LEARN NC

K–12 teaching and learning · from the UNC School of Education

Graphing Inequalities

This is an activity I use when I need to get my students into groups of two and review inequalties and perpendicular slopes.

A lesson plan for grades 7–12 Mathematics

By Shirlyn Sullins

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Learning outcomes

To review perpendicular slopes and linear inequalities.
Sometimes I use this activity to get “partners” for another activity. This activity helps reinforce the concepts of parallel and perpendicular as well as shading of inequalities.

Teacher planning

Time required for lesson

20 minutes

Materials/resources

-Index cards (one per student)
-Small grids of coordinate axis-- approximately one quarter of a sheet of paper (one per student)
-Construction paper (one per couple)
-Colored pencils (opt.)
-A few glue sticks

Technology resources

None

Pre-activities

Students need to know how to graph linear inequalities.

Activities

1. Prior to class, write one linear inequality on each index card. Be sure that each is perpendicular to exactly one other card.

2. Hand each student a card, coordinate grid. Have them graph the equation they have on the small square of graph paper.

3. Once all of them have completed their graphs, they must find the graph of a line of one of their classmates that is perpendicular to theirs. This will be their partner.

4. They then mount both equations and both graphs on one sheet of construction paper. I hang these up with both names on them.

5. Students are then “partnered” with that person for the next activity.

Assessment

Assessment is easy. Usually before they glue the two lines on, the students will have checked each other. Before I mount them on the wall,I check the graphs and equations.

Supplemental information

none

Related websites

none

Comments

I use this as a refresher, and to get random groups of two. It is short, and after the first time can be done in less than twenty minutes.

North Carolina Curriculum Alignment

Mathematics (2004)

Grade 7

  • Goal 5: Algebra - The learner will demonstrate an understanding of linear relations and fundamental algebraic concepts.
    • Objective 5.02: Translate among different representations of algebraic expressions, equations and inequalities.
    • Objective 5.03: Use and evaluate algebraic expressions, linear equations or inequalities to solve problems.

Grade 8

  • Goal 5: Algebra - The learner will understand and use linear relations and functions.
    • Objective 5.01: Develop an understanding of function.
      • Translate among verbal, tabular, graphic, and algebraic representations of functions.
      • Identify relations and functions as linear or nonlinear.
      • Find, identify, and interpret the slope (rate of change) and intercepts of a linear relation.
      • Interpret and compare properties of linear functions from tables, graphs, or equations.
    • Objective 5.03: Solve problems using linear equations and inequalities; justify symbolically and graphically.
    • Objective 5.04: Solve equations using the inverse relationships of addition and subtraction, multiplication and division, squares and square roots, and cubes and cube roots.

Grades 9–12 — Algebra 1

  • Goal 4: Algebra - The learner will use relations and functions to solve problems.
    • Objective 4.03: Use systems of linear equations or inequalities in two variables to model and solve problems. Solve using tables, graphs, and algebraic properties; justify results.

Grades 9–12 — Integrated Mathematics 1

  • Goal 4: Algebra - The learner will use relations and functions to solve problems.
    • Objective 4.03: Use systems of linear equations or inequalities in two variables to model problems and solve graphically.

Grades 9–12 — Integrated Mathematics 2

  • Goal 4: Algebra - The learner will use relations and functions to solve problems.
    • Objective 4.01: Use systems of linear equations or inequalities in two variables to model and solve problems. Solve using tables, graphs, and algebraic properties; justify steps used.

Grades 9–12 — Introductory Mathematics

  • Goal 4: Algebra - The learner will understand and use linear relations and functions.
    • Objective 4.01: Develop an understanding of function.
      • Translate among verbal, tabular, graphic, and algebraic representations of functions.
      • Identify relations and functions as linear or nonlinear.
      • Find, identify, and interpret the slope (rate of change) and intercepts of a linear relation.
      • Interpret and compare properties of linear functions from tables, graphs, or equations.
    • Objective 4.03: Solve problems using linear equations and inequalities; justify symbolically and graphically.