Whether calculating discount percent, sale price, original price, markup percent, or cost to store
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 do discounts and markups and to do a number of other calculations that involve percentages.
My experience teaching these concepts using percent proportions provided the inspiration for this product. In a 40-page product consisting of warm-up problems, guided notes, carefully orchestrated worksheets, detailed keys, and a math poetry and summary sheet, it allows the teacher to guide the students step by step through each of these concepts and provides a myriad of problems of various levels of complexity to ensure the concepts are practiced and retained.
NOTE THAT THIS PRODUCT CAN BE PURCHASED USING TWO SEPARATE METHODS:
1. If you are interested in purchasing products which address different types of more sophisticated percentage problems individually:
- purchase THIS PRODUCT
for discount and markup problems
, spread out over the course of four days AND/OR
- purchase Percent of Change (Increase or Decrease) and New Amount
to address percent increase and decrease problems
over the course of two days
2. If you are interested in purchasing a product that covers multiple complex uses of percentages in a bundled package, instead purchase Discounts, Markups, Percent Change, Tax, Tip Unit (using Percent Proportions)
. This 70-page, two-week product, sold at a discounted price, addresses percent of change, new amount, discounts, markups, and tax and tip, and contains a comprehensive unit assessment
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 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.
2. 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.
3. 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.
4. 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.
5. The POETRY and SUMMARY SHEET
– This fun poetry and comprehensive summary sheet cement concepts in the minds of the students, and can be saved for future reference
Good luck in your use of Discounts and Markups
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
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 this product.
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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