Pre-Algebra IA Grade Level 8

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1 Pre-Algebra IA Pre-Algebra IA introduces students to the following concepts and functions: number notation decimals operational symbols inverse operations of multiplication and division rules for solving equations by adding and subtracting integers exponents fractions graphing on the coordinate plane algebraic expressions statistics scatter plots definitions of basic geometric terms polygons and circles 1

2 TEACHERS' GUIDE COURSE DESCRIPTION: The Anywhere Learning System (ALS) Pre-Algebra IA course is a full semester course designed to help students bridge the gap from elementary studies into the more advanced and rigorous studies of high school mathematics courses. The Pre-Algebra IA content is designed to exceed the standards of Common Core Math, Grade 8, which many schools today refer to as the Pre-Algebra course. Students are provided foundational coursework in an easy-to-use interactive style, which encourages them to work problems thoroughly and check their work before moving on to the next task. COURSE FEATURES: Pre-Algebra IA is presented as a one-semester core course. All forty-four lessons contain a study guide, a practice test, and a mastery test. Each lesson contains interactive learning objects. Students click through each step of a problem in order to advance to the next step, providing students the opportunity to read and comprehend at the pace best suited for their individual needs. A glossary of terms and a calculator are provided in each study guide by clicking the Tools menu at the upper right. The built-in glossary helps students by reinforcing the key terms that are used across the title. They can also find key terms from previous lessons when they need them most. A virtual coach, Greek mathematician and philosopher Pythagoras, appears throughout the course to provide students with additional information about key concepts taught in the lesson. Students simply point at the image of Pythagoras in the lower left corner to read the information. 2

3 TEACHERS' GUIDE COURSE OBJECTIVES: Lessons are designed in units. Each unit groups related material as a foundation for the upcoming unit. Students should master a complete unit prior to moving to the next. Interactive sample problems are provided in each lesson. This allows students to immediately check their understanding as they move throughout the lesson. If they get the problems wrong, they can easily navigate to the previous page in order to review the module again. Pre-Algebra IA has an overall objective of laying the foundation for upper-level high school mathematics courses. Course materials are presented in a foundational method, and lessons become more complex as the student progresses. By the end of the course, students should have a solid working knowledge of the following key concepts: expressions, graphs, integers, exponents, rational numbers, square roots, equations, inequalities, statistics, and geometric shapes. COURSE CONTENT Course Name Number of Lessons Length of Course in Semesters Grade Level Built-in Calculator Glossary of Key Terms Pre-Algebra IA Yes Yes KEY TERMS Key terms, as listed in the following table, indicate new concepts that are introduced in each lesson. These concepts are listed as key terms in the course s glossary. When a lesson has no key terms listed, it typically means that the student will be working with concepts already introduced. 3

4 Unit 1: Expressions and Graphs Variables and Expressions Identify the parts of an expression, including terms, coefficients, constants, and variables. Evaluate algebraic expressions for given values of the variables. Key Terms: expression, numerical expression, algebraic expression, variable, term, coefficient, constant, substitution Writing Algebraic Expressions Translate words to numbers and numbers to words. Write an equation from a word problem. Solve a word problem Combining Like Terms Identify like terms in an expression. Simplify expressions by combining like terms. Simplify expressions using the distributive property. Key Terms: like terms, constant Graphing on a Coordinate Plane Graph a point given an ordered pair. Construct a line on a coordinate plane given a table. Solve an equation with two variables by using a table and coordinate plane. Key Terms: coordinate, plane, axes, x-axis, y-axis, ordered pair Interpreting Graphs and Tables Interpret information from a table. Interpret information from a graph. 4

5 Unit 2: Integers and Exponents Integers Define and recognize integers. Use a number line to compare two integers. Find the absolute value of an integer. Key Terms: integer, positive integer, negative integer, opposites, absolute value, zero pair Adding Integers Perform addition with positive and negative integers. Key Term: zero pair Subtracting Integers Perform subtraction with positive and negative integers Multiplying and Dividing Integers Multiply positive and negative integers. Divide positive and negative integers Exponents Evaluate expressions with exponents. Find the prime factorization of a number. Write a factorization with exponents. Key Terms: exponent, base, PEMDAS, prime number, factor tree Properties of Exponents State the laws of exponents. Simplify expressions with exponents. Multiply and divide terms with exponents. 5

6 02-07 Scientific Notation Convert from scientific notation to standard form. Convert from standard form to scientific notation Operations with Scientific Notation Add, subtract, multiply and divide numbers written in scientific notation. Add, subtract, multiply and divide when numbers in standard form and numbers in scientific notation are present in a problem Unit 3: Rational Numbers and Square Roots Rational Numbers Write fractions in simplest form. Convert fractions to decimals. Graph fractions on a number line. Compare two fractions or decimals. Key Terms: rational number, simplest form, mixed number, improper fraction Adding and Subtracting Rational Numbers Add and subtract rational numbers in decimal form. Add and subtract rational numbers in fraction form with like denominators Multiplying and Dividing Rational Numbers Multiply and divide rational numbers in decimal form. Multiply and divide rational numbers in fraction form. Key Terms: reciprocal, multiplicative inverse Adding and Subtracting with Unlike Denominators Add and subtract rational numbers in fraction form with unlike denominators. 6

