## Understanding Positive and Negative Numbers

#### Grade 6 Numbers - 6.NS.C.5

What Is the Difference Between Positive and Negative Numbers? We are all familiar with the plus and minus signs. We use these signs to add values together or find the difference between two values. These same signs can also be used to tell us the nature of a quantity as well. Numbers can broadly have a positive and/or negative presence in a system. Positive numbers have a plus sign and negative numbers have a minus sign with them. If no visible sign appears in front of them, it is assumed to be positive. Let's visualize the difference with the help of a number line. Any number that moves to the right of the number line is considered to be positive. And any number that runs to the left of the number line asserts a negative tone. Let us have a clearer idea of how the number line works. When adding two numbers on a number line, we go to the first addend, and from there we walk all the way to the second addend. Thus, for 5 + (-3) we will start at 5 and go three units to the left-to reach at our result at +2. So as we can see these are simple measures of how far from 0 these values are, in one direction or another.

### Printable Worksheets And Lessons

#### Homework Sheets

It was very difficult coming up with unique problem types and situations for these.

• Homework 1 - Max buys shares of Enron at \$785 on Monday. On Thursday, the stock falls to \$464, so he sells his shares. How much did he lose?
• Homework 2 - When the number is negative it means the quantity is decreasing. If the quantity increases that means the value is positive. So if the temperature drops that means the value is decreasing.
• Homework 3 - If the temperature were to drop 38 degrees, which number would display this best?

#### Practice Worksheets

We break out the number lines here to help make it clear for students.

• Practice 1 - Complete the following operation using the number line. They have a range of + to - 13.
• Practice 2 - We bring in decimals to see if that throws them off.
• Practice 3 - A mix of real world word problems and number lines.

#### Math Skill Quizzes

I have been petitioning the standards committee to consider a vertical numbers line. I see them online all the time.

• Quiz 1 - Display each value as an integer. These are real situations that you may come in contact with.
• Quiz 2 - 450 feet below sea level. The first problem will stump you.
• Quiz 3 - The stock market falls 66,864 points today. Wow! That is a bad day!

### When Will You Be Confronted with Negative Numbers in the Real World?

When students first come across the concept of a negative value, they are quickly confused because it is a little off from where they began their concept about integers. One of the first situations where you have to contemplate the meaning of a negative value is in the realm of temperature. If you are in a country that follows the metric system, you will see it more regularly, especially if you are far away from the equator. Negative values of the Celsius scale of temperature are cold. If you are on in a system that revolves around the Fahrenheit scale, those negative temperature values are overwhelming cold. As we can quickly realize negative values are somewhat relative to the scale you use to quantify it. You will also commonly ponder negative values in situation where you are quantifying financial values. This can be when you are measuring your bank balance or overall income. In most cases that is not a good thing. Vertical elevation is another place that we see this. If we think of sea level as the zero in our scale, it is an easy concept to grasp. There are many games that students play that also have values that can reduce their overall skill. They are often used to assess penalties or faults that they endure. When we are working with students it is often helpful to bring these real world measures to light to help them understand the of overall abstract nature of this concept.