# Lesson 12

Finding the Percentage

### Lesson Narrative

In this lesson, students consolidate what they have learned over the last few lessons and solve a variety of multi-step percentage problems involving taxes, tips, and discounts, including problems involving fractional percentages. They continue to move towards using equations to represent problems, which enable them to see the common underlying structure behind different problems (MP7). For example, $$1.2x$$ can represent

• a 20% increase in $$x$$.
• the total bill when 20% tax is added.
• the total bill when a 20% tip is added.
• the retail price when the wholesale price is marked up by 20%.

### Learning Goals

Teacher Facing

• Determine what information is needed to solve a problem involving sales tax and discounts. Ask questions to elicit that information.
• Explain (orally) how to calculate the percentage, given the dollar amounts before and after a sales tax, tip, or discount.
• Interpret (orally and in writing) tape diagrams that represent situations involving a sales tax, tip, or discount.

### Student Facing

Let’s find unknown percentages.

### Required Preparation

Print and cut up slips from the Info Gap: Sporting Goods blackline master. One copy of the blackline master is needed for every 4 students. A class set could be re-used if you have more than one class.

### Student Facing

• I can find the percentage increase or decrease when I know the original amount and the new amount.

Building On