Critical prealgebra skills for
7th and 8th grade math students

Whereas elementary school had one major theme, arithmetic, middle school focuses on prealgebra skills, which are primarily the following three topics:

• Higher arithmetic operations: fractions, decimals, mixed numbers.



• Percents, ratio and proportion, introductory geometry, and negative numbers.



• The concept of variable, meaning any number. That is, there needs to be some introduction to the concepts, symbolism and techniques of algebra.

Introduction to the algebraic concepts heralds in a very big step forward in abstraction!

Following are the main topics in a prealgebra curriculum. Some math departments will spread these topics out over 7th and 8th grade. Accellerated students may cram it all in during 7th grade math and then start alebra itself in 8th grade math.

The goal is to make sure your child achieves competency in all these topics, so that algebraic concepts will be more easily understandable, no matter when it is encountered.

If your child is doing pretty well with these prealgebra topics, you may be thinking of putting him or her in an accelerated math program. You should consider all the pros and cons of math course acceleration before moving forward with that decision.

If your own attempts at math skills practice with your child are not successful, and you are considering hiring a tutor, here are some tips to consider before hiring a math tutor.

Key Prelagebra Topics are:

• Operations with whole numbers: properties; expressions; inverse operations; exponents and square roots; order of operations; problem solving.



• Positive and negative numbers: four operations with positive and negative numbers; products with negative factors.



• Introduction to algebra: mathematical expressions; order of operations; equations and inequalities; properties of equality; writing mathematical expressions, solving equations and inequalities; word problems and equations.



• The decimal system: exponents and powers of ten; decimals; rounding; four operations with decimals; estimation.



• Number theory: factors and multiples; divisibility rules; square numbers and square roots; prime and composite numbers; greatest common factor; least common multiple.



• Rational numbers: positive and negative fractions; equivalent fractions; least common denominator; addition, subtraction, multiplication and division of fractions; mixed numbers; fractions and decimals.
• Ratio, proportion, and percent: ratio and proportion; scale drawings; percents, fractions, and decimals; percent of increase and decrease; commis¬sions, discounts, mark up, royalties; percents and proportions; simple and compound interest.



• Geometry: points, lines, segments, planes, circles, angles, special angles, parallel lines, triangles, special quadrilaterals, polygons, congruence. Area of rectangles, parallelograms, triangles, trape¬zoids, circles. Volume of prisms, cylinders, pyramids, cones, spheres. Surface area of prisms, cylinders, spheres. Mass and density. Graphs of ordered pairs and of equations.



• Polynomials: polynomial expressions; four operations with monomials and polynomials.



• Probability: permutations; combinations; probability of an event; odds in favor and odds against; mutually exclusive events and “overlapping events; independent and dependent events; estimating probabilities.
• Statistics: bar and line graphs; statistical measures; frequency distributions; stem-and-leaf plots; box-and-whisker plots; histograms; expected value of a random variable.

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