Pre Algebra
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Pre Algebra

AccelaStudy AI Pre-Algebra is a foundational mathematics course aligned to Common Core State Standards for grades 6–8 (domains: 6.NS, 6.RP, 6.EE, 6.SP, 7.NS, 7.RP, 7.EE, 7.G, 7.SP, 8.EE, 8.F, 8.G, 8.SP). It builds the essential bridge from arithmetic to formal algebra, developing fluency with rational numbers, proportional reasoning, algebraic expressions and equations, coordinate geometry, and introductory statistics and probability. Mastery prepares students to succeed in Algebra 1 and subsequent high-school mathematics courses.

Who Should Take This

Middle-school students in grades 6–8 who are transitioning from arithmetic to algebra, as well as any learner who wants to solidify foundational number sense, ratio reasoning, and early equation-solving skills before tackling Algebra 1.

What's Covered

1The Number System and Rational Number Operations
2Ratios, Rates, Proportions, and Percent
3Algebraic Expressions and Properties
4Equations and Inequalities
5Exponents and Scientific Notation
6Coordinate Plane and Linear Relationships
7Geometry: Area, Surface Area, Volume, and Angles
8Statistics and Data Analysis
9Probability

What's Included in AccelaStudy® AI

Adaptive Knowledge Graph
Practice Questions
Lesson Modules
Console Simulator Labs
Exam Tips & Strategy
13 Activity Formats

Course Outline

1The Number System and Rational Number Operations
2 topics

Integers and Absolute Value

  • Recall the definition of absolute value and identify the absolute value and opposite of any integer on a horizontal or vertical number line
  • Apply the rules for adding and subtracting integers by using number-line models and the additive-inverse property to solve multi-step problems (7.NS.A.1)
  • Apply sign rules for multiplying and dividing integers and explain why the product of two negatives is positive using the distributive property (7.NS.A.2a)

Rational Number Operations

  • Recall that every rational number has a terminating or repeating decimal representation and convert between fraction, decimal, and percent forms (7.NS.A.2d)
  • Apply the standard algorithms to add and subtract rational numbers in fraction and decimal form, including negative values, and verify using estimation (7.NS.A.1d)
  • Apply algorithms to multiply and divide rational numbers including mixed numbers and negative fractions, and interpret the sign of quotients in real-world contexts (7.NS.A.2b)
  • Analyse and order a mixed set of rational numbers including fractions, decimals, and percents on a number line and explain the ordering using equivalence (6.NS.C.7)
  • Solve multi-step real-world problems involving all four operations with rational numbers by selecting appropriate operation sequences and checking reasonableness of results (7.NS.A.3)
2Ratios, Rates, Proportions, and Percent
2 topics

Ratio and Rate Concepts

  • Recall the definition of a ratio and unit rate and express a ratio relationship in colon, fraction, and word form for given real-world data (6.RP.A.1)
  • Compute unit rates associated with ratios of fractions and decimals, including rates measured in like or different units such as miles per gallon or cost per ounce (7.RP.A.1)
  • Identify proportional relationships by testing for equivalent ratios in tables and determine whether a graph through the origin represents proportionality (7.RP.A.2a)

Percent Applications

  • Recall that percent means per hundred and use the percent equation part equals percent times whole to find any of the three unknowns in straightforward contexts (6.RP.A.3c)
  • Apply the percent change formula to calculate percent increase and decrease, markups, markdowns, discounts, and gratuities in multi-step real-world problems (7.RP.A.3)
  • Apply the simple interest formula I equals Prt to compute interest earned, principal, rate, or time and interpret results in the context of savings and loan scenarios (7.RP.A.3)
  • Analyse scale drawings by identifying the scale factor and computing actual dimensions from drawing measurements or creating scaled reproductions of figures (7.G.A.1)
3Algebraic Expressions and Properties
2 topics

Variables, Terms, and Expressions

  • Recall the meaning of variable, coefficient, constant, term, and expression and identify each component in a given algebraic expression (6.EE.A.2b)
  • Comprehend verbal descriptions of mathematical relationships and translate them into algebraic expressions using variables, including multi-operation expressions (6.EE.A.2a)
  • Apply order of operations (PEMDAS) to evaluate algebraic expressions with whole-number, fraction, and integer values substituted for variables (6.EE.A.1, 6.EE.A.2c)

Simplifying Expressions

  • Apply the properties of operations including commutative, associative, and distributive to combine like terms and simplify linear expressions with rational coefficients (7.EE.A.1)
  • Apply the distributive property to expand expressions of the form a times (b plus c) and factor expressions of the form ab plus ac, verifying equivalence by substituting values (6.EE.A.3)
  • Analyse whether two expressions are equivalent by testing multiple values of the variable and justify using algebraic properties of operations (6.EE.A.4)
4Equations and Inequalities
3 topics

