## Computing Costs

### Robert PauleyPalm Beach County Schools

#### Description

Students are expected to calculate the out-of-pocket money needed to purchase a discounted item taxed at a certain percentage of sales tax.

#### Objectives

The student solves real-world problems involving percents (for example, discounts, simple interest, taxes, tips).

#### Materials

-Pencils
-Notebook paper
-Calculators
-One copy of the student activity sheet per student (See Preparations)

#### Preparations

1. Distribute the necessary calculators, pencils and paper.
2. Ask the students if they are familiar with percentages, decimals and rounding.
3. Arrange the students in pairs or teams. Teamwork is encouraged, making certain everyone understands the concept.
4. Have the sample problem and similar problems listed in the procedures on a student activity sheet or overhead transparency.

#### Procedures

1.The student is given one activity sheet with a calculator, pencil and paper.

2. The students may work in pairs. If needed, warm-up exercises can review their math skills, including using simple handout items with price tags.) Ask them if they had an item for \$1.00, at 10% off, with a 5% tax how much would they pay. Work a few simple exercises on the overhead/board to get the teams acclimated to the task.

3. Ask them if they have ever purchased a CD player with their parents in a store.

4. Tell them you have located one at Wal-Mart, an excellent CD player marked at \$99.99. A sign above it reads “20% off!” and a sign by the register reads “A 6 1/2% sales tax is charged on all purchases.”

5. Explain to them the real-world scenario that would occur if they were using their own money to make the purchase. It is important to know how to calculate exactly how much they will pay out-of-pocket for this item.

6. Discuss their input on real-world purchases they have made with their parents.

7. At this time, groups attempt to solve the problem on their own. They are solving for the total price. If they are unfamiliar with the calculators used and explanation is necessary, especially of the multiplication (X) and the percentage (%) keys, review this. Many will not understand that 20% off means 80% on, so this must be explained to them. Many will not understand that a percentage must be changed to a decimal by moving the decimal point two places to the left, and this must be explained. Solve the problem on the overhead/board in stages as the students attempt to solve it at their desks. Allow groups to compare their calculations all along.

8. Many students will have difficulty rounding the decimal to two places since the answer must be in dollars and cents, and this should be explained to them.

9. Tell students: We have used an item you are familiar with and would likely purchase for your own use. Then tell students: CDs are 12.99 and the same discount and tax applies, so what is the cost of the CDs? By now they will have a much better concept of what must be done.

10. Allow groups to solve for the cost of the CDs.

11. Next, ask them to construct a formula to reflect what they have just calculated. The shortcut formula should be explained to them at this point: 1.065 x (Cost x 0.8) Help students to see the correctly written algebraic formula: 1.065(0.8C).

12. Tell students: Next we will check the formula by making a Best Buy purchase of a game cartridge listed at \$19.97. Assume a 15% discount and a 6.0% sales tax. The formula would now read 1.06 x (Cost x 0.85) or 1.06(0.85C) because the discount and tax amounts have changed. Again, allow groups to check their answers and to look for mistakes or correct calculations. Ask students to push their desks/chairs apart.

13. Give students this final problem to be turned in and assessed: A pair of Reeboks you want is on sale at the mall. The regular price is \$69.95 and the store is offering a 25% reduction. The tax in your county is 5 1/2 %. Tell students to set up the formula for this exercise and solve for the amount that will be paid to the clerk. This should be done individually.

#### Assessments

The problem that is turned in will be assessed for the students' grasp of solving real-world problems, using the calculator, using the formula and arriving at the correct answer. This is a formative assessment and students may need additional practice before demonstrating mastery.

#### Extensions

1. The student may confer with classmates and discuss shortcuts and alternate procedures. Some ways of solving the problem are easier than others.
2. The problems could be simplified for students with learning disabilities.
3. The lesson could be extended into an Excel computer program in a computer lab.