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Inequalities and Numbers Lines

6.NS.C.7a
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Aligned To Common Core Standard:

Grade 6 Numbers - 6.NS.C.7a

How to Write Inequalities on Numbers Lines - Suppose you are starting to take care of your health, and you have decided to reduce your calorie intake. So, let us suppose that the number of calories I am allowed to eat on a given day is represented by the letter C. C = number of calories And we want to lose some weight so. We want to consume less than 1500 calories a day. So how can this be expressed as an inequality? We can write this as: C < 1500 If we want to include 1500 in the mix as well and not just the values that are less than 1500, then we write - C ≤ 1500 If we want to write an inequality on a numbers line. Suppose we are plotting A > 4, then the plot on the numbers line would be an open circle with an arrow pointing the right of 4 and extending to the end of the line. Suppose If we are going for A ≤ 3. The plot on the number line would be a closed circle and an arrow pointing the end of the number line to the left. Pay attention that when we don't include the limit we defined, it is denoted by an open circle but, when adding the limit in the list of values, it is a filled circle.

Printable Worksheets And Lessons




Homework Sheets

The open and closed bubble is what gives most kids trouble.

  • Homework 1 - What inequality does this number line show?
  • Homework 2 - A filled-in circle includes the number it is located on. An open circle does not include the number it is located on.
  • Homework 3 - We want to write an inequality that says x can be anything shown by the arrow and circle.



Practice Worksheets

This skill gives many students great difficulty.

  • Practice 1 - A filled-in circle includes the number it is located on. An open circle does not include the number it is located on.
  • Practice 2 - The arrow pointing to the right means that x can also be any number greater than or equal to the value indicated.
  • Practice 3 - What inequality does this number line show?



Math Skill Quizzes

Once students have no trouble writing an inequality from a numbers line, they are good to go on this skill.

  • Quiz 1 - Explain each number line as an inequality.
  • Quiz 2 - You will explain what you see in a numeric expression.
  • Quiz 3 - More practice to see if you have this skill down.


Why Do We Graph Inequalities on a Number Line?

We first must understand what an inequality truly is to understand why we do this. Inequalities are equations that just are not equal or are lopsided. They state can start that one side is either less than or greater than the other. It can also state that we have a good idea but are not exactly certain the differences in value. This is displayed by using the greater than or equal to and less than or equal to values. They can also just not be equal to each other. When these values are expressed in a standard numeric inequality they can be read and understood. When we want to visualize this for ourselves or others to better communicate the notion, we use a number line to help explain the range of where the possible solution could be found. This will become much more helpful when you are beginning to consider the possibilities of compound inequalities. Which is composed of two or more statements. Visuals, in this case, are not only helpful but necessary to help understand possible solutions.