7 03-05 Squares, Cubes, and Roots Find squares of numbers. Identify perfect squares. Find the square roots of numbers. Find the cubes of numbers Identify perfect cubes. Find the cube roots of numbers. Key Terms: exponent, base, square, perfect square, radical symbol, square root, principal square root, cube, perfect cubes, cube root The Real Numbers Describe and give examples of irrational numbers. Define sets of numbers, including natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers, and classify numbers by one or more number sets. Key Terms: set, natural numbers, whole numbers, integers, rational number, terminating decimal, repeating decimal, irrational number, real numbers Unit 4: Solving Equations and Inequalities Solving Equations by Adding and Subtracting Identify the variable in an equation. Solve a simple equation using addition. Solve a simple equation using subtraction. Key Terms: variable, equation, inverse operation Solving Equations by Multiplying or Dividing Solve a simple equation using multiplication. Solve a simple equation using division. 7

8 04-03 Solving Two-Step Equations Solve two-step equations involving addition, subtraction, multiplication, and division Solving Multi-Step Equations Use the properties of equality to solve multi-step equations that require the use of the distributive property. Use the properties of equality to solve multi-step equations that require combining like terms. Use the properties of equality to solve multi-step equations with fractional coefficients. Key Terms: like terms, constant terms Solving Equations with Variables on Both Sides Use the properties of equality to solve two-step equations with variables on both sides of the equation. Use the properties of equality to solve multi-step equations with variables on both sides of the equation Solving for a Variable Use properties of equality to rearrange formulas to solve for a quantity of interest. Solve an equation in two or more variables for a specified variable. Key Term: formula Systems of Equations Determine whether an ordered pair is a solution of a system of equations. Solve a system of linear equations. Key Terms: system of equations, solution of a system of equations Inequalities Identify inequalities. Sketch inequalities on a number line. Describe the solutions of an inequality. Key Terms: inequality, number line 8

9 04-09 Solving Inequalities with Addition and Subtraction Solve a simple inequality with addition. Solve a simple inequality with subtraction. Graph the solution to a simple inequality. Key Terms: inequality, solution set Solving Inequalities with Multiplication and Division Solve an inequality with multiplication. Solve an inequality with division Solving Two-Step and Multi-Step Inequalities Evaluate a multi-step inequality. Evaluate a multi-step inequality involving negative numbers. Graph the solution for a multi-step inequality on a number line. Unit 5: Statistics Samples and Surveys Classify data and sampling methods. Identify possible sources of bias in sampling methods. Choose which sampling method is most appropriate for a given situation. Key Terms: population, sample, survey, simple random sampling, systematic sampling, stratified random sampling, convenience sampling, self-selected sampling, bias Organizing Data Organize data in tables. Organize data in stem-and-leaf plots. Key Terms: data, frequency table, stem-and-leaf plot, back-to-back stem-and-leaf plot 9

10 05-03 Measures of Central Tendency Calculate the mean, median, and mode of a set of data. Determine which measure of central tendency is most appropriate for a given data set. Key Terms: average, normal, median, measure of central tendency, mean, median, mode, outlier Variability Calculate the range of a data set. Find the five-number summary of a data set. Create a box plot of a data set. Key Terms: measure of variation, range, quartiles, first quartile, second quartile, third quartile, five-number summary, box plot Displaying Data Display data in bar graphs, pictographs, and histograms. Display data in line graphs. Recognize misleading graphs. Key Terms: bar graph, pictograph, histogram, line graph Scatter Plots Create a scatter plot. Describe a correlation for paired data sets. Use a scatter plot to make a prediction. Key Terms: scatter plot, correlation, positive correlation, negative correlation, no correlation 10

11 Unit 6: Geometric Shapes and Measurements Points, Lines, Planes, and Angles Identify basic geometric figures. Name and classify angles. Determine angle relationships. Use the properties of geometric figures to solve problems. Key Terms: point, line, plane, line segment, ray, angle, vertex, acute, right angle, obtuse, straight angle, congruent, complementary angles, supplementary angles, vertical angles, parallel lines, intersecting lines, perpendicular lines Parallel and Perpendicular Lines Identify congruent and supplementary angles formed by parallel lines intersected by a transversal. Find measures of angles formed by parallel lines intersected by a transversal, including cases in which the transversal is perpendicular to the parallel lines. Key Terms: transversal, alternate interior angles, alternate exterior angles, corresponding angles, same-side interior angles, congruent alternate interior angles, congruent alternate exterior angles, congruent corresponding angles, supplementary same-side interior angles Triangles Classify triangles by their side lengths and angle measures. Find unknown measures of angles in triangles. Key Terms: triangle, isosceles triangle, equilateral triangle, scalene triangle, right triangle, acute triangle, obtuse triangle, triangle sum theorem 11

12 06-04 Polygons and Circles Identify a polygon by its properties. Find unknown measures of angles in polygons. Identify special types of quadrilaterals. Identify the special segments contained in a circle. Key Terms: polygon, regular polygon, parallelogram, rhombus, square, trapezoid, quadrilaterals, pentagons, octagons, circle, center, radius, chord, diameter Coordinate Geometry Graph and classify polygons in the coordinate plane. Find the coordinates of vertices of polygons in the coordinate plane Congruence Determine whether two polygons are congruent. Use properties of congruent polygons to find unknown measures. Key Terms: correspondence, congruent figures, congruent angles, congruent segments, congruent polygons Transformations Identify translations, rotations, and reflections. Transform plane figures by using translations, rotations, and reflections. Key Terms: transformation, preimage, image, translation, reflection, rotation Symmetry and Tessellations Identify line symmetry in figures. Identify rotational symmetry in figures. Use symmetry to complete figures. Use patterns to create tessellations. Key Terms: line symmetry, rotational symmetry, tessellation 12

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