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Math Mammoth Percent teaches students the concept of percent, percentage of a number, discounts, sales tax, percent of change, circle graphs, and percent of comparison. It is suitable for 6th-8th grade (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 a student's understanding of fractions and decimals. Specifically, students should already 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, and one reason why I have emphasized finding a fractional part of a whole so much in the division and fraction materials 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 a whole, and can easily convert fractions to decimals, studying percent in middle school should not be difficult.
The first lesson, Percent, practices the concept of percent as 1/100, and how to write fractions and decimals as percentages. Next we study What Percentage? in order to cement the basic idea of questions where percentage (or how many percent) is asked: students write the asked part first as a fraction, and then convert that to a percentage.
The lesson that follows, Percentage of a Number, teaches how to find a certain percentage of a quantity using mental math techniques. For example, students find 10% of $400 by dividing $400 by 10. In the next lesson, students find a percentage of a quantity using decimal multiplication, including using a calculator. For example, to find 17% of 45 km, students multiply 0.17 × 45 km.
Then follow lessons about discounts and sales tax, important applications in everyday life. Next we go on to the lesson Practice with Percent, which contrasts the two types of problems: 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?”
I also present one optional lesson titled Backwards Questions with Percent, where students need to figure out “the whole” when a partial amount and a percentage are given. For example: “Three-hundred twenty students, which is 40% of all students, take additional PE. How many students are there in total?”
Then follows one lesson concentrating on tenth of a percent. Thus far, all the material has been with whole percents. From this lesson on, we will also use tenth of a percent (such as 13.4%). We go on to compare ratios, fractions, and percent in one lesson. Next, students study how to make a circle graph.
The last major topic is percent of change. This deals of course with decreases and increases in quantities (such as prices). We also study how to find the percent of change when the original and new amount are known.
Tying in with percent of change, there is one lesson on Comparisons with Percent. It ties in, because the way to solve comparisons involving percent (such as how many percent less/more is one thing than another) is identical to finding percent of change.
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 actually created a whole 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~
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