1. Estimation, Graphs, and Mathematical Models

2.  Use estimation techniques to arrive at an approximate answer to a problem.  Apply estimation techniques to information given by graphs.  Develop mathematical models that estimate relationships between variables.

3.  Estimation: the process of arriving at an approximate answer to a question.  For example, companies estimate the amount of their products consumers are likely to use, and economists estimate financial trends. ▪ Rounding numbers is also an estimation method.

4.  On your way home from work, you stopped at the market to pick up the items listed in the Table. You also would like to buy a half gallon of ice cream for $3.59, but you remember that you only have $20 in your wallet and you don’t want to be caught in the checkout line without enough money. Use rounding to the nearest ten cents to: a. Estimate the total cost of your purchases. b. Decide if it is safe to put the ice cream in your cart. Item Cost ($) Cereal4.29 Milk2.41 Bread1.89 Lunch Meat3.36 Pickles2.47 Dish-washing liquid 2.87 TOTAL:

5.  You do not need a calculator to add the estimated prices. For example to add $4.30 and $2.40, first add the dollars to get 2 + 4 = 6. Then add the cents to get 30 + 40 = 70 cents, so the total is $6.70. You can easily add in the other numbers one at a time to get the total. Doing this kind of mental arithmetic will make you a stronger mathematics student. ItemCost ($) Cereal4.29 Milk2.41 Bread1.89 Lunch Meat3.36 Pickles2.47 Dish-washing liquid2.87 TOTAL:

6. ItemCost ($) Cost Rounded to Nearest Ten cents Cereal4.29 Milk2.41 Bread1.89 Lunch Meat3.36 Pickles2.47 Dish-washing liquid 2.87 TOTALS:

7.  A carpenter who works full time earns $28 per hour. a. Estimate the carpenter’s weekly salary. b. Estimate the carpenter’s annual salary.

8.  Another way to make a quick estimate that is slightly different from rounding is to use compatible numbers.  When compatible numbers, instead of the numbers given in the problems, you simply substitute numbers that are easier to work with.  For example, instead of dividing 298 by 14, you could divide 300 by 15 to get 20.  Or, instead of multiplying 11 times 73, you could multiply 73 by 10 to get 730.

9.  Marc is buying 19 blank tapes at $2.89 each. Use compatible numbers to estimate the cost of the tapes.

10.  In 2001, the world’s population was approximately 6,157 million and the population of North America was 486 million. Estimate what fractional part of the world’s population lives in North America?

11.  The bar graph shows the average cost of tuition and fees for public four-year colleges, adjusted for inflation.

12.  Estimate the yearly increase in tuition and fees. Round to the nearest dollar.

13.  Write a mathematical model that estimates the average cost of tuition and fees, T, at public four-year colleges for the school year ending x years after 2000.

14.  Use the mathematical model to predict the tuition and fees for the school year ending in 2014.

15.  Classwork:  TB pg. 21/20 – 42 Even ▪ Must write problem and show ALL work to receive credit for the assignment.  Homework: