Math Mammoth Percent

81 pages
(includes answers)

Contents and sample lessons

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Este libro en español

Math Mammoth Percent is a worktext that covers all major percent-related topics usually studied in grades 6-7. The book contains both the instruction, written directly to the student, and a variety of practice exercises and problems. The lessons in the book cover the concept of percent and basic percentage calculations, discounts and sales tax, circle graphs, percentage of change, and simple interest.

I have made several videos to match the lessons from this book. You can watch them here.

The concept of percent builds on the student’s 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. One reason why I have emphasized finding a fractional part of a whole in the earlier grades of Math Mammoth materials is specifically to lay a groundwork for the concept of percent. Assuming the student has mastered this, 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 the 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 percentage 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 or quantity (the percentage is given), and questions that ask for the percentage. As an 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?”

In the lesson Finding the Total When the Percentage Is Known students practice 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.

After a review lesson in the middle of the book, we study some of the basics again in the lessons Percentage Basics 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 are originally written for 7th grade.

Circle Graphs is an optional lesson but it is an nice application that ties in statistics, percentages, and geometry.

The two lessons about percent equations and price changes cover how to solve basic percent problems using an equation. They also explain the usage of a percent proportion.

The next major topic is the percentage of change. Percentage of change means dealing 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?”

The last topic in the book is simple interest. Students learn to use the formula I = prt in a great variety of problems and situations, including both loans and savings accounts.

The text concludes with a review lesson of all of the concepts taught in the other lessons.

The PDF version of this book can be filled in on a computer, phone, or tablet, using the annotation tools found in many PDF apps. See more.

I have made several videos to match the lessons from this book. You can watch them here.