How to Make a Concrete Model of Integers
Integers occur everyday, all around us---in temperature, elevation and time. Understanding integers can be difficult, but some concrete examples will make it easier.
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Instructions
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Drawing a Vertical Number Line for Integers
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Draw a straight vertical line down the center of your paper. This will be your number line.
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Mark a point that indicates zero. This can be anywhere along your line, but typically, it is in the center.
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Make increments along the line. Each increment measures the same distance. If you have a ruler, the increments could each be 1 inch or 1/2 inch in length. These increments will move away from your zero point, both above and below.
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Write numbers next to each increment above the zero point. For this to be a concrete example, it has to represent something in the real world. Mark your increments with degrees Celsius to make a thermometer. Count up from zero, marking each degree as you go (1°C, 2°C, 3°C, etc).
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Count backward to write the temperatures below zero. Start at the zero point and count down, writing a negative sign in front of each number (-1°C, -2°C, -3°C, etc).
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Make your vertical number line stand for anything that has a zero point. It could be an elevator in a building or the elevation above or below sea level.
Drawing a Horizontal Number Line for Integers
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Draw a horizontal number line. Remember to mark your zero point, and draw increments moving away from zero to the left and right.
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Write numbers next to each increment starting at zero, and moving right. To make it a concrete example, these number could stand for days after today. The number line would be marked: +1 day, +2 days, +3 days, etc.
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Count backward to write the days before the zero point (today). The number line would be marked: -1 day, -2 days, -3 days, etc.
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Make your horizontal number line stand for anything that has a zero point. It could be an train moving past a station or money in your bank account.
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Tips & Warnings
Your increments don't always have to count by 1. You can just as easily count by 2s, 5s or 10s.
Make sure you understand what your zero point stands for. All integers are measured as their distance from zero.
Draw your increments using the same space between each one.
