Students will be able to use estimation to determine if they are on the right track in solving a problem and to quickly check results.

Their tools for solving math problems will include mental arithmetic, paper and pencil (especially with longer problems requiring multiple steps), calculators, and computer software.

Students learn to analyze numerical patterns and functions. For example, students exam how a quantity changes in relationship to another.

Students begin to learn algebraic concepts, such as the meaning of a variable or an equation. Algebraic techniques are used to solve real world word problems.

Students are introduced to probability concepts by comparing experimental data against mathematical predictions.

Students begin to study geometric concepts introduced in grades K-4. Students begin to work with areas and volumes. Relationships between 2D patterns and 3D objects are explored.

Student knowledge of measurements and unit systems is expanded. The concepts of rates of change and degree of accuracy in measurement is introduced.

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