NUMBERLINE AN IMPORTANT TOOL*
*One driving goal for elementary level mathematics education is to help children develop a rich understanding of numbers – their meanings, their relationships to one another, and how we operate with them.
One of the most overlooked tools of the elementary and middle school classroom is the number line. Typically displayed above the chalkboard right above the alphabet, the number line is often visible to children, though rarely used as effectively as it might be. When utilized in the elementary classroom, the number line has often used to help young children memorize and practice counting with ordinal numbers. Less often, perhaps, the number line is used like a ruler to illustrate the benchmark fractions like ½ or ¼. Beyond an illustration for these foundational representations of whole numbers and some fractions, however, the number line is underutilized as a mathematical model that could be instrumental in fostering number sense and operational proficiency among students.
importance of the number line as a tool for helping children develop greater flexibility in mental arithmetic as they actively construct mathematical meaning, number sense, and understandings of number relationships. Much of this emphasis has come as a result of rather alarming performance of young learners on arithmetic problems common to the upper elementary grades. For example, a study about a decade ago of elementary children in the Netherlands – a country with a rich mathematics education tradition – revealed that only about half of all students tested were able to solve the problem 64-28 correctly, and even fewer students were able to demonstrate flexibility in using arithmetic strategies. These results, and other research like them, prompted mathematics educators to question existing, traditional models used to promote basic number sense and computational fluency. Surprising to some, these research findings suggested that perhaps the manipulatives and mathematical models typically used for teaching arithmetic relationships and operations may not be as helpful as once thought. Base-10 blocks, for example, were found to provide excellent conceptual understanding, but *weak procedural representation of number operations.
Number line, is a wonderful concept for learning mathematics & spiritual science as well.
Anyone who tells you math is only about numbers is not telling you the whole truth. In the case of number lines, it’s also important to know your left from the right, as this is the whole basis of the concept. You see, a number line helps students decide which number is greater or larger. The further to the right a number falls on a number line, the greater it is. On the other hand, the further to the left a number falls on the line, the smaller it is.
The bottom line is that number line gives you a visual picture to determine whether two or more numbers are greater or smaller than the others *. Think of it as a number map letting you know the value of numbers in comparison to each other. However, beyond the simplistic usage most elementary school children master early on, the number line has more complex usages. In fact, our friend the number line models all real numbers, from -16,000 to 275 trillion and beyond. *The number line shouldn’t be confused counters, as counters do just that; they count. But, the number line is also about measurement, making it necessary to start with our hero, zero.
To paint a picture of this, when you’re counting items, you don’t start with 0. No, you start at 1. But when measuring, such as with a ruler, we line up the ruler at one end of the object, marking it Zero
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Now when you see a number line, you may think, hmmm, there are more numbers than that! A number line has the arrow on both sides for a reason. It shows that numbers go on forever. Additionally, just because there are small spaces between the numbers doesn’t mean other “numbers” don’t exist between them. After all, 1/2 or .5 could between the 0 and the 1. All numbers, fractions and decimals can also be placed on a number line.
Speaking of fractions, a common problem a great many students have is when they’re asked to put 1/2 on a number line. Their natural inclination is to put it between the 1 and the 2. However, of course, the right placement would be between the 0 and 1. This could be because 1 and 2 are the two numbers used in the 1/2 phrase or maybe because the common train of thought is that 1/2 means one of two.
It’s important to gain a good grasp of the number line early on in a child’s education, preparing him for use later on in high school Geometry and beyond. For example, math students will often scale numbers on the line with a logarthmic scale and using the scientific notation. They can use this method to show a sequence of events, such as in the history of the world, evolution, or distances to planets or stars etc. *
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Jai Hind Resp. sir..
Here I would like to add some extra important of Zero…😊
1) As a number, zero means nothing – the absence of other values. It plays a central role in mathematics as the identity element of integer, real number, and many other algebraic structures. As a digit, zero is used as a placeholder in the location value system. Historically, this was the last point in use..
2) Zero represents the absence of things. Zero is also an essential element of our number system. … Zero as a number on its own is also extremely important in maths. Zero is the ‘additive identity’, meaning any time I add a number to zero, I get that number back: 3 + 0 = 3.
3) Having a zero makes sense because if there were no zeros, a number line would go from -1 to 1 with nothing bridging the gap. … Without the zeros, one billion would just be 1. So zero is a placeholder, and therefore has a lot of value. Because “1” is nothing in 1,000,000,000 unless the zeros are there..
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