I’ve found that students have less trouble understanding these “rules” after working with temperature problems, for the rules make sense. Once students have done a fair amount of problems, gradually lead them to see two larger patterns: 1) If both numbers have the same sign, they keep the sign and add the numbers, and 2) If the numbers have different signs - one positive, the other negative - they take the sign of the larger number and subtract the numbers. When two negative integers are multiplied then also result. As long as the student has familiarity with temperatures and temps below 0, the student wills see that the new temperature will be – 7. Negative and Positive Rules When two positive integers are multiplied then the result is positive. Ask the student what the new temperature will be. 620 CE In India, the mathematician Brahmagupta created the first set of rules when working with positive and negative numbers. The second number, once again, tells how much the temperature changes during the day – 5 means the temperature FALLS 5 degrees. Tell students the first number is the temperature in the morning: – 2. That means they fall at either side of the number. Going back to examples, take another: – 2 – 5. Numbers higher than zero are called positive numbers, and numbers lower than zero are negative numbers. In time, try taking away the visual aid to see if students have internalized the temperature scale, thereby allowing them to do these kinds of problems in their mind. Students will use this as a vertical number line to figure out their answers, counting along the scale. When first using this approach, provide a temperature scale with 0 degrees in the middle, the positive temperatures above 0 and the negative temperatures below 0. Most students find it easy to intuitively see that the new temperature will be + 5 degrees, meaning the answer is + 5, or just 5. Ask the student what the new temperature will be. The second number tells how much the temperature changes during the day + 7 means the temperature ROSE 7 degrees. Using a temperature scale as a model for solving integer problems has several advantages:ġ) It’s a system students already know from everyday life.Ģ) The relationships among positive temperatures, negative temperatures, and 0 already make sense intuitively.ģ) Everything about how temperature works also works for positive and negative numbers. Kids struggle with positive and negative numbers … that’s a given.īut I’ve recently hit on a reliable way to eliminate the confusion … temperature.
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