Sample pages (PDF)
Contents & Introduction
Adding with Whole Tens
Going Over Ten
TwoDigit Numbers Ending in 9
Regrouping in Subtraction 1
Mental Subtraction Methods
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Math Mammoth Add & Subtract 2B is a continuation to the book Math Mammoth Add & Subtract 2A. The goal of this book is to study addition and subtraction within 0100, both mentally and in columns, especially concentrating on regrouping in addition (carrying) and in subtraction (borrowing).
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.
Mental math is important because it builds number sense. This book includes many lessons that practice mental math. For example, the child practices adding and subtracting twodigit numbers when one of the numbers is a whole ten (problems such as 30 + 14, or 66 − 20).
Also studied are problems such as 36 + 8 or 45 + 9. These problems use the idea of going over ten as in problems 6 + 8 and 5 + 9. The child knows that 6 + 8 fills the first ten and is four more than the ten. He/she will learn to use that fact when adding 36 + 8. The sum 36 + 8 fills the next whole ten (40), and is four more than that, or 44.
Simultaneously with this, the child learns adding twodigit numbers in columns, and regrouping with tens, or "carrying," which is illustrated and explained in detail with the help of visual models. These visual models take the place of baseten blocks or other manipulatives. You are welcome to use manipulatives to get the idea across, if you prefer. The main concept to understand is that 10 ones are regrouped to form a new ten, and this new ten is written using a little "1" in the tens column.
The next lessons teach subtracting in columns. First we only deal with the easy problems where you don't need to regroup (borrow). Then the following lessons practice in detail the process of regrouping or borrowing. You can use either term with your child, or even choose not to use either if you feel it is confusing. You can alternatively use the phrase "breaking a ten into ten ones."
First, the lesson Regrouping practices breaking down a ten into ten ones because we cannot subtract from the ones. It is crucial that the child understands what happens here. Otherwise, he/she might end up only memorizing the procedure, and will probably at some point misremember how it was done. That is why this lesson deals with the regrouping process in detail with plenty of visual exercises.
If you notice that the child does not understand the concept of regrouping, he/she may need more practice with concrete manipulatives or visual exercises before proceeding.
After learning regrouping, we practice mental subtraction in three separate lessons. One of them expounds on several methods for mental subtracting. Another is about Euclid's game—a fun game that also practices subtraction of twodigit numbers.
The video below shows a similar idea as to what is in the book about regrouping (borrowing).
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In other words, you are permitted to make copies for the students/children you are teaching, but not for other teachers' usage.
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