Course Title: 8 th Grade Pre-Algebra 8th Grade Math Course Map 2013 Duration: 2 semesters Frequency: Daily 44-51 minutes Year Updated: 2013 Text: Prentice Hall Pre-Algebra Other materials: Kagan Cooperative Learning Supplements; Algebra Tiles; Dale Seymour Middle School Math Warm-ups Areas to be evaluated: Students understanding of basic algebra concepts Additional activities: worksheets, board activities, Kagan activities: Find Someone Who, Showdown, Rally Coach, Simultaneous Roundtable, Quiz, Quiz, Trade Course Goals: The course objective for 8th grade will be to prepare students for Algebra I. The student successfully completing this course will learn to: - Recognize the consistency of mathematical truths demonstrates the orderliness, design and precision of God s creation. The study of mathematics should result in greater appreciation of the works of God in His creation. - Reason algebraically - Develop thinking skills using algebraic concepts - Develop problem solving skills using algebraic concepts Unit objectives will be met to achieve this overall objective. Course explanation: This course introduces students to algebraic concepts. Unit: Review of Computational skills Time frame: 20 days Kagan Cooperative Learning, Fraction Finders and Decimal Destinations by Evelyn Christensen, Wipe off boards, Daily Mental Math Unit objectives - Apply all math operations to fractions, decimals and percents. - Recognize and process Place Value problems to review concepts of fractions, decimal and percents -Assign problems from Evelyn Christensen s books -Find someone who -Showdown
Unit: Algebraic Expressions and Integers Kagan Structures, Graph paper 8.NS.1. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. Unit objectives Chapter 1 - Write algebraic expressions and evaluate them using the order of operations - Find absolute values of integers and use absolute value to compare integers - Use all mathematical operations with integers -Name coordinates, quadrants, and graph points on a coordinate plane -Showdown
Unit: Solving Onestep Equations and Inequalities Kagan Structures, Algebra Tiles and book, graph paper, Jeopardy NCTM Standards: 1. Number and operations; 2. Algebra; 3. Geometry; 4. Measurement; 5. Data Analysis and Probability; 6. Problem Solving; 7. Reasoning and Proof; 8. Communication; 9. Connections; 10. Representation 8.EE.1. Know and apply the properties of integer exponents to generate equivalent numerical expressions. Unit objectives Chapter 2 -Identify and use properties of numbers (commutative, associative, identity, distributive) -Simplify variable expressions -Solve one-step equations and inequalities using all mathematical operations -Graph and write inequalities -Showdown NCTM Standards: 1-4; 6-10 8.EE.1. Know and apply the properties of integer exponents to generate equivalent numerical expressions.
Unit: Decimals and Equations Calculators Unit objectives Chapter 3 -Find Mean, Median, and Mode and choose best measure -Use formulas -Solve equations involving decimals using all four operations -Identify appropriate metric measures and convert metric units -Statistics NTCM Standards: 1-6; 8-10 8.SP.1. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. Unit: Factors, Fractions, and Exponents Calculators Math Comics Unit objectives Chapter 4 -Review divisibility tests and exponents -Find prime factorization and GCF -Write fractions in simplest form -Evaluate fractions containing variables -Multiply and divide with the same base and find a power of a power -Write, evaluate and calculate scientific notations
-Math Comic worksheet -Science NTCM Standards: 1,2,4,5,6,8,9,10 8.EE.3. Use numbers expressed in the form of a single digit times a whole-number power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. 8.EE.4. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Unit: Operations with Fractions Time frame: 10 days Unit objectives Chapter 5 - Find LCM -Convert fractions to decimals and decimals to fractions -Review all math operations for fractions -Solve equations involving fractions using addition, subtraction, and
Calculators multiplication Unit: Ratios, Proportions and Percents Kagan Structures, Pennies, crayons, M and M s NCTM Standards: 1,2,6,7,8,9,10 8.NS.1. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. Unit objectives Chapter 6 - Write and simplify ratios and use to find unit rates -Solve proportions -Find probability and odds -Write percents as fractions and decimals -Use equations to solve percent problems
Unit: Solving Equations and Inequalities Kagan Structures NCTM Standards: 1-2; 4-10 8.EE.5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distancetime equation to determine which of two moving objects has greater speed. Unit objectives Chapter 7 -Write and solve multi-step equations and inequalities by combining like terms and using distributive property -Solve equations with variables on both sides -Solve formulas for a given variable
Unit: Linear Functions and Graphing Kagan Structures, graph paper NCTM Standards: 1-4; 6,8,9,10 8.EE.7. Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Unit objectives Chapter 8 -Identify and graph relations, functions, and solutions of two variable equations -Find the slope of a line and use slope to graph linear equations -Write rules for linear functions from words, tables, and graphs -Interpret and draw scatter plots -Graph systems of linear equations and inequalities
NCTM Standards: 2,5,6,7,8,9,10 Define, evaluate, and compare functions. 8.F.1. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. 1 8.F.2. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). 8.F.3. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. Use functions to model relationships between quantities. 8.F.4. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. 8.F.5. Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. Unit: Spatial Thinking Unit objectives Chapter 9 AIMS Circumference and Area of Circles, Kagan Structures -Name and recognize basic geometric figures -Draw and measure angles -Identify angle relationships -Classify triangles and quadrilaterals -Find circumference of a circle
-AIMS activities Unit: Area and Volume and Right Triangles Kagan Structures, AIMS Area Formulas for NCTM Standards: 3,4,6,7,8,9,10 8.G.1. Verify experimentally the properties of rotations, reflections, and translations: a. Lines are taken to lines, and line segments to line segments of the same length. b. Angles are taken to angles of the same measure. c. Parallel lines are taken to parallel lines. 8.G.2. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. 8.G.4. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. 8.G.5. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. Unit objectives Chapter 10-11 -Find areas of rectangles, parallelograms, triangles, and circles -Find surface areas and volumes of prisms, cylinders, cones, and spheres -Find square roots
parallelograms, triangles, and trapezoids -AIMS activities Unit: Nonlinear Functions and Polynomials Kagan Structures NCTM Standards: 1,2,3,4,6,7,8,9,10 8.G.9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. Unit objectives Chapter 13 -Identify arithmetic and geometric sequences -Graph quadratic and absolute value functions -Identify, evaluate, add, subtract and multiply polynomials -AIMS activities
NCTM Standards: 1,2,3,4,6,7,8,9,10 8.G.5. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.