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Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. ★
Standard #: MAFS.912.A-CED.1.2Archived Standard
Standard Information
General Information
Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Algebra: Creating Equations
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Create equations that describe numbers or relationships. (Algebra 1 - Major Cluster) (Algebra 2 - Supporting Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
Date Adopted or Revised: 02/14
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes
Related Courses
Related Resources
Educational Software / Tool
  • Free Graph Paper # A variety of graph paper types for printing, including Cartesian, polar, engineering, isometric, logarithmic, hexagonal, probability, and Smith chart.
Formative Assessments
  • Trees in Trouble # Students are asked to write a function that represents an annual loss of 3 percent each year.
  • Loss of Fir Trees # Students are asked to sketch a graph that depicts the exponential decline in the population of fir trees in a forest.
  • Model Rocket # Students are asked to graph a function in two variables given in context.
  • Hotel Swimming Pool # Students are asked to write an equation in two variables given a verbal description of the relationship among the variables.
  • Tech Repairs Graph # Students are asked to graph an equation in two variables given in context.
  • Tee It Up # Students are asked to write an equation in three variables from a verbal description.   Note: This task may assess skills that exceed the general expectation for this mathematical concept at this grade level.  The task is intended for students who have demonstrated mastery within the scope of instruction who may be ready for a more rigorous extensions of the content. As with all materials, ensure to gauge the readiness of students or adapt according to students needs prior to administration.
  • Tech Repairs # Students are asked to write an equation in two variables from a verbal description.
Lesson Plans
  • Compacting Cardboard # Students investigate the amount of space that could be saved by flattening cardboard boxes. The analysis includes linear graphs and regression analysis along with discussions of slope and a direct variation phenomenon.
  • Home Lines # Students will create an outline of a room and write equations of the lines that contain the sides of the room. This lesson provides an opportunity to review and reinforce writing equations of lines (including horizontal and vertical lines) and to apply the relationship between the slopes of parallel and perpendicular lines.
  • The Gumball Roll Lab # This lesson is on motion of objects. Students will learn what factors affect the speed of an object through experimentation with gumballs rolling down an incline. The students will collect data through experimenting, create graphs from the data, interpret the slope of the graphs and create equations of lines from data points and the graph. They will understand the relationship of speed and velocity and be able to relate the velocity formula to the slope intercept form of the equation of a line.
  • Solving Linear Equations in Two Variables # This lesson unit is intended to help you assess how well students can formulate and solve problems using algebra and, in particular, to identify and help students who have difficulties solving a problem using two linear equations with two variables and interpreting the meaning of algebraic expressions.
  • Equations of Circles 1 # This lesson unit is intended to help you assess how well students are able to use the Pythagorean theorem to derive the equation of a circle and translate between the geometric features of circles and their equations.
  • Cup-Activity: writing equations from data # This is a great lab activity that allows students to develop a true understanding of slope as a rate of change. Students are active and involved and must use higher order thinking skills in order to answer questions. Students work through an activity, measuring heights of cups that are stacked. Students them determine a "rate of change - slope". Students are then asked to put this into slope-intercept form. The important part here is in their determining the y-intercept of the equation. Students then take this further and finally attempt to create a linear inequality to determine how many cups, stacked vertically, will fit under a table.
  • Optimization Problems: Boomerangs # This lesson is designed to help students develop strategies for solving optimization problems. Such problems typically involve scenarios where limited resources must be used to greatest effect, as in, for example, the allocation of time and materials to maximize profit.
  • Don't Blow the Budget! # Students use systems of equations and inequalities to solve real world budgeting problems involving two variables.
  • Picture This! # This is a short unit plan that covers position/time and velocity/time graphs. Students are provided with new material on both topics, will have practice worksheets, and group activities to develop an understanding of motion graphs.
  • Exploring Slope Intercept Form with Graphs and Physical Activity # Students will work in pairs and compose three different linear equations in slope intercept form. They will discover and describe how different values for the slope and y-intercept affect the graph. After graphing lines on graph paper, they will do a physical activity involving graphing.
  • Movie Theater MEA # In this Model Eliciting Activity, MEA, students create a plan for a movie theater to stay in business. Data is provided for students to determine the best film to show, and then based on that decision, create a model of ideal sales. Students will create equations and graph them to visually represent the relationships. Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.
Original Student Tutorials
Perspectives Video: Professional/Enthusiast
Perspectives Video: Teaching Idea
Problem-Solving Tasks
  • Cash Box # The given solutions for this task involve the creation and solving of a system of two equations and two unknowns, with the caveat that the context of the problem implies that we are interested only in non-negative integer solutions. Indeed, in the first solution, we must also restrict our attention to the case that one of the variables is further even. This aspect of the task is illustrative of the mathematical practice of modeling with mathematics, and crucial as the system has an integer solution for both situations, that is, whether we include the dollar on the floor in the cash box or not.
