MATH APPLICATIONS CURRICULUM

Transcription

1 MATH APPLICATIONS CURRICULUM NEWTOWN SCHOOLS NEWTOWN, CT. August, 1997

2 MATHEMATICS PHILOSOPHY We believe mathematics instruction should develop students' ability to solve problems. We believe that the study of mathematics should prepare students with the skills necessary to interpret the multiple uses of numbers encountered in the real world. We believe that representing, discussing, reading, writing and listening to mathematics are vital parts of learning. We believe that students experience mathematics as sensible, logical and enjoyable when they are actively engaged in the learning process. We believe that students should be encouraged to appreciate the power of mathematical structures. We believe that mathematical strands should be connected to each other. We believe that mathematics education should be integrated with other curricular areas or disciplines. We believe that mathematics education should open opportunities for students to perform successfully in our scientific/technological/informational society. We believe that instructional strategies in mathematics should meet the learning needs and styles of all students. We believe that mathematics instruction should be a blend of concrete and abstract, application and theory, skills and concepts. We believe that assessments are essential tools for students' learning, growth and achievement.

3 MATHEMATICS GOAL Students will gain mathematical power as they learn to: Value mathematics. Become confident in their ability to do mathematics. Become mathematical problem solvers in theoretical and practical situations. Communicate mathematically. Reason mathematically. Demonstrate their ability through learning activities and assessments.

4 Students will be able to: CONTENT STANDARDS Use polynomial, rational, exponential, logarithmic, and (from law of sines and cosines) to solve world problems. Gather and analyze data from class experiments and real world problems. Use the equations of the conic sections to model real world phenomena and to solve real world problems. Use finance math to solve real world problems. Use matrices to solve systems of linear equations generated form real world problems. Use linear programming to solve real world problems. Describe, create, and observe mathematical patterns in geometry and art. Describe different math sequences and their applications to the real world.

5 CONTENT STANDARD Students will be able to use polynomial, rational, exponential, logarithmic, and trigonometric equations (from law of sines and cosines) to solve world problems. Use specific vocabulary including domain, range, asymptote and oblique triangle. Distinguish differences and similarities between these kinds of equations and their graphs. Sketch these equations without a calculator. Sketch these equations with a graphing calculator. Distinguish the differences and similarities between common logarithms and natural logarithms. Calculate missing sides and angles of a triangle using the jaw of sines and the law of cosines. Suggested Instructional Strategies, Classroom Activities and Assessments: Reports given by students on: Revenue, cost and profit History of logarithms Worldwide population growth Richter scale Guest speaker: architect, surveyor, chemist Supply and demand Carbon dating Radioactive decay ph scale Mathematics with Applications, Llal, Hungerford, Miller, 1995, Chapters 2,3,4 COMAP's High Schools Lessons in Mathematical Applications Integrated Mathematics Course 3, Kelly, Alexander, Atkinson, 1992, Chapter 13

6 Content Standard To gather and analyze data from class experiments and real world problems. Objective: Use specific vocabulary including rate of change, slope, median-median line, residual, scatter plot, measures of central tendency, mean deviation and standard deviation. Find and interpret slope as a rate of change. Draw a scatter plot. Draw the line of best fit and write its equation without and with a graphing calculator. Interpret the residual plot. Determine mean deviation and standard deviation. Suggested Instructional Strategies, Classroom Activities and Assessments Students' use of the graphing calculator and its statistics options Student project on data gathering and analysis Mathematics with Applications, Lial, Hungerford, Miller, 1995, Chapter 10 Integrated Mathematics Course 3 Kelly, Alexander, Atkinson, 1992, Chapter 14 NCTM Agenda Series: Data Analysis and Statistics

7 Content Standard To use the equations of the conic sections to model real world phenomena and to solve real world problems. Objective: Use specific vocabulary including conic section, parabola circle, ellipse, hyperbola, directrix, focus, standard form, vertex, eccentricity, focal endpoints, major and minor axbs of ellipse, focal segment. Sketch conies with and without a graphics calculator. Determine coordinates of vertex, focus, and equation of directrix for a parabola. Develop the equation of an ellipse. Suggested Instructional Strategies, Classroom Activities, and Assessments: Students' use of graphing calculator to graph conics Students' use of activities in Applications of Conic Sections, HRM, 1994 Students' construction of an original picture using equations of conic sections Video: Stand Up Comic Student reports on: LORAN system Kepler's Laws of Planetary Motion Development of telescopes Algebra and Trigonometry, Foerster, 1984, Chapter 9 Applications of Conic Sections, HRM, 1994 Suggested Instructional Strategies, Classroom Activities and Assessments: Guest speaker: Bank representative Students' completion of sample checks, check register, deposit slips, withdrawal slips donated by local banks Students' use of brochures on banking services from area banks for class discussion Student analysis of vocabulary found in bank ads in local newspapers Dollars and Sense, Gerver, Sgroi, 1989, Chapter 13 SAVINGS BONDS

