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Prealgebra tutor

Number Foundations

A short diagnostic on-ramp covering the number-sense skills a pre-algebra course assumes: recognizing factors, multiples, and prime structure; using divisibility shortcuts and finding the greatest common factor and least common multiple; writing and evaluating whole-number exponential notation; applying the order of operations to numerical expressions; and reading, rounding, and comparing whole numbers by place value. Topics: Factors, Multiples, and Prime Structure, Exponent Notation, Order of Operations, Place-Value Fluency.

Fractions and Decimals

Fluency with positive fraction and decimal arithmetic: simplifying and comparing fractions, adding, subtracting, multiplying, and dividing fractions and mixed numbers, and performing the same four operations with decimals. Topics: Fraction Operations, Mixed Numbers, Decimal Operations, Fraction-Decimal Conversion.

Integers and Rational Numbers

Extending arithmetic to negative numbers: plotting signed rational numbers on a number line, finding opposites and absolute value, and comparing and ordering signed numbers. Topics: Negative Numbers and Absolute Value, Integer Operations, Rational Number Operations.

Ratios and Rates

Ratio language and notation, equivalent ratios shown with tables, tape diagrams, and double number lines, unit rates including rates built from fractional quantities, comparing rates, and converting measurement units by multiplying by a rate. Topics: Ratio Language and Equivalence, Ratio Representations, Rates and Unit Rates, Rate-Based Unit Conversion.

Percents

Percent as a rate per 100, converting among percents, fractions, and decimals, finding a part, whole, or percent in a percent relationship, common percent applications such as tax, tip, discount, markup, and commission, percent increase and decrease, percent error, and simple interest. Topics: Percent Meaning and Conversion, Finding the Part, Whole, or Percent, Percent Applications, Percent Change and Error, Simple Interest.

Proportional Relationships

Deciding whether a relationship shown in a table, graph, or equation is proportional, finding and interpreting the constant of proportionality, writing and graphing equations of the form y = kx, solving proportions and multi-step proportional word problems, and using scale drawings and scale factor. Topics: Identifying Proportional Relationships, Finding the Constant of Proportionality, Representing and Interpreting Proportional Relationships, Solving Proportions and Applications, Scale Drawings.

Expressions

Algebraic expression language and fluency: naming the parts of an expression, evaluating expressions by substitution, translating between verbal descriptions and symbolic form, and rewriting expressions into equivalent forms using properties of operations, the distributive property, and combining like terms. Topics: Expression Language, Evaluating Expressions, Equivalent Expressions.

Equations and Inequalities

Solving equations and inequalities in one variable and writing them to model real-world situations: checking solutions, solving one-step through multi-step equations, recognizing equations with one, no, or infinitely many solutions, and solving and graphing one-variable inequalities, including the sign reversal that comes from multiplying or dividing by a negative number. Topics: Equation Basics, Multi-Step Equations, Equation Modeling, Solving Inequalities, Inequality Modeling.

Exponents, Roots, and Scientific Notation

A toolkit of number and expression skills built on powers and roots: the laws of integer exponents, including zero and negative exponents, evaluating and simplifying exponential expressions, square and cube roots and the equations they solve, the distinction between rational and irrational numbers, estimating irrational numbers on a number line, and reading, comparing, and operating with scientific notation. Topics: Exponent Rules, Square and Cube Roots, Rational and Irrational Numbers, Scientific Notation.

Linear Relationships and Functions

Linear relationships studied through the coordinate plane, slope, and the general idea of a function: plotting and reflecting points, finding the distance between points that share a coordinate, computing and interpreting slope from different representations, writing and graphing equations in slope-intercept form, determining whether a relationship is a function and whether it is linear, comparing functions given in different representations, reading qualitative graphs of real situations, and solving simple systems of two linear equations. Topics: Coordinate Plane, Independent and Dependent Variables, Slope, Slope-Intercept Form, Functions, Systems of Linear Equations.

Geometry and Measurement

Area, surface area, volume, and other measurement relationships for two- and three-dimensional figures, together with the angle and triangle facts that describe how shapes fit together. Topics: Area of Polygons, Nets and Surface Area, Circles, Volume of Solids, Angle Relationships, Triangle Side and Angle Conditions, Cross-Sections of Solids.

Transformations and the Pythagorean Theorem

Rigid motions, congruence, dilations, and similarity of figures on a coordinate plane, the angle facts that come from parallel lines and triangles, and the Pythagorean theorem. Topics: Translations, Reflections, and Rotations, Congruence, Dilations, Similarity, Parallel Lines and Triangle Angles, The Pythagorean Theorem.

Statistics and Probability

Statistical questions and data displays, measures of center and spread, sampling and population inference, comparing two data sets, probability, and bivariate data through scatter plots and two-way tables. Topics: Statistical Questions and Data Displays, Measures of Center and Spread, Sampling and Population Inference, Comparing Two Populations, Probability, Scatter Plots and Association, Two-Way Tables.