Math: It Adds to Your Life Math Pathways take students where they need to go
Number Systems Solution • Arithmetic, Exponents
Oil Spill • An oil spill breaks up over the sea in smaller and larger sections. An aerial photograph is taken of the area and it is estimated that the sections of oil and open water can be enclosed by a 4 by 5 kilometer rectangle.
Oil Spill Solution • Probability and Ratios • Monte Carlo Method • The photo is digitized and fed into a computer, then random points are programmed and noted whether they hit the sought area. The greater the total number of points the more reliable the estimate.
Pulse Rate • Do you see any patterns in this chart?
Pulse Rate Solution • Algebra and Geometry, Biology • Plotting points, Graphing a line, estimating surface area
Circumference of the Earth • On the day of the summer solstice, the sun’s rays shine directly into the bottom of a well without illuminating the side of the well; 800 km away the sun’s rays are measured to be 7⁰ from vertical. What is the circumference of the Earth?
Circumference of the Earth Solution • Geometry and Ratios • Eratosthenes did this calculation around 230BC
Turkey Time • A turkey is taken from the refrigerator at 2⁰C and placed in an oven preheated to 200⁰C and kept at that temperature; after 30 minutes the internal temperature of the turkey has risen to 16⁰C. The fowl is ready to be taken out when it internal temperature reaches 88⁰C. • Determine the cooking time required.
Turkey Time Solution • Calculus, Science of Heat Transfer
What these problems tell us • We look for solutions to problems from what we know • Skill development doesn’t automatically lead to mathematical thinking • History brings a new perspective to math • Mathematical modeling connects math to life
Math Presenters • John Squires – Chattanooga State CC • Betty Frost – Jackson State CC • Myra Snell – Los Medanos CC • Amy Getz/ Uri Treisman – UT Austin • Tristan Denley – Austin Peay Stat University
From Myra Snell’s presentation For students placing two levels below a college course in English/Math, there are 5 “exit points” where they fall away: • Do they pass the first course? • If they pass, do they enroll in the next course? • If they enroll, do they pass the second course? • If they pass, do they enroll in the college-level course? • If they enroll, do they pass the college-level course? Students placing three levels down have 7 exit points.
From Myra Snell’s Presentation • (0.66)(0.93)(0.75)(0.91)(0.78)= 33%
MAT 030 • I. Calculate using whole and decimal numbers without a calculator. • II. Demonstrate knowledge and usage of whole numbers. • III. Demonstrate knowledge and usage of fractions and mixed numbers. • IV. Demonstrate knowledge and usage of decimals. • TOPICAL OUTLINE: • I. Demonstrate competency in the usage of whole numbers. • A. Describe the structure of our number system. • B. Read and write whole numbers through trillions. • C. Compute the sum, difference, product, and quotient of whole numbers. • D. Round whole numbers to the indicated place. • E. Estimate answers to whole number calculations. • F. Evaluate numbers written in exponential form and identify base, exponent, and factors of such numbers. • G. Determine square and cube roots. • H. Apply the correct order of operations to evaluate arithmetic expressions. • I. Solve word problems involving whole numbers. • J. Identify numbers as prime or composite. • K. Determine the prime factorization of a number using divisibility rules. • II. Demonstrate knowledge and usage of fractions and mixed numbers. • A. Interpret a fraction as parts of a whole, or as an indicated division. • B. Identify and understand the meaning of numerator and denominator. • C. Determine the least common multiple/lowest common denominator of a set of numbers. • D. Use the identity property to rename fractions. • E. Arrange fractions in order, smallest to largest. • F. State the reciprocal of any given number. • G. Change improper fractions to mixed numbers and vice versa. • H. Compute the sum, difference, product and quotient of commonly used fractions and mixed numbers writing the answer in simplest form. • I. Use fractions in applications. • III. Demonstrate knowledge and usage of decimals. • A. Read and write decimal numerals to millionths place. • B. Write common fractions as equivalent decimals and vice versa. • C. Arrange decimal numerals in order, smallest to largest. • D. Round decimal numerals to indicated place. • E. Compute the sum, difference, product and quotient of decimals. • F. Apply the shortcut method of moving the decimal point when multiplying or dividing by powers of ten. • G. Rewrite standard decimal numerals in scientific notation and vice versa. • H. Solve word problems involving decimals.
MAT 060 • I. Calculate using whole, fractional and decimal numbers both with and without a calculator. • II. Demonstrate knowledge and usage of fractions and mixed numbers. (I) • III. Demonstrate knowledge and usage of ratio and proportion. (II) • IV. Demonstrate knowledge and usage of percent. (III)
MAT 060 Con’t • V. Demonstrate knowledge and usage of measurement, area and perimeter. (IV) • VI. Demonstrate knowledge and usage of integers. (V) • VII. Demonstrate knowledge and usage of algebraic expressions. (Optional) (VI) • VIII. Demonstrate knowledge and usage of basic first-degree equations. (Optional) (VII)
MAT 090 • I. Demonstrate knowledge and usage of first-degree equations, inequalities and formulas. (I) • II. Demonstrate knowledge and usage of polynomials. (II) • III. Demonstrate knowledge and usage of factoring and solving quadratic equations by factoring. (III)
MAT 090 con’t • IV. Demonstrate knowledge and usage of coordinate geometry. (IV) • V. Demonstrate knowledge and usage of algebraic fractions. (V) (Optional) • VI. Demonstrate knowledge and usage of linear systems. (VI) (Optional
MAT 120 • I. Solve problems involving principles of set theory and logic. • II. Solve problems involving mathematical modeling. • III. Solve problems involving probability. • IV. Solve problems involving statistics.
MAT 120 con’t • V. Solve problems involving consumer mathematics. • VI. Read, analyze, and apply to new situations, written material related to the study of mathematics. • VII. Write and speak clearly and logically in presentations and essays about topics related to mathematics.
MAT 120 con’t • VIII. Demonstrate the ability to select and apply contemporary forms of technology to solve problems or compile information in the study of mathematics.
MAT 120 con’t • IX. One of the following competencies is also required. • A. Solve problems involving Euclidean geometry. • B. Solve problems involving varying numeration systems. • C. Solve problems involving mathematics of social choice. • D. Solve problems involving management science.