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.
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.
Code | Description |
MAFS.912.A-REI.4.10: | Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). |
MAFS.912.A-REI.4.11: | Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. ★ |
MAFS.912.A-REI.4.12: | Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. |
Access Point Number | Access Point Title |
MAFS.912.A-REI.4.In.10a: | Identify and graph the solutions (ordered pairs) on a graph of an equation in two variables. |
MAFS.912.A-REI.4.In.11a: | Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically. |
MAFS.912.A-REI.4.In.12a: | Graph a linear inequality in two variables using at least two coordinate pairs that are solutions. |
MAFS.912.A-REI.4.In.12b: | Graph a system of linear inequalities in two variables using at least two coordinate pairs for each inequality. |
Access Point Number | Access Point Title |
MAFS.912.A-REI.4.AP.10a: | Identify and graph the solutions (ordered pairs) on a graph of an equation in two variables. |
MAFS.912.A-REI.4.AP.11a: | Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically |
MAFS.912.A-REI.4.AP.12a: | Graph a linear inequality in two variables using at least two coordinate pairs that are solutions. |
MAFS.912.A-REI.4.AP.12b: | Graph a system of linear inequalities in two variables using at least two coordinate pairs for each inequality. |
Name | Description |
Graphing Linear Inequalities: | Learn to graph linear inequalities in two variables to display their solutions as you complete this interactive tutorial. |
Finding Solutions on a Graph: | Learn to determine the number of possible solutions for a linear equation with this interactive tutorial. |
Solving an Equation Using a Graph: | Follow as we learn why the x-coordinate of the point of intersection of two functions is the solution of the equation f(x) = g(x) in this interactive tutorial. |
Name | Description |
Solving Inequalities: Inequalities and Graphs of Inequalities: | In this challenge game, you will be solving inequalities and working with graphs of inequalities. Use the "Teach Me" button to review content before the challenge. During the challenge you get one free solve and two hints! After the challenge, review the problems as needed. Try again to get all challenge questions right! Question sets vary with each game, so feel free to play the game multiple times as needed! Good luck! |
Name | Description |
Free Graph Paper: | A variety of graph paper types for printing, including Cartesian, polar, engineering, isometric, logarithmic, hexagonal, probability, and Smith chart. |
Name | Description |
Using Technology: | Students are asked to use technology (e.g., spreadsheet, graphing calculator, or dynamic geometry software) to estimate the solutions of the equation f(x) = g(x) for given functions f and g. |
Case In Point: | Students are asked to explain the relationship between the set of solutions and the graph of an exponential equation. |
What Is the Point?: | Students are asked to explain the relationship between a given linear equation and both a point on its graph and a point not on its graph. |
Finding Solutions: | Students are asked to explain the relationship between a given linear equation and both a point on its graph and a point not on its graph. |
Graphs and Solutions - 2: | Students are asked to find the solution(s) of the equation f(x) = g(x) given the graphs of f and g and explain their reasoning. |
Using Tables: | Students are asked to find solutions of the equation f(x) = g(x) for two given functions, f and g, by constructing a table of values. |
Graph a System of Inequalities: | Students are asked to graph a system of two linear inequalities. |
Which Graph?: | Students are asked to select the correct graph of the solution region of a given system of two linear inequalities. |
Graphs and Solutions -1: | Students are asked to explain why the x-coordinate of the intersection of two functions, f and g, is a solution of the equation f(x) = g(x). |
Linear Inequalities in the Half-Plane: | Students are asked to graph all solutions for a non-strict <= or >= linear inequality in the coordinate plane. |
Graphing Linear Inequalities: | Students are asked to graph a strict < or > linear inequality in the coordinate plane.
