Sample pages (PDF)
Contents and Introduction
Review
What Percentage...?
Percentage of a Number
Discounts
Percent of Change
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Math Mammoth Percent teaches students the concept of percent, how to calculate the percentage of a number, to figure discounts, sales tax, and interest, to draw circle graphs, to differentiate between a percent of change and a percent of comparison, and to know how to calculate both. The text is suitable for grades 6 through 8 (middle school).
I have made several videos to match the lessons from this book. You can watch them here.
The concept of percent builds on the students' understanding of fractions and decimals. Specifically, students should be very familiar with the idea of finding a fractional part of a whole (such as finding 3/4 of $240). Students who have used Math Mammoth have been practicing that concept since 4th grade. One reason why I have emphasized finding a fractional part of a whole so much in the earlier grades is specifically to lay a groundwork for the concept of percent. Assuming the student has mastered how to find a fractional part of a whole, and can easily convert fractions to decimals, then studying the concept of percent should not be difficult.
The first lesson, Percent, practices the concept of percent as a hundredth part, and how to write fractions and decimals as percentages. Next, we study how to find a percentage when the part and the whole are given (for example, if 15 out of 25 club members are girls, what percentage of them are girls?).
The following two lessons have to do with finding a certain percentage of a given number or quantity. First, we study how to do that using mental math techniques. For example, students find 10% of $400 by dividing $400 by 10. Next, students find a percentage of a quantity using decimal multiplication, including using a calculator. For example, students find 17% of 45 km by multiplying 0.17 × 45 km.
I prefer teaching students to calculate percentages of quantities using decimals, instead of using percent proportion or some other method (such as changing 17% into the fraction 17/100 for calculations). That is because using decimals is simpler: we simply change the percentage into a decimal, and multiply, instead of having to build a proportion or use fractions. Also, decimals will be so much easier to use later on, when solving word problems that require the usage of equations.
Next is a lesson about discounts, which is an important application in everyday life. Then, we go on to the lesson Practice with Percent, which contrasts the two types of problems students have already studied: questions that ask for a certain percentage of a number (the percentage is given), and questions that ask for the percentage. For example, the first type of question could be "What is 70% of $380?", and the second type could be "What percentage is $70 of $380?"
Finding the Total When the Percent Is Known lets students find the total when the percentage and the partial amount are known. For example: "Threehundred twenty students, which is 40% of all students, take PE. How many students are there in total?" We solve these with the help of bar models.
After a review lesson in the middle of the book, we study some of the basics again in the lessons Percentage and Solving Basic Percentage Problems. While the concepts are the same as in the lessons in the beginning of this book, this time we include more decimal digits and the coverage is faster, as these two lessons were originally written for 7th grade.
Percent Equations is meant for prealgebra students and covers how to solve basic percent problems using an equation. It also explains the usage of a percent proportion.
The next major topic is the percentage of change, which is covered in a twolesson sequence. The concept of percentage of change deals with percentage increases and decreases in quantities (especially prices). For example: "If an airline ticket that costs $120 now goes up by 10%, then what will the new price be?" Students will also learn how to find an unknown percentage of change when the original and new quantities are known. For example, "If a shirt cost $24 and is now discounted to $18, then what percentage was the discount?"
Tying in with percentage of change, there is one lesson on Comparing Values Using Percentages. Students learn to solve comparisons involving percent (such as how many percent more (or less) one thing is than another) through applying concepts that they learned in finding the percentage of change and to differentiate clearly among the various types of comparison questions that can be asked.
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 thorough review lesson of all of the concepts taught in the other lessons.
I have made several videos to match the lessons from this book. You can watch them here.
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