Functional Math II. Information CourseTitle. Types of Instruction

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1 Functional Math II Course Outcome Summary Riverdale School District Information CourseTitle Functional Math II Credits 0 Contact Hours 135 Instructional Area Middle School Instructional Level 8th Grade Organization Riverdale School District Department Mathematics Developer(s) Bruce Borchardt Development Date 02/27/2009 Types of Instruction Type of Instruction Contact Hours Outside Hours Credits Group Instruction Cooperative Learning Exploration Homework Totals Target Population Special education students or struggling math students that need more individual instruction and a slower pace to understand 8th grade mathematic concepts. Description Students will build on math skills from seventh grade. Students will focus on rational numbers and their operations, equations, and inequalities. Students will build their understanding of these concepts using models. Students will also integrate and expand on real number properties, geometric formulas, and averages. They will also work with linear equations and their graphs, geometric transformations, and probability. Prerequisites 1. Pass 7th grade Math 2. WKCE scores 3. MAPS scores Textbooks 1. Larson, Bowell, Kanold, Stiff. McDougal Littel Math Course 3. Edition: 1st Edition. Publisher: McDougal Littel, a divison of Houghton Mifflin. Year: ISBN: 13: Pages: 830. Required. Supplies Calculator. Manufacturer: TI-30XA. Price: Required /qtr Pencils. Manufacturer: No. 2. Price: Required.

2 General Education Outcomes A. Students will make satisfactory progress toward IEP goals. Core Abilities A. Demonstrate maturity, responsibility, dependability, and respect for others. B. Achieve desired results by interpreting and executing instructions, plans, models, and diagrams. C. Access and use appropriate information resources. D. Use technology appropriately. E. Apply effective problem solving strategies. F. Show respect for diversity. Competencies, Linked Exit Learning Outcomes, and Performance Standards 1. Review important foundational skills in calculation, data analysis, algebra, and problem-solving. Comprehension Essential WI.MA.A. Mathematical Processes--Students will draw on a broad body of mathematical knowledge and apply a variety of mathematical skills and strategies when solving mathematical real-world and non routine problems. WI.MA.B.8.1 Read, represent, and interpret various rational numbers (whole numbers, integers, decimals, fractions and percents) with verbal descriptions, geometric models, and mathematical notation (e.g., expanded, scientific, exponential) WI.MA.B.8.6 Model and solve problems involving number-theory concepts o based on individual student IEP goals o you solve 10 out of 12 basic math problems at 60% accuracy. a. Use graphs to analyze data b. Apply order of operations to evaluate numerical expressions. c. Write and evaluate variable expressions. d. Evaluate expressions with powers. e. Use formulas to find unknown values. 2. Acquire knowledge to do operations when numbers with values less than zero are included. Explore number properties as they apply to expressions including integers.

3 WI.MA.B.8.1 Read, represent, and interpret various rational numbers (whole numbers, integers, decimals, fractions and percents) with verbal descriptions, geometric models, and mathematical notation (e.g., expanded, scientific, exponential) WI.MA.B.8.2 Perform and explain operations on rational numbers WI.MA.B.8.4 Express order relationships among rational numbers using appropriate symbols (>, <, =) WI.MA.B.8.7 In problem-solving situations, select and use appropriate computational procedures with rational numbers o you add and subtract integers correctly 80% of the time. o you multiply and divide integers correctly 80% of the time. o you apply correctly the appropriate property to evaluate expressions o you indetify and plot points on a coordinate graph 80% of the time. a. Investigate integers. b. Add and subtract integers. c. Multiply and divide integers. d. Apply properties to evaluate expressions. e. Administer the distributive property f. Identify and plot points in a coordinate graph 3. Develop an understanding of core algebra concepts from evaluating and solving equations and inequalities. Synthesis High WI.MA.B.8.1 Read, represent, and interpret various rational numbers (whole numbers, integers, decimals, fractions and percents) with verbal descriptions, geometric models, and mathematical notation (e.g., expanded, scientific, exponential) WI.MA.B.8.2 Perform and explain operations on rational numbers WI.MA.B.8.6 Model and solve problems involving number-theory concepts WI.MA.B.8.7 In problem-solving situations, select and use appropriate computational procedures with rational numbers WI.MA.F.8.1 Work with algebraic expressions in a variety of ways WI.MA.F.8.5 Recognize and use generalized properties and relations o o under the direct supervision of a certified classroom teacher lecture