8 Use specific vocabulary Including purchase price, holding period, education tax exclusion benefit, maturity time, face value, Series SE bond. Determine types of savings bonds. List denominations available. Understand minimum holding period Suggested Assessment: Student research project about savings bonds by visits to local banks and interviews with bank representatives. INCOME TAX Use specific vocabulary including gross pay, net pay, dependent, tax liability, Form 1040 EZ, Form W-4, Form W-2, FICA. Do problems involving income tax. Read a tax table. Read a Form W-2. Fill out a Form 1040EZ. Suggested Instructional Strategies, Classroom Activities, and Assessments: Class discussion of income tax forms and income tax booklets available at local post office Student generated discussion about their own Form W-2 Student report on history of the Income tax Dollars and Sense, Gerver, Sgroi, 1989, Chapter 10. LOANS AND ANNUITIES Use specific vocabulary including simple interest note, simple discount note, proceeds, geomethc sequence, geometric series, annuity, ordinary annuity, annuity due, payment period, term of annuity, future value of annuity. Describe the pattern of a geometric sequence of numbers.

9 Find the sum of numbers in a geometric sequence. Find the future value of an ordinary annuity. Find the future value of an annuity due. Suggested Instructional Strategies, Classroom Activities, and Assessments: Guest speaker: financial advisor Mathematics with Applications, Lial, Hungerford, Miller, 1995, Chapter 5 INTEREST Use specific vocabulary including simple interest, compound interest, compounded continuously, present value, compounding periods, APR, nominal rate, effective rate, rule of 70, credit report. Calculate simple interest and use formula i=prt. Calculate compound interest and generate formula A=P(1 + r/n)nt. Calculate interest compounded continuously and use formula A=Pert. Calculate present value with interest compounded continuously and use formula P=A/ert Calculate present value with compound interest and use formula P=A/(l+r/n)nt. Calculate nominal rate. Use rule of 70, T=(ln 2) /r. Suggested Instructional Strategies, Classroom Activities and Assessments: Bank advertisements distributed to students to generate a list of unfamiliar words or symbols Guest speaker: accountant Students' use of graphics calculator and its programming features to write programs to apply the above formulas Students comparing and contrasting interest rates found in newspaper ads Mathematics with Applications, Lial, Hungerford, Miller, 1995, Chapter 5

10 Content Standard To use matrices to solve systems of linear equations generated from real world problems. Use specific vocabulary including mathx, augmented matrix, dimension, multiplicative inverse. Write a system of equations in matrix form. Perform row operations. Transform an augmented matrix to the Identity matrix. Solve a system of equations. Form the multiplicative inverse. Identify the dimension of a matrix. Add, subtract, and multiply matrices. Suggested Instructional Strategies, Classroom Activities and Assessments: Students' use of graphing calculators to perform matrix arithmetic Students' use of graphing calculators to find multiplicative inverse matrix Student generation of matrix menu developed from local pizza parlor menus Mathematics with Applications, Lial, Hungerford, Miller, 1995, Chapters

11 Content Standard To use linear programming to solve real world problems. Objective: Use specific vocabulary Including objective function, feasible region, optimal value. Graph linear inequalities in two variables. Solve a system of linear inequalities. Write the objective function and all necessary constraints. Identify the feasible region. Determine the coordinates at each corner point. Find the optimal value (maximum or minimum). Mathematics with Applications, Lial, Hungerford, Miller, 1995, Chapter 7 Algebra and Trigonometry, Foerster, 1984, Chapter 4

12 Content Standard To describe, create, and observe mathematical patterns in geometry and art. Use specific vocabulary including tessellation, regular tessellation, regular polygon, dissecting, tile designs. Determine which regular polygons fit exactly around a point. Tile a design using 2 or more different polygons. Start with a square, alter it, and tessellate the design by translation. Suggested Instructional Strategies, Classroom Activities, and Assessments: Use of CD ROM Tesse Use of game Pentaminos Student construction of design using templates for triangle, square, pentagon, hexagon, octagon Student report on Maurits Escher Moving on with Tanarams, 1988 Creative Publications Introduction to Tessellations, Dale Seymour

13 Content Standard To describe, create, and observe mathematical patterns In geometry and art. Use specific vocabulary including tessellation, regular tessellation, regular polygon, dissecting, tile designs. Determine which regular polygons fit exactly around a point. Tile a design using 2 or more different polygons. Start with a square, alter it, and tessellate the design by translation. Suggested Instructional Strategies, Classroom Activities, and Assessments: Use of CD ROM Tesse Use of game Pentaminos Student construction of design using templates for triangle, square, pentagon, hexagon, octagon Student report on Maurits Escher Moving on with Tanarams, 1988 Creative Publications Introduction to Tessellations, Dale Seymour

14 Content Standard To describe different math sequences and their applications to the real world. Use specific vocabulary including arithmetic sequence, geometric sequence, common difference, and common ratio. Determine if a sequence is arithmetic or geometric. Find the sum of a finite arithmetic and geometric sequence. Find the sum of an infinite geometric sequence. Suggested Instructional Strategies, Classroom Activities, and Assessments: Reports given by students on: the golden ratio and its art connection spirals and the Fibonacci sequence Students' use of graphing calculator to graph spirals Mathematics A Human Endeavor, Jacobs, 1994 Algebra and Trigonometry, Foerster, 1984, Chapter 11