Applying Tax, Tip, and Discount: Using Proportions and Scale Factors

This lesson teaches how to apply taxes, tips, and discounts using proportions and scale factors. It explains the concept of proportions, provides a real-life example of calculating a discount on sneakers, and uses bar models to verify calculations. Common misunderstandings are addressed, emphasizing the importance of distinguishing between discounts and final sale prices. The lesson concludes with a summary of the key concepts.

What is a proportion in mathematical terms?

• A statement that two ratios or rates are equal through subtraction.

• A statement that two ratios or rates are equal through multiplication by a scale factor.

• A statement that two ratios or rates are equal through division.

• A statement that two ratios or rates are equal through addition.

How do you determine the scale factor in a proportion?

• By multiplying the two numbers in the proportion.

• By dividing one number by the other in the proportion.

• By subtracting the smaller number from the larger number.

• By adding the two numbers in the proportion.

In the example of the sneakers, what does the $75 represent?

• The final sale price.

• The discount amount.

• The original price of the sneakers.

• The tax amount.

What is the scale factor used to calculate the discount on the sneakers?

• 1/2

• 4/3

• 3/4

• 2/3

How much is the discount on the sneakers?

• $10

• $20

• $25

• $15

What is a common mistake students make when calculating discounts?

• Calculating the discount as a percentage of the final price.

• Using the wrong scale factor.

• Adding the discount to the original price.

• Confusing the discount amount with the final sale price.

Why is keeping a receipt helpful when calculating discounts?

• It helps in organizing work and avoiding mistakes.

• It provides a detailed breakdown of taxes.

• It shows the original price of the item.

• It automatically calculates the discount for you.