About This Chapter
Standard: 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. (CCSS.Math.Content.7.RP.A.3)
About This Chapter
Comprehension of the material in this chapter will increase students' competence in working with ratios as a percentage, particularly in the context of word problems. This will enhance their mathematics capacity and test-readiness in general, but this chapter has the added benefit of being incredibly relatable in day-to-day situations. This helps students become more competent in the arithmetic of daily life. The concepts covered in this chapter cover:
- Understanding proportional relationships in multistep ratio and percent problems
- Constructing proportions while solving real-world problems
- Solving interest, commissions, tip, price markup, and tax/discount problems
- Calculating percentage increase and decrease
Students will exhibit mastery of the lessons in this chapter when they are able to deconstruct common word problems involving various percentage-based ratios, reorder or change the notation of incongruent elements of the equation, and solve for the missing element(s). Their understanding of these topics will be readily evident in both the classroom and to their parents at home as they navigate the very problems presented here in real life.
How to Use These Lessons in Your Classroom
Looking for an interactive way to incorporate these lessons into your classroom instruction? Here are some examples of how you might do so.
Who wants to be a used car salesperson?
Have students watch the How to Calculate Sales Commissions video. Pair students off with one acting as a car salesperson and the other as a prospective client. Give each student in the pair a type of car and its worth as rated on a common used car site. Provide the salesperson with a commission rate and minimum commission goal. Provide the client with a maximum budget (they are paying cash). Negotiations begin with the salesperson presenting a figure which benefits them greatly and they think the client may go for. The client then determines if the price is within their budget, declining the offer if it is not. Negotiations continue until the salesperson makes an offer which fits in the client's budget but still makes a profit for them and the company. Switch roles to give each student practice on both sides of the negotiation.
Calculating markups homework
Assign the How to Markup a Price video as homework. Have students watch the video and then develop a business plan for selling their own t-shirts. Have them research t-shirt vendors and screen printers to determine the costs of running such a business from their home (no overhead). After finding an appropriate vendor and determining the price of creating their shirts, they will decide how much they are going to sell the product for to make a target profit (e.g. $10 per shirt).
Take a coupon page out of the local newspaper or print information on a sales event from an online source. Have students work out the missing starting/ending prices, percentages, or total savings. For example, an ad offering a 30% discount on cardigans, now costing only $70, has two missing elements: initial price and amount of savings ($100 and $30 respectively). Of course each ad must have at least two of the four elements for the math to work out: an ad indicating only a percentage off without prices would be impossible to work with. This can be assigned as homework, in-class work, or a quiz.
1. Proportional Relationships in Multistep Ratio & Percent Problems
This lesson introduces the concepts of ratios, rates, and proportions. It will show you how to use rates and ratios to develop proportional relationships. Using proportions to solve problems is very common in mathematics, because oftentimes many rates and ratios are constant.
2. Constructing Proportions to Solve Real World Problems
In this lesson, we will concentrate on proportions. Through definition and example, we will learn how to construct proportions and how to use proportions to solve real world problems.
3. How to Solve Interest Problems: Steps & Examples
If you want to know how your money can earn money, then it's essential to learn about solving interest problems. In this lesson, we'll practice calculating interest amounts and interest rates.
4. How to Calculate Sales Commissions
In this lesson, we'll define sales commission. We'll also discuss three types of sales commission: percent of sales, stair step and fixed amount. You'll also learn when to utilize each type.
5. How to Calculate a Tip
Tips are quantities of money that are often added onto to the original cost of a bill. Figuring out these items is as simple as setting up a ratio between the tip percentage and the bill amount. In this lesson learn how easy it is to calculate a tip.
6. How to Mark Up a Price
Marking up prices to cover costs and earn a profit is a common business practice. This lesson explains the standard formula to mark up a price, and provides examples of markups.
7. Taxes & Discounts: Calculations & Examples
When you go shopping, you don't want to be surprised by the amount of tax on an item. You also want to fully understand discounts to know how much you can save. In this lesson, we'll practice calculating both tax and discounts.
8. Percentage Increase and Decrease: Calculation and Examples
After watching this video lesson, you will be able to calculate the percentage increase and decrease of changes that happen over time. You will also learn what you need in order to make your calculations.
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Other chapters within the Common Core Math Grade 7 - Ratios & Proportional Relationships: Standards course