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Math Mammoth Subtraction 1 deals with various concepts related to basic subtraction, and with basic addition and subtraction facts within 0-10. Most of the problems in the book only use numbers up to 10, but a few include numbers between 10 and 20.
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.
The concept of subtraction is easy to illustrate with the idea of "taking away". If your child does not yet know the word "minus", it is a good idea to introduce it first orally. Simply use blocks, rocks, or other concrete objects. For example, show the child eight blocks, and take away three blocks. Then use both kinds of wordings: "Eight blocks, take away three blocks, leaves five blocks. Eight blocks minus three blocks equals five blocks."
Play with the blocks or other concrete objects until the child can use the words "minus" and "equals" in his/her own speech. This will make it much easier to introduce the actual written symbols.
The next step would be to abandon concrete objects and use semi-concrete illustrations or pictures. That is where this book starts with the lesson Subtraction Is "Taking Away". At this stage, the child can still figure out the subtraction problems by simply counting how many objects are left.
So, how does the student learn how to subtract without actually counting concrete objects or pictures? As a transitional strategy, we will study counting down: the student solves 9 − 3, for example, by counting down three steps from nine: eight, seven, six. So the answer is six.
However, the final goal is to learn to use the addition facts to find the answer to subtraction problems. For example, once the student knows that 5 + 5 = 10, then this fact is used to solve 10 − 5 = 5. For this purpose, the student must learn well the connection between addition and subtraction. This is why this book concentrates heavily on the connection between addition and subtraction with several lessons, ending up with the concept of fact families.
Besides "taking away", subtraction is also used for these two situations:
- Finding how much more one number is than another. Note that no one "takes away" anything in this situation. For example, if you have 3 dollars and you need 6 dollars, how many more dollars do you need? The student is instructed to write a "how many more" addition problem for this, which looks like this: 3 + ___ = 6. We also call these problems "missing addend" problems. It can be solved by remembering the addition fact 3 + 3 = 6, or by subtracting 6 − 3 = 3.
- Two (or more) parts (of something) make up a whole. If you know the whole and one of its parts, you can figure out the other part. For example, if there are 10 white and red flowers, and seven of them are white, how many are red? We know the "parts" (the red and white flowers) add up to 10, so we write an addition 7 + __ = 10. Again, this can be solved by subtracting, or simply by knowing the addition fact 7 + 3 = 10.
These two situations are dealt with in several lessons in the book and are found in various word problems throughout the book.
In the latter part of the book, we encounter several lessons named Addition and Subtraction Facts with... They aim at helping the child to memorize the basic addition and subtraction facts. We are approaching it from the concept of fact families.
These lessons have a lot of practice problems. Use your judgment as to whether your child will need to do all of the problems. If he/she masters the facts quickly, you can skip some of them.
Besides the written problems, I encourage you to use games that are explained below. Children like to play, and using the addition and subtraction facts in a game gives them fun and education in the same "package".
While this book is not tied to any grade level, it is most suitable for first grade.
About the Seller
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.