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A number line is a useful tool for teaching arithmetic, including fractions and negative numbers. It can be a line or segment with positive numbers to the right and negative to the left. Children learn to draw coordinates on the line, which helps with graphing and understanding (x, y) axes.
A number line can be a line of any length listing positive and sometimes negative numbers. Such lines are commonly used for young children learning arithmetic functions such as addition and subtraction. They are also used when children are being taught “intermediate numbers” such as fractions. Being able to draw fractions or decimals on a line is a useful way to understand the true size of a fraction and its comparative nature with other fractions.
In the standard horizontal number line, zero is called the origin. The points to the right of the origin are positive numbers and the points to the left are negative numbers. Any number drawn on the line is called a coordinate. At the beginning of counting, children can simply learn to draw coordinates on a line. The line is usually terminated on each side with arrows, suggesting that the line could continue essentially forever to either the left or right.
Sometimes, in early math lessons, the number line is not a line but a line segment or radius. The zero origin point is the start of the line and is indicated by a dot rather than an arrow pointing to the side of the negative number. This is usually done to help young children with basic counting skills, as the concept of negative numbers isn’t introduced until children are in the fourth or fifth grade.
When negative numbers are being taught, the number line can be a useful aid as one can simply count the coordinates to arrive at the appropriate answer. For example, if a child is given problem 5-7, she can count seven spaces backwards to arrive at the appropriate answer of -2. Similarly, the -3 + 4 problem can be solved by counting forward four spaces to arrive at the +1 answer. Note that this will only work when the coordinates on the number line are integers or the child knows not to count coordinates that are not integers.
Learning to use a number line is great preparation for learning how to graph numbers. When students are learning to graph coordinates, their familiarity with the horizontal number line makes it easier to understand vertical number lines and the intersection of two numbers that are based on an (x, y) axis. Sometimes, in preparation for learning how to find coordinates, students work for a short time with vertical rather than horizontal lines, so their familiarity with finding numbers from left to right and bottom to top increases.
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