Pre-Algebra

Course Duration: Full Year

Category: High School, Mathematics

Assessment: Pre-Test, Lesson Practice, Unit Exams, Mid-Term Exam, Final Exam

Language: English

Course Overview

The Pre-Algebra course was developed to ensure that students have a strong foundation in basic mathematical concepts prior to introducing them to more advanced topics. We have found that students often have difficulty in Algebra when they have a weak foundation in mathematics. Acellus Pre-Algebra helps to fill in the holes in student understanding, providing them with a strong foundation of basic mathematical concepts upon which they can build. It is recommended that students take Acellus Pre-Algebra at either grade 7 or 8, prior to going into Algebra. A Spanish version of Pre-Algebra is also available. Course topics include:

Whole Number Operations
Order of Operations
Fractions/Decimals/Percentages
Probabilities (including permutations and combinations)
Statistics (mean, median, mode, range, and graphs)
Planes, Points, Lines, and Angles
Polygons (types of polygons and several properties)
Perimeter, Area, and Volume
Square Roots
Pythagorean Theorem
Absolute Value
Integer Operations
Basic Graphing
Operations using Rational Numbers
One- and Two-Step Equations
Basic Inequalities

Course Objectives & Student Learning Outcomes

Upon completion of Acellus Pre-Algebra, students will be able to add, subtract, multiply, and divide whole numbers; determine divisibility; compare and contrast prime and composite numbers calculate greatest common factors; factor; choose place value; estimate; implement order of operations; utilize formulas with variables; calculate ratios, rates, and proportions; compare and contrast and manipulate improper and mixed fractions; simplify fractions; find least common multiples; add, subtract, multiply, and divide fractions, mixed numbers, simple fractions, and mixed numbers; add, subtract and multiply decimals; divide decimals by whole numbers; compare and order decimals; divide decimals by powers of ten; and solve terminating and repeating decimal problems. Students will also be able to utilize standard and scientific notation; find or convert measures to the metric system; solve percent, simple interest, and applied percent problems; create and read circle graphs; implement counting principle and create and read tree diagrams; calculate basic probability; choose, compare and contract independent and dependent events; predict with probability; identify factorials; find permutations in ordered subsets and combinations in unordered subsets; find mean, median, mode and range; read and interpret frequency tables, pictographs, and bar graphs, broken line graphs and other graphs; and judge misleading statistics. Students will be able to identify, create and measure planes, points, and lines to include parallel lines and transversals; read and use geometry symbols; find the sum of angles of a triangle and regular polygons; classify triangles, quadrilaterals, and other polygons; compare and contrast congruent versus similar triangles; find length and perimeter; and find area, volume and surface area for 2-dimensional shapes and 3-dimensional figures. Finally, students will be able to calculate square roots and implement the Pythagorean Theorem; identify, classify, and measure circles and transformations; find symmetry; implement set notation; identify, create, and read Venn Diagrams; compare and order integers; find absolute value; add, subtract, multiply, and divide integers; use order of operations with integers; solve problems with zero and with identify, commutative, associate, and distributive properties; create, read, and manipulate basic graphs, ordered pairs, and the coordinate plane; compare, order, add, subtract, multiply, and divide rational numbers to include decimals and fractions; discriminate expressions from equations; solve problems using order of operations with and without variables; translate algebraic words to symbols; solve one-step and two-step equations; use formulas and literal equations; identify patterns and functions; graph straight lines; find slope of a line; solve basic inequalities problems; find and use significant figures and significant digits with decimals; judge degree of precision; and add and subtract numbers in scientific notation.

Scope and Sequence

Unit 1 – Introduction and Basic FoundationIn this unit students explore addition, subtraction, multiplication, and division of whole numbers, divisibility rules, and prime and composite numbers. They study greatest common factors, prime factorization, place value, estimating, order of operations, powers of ten, and formulas and variables.Unit 2 – FractionsNext students discuss ratios, rates, proportions, improper and mixed fractions, and simplifying fractions. They explore least common multiples and adding, subtracting, multiplying, and dividing fractions and mixed numbers.Unit 3 – DecimalsIn this unit students investigate adding, subtracting, and multiplying decimals, as well as dividing decimals by whole numbers and by powers of ten. They discuss comparing and ordering decimals, and terminating and repeating decimals.Unit 4 – Decimals and FractionsStudents continue by studying standard and scientific notation, the metric system, and forms and types of percent. They investigate simple interest, applied percent, and circle graphs.Unit 5 – ProbabilityNext students learn about the counting principle, tree diagrams, basic probability, and independent and dependent events. They learn about using probability for prediction, as well as about factorials, permutations (ordered subsets), and combinations (unordered subsets).Unit 6 – StatisticsStudents begin the study of statistics, exploring mean, median, mode, range, frequency tables, and pictographs. They study reading and interpreting graphs; bar, broken-line, and other graphs; and misleading statistics. Following this unit students are presented with the Mid-Term Review and Exam.Unit 7 – Geometry of Angles and LinesIn this unit students discuss geometry symbols, planes, and points. They explore lines (including parallel lines and transversals), and angles.Unit 8 – PolygonsNext students investigate the sum of the angles of a triangle, how to classify a triangle, and the difference between congruent and similar triangles. They explore quadrilaterals and other polygons, as well as angles in regular polygons.Unit 9 – Perimeter, Area, and VolumeIn this unit students learn about perimeter and area in two-dimensional shapes. They also investigate volume and surface area in three-dimensional shapes.Unit 10 – Miscellaneous GeometryBeginning this unit with square roots and the Pythagorean Theorem, students continue by studying circles. They also learn about transformations and symmetry.Unit 11 – Pre-AlgebraIn this unit students explore set notation and Venn Diagrams, as well as comparing, ordering, adding, subtracting, multiplying and dividing integers. They investigate absolute value, as well as adding, subtracting, multiplying, and dividing integers. They study the order of operations and the properties of mathematics. They consider basic graphing.Unit 12 – Beginning AlgebraNext students discuss comparing, ordering, adding, subtracting, multiplying, and dividing rational numbers. They study expressions and equations, order of operations with and without variables, and the meaning of algebraic symbols. They also explore one- and two-step equations, as well as decimals and fractions. They analyze formulas, literal equations, patterns, functions, graphing straight lines, and basic inequalities.Unit 13 - Precision and Scientific NotationTo complete their study of math in this course, students study significant figures, including those with a decimal. They discuss degree of precision and learn to add and subtract numbers in scientific notation. They practice using scientific notation in real-world situations. Following this unit students are presented with the Final Review and Exam.

This course was developed by the International Academy of Science. Learn More