In the unit Percent, Grade 7 we begin by reviewing the concept of percent as “per hundred” or as hundredth parts and how to convert between fractions, decimals, and percentages. The second lesson in the unit, Solving Basic Percentage Problems, is intended for review of sixth grade topics, focusing on finding a known percentage of a number (such as 21% of 56) or finding a percentage when you know the part and the total.
We take a little different perspective of these concepts in the lesson Percent Equations. Students write simple equations for situations where a price increases or decreases (discounts). This lesson also explains what a percent proportion is. Personally, I prefer not to use percent proportion but to write the percentage as a decimal and then write an equation. I feel that approach adapts better to solving complex problems than using percent proportion.
Here is a quick example to show the difference between the two methods. Let’s say an item is discounted by 22% and it now costs $28. Then, the new price is 78% of the original. If we let p be the price of the item before the discount, we can write the percent proportion $28/p = 78/100 and solve for p. If, we write the percentage 78% as the decimal 0.78, we get the equation 0.78p = $28. Personally, I consider percent proportion to be an optional topic, and the reason I have included it here is to make this curriculum fully meet the Common Core Standards for seventh grade.
The lesson Circle Graphs provides students a break from new concepts and allows them to apply the concept of percent in a somewhat familiar context. Next, we delve into the percentage of change. Students sometimes view the percentage of change as a totally different concept as compared to other percentage topics, but it is not that at all. To calculate the percentage of change, we still use the fundamental idea of percentage = part/total, only this time, the “part” is how much the quantity in question changes (the difference) and the “total” is the original quantity.
Tying in with percentage of change, students also learn to compare values using percentages, such as how many percent more or less one thing is than another. Once again, this is not really a new concept but is based on the familiar formula percentage = part/total. The percentage difference (or relative difference) is the fraction (actual difference)/(reference value).
Simple Interest is a lesson on the important topic of interest, using as a context both loans and savings accounts. Students learn to use the formula I = prt in a great variety of problems and situations.
The text concludes with a review lesson of all of the concepts taught in the unit.