# Graphing Systems of Linear Inequalities Activities

Instructor: Heather Jenkins

Heather has a bachelor's degree in elementary education and a master's degree in special education. She was a public school teacher and administrator for 11 years.

When students are learning about inequalities, consider teaching them how to graph systems of linear inequalities. Use these activities to help students graph systems of linear inequalities and interpret the graphs.

## Examining Possible Solutions

Whether it's a construction worker figuring out possible dimensions to meet a customer's demands or a financial officer exploring budget scenarios, graphing systems of linear inequalities is an important skill to learn.

When students learn how to graph systems of linear inequalities they can solve more complex mathematical problems that address different variables and criteria. Let's look at some activities to help students learn about graphing systems of linear inequalities.

## Jump Ropes and Chalk

Use this kinesthetic activity to help students graph systems of linear inequalities using jump ropes and sidewalk chalk.

### Materials

• Jump ropes
• Sidewalk chalk
• Coordinate grid
• Index cards

### Teacher Directions

#### Preparation

• Create index cards with a system of two linear inequalities written on each.

#### Activity

• Show students how to graph systems of linear inequalities using a coordinate grid.
• Divide the class into groups of four students and provide each group with two jump ropes and sidewalk chalk.
• Take students outside to a large paved area where students can use sidewalk chalk, such as a blacktop basketball court, a larger sidewalk, or an unused parking lot.
• Provide each group with one of the index cards you created.
• Students will use the sidewalk chalk to create a coordinate grid on the ground. They will use the jump ropes to represent the two linear inequalities from the system on their index card. Students will use sidewalk to shade in the appropriate areas of the coordinate grid that correspond to the inequalities on the index card.
• If space is a concern, students can create their graphs with the jump ropes inside by creating a coordinate grid on the floor of the classroom using tape. Instead of shading with sidewalk chalk, students can just point to the area(s) that would be shaded.

### Discussion Questions

• What steps did you follow to graph your system of linear inequalities?
• What was the most difficult part of graphing systems of linear inequalities?

## Linear Inequalities Art

Students can use their creative skills to design art by graphing systems of linear inequalities.

### Materials

• Copies of a coordinate grid
• Pencils
• Colored pencils

### Teacher Directions

• Draw two lines on a coordinate grid and color an area on the coordinate grid that could represent a system of linear inequalities.
• Model for students how to find the linear inequalities represented by each line and the system of linear inequalities that would include the colored area on the coordinate grid.
• Give each student a copy of a coordinate grid, pencils, and colored pencils.
• Have them draw two lines on the coordinate grid.
• Students should then choose a different color to color each section of the coordinate grid that was created drawing the lines (see example).
• Students should then determine a system of linear inequalities that would include each differently colored section of the coordinate grid.
• When students are finished, they should share their artwork with the class.

### Discussion Questions

• How did you go about determining the system of linear inequalities for each colored section?
• Why would someone need to figure out a system of linear inequalities that includes a certain point or set of points?

## States on a Map

Have students identify which graph of a system of linear inequalities would include specific points on a map.

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