Mathematical Literacy: A Math Course Students WANT to Take Jack Rotman AMATYC 2011 (Austin, TX) Math119 at Lansing CC (Math: Applications for Living)
Area Quantities
Topics (outcomes) Units for measurements; Geometry Proportional reasoning; Conversions & dimensional analysis Magnitude; Significant digits, precision Percent Absolute versus relative change Percent change written as expression Finance Simple, Compound Interest Savings plans & payments; loan payments Statistics Samples, Populations; bias Confidence intervals; margin of error Charts (bar, frequency, histogram, line) Correlation Median, mode, mean; 5-number summary; Box-whisker Distributions; symmetry; skewed Standard deviation; Statistical significance Hypotheses (null, alternative) Probability Independent, dependent; Theoretical probability Probability of A not happening Probability of A happening at least once Law of Large Numbers; Expected value Arrangements, Permutations, Combinations Functions & Modeling Linear models – slope & y-intercept Exponential models – initial value; rate Additive versus multiplicative change Doubling time, half life Population growth with limit (logistic) Logarithmic scales (decibels, pH) Regression (linear, exponential) The course emphasizes numeric and graphical methods, more than symbolic. Lists of formulas are provided for tests & final – without explanation Prerequisite: pass beginning algebra OR the algebra placement test Students need basic skills with equations (linear), like terms, and basic exponent rules (products, quotients). Graphing calculator required. Math119 transfers to about half of the Michigan universities, usually as a general education requirement. Also satisfies a state transfer articulation agreement (part of math & science requirement). Math119 is intended to meet the graduation requirement for some occupational programs, and for some transfer (university) programs.
Mathematical Literacy (Rotman)
AMATYC 2011
www.devmathrevival.net
Examples from Math119 Final Exam
Quantities and Percents 25. A family is filling a child’s “swimming pool” – a round pool that is 6 feet in diameter (3 feet radius). They will fill the pool to a depth of 2 feet, and will be using a garden hose to fill the pool. We know that there are about 7.5 gallons of water in 1 cubic foot, and the hose will deliver about 10 gallons per minute. How long will it take to fill the pool, starting from empty, to the desired volume of water? For problems 3 and 4, use this situation. Car sales at a certain company have reached $28 million per year, and are growing at 9% annually. 3. At this rate, what will the amount of sales be next year (nearest tenth of million)? 4. If this exponential growth continues, what would the equation be to find the sales (y) based on the year in the future (x)? 7. Use the correct precision to answer the question: One hundred eighty apples weigh a total of 42 pounds. What is the average weight of these apples (in pounds)? 26. For a new play area, a school is using 200 meters of fencing. Find the area of a square enclosure, and of a circular enclosure, using this amount of fencing. Finance 8. Mr. Smith and Mr. Jones put $250 per month in an investment plan that pays an APR of 4% compounded monthly. (A) How much money will they have in 16 years? (B) How much interest will be earned in those 16 years? 9. For a vacation, a family wants to have $6000 after 4 years. They find a plan to put monthly payments into an account that pays 2% annual interest, compounded monthly. What is the amount needed for each monthly payment? Probability 16. Two marbles are drawn without replacement from a bowl that has 4 white, 3 green, and 2 red marbles. Find the probability that both selected marbles are green. 17. A family is going to have 4 children. Assuming that boys and girls are equally likely, what is the probability of having 2 boys followed by 2 girls? 18. The probability of a major earthquake in a given year is 0.06 for a region in California. What is the probability that the region will have at least one major earthquake in the next 5 years? Statistics 12. When the unemployment rate rises, the sales of luxury cars falls. State whether this correlation is positive or negative, and whether the correlation is most likely due to coincidence, a common underlying cause, or a direct cause. 14. In a poll of 1200 adults, 62% said they usually try to eat healthy foods. Find the 95% confidence interval. Functions & Modeling 21. A company finds that it costs $2.50 per glass, in addition to a basic set up cost of $80. (A) Write the linear function for the total cost based on the number of items. (B) Graph this function for a domain 0 to 100. 23. A radioactive substance has a half-life of 30 hours. If we start with 100 milligrams of this substance, how much will remain in 40 hours? Use the exact formula. 22. Fred’s family is investing $1000 in an account that pays 6% APR, compounded annually. (A) Write the exponential function for the account balance based on the number of years. (B) Graph this function for a domain 0 to 20.
Mathematical Literacy (Rotman)
AMATYC 2011
www.devmathrevival.net