4 o you create and solve equations or multi-step equations using addition and subtraction accurately 80% of the time. o you create and solve equations or multi-step equations using multiplication and division accurately 80% of the time. o you accurately apply formulas for perimter and area 80% of the time. o you create and solve inequalities using addition and subtraction accurately 80% of the time. o you create and solve inequalities using multiplication and division accurately 80% of the time. a. Evaluate equations using addition or subtraction. b. Solve equations using multiplication or division. c. Assess two-step equations. d. Solve two-step equations. e. Apply formulas for perimeter and area. f. Evaluate inequalities using addition or subtraction. g. Solve inequalities using multiplication or division. 4. Build on the core fraction concepts, such as comparing fractions to performing operations with fractions and exponents. Essential WI.MA.B.8.1 Read, represent, and interpret various rational numbers (whole numbers, integers, decimals, fractions and percents) with verbal descriptions, geometric models, and mathematical notation (e.g., expanded, scientific, exponential) WI.MA.B.8.2 Perform and explain operations on rational numbers WI.MA.B.8.3 Generate and explain equivalencies among fractions, decimals, and percents WI.MA.B.8.4 Express order relationships among rational numbers using appropriate symbols (>, <, =) WI.MA.B.8.5 Apply proportional thinking in a variety of problem situations WI.MA.B.8.6 Model and solve problems involving number-theory concepts WI.MA.B.8.7 In problem-solving situations, select and use appropriate computational procedures with rational numbers o you explain the prime factorization of numbers 80% of the time. o you discover the greatest common factor or least common multiple of numbers 80% of the time. o you simplify fractions 80% of the time.

5 o you compare and order fractions and mixed numbers 80% of the time accurately. o you simplify expressions with negative exponents 80% of the time. o you read and write numbers in scientific notation accurately 80% of the time. a. Write the prime factorization of numbers. b. Find the greatest common factor of two or more numbers. c. Simplify fractions. d. Discover the least common multiple of two or more numbers. e. Apply multiplication and division to expressions with exponents. f. Simplify expressions with negative exponents. g. Read and write numbers using scientific notation. 5. Apply a variety of methods for exploring fraction concepts, mixed numbers, and decimals. Analyze data. WI.MA.B.8.1 Read, represent, and interpret various rational numbers (whole numbers, integers, decimals, fractions and percents) with verbal descriptions, geometric models, and mathematical notation (e.g., expanded, scientific, exponential) WI.MA.B.8.2 Perform and explain operations on rational numbers WI.MA.B.8.3 Generate and explain equivalencies among fractions, decimals, and percents WI.MA.B.8.4 Express order relationships among rational numbers using appropriate symbols (>, <, =) WI.MA.B.8.5 Apply proportional thinking in a variety of problem situations WI.MA.B.8.6 Model and solve problems involving number-theory concepts WI.MA.B.8.7 In problem-solving situations, select and use appropriate computational procedures with rational numbers o you add and subtract fractions and mixed numbers accurately 80% of the time. o you multiply and divide fractions and mixed numbers accurately 80% of the time. o you accurately convert fractions to decimals and decimals to fractions. o you add and subtract decimals accurately 80% of the time. o you multiply and divide decimals accurately 80% of the time. o you accurately describe data sets using mean, median, mode, and range. a. Add and subtract fractions with common and unlike denominators. b. Multiply and divide fractions and mixed numbers. c. Convert fractions to decimals and decimals to fractions.

6 d. Apply addition and subtraction to decimals. e. Use multiplication and division with decimals. f. Describe data sets using mean, median, mode, and range. 6. Evaluate equations and inequalities with multi-steps and apply to real-world problems. High WI.MA.B.8.1 Read, represent, and interpret various rational numbers (whole numbers, integers, decimals, fractions and percents) with verbal descriptions, geometric models, and mathematical notation (e.g., expanded, scientific, exponential) WI.MA.B.8.4 Express order relationships among rational numbers using appropriate symbols (>, <, =) WI.MA.B.8.5 Apply proportional thinking in a variety of problem situations WI.MA.B.8.7 In problem-solving situations, select and use appropriate computational procedures with rational numbers WI.MA.F.8.1 Work with algebraic expressions in a variety of ways WI.MA.F.8.3 Recognize, describe, and analyze functional relationships by generalizing a rule that characterizes the pattern of change among variables. These functional relationships include exponential growth and decay (e.g., cell division, depreciation) WI.MA.F.8.4 Use linear equations and inequalities in a variety of ways WI.MA.F.8.5 Recognize and use generalized properties and relations o you create and solve multi-step equations accurately 80% of the time. o you explore circumference of a circle accurately 80% of the time. o you create and solve multi-step inequalities accurately 80% of the time. a. Solve equations by using two or more steps. b. Explain equations that have variables on both sides. c. Discover equations with fractions and decimals. d. Explore the circumference of a circle. e. Use two or more steps to solve inequalities. f. Solve multi-step inequalities. 7. Create ratios, extending to rates, unit rates, and scale factors to help solve proportions. Discover percents and apply to real-world problems. Synthesis

