Whether doing discount percent, markup percent, percent of change (increase or decrease), or tax and tip problems, all of which involve percent calculations, I have found that using percent proportions
is the best way to do so. There are no decimal shifts (as there are when students use the percent equation, p = % • w) to cause errors, the amount of memorization is minimal (the percent proportion, part/whole = percent/100
, with some careful thinking before and/or after applying it, is all that is needed), and the problems can be solved relatively simply. After spending years attempting to use and manipulate the percent equation and watching my students struggle, I now gleefully observe them thriving as they use proportions to solve these types of problems (yes, many have actually called it “fun”!). Students who have been well trained in the use of proportions to solve general problems (see Ratios, Rates, and Proportions Galore
if you need a unit which serves as a comprehensive introduction to these concepts) and have attempted to solve simple percentage problems (see Percent Proportions
if you need a unit to train them on part/percent/whole percentage calculations using proportions) quickly pick up how to use proportions to find percent of change, new amount, discount percent, markup percent, original price, sale price, cost to store, sales tax, tip, and total cost of the meal.
My experience teaching these concepts using percent proportions provided the inspiration for this product. In 74 pages of warm-up problems, guided notes, carefully orchestrated worksheets, and detailed keys (with some poetry thrown in!), it first allows the teacher to guide the students step by step through each of these concepts, then provides a myriad of problems of various levels of complexity to ensure the concepts are practiced and retained, and concludes with a comprehensive unit assessment.
The time required for this unit will vary depending upon the ability and experience level of the class and whether the teacher elects to use all or just some of the activities, but experience has shown this unit will take eight to ten days to complete.
The content areas included in this unit will summarized below. Generally though, each "section" of the unit consists of a warm-up activity, guided notes page(s) and a worksheet. The purpose of these activities is as follows:
1. The Warm-ups
are meant to review previous concepts, get students’ creative juices flowing, and stimulate preliminary thinking and speculation about the topic of the day. Teachers then go over the Review
problems in detail and have a discussion about student answers to the New
problems before diving into the guided notes.
2. The Guided Notes
pages are intended to allow the students to take notes and absorb concepts in a structured method. Ideally, the teacher should have the same notes page that the students have in their hands projected onto a screen, and have the answer key beside him or her for his or her own use. The teacher should then guide the students through the step by step process, allowing the students to take notes, ask questions, provide answers, and have rich discussion along the way.
3. The Worksheets
are provided for the students to practice what they learned in the guided notes pages. All include both computation problems and word problems and are pictorially illustrated. Later worksheets include spiral review of previous concepts. These pages can be completed for homework if it appears the students have the basic concepts down.
The different days of activities are:
1. Calculating PERCENT OF CHANGE
– Includes a warm-up activity, two pages of guided notes, and one-page worksheet. Focuses on transforming the percent proportion to use to find percent of change when original and new amounts are given.
2. Calculating NEW AMOUNT
– Includes a warm-up activity, a page of guided notes, and a one-page worksheet. Here the focus shifts to finding the new amount when a percent of change (increase or decrease) is provided.
3. The POETRY and SUMMARY SHEET
– Now that the students have gotten their feet wet in solving two types of problems, it is time for some fun poetry and a summary sheet both to cement concepts already covered and to show students that all concepts to come will be handled using the percent proportion in a similar, but not identical, fashion. There are a variety of ways, and even a variety of locations in the unit, to introduce the poetry and summary sheet. I like to introduce it after percent change and new amount have been covered, refer back to it as each additional concept is covered to show the students how that concept fits into the overall picture, and then tell the students to use it to study for the end of unit assessment.
4. Calculating DISCOUNT % and SALE PRICE
– Includes a warm-up activity, two pages of guided notes, and a two-page worksheet. The focus here is on calculating discount percent when original and sale price are provided, and calculating sale price when original price and discount percent are provided. It is here that the students are first introduced to the fact that there is more than one way to solve these types of problems. The guided notes in this section allow the teacher to show the students both the “Thinking After” method, in which the student performs an extra calculation AFTER using the proportion, and the “Thinking Before” method, in which the student performs an extra calculation BEFORE using the proportion.
5. Calculating ORIGINAL PRICE
– Includes a warm-up activity, a page of guided notes, and a two-page worksheet. The focus here is on calculating the original price when sale price and discount percent are given.
6. Calculating MARKUP % and SALE PRICE
- Includes a warm-up activity, two pages of guided notes, and a two-page worksheet. The focus here is on calculating markup percent when cost to store and a sale price are provided, and calculating sale price when cost to store and markup percent are provided.
7. Calculating COST TO STORE
– Includes a warm-up activity, a page of guided notes, and a two-page worksheet. The focus here is on calculating the cost to the store when sale price and markup percent are given.
8. Calculating TAX, TIP and TOTAL COST
– Includes a warm-up activity, two pages of guided notes, and a two-page worksheet. This wraps up the unit by covering both the calculation of sales tax (without tip) and total cost when an item is purchased, and also the calculation of tax, tip, and total cost when a meal is purchased. Students are generally semi-experts at this point, and therefore tax and tip should not present a problem.
9. UNIT ASSESSMENT
- The culmination of the unit, this test contains a variety of problems from all sections of the unit. It is broken out cleanly by content area, allowing the teacher to eliminate certain types of problems if he or she elected not to cover them as part of this unit. This test should be able to be completed in a one-hour class period.
Good luck in your use of Percent of Change, Discounts, Markups, Tax, Tip
Other products which deal with rates, ratios, and proportions include:
Ratios, Rates, and Proportions Galore
- This complete unit teaches students the basics of ratios, rates, and proportions and is the ideal predecessor to Percent Proportions - The Complete Unit
- This complete unit teaches students how to use proportions to find part, percent and whole. It is the ideal predecessor to Percent of Change, Discounts, Markups, Tax, Tip
Similar Figures in the Real World, An Outdoor Lesson
- Uses proportions to solve real world problems involving similar triangles.
- Uses ratios and rates to convert between measures and rates with different units.
Another product which deals with percentages is Tape Diagrams and Percent Made Easy for Common Core Standards
- a product similar to Percent Proportions - The Complete Unit
, but in which tape diagrams, rather than proportions, are used to calculate part, whole, or percent. Ideal for sixth grade Common Core standards.
Also feel free to check out a growing number of other products that use poetry, songs, games, worksheets, and assessments to make math fun and help students to learn a variety of common core math standards.
Click here to view Algebraic Equation Products
Click here to view Divisibility Rule Products
Click here to view Elementary to Middle School Transition Products
Click here to view Fraction Products
Click here to view Geometry Products
Click here to view Integer and Order of Operations Products
Click here to view Probability Products
Click here to view Ratio-Rate-Proportion Products
Click here to view Riddle Card Products that Help Retain Math Essentials
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