  • Global Positioning System I # This question examines the algebraic equations for three different spheres. The intersections of each pair of spheres are then studied, both using the equations and thinking about the geometry of the spheres.
  • Bernardo and Sylvia Play a Game # This task presents a simple but mathematically interesting game whose solution is a challenging exercise in creating and reasoning with algebraic inequalities. The core of the task involves converting a verbal statement into a mathematical inequality in a context in which the inequality is not obviously presented, and then repeatedly using the inequality to deduce information about the structure of the game.
  • Regular Tessellations of the Plane # This task examines the ways in which the plane can be covered by regular polygons in a very strict arrangement called a regular tessellation. These tessellations are studied here using algebra, which enters the picture via the formula for the measure of the interior angles of a regular polygon (which should therefore be introduced or reviewed before beginning the task). The goal of the task is to use algebra in order to understand which tessellations of the plane with regular polygons are possible.
Tutorials
Unit/Lesson Sequences
  • Sample Algebra 1 Curriculum Plan Using CMAP #
    This sample Algebra 1 CMAP is a fully customizable resource and curriculum-planning tool that provides a framework for the Algebra 1 Course. The units and standards are customizable and the CMAP allows instructors to add lessons, worksheets, and other resources as needed. This CMAP also includes rows that automatically filter and display Math Formative Assessments System tasks, E-Learning Original Student Tutorials and Perspectives Videos that are aligned to the standards, available on CPALMS. Learn more about the sample Algebra 1 CMAP, its features and customizability by watching the following video:

    Using this CMAP

    To view an introduction on the CMAP tool, please . To view the CMAP, click on the "Open Resource Page" button above; be sure you are logged in to your iCPALMS account.To use this CMAP, click on the "Clone" button once the CMAP opens in the "Open Resource Page." Once the CMAP is cloned, you will be able to see it as a class inside your iCPALMS My Planner (CMAPs) app. To access your My Planner App and the cloned CMAP, click on the iCPALMS tab in the top menu.All CMAP tutorials can be found within the iCPALMS Planner App or at the following URL: http://www.cpalms.org/support/tutorials_and_informational_videos.aspx
  • Linear Functions and Slope # This session on linear function and slope contains five parts, multiple problems and videos, and interactive activities geared to help students recognize and understand linear relationships, explore slope and dependent and independent variables in graphs of linear relationships, and develop an understanding of rates and how they are related to slopes and equations. Throughout the session, students use spreadsheets to complete the work, and are encouraged to think about the ways technology can aid in teaching and understanding. The solutions for all problems are given, and many allow students to have a hint or tip as they solve. There is even a homework assignment with four problems for students after they have finished all five parts of the session.
Video/Audio/Animations
  • Using Systems of Equations Versus One Equation # When should a system of equations with multiple variables be used to solve an Algebra problem, instead of using a single equation with a single variable?
  • Systems of Linear Equations in Two Variables # The points of intersection of two graphs represent common solutions to both equations. Finding these intersection points is an important tool in analyzing physical and mathematical systems.
  • Point-Slope Form # The point-slope form of the equation for a line can describe any non-vertical line in the Cartesian plane, given the slope and the coordinates of a single point which lies on the line.
  • Two Point Form # The two point form of the equation for a line can describe any non-vertical line in the Cartesian plane, given the coordinates of two points which lie on the line.
  • Graphing Lines 1 # Khan Academy video tutorial on graphing linear equations: "Algebra: Graphing Lines 1"
Virtual Manipulative
  • Linear Equations # This resource provides guided practice for writing and graphing linear functions.
STEM Lessons - Model Eliciting Activity
  • Movie Theater MEA # In this Model Eliciting Activity, MEA, students create a plan for a movie theater to stay in business. Data is provided for students to determine the best film to show, and then based on that decision, create a model of ideal sales. Students will create equations and graph them to visually represent the relationships. Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.
MFAS Formative Assessments
  • Hotel Swimming Pool # Students are asked to write an equation in two variables given a verbal description of the relationship among the variables.
  • Loss of Fir Trees # Students are asked to sketch a graph that depicts the exponential decline in the population of fir trees in a forest.
  • Model Rocket # Students are asked to graph a function in two variables given in context.
  • Tech Repairs # Students are asked to write an equation in two variables from a verbal description.
  • Tech Repairs Graph # Students are asked to graph an equation in two variables given in context.
  • Tee It Up # Students are asked to write an equation in three variables from a verbal description.   Note: This task may assess skills that exceed the general expectation for this mathematical concept at this grade level.  The task is intended for students who have demonstrated mastery within the scope of instruction who may be ready for a more rigorous extensions of the content. As with all materials, ensure to gauge the readiness of students or adapt according to students needs prior to administration.
  • Trees in Trouble # Students are asked to write a function that represents an annual loss of 3 percent each year.
Original Student Tutorials Mathematics - Grades 9-12
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