7 Essential WI.MA.B.8.5 Apply proportional thinking in a variety of problem situations WI.MA.B.8.6 Model and solve problems involving number-theory concepts WI.MA.B.8.7 In problem-solving situations, select and use appropriate computational procedures with rational numbers o you discover ratios and unit rates in real-world situations. o you write and solve proportions accurately 80% of the time. o you write and solve percent problems using proportions or the percent equation accurately 80% of the time. o you convert fractions, decimals, and percents with 80% accuracy. o you explore percents of change with 80% accuracy. o you find probabilities of events in real-world situations. a. Find ratios and unit rates. b. Solve proportions. c. Discover percent problems using proportions. d. Convert fractions, decimals, and percents. e. Explore problems with percent of increase or decrease. f. Explain percent application problems. g. Apply the percent equation to solve percent problems. h. Discover probabilities of events. 8. Discover intersecting lines, geometric figures, and congruency. Explore transformations of figures on a coordinate plane. Psychomotor Practice WI.MA.C.8.1 Describe special and complex two- and three-dimensional figures (e.g., rhombus, polyhedron, cylinder) and their component parts (e.g., base, altitude, and slant height) WI.MA.C.8.2 Identify and use relationships among the component parts of special and complex two-and threedimensional figures (e.g., parallel sides, congruent faces) WI.MA.C.8.3 Identify three-dimensional shapes from two-dimensional perspectives and draw two-dimensional sketches of three-dimensional objects preserving their significant features WI.MA.C.8.4 Perform transformations on two-dimensional figures and describe and analyze the effects of the transformations on the figures

8 o you use equations to solve angle measures with 80% accuracy. o you can classify angles, triangles, and quadrilaterals with 80% accuracy. o you discover angle measures in polygons with 80% accuracy. o you can identify and name congruent polygons. o you create reflections of figures and discover lines of symmetry. o you translate or rotate figures in a coordinate plane with 80% accuracy. a. Discover angle measures. b. Classify angles and triangles. c. Categorize quadrilaterals. d. Find angle measures in polygons. e. Identify and name congruent polygons. f. Reflect figures and identify lines of symmetry. g. Translate or rotate figures in a coordinate plane. 9. Explore measurement in geometry, including square roots, real numbers, special triangles, and discover the Pythagorean Theorem. High WI.MA.C.8.1 Describe special and complex two- and three-dimensional figures (e.g., rhombus, polyhedron, cylinder) and their component parts (e.g., base, altitude, and slant height) WI.MA.C.8.2 Identify and use relationships among the component parts of special and complex two-and threedimensional figures (e.g., parallel sides, congruent faces) WI.MA.C.8.3 Identify three-dimensional shapes from two-dimensional perspectives and draw two-dimensional sketches of three-dimensional objects preserving their significant features WI.MA.C.8.4 Perform transformations on two-dimensional figures and describe and analyze the effects of the transformations on the figures o project o textbook problems or worksheets o you find and approximate square roots with 80% accuracy. o you can work accurately with irrational numbers. o you can apply the Pythagorean Theorem to solve real-world problems with 80% accuracy. o you use speical right triangles to solve real-world problems with 80% accuracy.

