Math Mammoth Division 1 is a worktext about basic single-digit division, remainder, and divisibility. It is most suitable for third grade, after the student knows the multiplication tables.
The division concept in itself is not very difficult - after all, it is like backwards multiplication. However, children can have difficulties in related concepts, such as the remainder, divisibility, and later in factoring and long division (the latter two are not dealt with in this book).
The aim of Math Mammoth Division 1 is to lay a good foundation in basic division, cementing the link between multiplication and division, and then to solidly study the concepts of the remainder and divisibility. Understanding these is required when studying (later) factoring and long division.
There are basically two ways of illustrating division with concrete objects. The first method has to do with dividing objects between a certain number of persons. For example, the problem 12 ÷ 3 would be, "If you have 12 bananas and 3 people, how many bananas does each one get?"
The second method has to do with grouping. The problem 12 ÷ 3 would be: "If you have 12 people, how many groups of 3 people can you make?" These two interpretations of division are important to understand so that your child can solve problems of everyday life.
The book at hand provides plenty of practice and stresses understanding of concepts. I don't wish the student to memorize procedures without understanding the "why" (rote memorization).
For example, when studying the remainder, the student first finds the remainder with the help of pictures - which is equivalent to using manipulatives. Then he explores the pattern found in dividing sequential numbers by the same number, such as 25 ÷ 3, 26 ÷ 3, 27 ÷ 3, 28 ÷ 3, etc. After that, it is explained that you can find the remainder by looking at a certain difference, and finally the typical school-book method is presented.
The prerequisite for this book is knowing the times tables fairly well. The child can start studying division even if he still needs some practice with the multiplication tables, but he should finish mastering the tables before advancing very much with the lessons of this book.
This book is enabled for annotation, which means you can fill it in on a computer (with Adobe Reader 9 or higher) or on a tablet using a PDF app with annotation tools.
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Maria Miller, the author of the Math Mammoth books, is a math teacher turned homeschooler. She has a master's degree in mathematics with the teacher educational studies, and minors in physics and statistics. The aim of her math books is first and foremost to explain math in very simple terms, yet rigorously, concentrating on understanding of concepts.