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 to understand the concept of percent, to calculate the percentage of a number, to figure discounts and sales tax, 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, in what is often termed middle school.
The PDF version of this book is enabled for annotation. This means that if you prefer, your student can fill it in on the computer, using the typewriter and drawing tools in Adobe Reader version 9 or greater.
I have created a set of videos to go with this book. Please access them on this web page: Percent videos.
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: "Three-hundred 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.
Thus far in the text, all the material has used whole percents. Now follows a lesson that introduces calculations with tenths of a percent (quantities like 13.4%). From this lesson on, the lessons will continue to use tenths of a percent. In Ratios, Fractions, and Percents we compare those three ways of expressing the same relations among members of a group. In the next lesson, students study how to make a circle graph.
The last major topic is percent of change, which is treated in a three-lesson sequence. The concept of percent 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 percent of change when the original and new quantities are known. For example, "If a shirt cost $24 and now is discounted to $18, then how many percent was the discount?"
Tying in with percent of change, there is one lesson on Comparisons with Percent. 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 percent of change and to differentiate clearly among the four types of comparison questions that can be asked.
The text concludes with a thorough review lesson of all of the concepts taught in the other lessons.
As an example how this book teaches percent topics, please see these videos of mine. They are based on the lessons in the book. I have created a set of videos to go with this book, which you can access for free.
I have never really been in a position to write one of those glowing testimonials that every product puts on their website, but I just had to tell you that I truly AM thrilled with Math Mammoth. Amanda just finished the Percent book in record time and actually seemed to enjoy it. In the course of two books, she has gone from super-frustrated, tightened-down, hating math of all kinds to deciding that it's not bad after all and just breezing through it. Practically miraculous, if you ask me. She thinks ratios are fun (Is this really my child??) so we are doing Ratios and Proportions next, and life is just a whole lot easier at this homeschool than it used to be.
Many thanks for a wonderful product that I can actually afford.
Blessings to you, Maria~
Ronda
March 2011
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