9 o you apply trigonometric ratios with 80% accuracy. a. Explore and approximate square roots of numbers. b. Work with irrational numbers. c. Apply the Pythagorean Theorem to solve problems. d. Analyze real-world problems using the Pythagorean Theorem. e. Utilize special right triangles to solve real-life problems. 10. Classify and sketch solids and three-dimensional figures. Apply formulas to measure surface area and volume. Synthesis WI.MA.C.8.1 Describe special and complex two- and three-dimensional figures (e.g., rhombus, polyhedron, cylinder) and their component parts (e.g., base, altitude, and slant height) WI.MA.C.8.2 Identify and use relationships among the component parts of special and complex two-and threedimensional figures (e.g., parallel sides, congruent faces) WI.MA.C.8.3 Identify three-dimensional shapes from two-dimensional perspectives and draw two-dimensional sketches of three-dimensional objects preserving their significant features WI.MA.C.8.4 Perform transformations on two-dimensional figures and describe and analyze the effects of the transformations on the figures WI.MA.C.8.5 Locate objects using the rectangular coordinate system o you find areas of parallelograms, trapezoids, and circles with 80% accuracy. o you classify and sketch solids. o you find surface areas of prisms, cylinders, pyramids, and cones with 80% accuracy. o you discover volume of prisms, cylinders, pyramids, cones, and spheres with 80% accuracy. a. Explore the areas of parallelograms and trapezoids. b. Discover the areas of circles. c. Classify and sketch solids. d. Find the surface areas of prisms and cylinders. e. Discover the volumes of prisms and cylinders. f. Explore the volumes of pyramids and cones. 11. Explore linear relationships using tables, graphs, and equations.

10 WI.MA.F.8.1 Work with algebraic expressions in a variety of ways WI.MA.F.8.2 Work with linear and nonlinear patterns and relationships in a variety of ways WI.MA.F.8.3 Recognize, describe, and analyze functional relationships by generalizing a rule that characterizes the pattern of change among variables. These functional relationships include exponential growth and decay (e.g., cell division, depreciation) WI.MA.F.8.4 Use linear equations and inequalities in a variety of ways WI.MA.F.8.5 Recognize and use generalized properties and relations o you use tables to represent functions with 80% accuracy. o you make and interpret scatter plots with 80% accuracy. o you discover solutions of equations with two variables with 80% accuracy. o you sketch the graph of a linear equation. o you find x-and y-intercepts with 80% accuracy o you determine the slope of a line with 80% accuracy. o you write and graph equations in slope-intercept form with 80% accuracy. o you graph inequalities with 80% accuracy. a. Apply tables to represent functions. b. Create and interpret scatter plots. c. Discover solutions of equations with two variables. d. Sketch the graph of a linear equation. e. Determine the x- and y- intercepts of lines. f. Explore and interpret slopes of lines. g. Write and graph equations in slope-intercept form. h. Graph linear inequalities. 12. Uncover ways to display and analyze data sets and apply to real-world events. Analysis WI.MA.A.8.3 Analyze nonroutine problems by modeling, illustrating, guessing, simplifying, generalizing, shifting to another point of view, etc. WI.MA.F.8.1 Work with algebraic expressions in a variety of ways WI.MA.F.8.2 Work with linear and nonlinear patterns and relationships in a variety of ways

11 o you create and interpret stem-and-leaf plots accurately. o you make and interpret box-and-whisker plots accurately. o you organize data using circle graphs and line graphs with 80% accuracy. o you apply various methods to count possibilities with 80% accuracy. o you explore the odds in favor of events with 80% accuracy. a. Make and interpret stem-and-leaf plots. b. Create and interpret box-and-whisker plots. c. Organize data using circle graphs and line graphs. d. Use counting methods to count the number of choices. e. Apply permutations to count possibilities. f. Administer combinations to count possibilities. g. Discover the odds in favor of events. h. Study independent and dependent events. 13. Identify and operate with polynomials and graph functions. High WI.MA.E.8.3 Extract, interpret, and analyze information from organized and displayed data WI.MA.E.8.4 Use the results of data analysis WI.MA.F.8.3 Recognize, describe, and analyze functional relationships by generalizing a rule that characterizes the pattern of change among variables. These functional relationships include exponential growth and decay (e.g., cell division, depreciation) WI.MA.F.8.5 Recognize and use generalized properties and relations o you simplify polynomials with 80% accuracy. o you add and subtract polynomials with 80% accuracy. o you apply accurately properties of exponents to monomials. o you multiply binomials with 80% accuracy.

12 o you use function notation and graph nonlinear functions with 80% accuracy. a. Simplify polynomials by combining like terms. b. Add and subtract polynomials. c. Apply properties of exponents to monomials. d. Multiply binomials. e. Use function notation and graph nonlinear functions

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