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Pre-Algebra

Pre-Algebra

Course Features

Course Duration: Full Year
Category: , , ,
Assessment: Pre-Test, Lesson Practice, Unit Exams, Mid-Term Exam, Final Exam
Language: English

Course Details

Course Overview

Acellus Pre-Algebra provides a comprehensive introduction to foundational concepts in algebra and geometry, equipping students with essential mathematical skills for higher-level studies. Students will explore integers, rational numbers, exponents, and real numbers, mastering operations and their applications in algebraic expressions and equations. The course delves into geometric concepts, including the coordinate plane, transformations, and measurements of two- and three-dimensional figures. Additionally, students will learn about proportions, percents, data analysis, probability, and functions, culminating in an introduction to polynomials. Through hands-on problem-solving and real-world applications, students will develop critical thinking and analytical skills, preparing them for advanced mathematical challenges.

Sample Lesson - Introduction to Pre-Algebra

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Scope and Sequence

Unit 1: Integers and Algebraic Expressions This unit introduces students to the basics of algebra by focusing on integers and algebraic expressions. Students will learn to identify variables, simplify expressions by combining like terms, and apply the order of operations. They will explore integers, their opposites, and absolute values, while also mastering addition, subtraction, multiplication, and division of integers. The unit covers number properties, including the distributive, associative, and commutative properties, and introduces solving one-step equations involving addition, subtraction, multiplication, and division. By the end, students will be able to evaluate algebraic expressions, compare integers using inequalities, and apply these skills to solve basic algebraic problems.

Unit 2: Rational Numbers In this unit, students dive into rational numbers, learning to work with fractions, decimals, and their conversions. They will explore prime and composite numbers, prime factorization, and the greatest common factor to simplify fractions. Students will convert between mixed numbers, improper fractions, and decimals, including terminating and repeating decimals. The unit emphasizes finding the least common multiple to compare and perform operations (addition, subtraction, multiplication, and division) on rational numbers in both fraction and decimal forms. By the end, students will be proficient in manipulating rational numbers and applying these skills to real-world scenarios.

Unit 3: Powers and Exponents This unit focuses on powers, exponents, and their applications. Students will learn to simplify and evaluate expressions with exponents, including those with zero and negative exponents. They will explore rules for multiplying and dividing powers with the same base, raising powers to powers, and using the order of operations with exponents. The unit introduces scientific notation, teaching students to convert numbers between standard form and scientific notation, compare numbers in scientific notation, and perform multiplication and division with them. By the end, students will confidently handle exponential expressions and apply scientific notation in practical contexts.

Unit 4: Real Numbers and the Coordinate Plane This unit introduces real numbers and the coordinate plane, covering both rational and irrational numbers. Students will learn to evaluate square and cube roots, estimate non-perfect square roots, and solve equations using square roots. The Pythagorean Theorem is explored to calculate distances in right triangles. Students will graph ordered pairs, calculate distances on the coordinate plane, and perform transformations such as translations, reflections, and rotations. The unit concludes with identifying congruent transformations, enabling students to classify numbers and manipulate geometric figures on the coordinate plane effectively.

Unit 5: Proportions This unit focuses on ratios, proportions, and their applications in geometry and real-world problems. Students will learn to compare quantities using ratios, calculate unit rates, and convert units using conversion factors. They will determine proportionality using cross products and solve proportions to find missing values. The unit extends to similar figures, where students use proportions to find missing side lengths and explore dilations and similarity transformations. Students will also apply proportions to scale models, drawings, and indirect measurements, mastering practical applications of proportional reasoning.

Unit 6: Percent In this unit, students explore percents and their applications in real-world contexts. They will learn to convert fractions and decimals to percents and solve percent problems using proportions and the percent equation. The unit covers calculating percent change, markups, discounts, and simple interest, providing students with practical financial literacy skills. By the end, students will be able to confidently handle percent-related calculations and apply them to scenarios such as shopping, budgeting, and interest calculations.

Unit 7: Equations and Inequalities This unit builds on algebraic skills by focusing on solving multi-step equations and inequalities. Students will solve two-step equations, simplify expressions using the distributive property and combining like terms, and tackle equations with variables on both sides. They will determine whether equations have one, no, or infinite solutions. The unit also covers graphing and solving inequalities using addition, subtraction, multiplication, and division, including multi-step inequalities. By the end, students will be proficient in solving complex algebraic equations and inequalities and interpreting their solutions.

Unit 8: Geometry This unit explores geometric concepts, including angle relationships and measurements of two-dimensional shapes. Students will learn about vertical, adjacent, complementary, and supplementary angles, as well as angle relationships in parallel lines cut by a transversal. They will calculate interior and exterior angles in triangles and polygons, and compute perimeters and areas of rectangles, triangles, parallelograms, trapezoids, and circles. By the end, students will be able to analyze and calculate measurements of various shapes, applying geometric principles to solve problems.

Unit 9: Measurements This unit focuses on three-dimensional figures and their measurements. Students will identify nets of geometric solids and calculate surface areas and volumes of prisms, cylinders, pyramids, cones, and spheres. The unit also covers proportions in similar solids, enabling students to calculate lengths, surface areas, and volumes of scaled figures. By the end, students will be adept at visualizing and computing measurements of three-dimensional objects, applying these skills to real-world scenarios such as architecture and engineering.

Unit 10: Analyzing Data This unit introduces data analysis, teaching students to calculate measures of central tendency (mean, median, mode) and range. They will explore mean absolute deviation to assess data dispersion and learn to represent data using line plots, histograms, stem-and-leaf plots, box-and-whisker plots, and circle graphs. Students will analyze two-way tables for relative frequency, use Venn diagrams, and critically evaluate graphs for accuracy. The unit concludes with using scatter plots to make predictions, equipping students with tools to interpret and visualize data effectively.

Unit 11: Probability This unit covers the fundamentals of probability, including theoretical and experimental probability. Students will calculate probabilities, make predictions using survey data, and design valid surveys. They will distinguish between independent and dependent events, compute their probabilities, and apply the counting principle, factorials, permutations, and combinations to determine possible outcomes. By the end, students will be able to analyze probabilistic scenarios and apply these concepts to real-world decision-making.

Unit 12: Functions - Part I This unit introduces functions, focusing on sequences and their graphical representations. Students will explore arithmetic and geometric sequences, identify functions from tables, and classify functions as linear or nonlinear, increasing or decreasing. They will evaluate functions using function notation, graph functions using tables, and calculate slopes from graphs, tables, and unit rates. The unit also covers slopes of horizontal, vertical, parallel, and perpendicular lines, providing students with a solid foundation in functional analysis and graphing.

Unit 13: Functions - Part II Building on the previous unit, this unit delves deeper into functions, focusing on linear and nonlinear functions. Students will solve and graph direct variation equations, write linear function rules from tables, graphs, and verbal descriptions, and use them to predict real-world outcomes. They will explore systems of linear equations, quadratic functions, and exponential functions, and calculate compound interest. The unit concludes with analyzing financially responsible decisions, equipping students with practical applications of functions in real-world contexts.

Unit 14: Polynomials This unit introduces polynomials, teaching students to simplify, add, subtract, and multiply them. Students will learn to combine like terms in polynomials, multiply monomials, and multiply monomials by binomials and binomials by binomials. By the end, students will be proficient in manipulating polynomial expressions, laying the groundwork for advanced algebraic studies and applications in higher mathematics.

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