New Year`s tips

unit pricing, calculations, fractions, mathematical facts

Ann’s New Year’s Math Resolutions 2008

1. Saving money through unit pricing
• Learning unit pricing can save you in shopping.  Although many stores have  unit pricing labels on shelves, you can still compare prices by doing the unit pricing calculations yourself.  Calculate the unit price of an item by dividing more than $.20 per ounce.  Compared to a 34-ounce can of that same coffee  costing $5,69, the smaller can is about two cents more expensive per ounce than the larger can, which  weighs in at about sixteen cents per ounce.
• Carry a small calculator with you in your purse or pocket so you can easily calculate unit prices while in the store.the price of the package by the unit by which it is measured.  For instance, a 13-ounce can of coffee which costs $269 costs $2.69/13 per ounce, or a little
2. Organizing time
• When making appointments, use a planner such as a calendar and allow sufficient time for transitions and breaks from work.
• Teach children to schedule rest periods and breaks when studying for exams and when planning chores.  Children who are raised with digital watches often need to be reminded that there are sixty minutes to the hour and that time can be broken down into fractions of hours.  
• Have children schedule themselves in fractions of hours, such as ¼ or ½ hour periods.  Then work with them to add these periods to see the total time a job will take.
3. Some little known mathematical facts on consumer spending
Your car:
•   Keeping your tires inflated can save between 3.3% and 10% of your fuel bill, not to mention keeping your brakes and suspension systems working optimally.
• A dirty air filter can cost you up to 10% of your fuel cost.  Check your owner’s manual for recommended replacement times.
Your house or apartment:
• Your water heating bill may eat up to 25% of your heating bill.   Studies have found that electric hot water heaters consume more energy per BTU than gas heat and recovery time is shorter with gas heat.  You might want to check with an authority in your area, either with a commercial entity or a business or government group , to see if you can save money on this big ticket item.
Your diet:
• Many cookbooks and prepared food labels list number of servings per recipe or per unit of food.  Paying attention to nutritional information can prevent you from overeating and keep your waistline from growing.
• Learning unit pricing can save you in shopping.  Although many stores have  unit pricing labels on shelves, you can still compare prices by doing the unit pricing calculations yourself.  Calculate the unit price of an item by dividing the price of the package by the unit by which it is measured.  For instance, a 13-ounce can of coffee which costs $269 costs $2.69/13 per ounce, or a little more than $.20 per ounce.  Compared to a 34-ounce can of that same coffee  costing $5,69, the smaller can is about two cents more expensive per ounce than the larger can, which  weighs in at about sixteen cents per ounce.

Snowtime fun problem
Alex and Alicia have piled up the snow in their front yard so that their children can learn some math and have some fun.  They have made a conical pile of snow six feet high and eight feet across.  They will let their children, Sandy and Sam, slide down the hill if the children can determine (a) the volume of the snow piled up to make the hill and (b) the angle down which they will slide from the top.  Can you help Sandy and Sam to find the volume and the angle?

Answers:  The volume of a cone is calculated using the formula V= 1/3pi r^2(h), or 1/3 the number pi (approximately 3.14) times the radius squared times the height.  Alex and Alicia’s snow cone is eight feet across, which means that the radius is four feet. The height is six feet.  Therefore, that volume is 1/3 (3.14) (4^2) (6), 100.48, or a little over 100 cubic feet.  That’s’ a lot of snow for parents to shovel!

The angle down which they slide may be calculated by the dimensions of the triangle formed by the mound.  If the height is 6 and the base of the triangle  is 4, as shown above,
using the Pythagorean theorem shows us that the outside(or the hypotenuse of the triangle) is the square root of the sum of the squares of 4 and 6, or the square root of 52.  Using the arcsin function of 6/square root of 52, the angle is approximately 56 degrees. Sam and Sandy will surely have a wild ride down their manmade mountain!

unit pricing, calculations, fractions, mathematical facts