Mathematics Standards of Learning
Reprinted with permission from:

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Intro | Kindergarten | Grade 1 | Grade 2 | Grade 3 | Grade 4 | Grade 5 | Grade 6 | Pre Algebra | Algebra I | Geometry

Pre-Algebra

These Standards list skills that students should master. They need not be taught in the order presented. Some topics may appear in slightly different forms in different areas. These Standards mention a number of specific skills as well as solving "word" or "real world" problems. Even when not mention explicitly, students should practice and be able to use the component skills in the context of solving "word" or "real world" problems.

Some of these Standards will have been met by students in an appropriate K-6 program. If not, students expecting to take Algebra are expected to meet these Standards in their Pre-Algebra course. For some students, such a course might be designed to take two years. A number of different textbooks should be able to prepare students to meet these Standards, but textbooks that are clearly lacking in large portions of these Standards should not be used for courses that serve as the course before Algebra. Although some textbooks or classroom methods may involve calculators as pedagogical aids, it is expected that a student will demonstrate mastery of the material described in these Standards without the use of a calculator.

Properties of the Number System

• PA-1 The student will know and identify the following properties or operations with real numbers and use them to justify individual steps in the solution of problems:
  • the commutative and associative properties for addition and multiplication;
  • the distributive property;
  • the additive and multiplicative identity properties;
  • the additive and multiplicative inverse properties; and
  • the multiplicative property of zero.
• PA-2 The student will be able to perform operations with exponents, including operations with positive, negative and fractional exponents. The student should also be able manipulate numbers expressed as powers of 10 and in scientific notation.
• PA-3 The student will break numbers into their prime factors.
• PA-4 The student will know the squares of numbers up to 16 and be able to determine the value, to between any two integers, of the square root of any number less than 256.
• PA-5 The student will know and use the rules for order of operations to evaluate numerical expressions, to evaluate algebraic expressions in which the variables are replaced by specific values, to simplify algebraic expressions containing up to three variables and to solve linear algebraic equations of a single variable.

Fractions, Decimals, Percents, Proportions, Ratios and Probability

• PA-6 The student will add, subtract, multiply and divide fractions, including fractions with unlike denominators and negative fractions.
• PA-7 The student will add, subtract, multiply and divide decimals, and decimals expressed as powers of ten or in scientific notation.
• PA-8 The student will convert fractions to decimals, decimals to fractions, fractions to percents, percents to fractions, decimals to percents, and percents to decimals.
• PA-9 The student will solve "word" or "real world" problems using fractions, decimals and percents, including problems involving determining what fraction or percent of one quantity another quantity is, or determining what value is a set fraction or percent of a given quantity. This will include problems involving money such as computation of tips, discounts, sales tax, and simple interest.
• PA-10 The student will recognize and compute proportions and ratios as a fraction of a total and in addition, will calculate ratios as the relationship of two parts of a total.
• PA-11 The student will solve "word" or "real world" problems involving proportions and ratios.
• PA-12 The student will use proportions/ratios to evaluate scale drawings and to produce scale drawings.
• PA-13 The student will recognize the relationship between probability statements and fractions, decimals and percents, will determine the expected number of events based on a given probability, and will be able to estimate the probability of an event based on a given distribution of previous events.
• PA-14 The student will determine the theoretical probability of events in simple systems such as the chance of drawing a "heart" or an "ace" from the a deck of cards, the chance of rolling a particular number with one die or a pair of dice, or the chance of a particular result on a spinner.

Algebraic Manipulations

• PA-15 The student will evaluate expressions in one, two or three variables when given specific numerical values for each variable using any or all of the processes covered above.
• PA-16 The student will simplify expressions involving one, two or three variables such as
  
  • m^3p + mpm^2 -m^3+ 3pmp^2 or
  • a^2bc/ab^3
• PA-17The student will solve linear equations and inequalities in one variable such as
  
  • 2x/5 = -10 or
  • 5y -2.7 = -12.7y or
  • 3r - 6/5 = 9/3
• PA-18 The student will, given various "word" or "real world" problems, write and solve linear equations of a single variable and convert these solutions into answers to the problems.

Graphing of Data and Equations

• PA-19 The student will understand the terms domain, range, x-axis, y-axis, x-coordinate, y-coordinate, slope, x-intercept and y-intercept.
• PA-20 The student will plot ordered pairs of points in all quadrants of the coordinate plane.
• PA-21 The student will plot data in various graphical formats and will answer questions and make predictions based on information given in graphs.
• PA-22 The student will calculate the mean, median, mode and range of a set of data.

Geometry

• PA-24 The student will calculate the area and perimeter of rectangles, parallelograms, trapezoids, triangles and circles. The student will also calculate the are of more complicated shapes by breaking them into pieces such as rectangles, triangles and fractions of circles.
• PA-25 The student will calculate the volume and surface area of right angle boxes and spheres. The student will also calculate the volume and surface area of rectangular prisms with known heights and irregular bases.
• PA-26 The student will use the Pythagorean Theorem to calculate the length of the missing side of a right triangle and to determine if a triangle is a right triangle.
• PA-27 The student will recognize and name polygons with up to 10 sides as well as dodecagons.
• PA-28 The student will recognize congruent and similar polygons and will use proportions to determine the lengths of unlisted sides.