One-Step Equations

  • Recall the definition of a solution to an equation and identify whether a given value satisfies an equation by substitution (6.EE.B.5)
  • Apply inverse operations including addition and subtraction and multiplication and division to solve one-step equations with rational number coefficients and verify the solution (6.EE.B.7)

Two-Step and Multi-Step Equations

  • Apply a two-step solution process to equations of the form px plus q equals r and p times (x plus q) equals r with rational numbers and justify each algebraic step (7.EE.B.4a)
  • Solve multi-step real-world and mathematical problems by writing and solving a two-step equation, identifying the variable, and interpreting the solution in context (7.EE.B.3)
  • Apply the distributive property and collect like terms to solve multi-step linear equations with rational number coefficients, including equations with variables on both sides (8.EE.C.7b)

Inequalities

  • Recall the meaning of the inequality symbols and represent simple inequality solution sets on a number line using open and closed circles (6.EE.B.5)
  • Apply inverse operations to solve one- and two-step inequalities of the form px plus q greater than r, recognizing that multiplying or dividing by a negative reverses the inequality symbol (7.EE.B.4b)
  • Analyse a real-world constraint scenario, write a two-step inequality, solve it, graph the solution set, and interpret what values satisfy the constraint (7.EE.B.4b)
5Exponents and Scientific Notation
2 topics

Laws of Exponents

  • Recall the meaning of integer exponents including positive, zero, and negative and evaluate powers of integers and unit fractions without a calculator (8.EE.A.1)
  • Apply the product rule, quotient rule, and power rule to simplify numerical expressions with integer exponents and generate equivalent forms (8.EE.A.1)
  • Apply square root and cube root notation to solve equations of the form x-squared equals p and x-cubed equals p for positive rational p, evaluating perfect squares through 225 and perfect cubes through 125 (8.EE.A.2)

Scientific Notation

  • Recall the form of scientific notation as a times 10 to the n power where a is at least 1 and less than 10, and convert between standard decimal notation and scientific notation (8.EE.A.3)
  • Apply the laws of exponents to multiply and divide numbers in scientific notation and express results in proper scientific notation, including problems that mix decimal and scientific forms (8.EE.A.4)
  • Analyse the relative size of quantities expressed in scientific notation to estimate how many times larger one quantity is than another in real-world science and astronomy contexts (8.EE.A.3)
6Coordinate Plane and Linear Relationships
3 topics

The Coordinate Plane

  • Recall the structure of the four-quadrant coordinate plane and plot ordered pairs of integers and rational numbers, identifying the quadrant or axis location (6.NS.C.6c)
  • Apply absolute value to calculate the distance between two points on a coordinate plane that share the same x-coordinate or y-coordinate, and connect this to real-world map problems (6.NS.C.8)

Slope and Linear Equations

  • Comprehend slope as the constant rate of change expressed as rise over run and identify slope from a graph, a table of values, and the equation y equals mx for a proportional relationship (7.RP.A.2b, 8.EE.B.5)
  • Comprehend the slope-intercept form y equals mx plus b, identify the slope and y-intercept from the equation, and connect both values to the graph of the line (8.EE.B.6)
  • Apply knowledge of slope and y-intercept to graph a linear equation y equals mx plus b by plotting the y-intercept and using the rise-over-run ratio to locate additional points (8.EE.B.6)

Introduction to Functions

  • Recall the definition of a function as a rule assigning exactly one output to each input and identify functions from mapping diagrams, tables, and sets of ordered pairs (8.F.A.1)
  • Comprehend multiple representations of a linear function including equation, table, graph, and verbal description and move fluently among these forms (8.F.A.2)
  • Apply a linear function to model a real-world relationship, construct the equation from context using initial value and rate of change, and predict values for inputs outside the given data (8.F.B.4)
  • Analyse graphical representations to distinguish linear from nonlinear functions by checking whether the rate of change is constant and cite evidence from slope calculations between multiple point pairs (8.F.A.3)
7Geometry: Area, Surface Area, Volume, and Angles
3 topics

Area and Circumference

  • Recall area formulas for triangles, parallelograms, and trapezoids and apply them to compute area of composite plane figures formed by combining these shapes (6.G.A.1)
  • Apply the formulas A equals pi r-squared and C equals 2 pi r to compute the area and circumference of circles and solve problems with semicircles and composite figures containing circular parts (7.G.B.4)

