Graphing Inequalities on a Number Line: Visualizing Solutions

Algebra 1 Grades High School 2:07 Video
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Lesson Description

This lesson teaches students how to represent and interpret inequalities on a number line. Students will learn to distinguish between strict and inclusive inequalities, and how to visually represent them.

Video Resource

How to plot inequalities on a number line | Pre-Algebra | Khan Academy

Khan Academy

Duration: 2:07
Watch on YouTube

Key Concepts

  • Inequalities and their symbols (>, <, ≥, ≤)
  • Number line representation
  • Open vs. closed circles on a number line
  • Interpreting the solution set of an inequality

Learning Objectives

  • Students will be able to identify and differentiate between the inequality symbols.
  • Students will be able to represent inequalities on a number line correctly.
  • Students will be able to interpret the meaning of a graphed inequality in context.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the meaning of inequality symbols (>, <, ≥, ≤) and their corresponding verbal descriptions (greater than, less than, greater than or equal to, less than or equal to). Ask students to provide real-world examples of situations involving inequalities (e.g., age restrictions, speed limits).
  • Video Presentation (7 mins)
    Play the Khan Academy video: 'How to plot inequalities on a number line | Pre-Algebra | Khan Academy'. Instruct students to take notes on the key concepts presented in the video, especially the difference between open and closed circles on the number line.
  • Guided Practice (10 mins)
    Work through example problems on the board, demonstrating how to graph inequalities on a number line. Emphasize the importance of choosing the correct circle type (open or closed) and shading the correct direction. Examples: x > 3, y ≤ -2, z ≥ 0, a < 5.
  • Independent Practice (10 mins)
    Provide students with a worksheet containing various inequalities. Have them graph these inequalities on number lines. Circulate to provide assistance and answer questions.
  • Discussion and Wrap-up (8 mins)
    Lead a class discussion to review the concepts covered in the lesson. Address any remaining questions or misconceptions. Preview the next lesson on solving inequalities.

Interactive Exercises

  • Number Line Game
    Divide the class into teams. Provide each team with a number line and a set of inequality cards. Teams take turns drawing a card and graphing the inequality on the number line. The first team to correctly graph the inequality wins a point.
  • Inequality Match
    Create cards with inequalities and corresponding number line graphs (some correct, some incorrect). Students must match the correct inequalities with their corresponding number line representations.

Discussion Questions

  • How does the symbol used in an inequality (>, <, ≥, ≤) affect its representation on a number line?
  • Explain the difference between an open circle and a closed circle when graphing inequalities. When do you use each?
  • Can you think of a real-world situation that can be modeled by an inequality? How would you represent it on a number line?

Skills Developed

  • Visual representation of mathematical concepts
  • Critical thinking and problem-solving
  • Understanding of inequality symbols and their meanings
  • Number sense and fluency

Multiple Choice Questions

Question 1:

Which of the following inequalities represents 'x is greater than 5'?

Correct Answer: x > 5

Question 2:

On a number line, how is 'x is less than or equal to 2' represented at the point 2?

Correct Answer: Closed circle

Question 3:

Which inequality is represented by an open circle at -3 on a number line, with the line shaded to the right?

Correct Answer: x > -3

Question 4:

What does the inequality symbol '≥' mean?

Correct Answer: Greater than or equal to

Question 5:

Which of the following values is a solution to the inequality x < 7?

Correct Answer: 6

Question 6:

How would you represent 'x is at least 10' as an inequality?

Correct Answer: x ≥ 10

Question 7:

Which inequality is represented by a closed circle at 4 and shaded to the left?

Correct Answer: x ≤ 4

Question 8:

Which of the following is NOT a solution for x > -2?

Correct Answer: -2

Question 9:

What does an open circle on a number line signify when graphing an inequality?

Correct Answer: The value is not included in the solution

Question 10:

Which inequality means 'x is no more than 3'?

Correct Answer: x ≤ 3

Fill in the Blank Questions

Question 1:

The symbol '>' means _________ than.

Correct Answer: greater

Question 2:

On a number line, a closed circle indicates that the value is _________ in the solution set.

Correct Answer: included

Question 3:

The inequality 'x ≤ 5' means that x is less than or _________ to 5.

Correct Answer: equal

Question 4:

An open circle on a number line means that the boundary point is _________ from the solution.

Correct Answer: excluded

Question 5:

The inequality 'x ≥ -2' includes all numbers that are greater than or equal to _________.

Correct Answer: -2

Question 6:

When graphing 'x < 4' on a number line, you would use a(n) _________ circle at 4.

Correct Answer: open

Question 7:

If an inequality includes the possibility of the number being equal to the constant, then the circle is _________.

Correct Answer: closed

Question 8:

The values that make an inequality true are called the _________ set.

Correct Answer: solution

Question 9:

The phrase 'at least' is represented by the symbol _________.

Correct Answer: ≥

Question 10:

The phrase 'no more than' translates to the inequality symbol _________.

Correct Answer: ≤

Educational Standards

A1.A.2:Represent and solve real-world and mathematical problems using linear inequalities and compound inequalities; interpret solutions in the original context. A1.A.2.1:Represent relationships using mathematical models with linear inequalities; solve the resulting inequalities, graph on a coordinate plane, and interpret the solutions. A1.A.2.2:Represent relationships using mathematical models with compound and absolute value inequalities and solve the resulting inequalities by graphing and interpreting the solutions on a number line.

Teaching Materials

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