Numbers can also be abstracted in a variety of ways, including mathematical objects like matrices and sets. In some sense, complex numbers mark the "end" of numbers, although mathematicians are always imagining new ways to describe and represent numbers. Rather, the word rational is related to the word found within the first five letters: ratio.Ī rational number is any number that can be written as the ratio of two integers, such as \(\fraci\)). The name has nothing to do with the numbers being sensible, although it opens up a chance to discuss ELA in math class and show how one word can have many different meanings in a language and the importance of being precise with language in mathematics. Notice that 0 is the only number whose opposite is itself.Įxpanding the concept of number further brings us to rational numbers. The integer numbers (or simply integers) extend whole numbers to their opposites too. Different people may give different names to these sets, even sometimes reversing which one they call natural and which one they call whole! Open it up to your students: what would they call the set of numbers 1, 2, 3.? What new name would they give it if they included 0? While these are standard terms, this is also a chance to share how math is ultimately a human endeavor. If we start counting from 0 instead, the set of numbers are instead called whole numbers. These are the counting numbers that start with 1, 2, and 3, and go on forever. The most common numbers that we encounter-in everything from speed limits to serial numbers-are natural numbers. The notion of number has evolved over millennia and has, at least apocryphally, cost one ancient mathematician his life. It was not always known, for example, how to write and perform arithmetic with zero or negative quantities. They are often our introduction into math and a salient way that math is found in the real world. But ask someone what math is, and you will almost always hear an answer involving numbers. It includes shapes, logic, symbols, spaces, and broad practices like critical thinking and attending to precision, along with applications far and wide in everything from physics to physical education. The Center for Model Schools (formerly ICLE)Ĭustomer Service & Technical Support Portal Into Algebra 1, Geometry, Algebra 2, 8-12 Science & Engineering Leveled Readers, K-5
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