Compound Inequalities on the Number Line

Learning Resource Type

Classroom Resource

Subject Area

Mathematics

Grade(s)

8, 9, 10, 11, 12

Overview

In this Desmos activity, students explore compound inequalities and make connections among multiple representations (including algebraic expressions, verbal statements, number line graphs, and solution sets). There are a series of 3 videos available to fully teach this concept. The videos are labeled "Inequalities on the Number Line," "Compound Inequalities on the Number Line," and "Absolute Value Inequalities on the Number Line." This activity should be used to help teach a lesson on solving linear inequalities. This Desmos activity offers sample student responses and a teacher guide.

Mathematics (2019) Grade(s): 8 - Grade 8 Accelerated

MA19.8A.13

Create equations and inequalities in one variable and use them to solve problems in context, either exactly or approximately. Extend from contexts arising from linear functions to those involving quadratic, exponential, and absolute value functions. [Algebra I with Probability, 11]

UP:MA19.8A.13

Vocabulary

  • Inequality
  • Variable
  • Solution set
  • Linear relationship-Quadratic relationship
  • Exponential relationship
  • Absolute value

Knowledge

Students know:
  • When the situation presented in a contextual problem is most accurately modeled by a linear, quadratic, exponential, or absolute value relationship.

Skills

Students are able to:
  • Write equations or inequalities in one variable that accurately model contextual situations.
  • Solve equations and inequalities.

Understanding

Students understand that:
  • Features of a contextual problem can be used to create a mathematical model for that problem.
Mathematics (2019) Grade(s): 8 - Grade 8 Accelerated

MA19.8A.15

Represent constraints by equations and/or inequalities, and solve systems of equations and/or inequalities, interpreting solutions as viable or nonviable options in a modeling context. Limit to contexts arising from linear, quadratic, exponential, absolute value, and linear piecewise functions. [Algebra I with Probability, 13]

UP:MA19.8A.15

Vocabulary

  • Constraints
  • System of equations
  • System of inequalities
  • Solutions
  • Feasible region
  • viable and non
  • viable options
  • linear
  • quadratic
  • Exponential
  • Absolute value
  • linear piecewise
  • Profit
  • Boundary
  • Closed half plane
  • Open half plane
  • Half plane
  • Consistent
  • Inconsistent
  • Dependent
  • Independent
  • Region

Knowledge

Students know:
  • When a particular system of two variable equations or inequalities accurately models the situation presented in a contextual problem,
  • Which points in the solution of a system of linear inequalities need to be tested to maximize or minimize the variable of interest.

Skills

Students are able to:
  • Graph equations and inequalities involving two variables on coordinate axes.
  • Identify the region that satisfies both inequalities in a system.
  • Identify the point(s) that maximizes or minimizes the variable of interest in a system of inequalities.
  • Test a mathematical model using equations, inequalities, or a system against the constraints in the context and interpret the solution in this context.

Understanding

Students understand that:
  • A symbolic representation of relevant features of a real-world problem can provide for resolution of the problem and interpretation of the situation and solution.
  • Representing a physical situation with a mathematical model requires consideration of the accuracy and limitations of the model.
Mathematics (2019) Grade(s): 09-12 - Algebra I with Probability

MA19.A1.11

Create equations and inequalities in one variable and use them to solve problems in context, either exactly or approximately. Extend from contexts arising from linear functions to those involving quadratic, exponential, and absolute value functions.

UP:MA19.A1.11

Vocabulary

  • Variable
  • Equation
  • Inequality
  • Solution Set
  • Identity
  • No solution for a given domain
  • Approximate solutions

Knowledge

Students know:
  • When the situation presented in a contextual problem is most accurately modeled by a linear, quadratic, exponential, or rational functional relationship.

Skills

Students are able to:
  • Write equations in one variable that accurately model contextual situations.

Understanding

Students understand that:
  • Features of a contextual problem can be used to create a mathematical model for that problem.
Mathematics (2019) Grade(s): 09-12 - Algebra I with Probability

MA19.A1.13

Represent constraints by equations and/or inequalities, and solve systems of equations and/or inequalities, interpreting solutions as viable or nonviable options in a modeling context. Limit to contexts arising from linear, quadratic, exponential, absolute value, and linear piecewise functions.

UP:MA19.A1.13

Vocabulary

  • Constraint
  • System of equations
  • System of inequalities
  • Profit
  • Boundary
  • Closed half plane
  • Open half plane
  • Half plane
  • Consistent
  • Inconsistent
  • Dependent
  • Independent
  • Region

Knowledge

Students know:
  • When a particular system of two variable equations or inequalities accurately models the situation presented in a contextual problem.
  • Which points in the solution of a system of linear inequalities need to be tested to maximize or minimize the variable of interest.

Skills

Students are able to:
  • Graph equations and inequalities involving two variables on coordinate axes.
  • Identify the region that satisfies both inequalities in a system.
  • Identify the point(s) that maximizes or minimizes the variable of interest in a system of inequalities.
  • Test a mathematical model using equations, inequalities, or a system against the constraints in the context and interpret the solution in this context.

Understanding

Students understand that:
  • A symbolic representation of relevant features of a real-world problem can provide for resolution of the problem and interpretation of the situation and solution.
  • Representing a physical situation with a mathematical model requires consideration of the accuracy and limitations of the model.

CR Resource Type

Learning Activity

Resource Provider

Desmos

License Type

Custom
https://teacher.desmos.com/activitybuilder/custom/57b7f808ce9904f705558c4e

Custom License Type (URL)

https://www.desmos.com/terms

Accessibility

Text Resources: Content is organized under headings and subheadings

Comments or Notes

Desmos's mission is to help every student learn math and love learning math. Teachers can explore and enjoy Desmos collections of free digital math activities that include:

  • Meaningful feedback by showing students what their answers mean, then give them the opportunity to improve their thinking and revise their work.
  • Collaboration by using devices to connect students, not to isolate them. Students see their classmates' thinking. They ask each other questions and create challenges for each other.
  • Invite students to solve challenging problems using the tools they already have.

If the teacher does not have an account, he/she will need to create a FREE account. (More information on how Desmos works can be found at Getting Started.)

Once the teacher has selected an activity to run, he/she will need to click on the "Create Class Code" button. This will generate a unique class code and a link to view the dashboard. (More information can be found at Creating a Class Code.) Every new activity will need a new class code in order to start a session. Students cannot start the activity until they have the class code so sessions can be started days, hours, or mere minutes before the teacher plans to run the activity. When the teacher is ready to have students start, have the students go to student.desmos.com and enter the class code. Although it is not required, Desmos strongly encourages students to sign in with their Desmos Student Account. Signing in allows students to resume and view their past activity work. 

Approved Date

Owner (Author)

yvetteakridge
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