Math Mammoth Division 1

57 pages
(answers included)

Sample pages (PDF)
Contents
Dividing Evenly into Groups
Multiplication and Division Fact Families
Multiplication and Division Word Problems

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Este libro en español

Math Mammoth Division 1 is a worktext that covers the concept of division, finding whole-number quotients within 0-100 (essentially, the basic division facts), and bar graphs and pictographs. It is most suitable for third grade, after the student knows the multiplication tables.

I recommend the student know the multiplication tables fairly well before starting this book. In fact, the approach taken here to teach division facts is to simply base them on the multiplication tables, and not to teach them as a separate set of facts to memorize. This is very efficient, and works well when the student knows the times tables, but is nearly useless for someone who doesn't know them. Several lessons in the book focus on this basic concept that division problems can be solved by thinking of multiplication.

There are basically two ways to interpret division, and thus to illustrate it with concrete objects. The first way has to do with grouping. The problem 12 ÷  3 is interpreted as, “How many groups of three items can you make out of 12 items?” This is also called measurement division.

The second way to interpret division is equal sharing: we divide or share items equally between people or other items. For example, the problem 12 ÷  3 can be interpreted as, “If you share 12 bananas equally between 3 people, how many bananas does each one get?”

Both of these interpretations of division are important to understand so that the student can solve real-life and mathematical problems involving division.

We also study division by zero. In that lesson, students should recognize that division by zero “does not work.” I realize that in higher forms of mathematics, division by zero may be defined (such as 1 ÷ 0 = infinity), but for now, this is how we present it for third graders.

The latter part of the book deals with bar graphs and pictographs. Earlier (in 2nd grade), students have drawn pictographs and bar graphs with single-unit scale. Now, they draw scaled pictographs and bar graphs from the given data, choosing the scale, or how many items one block in the bar graph or one picture in the pictograph signifies. This process provides practice in using both division and multiplication.

Lastly, the book includes an optional lesson on the concept of remainder. It focuses on finding the remainder by using visual models. It is optional because this concept technically belongs to 4th grade.

This book will be relatively easy for students who have mastered the multiplication tables, since division facts are just multiplication tables “backwards”. So, students can focus on another important skill: recognizing real-life situations in word problems that mathematically relate to either division or multiplication. This is very important to master so that the student can later on translate more complex situations into equations (modeling with mathematics).

Like already mentioned, in this book, students will find quotients (answers to division problems) by thinking of the multiplication tables. In continuation (in 4th and 5th grades), they will divide larger numbers, primarily using long division, though thinking of multiplication will still be used for some types of division problems. The basic concept of division is also the foundation for finding factors of a number and prime factorization, which are typically studied in 4th and 5th grades.

You can find free videos covering topics of this book at https://www.mathmammoth.com/videos/ (choose 3rd grade, then division).

The answer key is appended.

The digital version (PDF) of this book can be filled in on a computer or on a tablet using a PDF app with annotation tools.