Lesson 7.1.3 – Teacher Notes Standard: 7.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. 7.EE.A.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that "increase by 5%" is the same as "multiply by 1.05." 7.NS.A.3 Solve real-world and mathematical problems involving the four operations with rational numbers. Full mastery can be expected by the end of the chapter. Lesson Focus: The focus of the lesson is to provide additional practice of solving real-world problems. The questions are balanced between one-step and multi-step. (7-27, 7-29, and the additional challenge) I can investigate and solve real-world rational number word problems. Calculator: No Literacy/Teaching Strategy: Red-Light-Green-Light (7-27); Participation Quiz (Whole Lesson)

Bell Work

As you have seen many times in this course, there is usually more than one way to solve a problem.  When a problem uses portions (fractions, decimals, or percents), there are different ways to write the numbers and different solving strategies to choose from.  Today you will look at the different multipliers that can scale a quantity and see what each of them will help you find.  As you work with your team today, consider the questions  below. What multiplier (scale factor) should I use? How can I write an equation?

7-27. Hugo and his family were shopping and purchased a new bed.  The bed was a great deal at 60% off of the original cost.  The bed originally cost $245.    a. If Hugo scales (multiplies) the original price of the bed by 60%, what will his result represent?     b. What should Hugo scale (multiply) the original price by to find the new price of the bed?  c. Work with your team to find the sale price of the bed in two different ways, that is, using two different multipliers (scale factors).  How do your answers from your two methods compare?   

7-28. Hugo’s older sister, Sandra, had the same summer job for the past two years.  Last year, she worked the entire summer and was paid a salary of $3,000.  This summer, she is going to get a 6% raise in pay.  To figure out how much she will make, Sandra drew the following diagram. a. Copy the diagram on your paper and fill in the missing information.  b. Since Sandra’s salary is increasing, does it make sense that her scale factor (multiplier) should be less than 1, equal to 1, or more than 1?  Why?  c. The diagram shows Sandra’s original salary and the amount of the increase.  What is the scale factor (multiplier) between her original salary and her new salary?  That is, what number could Sandra multiply the original salary by to get the new salary?    d. Show two ways that use different scale factors (multipliers) that Sandra can use to compute her new salary. 

7-29. Miranna teaches gymnastics lessons at summer camp.  She is paid $12.50 per hour. a. If Miranna were offered a raise of 100% per hour, what would her new hourly rate be?  What percent of her original pay would she be paid? b. Miranna is offered a raise of 75% of her hourly rate to teach a private lesson.  How much per hour would she be paid for the private lesson?  What percent of her original pay would she get?   c. What is the relationship between the percent raise that Miranna gets and her new pay as a percent of her original pay?  How is this related to the scale factor  (multiplier) between her original pay and her new pay?   

7-31. Additional Challenge: Ramon went to the corner store and bought more notebook paper to do his homework.  The cost for the paper was $7.50, but he also had to pay the 8.1% sales tax.  How much will the notebook paper cost Ramon?  If Ramon gives the clerk $10, how much change should he receive?

Practice Emily buys a toaster during the sale for 10% off. If Ellen pays $36, what was the original price? 2. Zack has an old car. He wants to sell it for 60% off the current price. The market price is $500. How much money would he receive in exchange for the car if he were able to sell it at that rate? 3. A football is selling for 35% off the original price. The original price was $60. What is the sale price of the football? 4. A boat is marked up 20% on the original price. The original price was $50. What is the sale price of the boat before sales tax? 5. Kevin's Furniture Store buys a sofa at a wholesale price of $117.00. If the markup rate at Kevin's Furniture Store is 60%, what is the markup for the sofa?