A in Math

Price = $10

This math book teaches the Decimal Place Value – the system by which we name numbers. It is a critical book even though it is a simple one. It is also the ONLY book of its type. No other book explains ALL the mathematical ideas and rules associated with the Decimal Place Value system.

Often, problems with Operations, Decimals, or later with Algebra or Calculus, have roots in not understanding the Decimal Place Value system well. The concepts of numbers, and how they work, can be tricky. If those concepts are not understood well, then later, when they are needed in order to understand other concepts, problems arise. The Decimal Place Value Systems is not a trivial one! It took mathematicians many centuries to get it right, especially because the concept of Zero had to be understood well before the system could work well.

This Place Value (Decimal) book explains this concept of zero (more than one idea, actually) as well as positive and negative numbers, although for a full explanation of those you should buy the Integers book.

This math book has place value worksheets or exercises as part of it. Each lesson is followed by a place value worksheet to be completed. The explanations are done with place value charts illustrating the ideas, and are very graphic in nature.

By the end of the book, even 6 – 7 years olds can name or write numbers with 18 digits! They may not be able to yet understand all the concepts fully, but they will understand how numbers work. It is recommended that students at 3 – 5 grades read it again, and then just before starting Algebra.
If a student has problems with Operations (most pronounced in long division), Decimal Fractions, variables in Algebra, or Calculus, it is recommended that they first study the Decimal Place Value book. How we think about variables is strongly affected by how we think about numbers, a connection not made, understood, discussed, or treated in the education system.

You get pagesand practice questionsand it only takes AT MOST 5 Hours!!! (Including doing all the practice questions)

Q: Who is it intended for?

It is intended for three groups:

• For 1 - 2 graders who will love being able to name and write HUGE numbers. They enjoy this power :-) They will go around to adults (or older siblings!) and challange them - I have seen it happen with my own kids and other parents reported a similar phenomenon.

• For 3 - 5 graders who studied the Ones-Tens-Hundred type of books about Place Value and are ready to learn the full ideas behind Place Value.

• For higher grades students who have mastered the mechanics of the decimal system but most likely do not know and understand all the ideas behind Place Value, since no other book teaches it.

• For parents and teachers who are working with their children or students on Place Value and could use a guide book about the mathematical ideas of the system; ideas that can be quite complex and abstract.

Q: Why does my child need to know that? After all, s/he knows how to count and write numbers.

The Place Value system is the basis for our system of numbers. Without fully understanding it, your child would not fully understand many concepts that come later, such as derivatives in calculus, or the roots of a cubic equation.

Q: What is the difference between your book and all the other books?

It is easy to answer since NO OTHER book fully explains the Place Value System. The way all books teach it is through the one idea of grouping, then doing many exercises about Ones and Tens, then Ones-Tens-Hundreds (and possibly Thousands). However, the Place Value system is complex and took the efforts of many great mathematicians over millennia. The concept of Zero was not developed in most of those cultures (including the Greeks) and division by Zero, which is meaningless, was completely misunderstood, and is often still so. This book is the only book I know of that explains the Place Value System completely and thoroughly in a way that children can understand.

Q: How do I know if my child, who knows numbers and Place Value, needs the book? And how do I know if I need it?

To check whether your children need it, check their understanding and knowledge of the following three questions:

1. What is the meaning of Zero? [You should have two answers, not one...]
2. Can you divide by Zero? If yes, what is the result? If no, why? [The answer is you cannot...]
3. What are the rules/ideas of the Place Value system? [You should have 5-6 depending on how the answer is phrased]

If your child knows the answers to those questions, then you should not buy the Place Value book, but if s/he doesn't, then you should but it to ensure their deeper understanding of the Place Value System, and therefore better understanding of other concepts in Math.