Math Problems With Positives and Negatives

Thermometers are often used for problem solving with negative numbers.
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In math, numbers can be classified as positive or negative based on their value in relation to zero and position on the number line. The symbol (-) is placed in front of negative numbers at all times. The symbol (+) may or may not be placed in front of positive numbers, and numbers without a symbol are assumed to be positive. When introduced to problems using negative numbers, a number line is a helpful tool for students to use.


Temperature is measured with a thermometer that resembles a number line. Temperatures above zero are considered positive while those below zero are negative. Math problems with temperatures involve real world examples of temperature change. For example, on a cold day the morning temperature is -3 degrees. Ask your students to determine the temperature if it increases by 12 degrees. Students can use the thermometer, as a number line, to count up 12 degrees to see that the new temperature is +9 degrees or 9 degrees above zero.


Problems involving money are useful to reinforce the concept of positive and negative numbers. Saving or depositing money in an account is expressed as addition, and a balance above zero is a positive value. Spending or withdrawing money is expressed as subtraction, and being in debt or owing money is an example of a negative balance. A savings account starts off with a positive balance of $25. If you write a check for $35, the account will show a negative balance of -$10.


Measuring altitude involves positive and negative number applications. Mountains can be measured as above sea level with a positive number while land below sea level can be measured with negative numbers. Give students the following problem: if you are on land at 40 feet above sea level and travel to land that is 10 feet below sea level, how far did you travel? By using a number line, students can determine that they traveled 40 feet to get to sea level and another 10 to get to the distance below sea level. Adding 40 feet to 10 feet results in a total distance traveled of 50 feet.

Modeling With Chips

Students can use manipulatives to model adding and subtracting positive and negative numbers. Using a number line, red chips to model negative numbers and blue chips to model positive numbers, students can add and subtract them. For example, starting with three red chips to represent -3, students can model adding five by first getting back to zero with the three red chips, then using two blue chips. This represents that - 3 plus 5 is equal to +2.

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