Course Description: Seventh Grade Mathematics

Introduction

The general application and transformation of formulas and equations in practical life situations forms a central part of the seventh grade math curriculum. The students are beginning to encounter the practical laws of cause and effect, and with this, they can start working strongly with estimation in their computation. However, computational skills must be firmly established, or work with estimation will be difficult to verify. Extensive mental arithmetic, using sets and distribution as in 3(3+4), are used to challenge the students. Continued mastery of the four processes using whole numbers, fractions, decimals, measurements, and word problems are reinforced.

Work also continues in business math, solving budget, percentage, and discount problems. Ratio and simple proportion problems continue, as do problems with simple formulae (P = BR; P = RT; A = lw; etc.) Facility with simple algebraic equations and work with prime and square numbers is furthered. Absolute value, signed numbers, powers, and roots are introduced. Conscious work with geometric proofs continues, building up through triangles and parallelograms to deductive proofs of the Pythagorean theorem. Familiarity and precision are developed with all basic geometric constructions. During this time when thinking skills are active, word problems are worked with extensively. Appropriate discriminatory strategies and skills in analyzing word problems are further developed.

History of Mathematics

An understanding of the story of mathematics is vital to realizing the phenomenal effect mathematics has had, and continues to have, on all that we do, think and believe. Students should be familiar with the major contributions of various cultures, in particular Egypt, Babylonia, India, Ancient Greece, Persia, Arabia, and Europe. The questions, challenges, tragedies, and triumphs of key mathematicians are given life within the classroom. Some examples include Archimedes, Pythagoras, Plato, Aristotle, Euclid, Hypatia, Copernicus, Galileo, Kepler, Descartes, Newton, Leibniz, Euler, Gauss, and Einstein.

Number Sense and Theory

All mathematics is based on a surprisingly small set of ideas. To avoid a superficial understanding of mathematics, these core assumptions are carefully considered. Topics include: The mathematics within us; The number one, and it's infinite divisions and multiples; The operation of counting, and its four variations; The “devilish” discovery of zero; The counter-intuitive fact of negative numbers; Variations of number systems and notation. Some typical questions to explore include: What is knowledge, and how do we know? What is a number? What is the biggest/smallest number? Are numbers real or imagined? Is mathematics invented or discovered? What is truth? What is a mathematical proof? Why does mathematics work so well? What exactly is mathematics?

Measurement and Geometry

Measurement is the act or process of assigning numbers to phenomena according to a rule. It is this application of numbers to qualities of things that makes practical mathematics possible. Students study common forms of measurement such as time, distance, mass, length, volume, rates of exchange, and temperature.

Students explore the nature of basic geometric shapes, such as points, lines, squares, triangles, circles, etc. Students use the compass and straight measure to create a variety of shapes. Seventh grade focuses exclusively on Euclidean geometry.

Algebra and Functions

Symbolic reasoning and calculations with symbols are central in algebra. Through the study of algebra, a student develops an understanding of the symbolic language of mathematics and the sciences. In addition, algebraic skills and concepts are developed and used in a wide variety of problem-solving situations. Seventh graders learn the basic vocabulary and techniques of algebra including the nature of linear equations, variables, unknown values, and constants. Probability Probability is a technique for measuring the edge of what is measurable. It explores patterns of chance and risk. Seventh grade students can begin to explore probability through various games of chance, and make simple predictions, such as the odds that the roll of a die will be 4, or that three consecutive rolls of the die will all result in even numbers.

The Future of Mathematics

Many schools teach only mathematical facts discovered thousands of years ago. They often fail to share the drama of those discoveries or to historically link them to modern life. Student's often find such instruction boring and irrelevant. However, the future of mathematics is immeasurably greater than its past. Mathematics continues to grow at a phenomenal rate. There is no end in sight, and the applications of mathematics becomes greater all the time. The infinitely larger world of the unknown waits to be discovered by a new generation of students. Seventh grade students can begin to explore today's greatest mathematical questions.