Shodor Interactivate: Linear Inequalities

1. Engage: Start by asking students a real-world question where inequalities apply, such as, “If you had a limited budget to buy snacks for a party, how would you represent your spending limitations mathematically?”
2. Collaborate: Have students share their ideas with a partner or small group to discuss how inequalities can be used to represent real-world situations.
3. Discuss: Briefly introduce the idea that inequalities can be graphed just like equations but cover a range of values.

1. Explain: Give an overview of what a linear inequality is, focusing on how it differs from a linear equation.
2. Visualize: Show an example of a graph with a shaded region representing the solutions to a linear inequality.
3. Relate to Students: Explain that today, they will use an online tool to graph linear inequalities and verify their work.

1. Demonstrate: Show how to use the interactive graphing tool by inputting inequalities into the tool (project the steps on the screen for all to see).
   • Step-by-step, enter values in the boxes (before x, before y, select inequality sign, and last value).
   • Explain how the “Plot/Update” button works.
   • Show how inequalities are represented by a shaded region and how students can graph up to four inequalities at a time.
2. Interactive Practice: Ask students to suggest inequalities to graph, and plot them live to ensure comprehension.
3. Group Participation: Get students to vote or decide together which inequality to input.

1. Worksheet Activity: Hand out prepared worksheets with a list of linear inequalities for students to graph using the online tool.

Here is a list of linear inequalities for students to graph using the online tool:

1. 1. 2x+3y≤6
   2. −x+4y>8
   3. 3x−2y≥5
   4. x+y<4
   5. −2x+y≥−3
   6. 4x−5y≤10
   7. −3x+y>7
   8. 5x−y≤12
   9. x−3y>−2
   10. 2x+y≥3

• • Students work individually or in pairs to input the inequalities into the tool and graph them.

1. Collaboration: Encourage students to work in small groups, comparing their solutions and discussing how they derived them.
2. Real-Time Feedback: Walk around the classroom, offering guidance, answering questions, and helping troubleshoot any issues with the tool

1. Check Understanding: Once students have graphed all the inequalities, have them cross-check their work using graph paper and solve the same inequalities manually.
2. Discussion: Bring the class together and ask students to explain the solutions they found. Focus on identifying any common errors and troubleshooting them as a group.
3. Peer Review: Allow students to check each other's work in pairs, fostering peer feedback and correction.

1. Real-World Example: Challenge students to think of a real-life situation where linear inequalities apply (e.g., budgeting, limiting resources, etc.), and have them write an inequality to represent that situation.
2. Extended Learning: Suggest students explore inequalities in economics, like supply and demand curves, to see how this mathematical concept applies beyond the classroom.
3. Homework: Assign a real-world scenario for students to create and solve their own linear inequalities.