Surface Area and Volume

  • Comprehend the relationship between a three-dimensional solid and its net, and apply the net to compute surface area of rectangular prisms, triangular prisms, and pyramids (6.G.A.4)
  • Apply volume formulas V equals Bh for prisms and V equals one-third Bh for pyramids to compute volume of right prisms and pyramids with rational number dimensions (7.G.B.6)
  • Apply lateral and total surface area formulas for cylinders and cones, and solve real-world packaging and design problems requiring selection of the correct formula (7.G.B.6)

Angle Relationships

  • Recall the definitions of complementary, supplementary, vertical, and adjacent angles and identify each type in diagrams with intersecting and parallel lines (7.G.B.5)
  • Apply complementary and supplementary angle relationships to write and solve one-step equations that find unknown angle measures in geometric diagrams (7.G.B.5)
  • Apply the triangle angle-sum theorem of 180 degrees and the exterior angle theorem to find missing angle measures in triangles, including multi-step and algebraic problems (8.G.A.5)
8Statistics and Data Analysis
3 topics

Data Displays and Distributions

  • Recall the distinction between statistical and non-statistical questions and explain that data distributions have variability that can be described by center, spread, and shape (6.SP.A.1)
  • Comprehend and construct dot plots, histograms, stem-and-leaf plots, and box plots from a data set and identify the shape of the distribution as symmetric, skewed, or uniform (6.SP.B.4)

Measures of Center and Spread

  • Recall the definitions of mean, median, and mode, compute each from a data set, and identify which measure best represents center for symmetric versus skewed distributions (6.SP.A.3)
  • Apply range and interquartile range to measure the spread of a data set, compute the first and third quartiles and IQR, and identify potential outliers using the 1.5 times IQR rule (6.SP.B.5c)
  • Analyse two data sets using parallel box plots or histograms, comparing their centers, spreads, and shapes to draw evidence-based conclusions about the populations (7.SP.B.4)

Sampling and Inference

  • Comprehend that random sampling produces representative samples and use a sample statistic such as mean or proportion to make a valid inference about the population from which it was drawn (7.SP.A.1, 7.SP.A.2)
  • Comprehend a scatter plot as a tool for exploring association between two quantitative variables and identify positive, negative, or no association and linear or nonlinear patterns from the graph (8.SP.A.1)
  • Apply a line of best fit to a scatter plot by drawing it informally or using a given equation and make predictions within the range of the data by substituting input values (8.SP.A.2, 8.SP.A.3)
9Probability
2 topics

Basic Probability Concepts

  • Recall the probability scale from 0 to 1 and define probability as the ratio of favorable outcomes to total equally likely outcomes, classifying events as impossible, unlikely, equally likely, likely, or certain (7.SP.C.5)
  • Apply the theoretical probability formula P of E equals favorable outcomes divided by total outcomes to compute probabilities of simple events for uniform sample spaces such as dice, spinners, and card draws (7.SP.C.6)
  • Comprehend the difference between theoretical and experimental probability and explain why repeated trials cause experimental probability to converge toward theoretical probability (7.SP.C.6)

Compound Events

  • Apply organized lists, tables, and tree diagrams to represent the sample space of a compound event and systematically count the total number of equally likely outcomes (7.SP.C.8a)
  • Apply the multiplication rule P of A and B equals P of A times P of B to compute probabilities of compound independent events and verify by listing the complete sample space (7.SP.C.8b)
  • Apply the complement rule P of not-E equals 1 minus P of E to compute complementary probabilities and use it to simplify problems where counting what does not happen is easier (7.SP.C.7b)
  • Analyse a real-world game or scenario involving compound events, compute theoretical probabilities using multiple methods including lists, tables, and tree diagrams, and evaluate whether the game is mathematically fair (7.SP.C.8c)

Scope

Included Topics

  • Integers and rational number operations (7.NS)
  • Ratios, rates, proportions, and percent applications (6.RP, 7.RP)
  • Algebraic expressions, properties, and simplification (6.EE, 7.EE)
  • One- and two-step equations and inequalities (7.EE.B.4)
  • Coordinate plane and linear relationships (6.NS.C.6, 8.EE.B)
  • Integer exponents and scientific notation (8.EE.A)
  • Area, surface area, volume, and angle relationships (7.G)
  • Introductory statistics: data displays, center, spread, and sampling (6.SP, 7.SP)
  • Probability models and compound events (7.SP.C)
  • Introduction to functions and linear models (8.F)

Not Covered

  • Formal proof and deductive geometry (Euclidean)
  • Quadratic and polynomial functions
  • Systems of equations beyond two-variable linear
  • Trigonometry and right-triangle ratios
  • Complex numbers and irrational number theory
  • Calculus concepts (limits, derivatives, integrals)

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