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Name | Description |
Solving Systems of Inequalities: | Students will learn to graph a system of inequalities and identify points in the solution set. This lesson aligns with the Mathematics Formative Assessment System (MFAS) Task Graph a System of Inequalities (CPALMS Resource #60567). In this lesson, students with similar instructional needs are grouped according to MFAS rubric levels: Getting Started, Moving Forward, Almost There, and Got It. Students in each group complete an exercise designed to move them toward a better understanding of solutions of systems of inequalities and their graphs. |
Steel vs. Wooden Roller Coaster Lab: | This lesson is a Follow Up Activity to the Algebra Institute and allows students to apply their skills on analyzing bivariate data. This STEM lesson allows students the opportunity to investigate if there is a linear relationship between a coaster's height and speed. Using technology the students can determine the line of best fit, correlation coefficient and use the line for interpolation. This lesson also uses prior knowledge and has students solve systems of equations graphically to determine which type of coaster is faster. |
Pendulum Conundrum Inquiry Lab: | In this exploration, students will answer the following essential questions:
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Whose Line Is It Anyway?: | In this lesson, students will use graphing calculators to explore linear equations in the form y = mx + b. They will observe the graphs of equations with different values of slope and y-intercept. They will draw conclusions about how the value of slope and y-intercept are visible in the appearance of the graph. |
Defining Regions Using Inequalities: | This lesson unit is intended to help you assess how well students are able to use linear inequalities to create a set of solutions. In particular, the lesson will help you identify and assist students who have difficulties in: representing a constraint by shading the correct side of the inequality line and understanding how combining inequalities affects a solution space. |
Name | Description |
Taxi!: | This simple conceptual problem does not require algebraic manipulation, but requires students to articulate the reasoning behind each statement. |
Solution Sets: | The typical system of equations or inequalities problem gives the system and asks for the graph of the solution. This task turns the problem around. It gives a solution set and asks for the system that corresponds to it. The purpose of this task is to give students a chance to go beyond the typical problem and make the connections between points in the coordinate plane and solutions to inequalities and equations. Students have to focus on what the graph is showing. When you are describing a region, why does the inequality have to go one way or another? When you pick a point that clearly lies in a region, what has to be true about its coordinates so that it satisfies the associated system of inequalities? |
Population and Food Supply: | In this task students use verbal descriptions to construct and compare linear and exponential functions and to find where the two functions intersect (F-LE.2, F-LE.3, A-REI.11). |
Fishing Adventures 3: | This task is the last in a series of three tasks that use inequalities in the same context at increasing complexity in 6th grade, 7th grade and in HS algebra. Students write and solve inequalities, and represent the solutions graphically. |
Two Squares are Equal: | This classroom task is meant to elicit a variety of different methods of solving a quadratic equation (A-REI.4). Some are straightforward (for example, expanding the square on the right and rearranging the equation so that we can use the quadratic formula); some are simple but clever (reasoning from the fact that x and (2x - 9) have the same square); some use tools (using a graphing calculator to graph the functions f(x) = x^2 and g(x) = (2x-90)^2 and looking for values of x at which the two functions intersect). Some solution methods will work on an arbitrary quadratic equation, while others (such as the last three) may have difficulty or fail if the quadratic equation is not given in a particular form, or if the solutions are not rational numbers. |
Name | Description |
Graph the solution to a system of inequalities.: | This video will demonstrate how to graph the solution to a system of inequalities. |
Introduction to the Coordinate Plane: | In this video, you will learn about Rene Descartes, and how he bridged the gap between algebra and geometry. |
Dependent and independent variables exercise: graphing the equation: | It's helpful to represent an equation on a graph where we plot at least 2 points to show the relationship between the dependent and independent variables. Watch and we'll show you. |
Name | Description |
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 CMAPTo 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 |
Name | Description |
Graphing Lines 1: | Khan Academy video tutorial on graphing linear equations: "Algebra: Graphing Lines 1" |
Name | Description |
Graph a Line Using Y-Intercept and Slope: | This tutorial will help you to graph a line using its slope and y-intercept, or to identify the slope and y-intercept from a linear equation written in slope-intercept form. |
Equation Grapher: | This interactive simulation investigates graphing linear and quadratic equations. Users are given the ability to define and change the coefficients and constants in order to observe resulting changes in the graph(s). |
Title | Description |
Graphing Linear Inequalities: | Learn to graph linear inequalities in two variables to display their solutions as you complete this interactive tutorial. |
Finding Solutions on a Graph: | Learn to determine the number of possible solutions for a linear equation with this interactive tutorial. |
Solving an Equation Using a Graph: | Follow as we learn why the x-coordinate of the point of intersection of two functions is the solution of the equation f(x) = g(x) in this interactive tutorial. |
Title | Description |
Solving Inequalities: Inequalities and Graphs of Inequalities: | In this challenge game, you will be solving inequalities and working with graphs of inequalities. Use the "Teach Me" button to review content before the challenge. During the challenge you get one free solve and two hints! After the challenge, review the problems as needed. Try again to get all challenge questions right! Question sets vary with each game, so feel free to play the game multiple times as needed! Good luck! |
Title | Description |
Taxi!: | This simple conceptual problem does not require algebraic manipulation, but requires students to articulate the reasoning behind each statement. |
Solution Sets: | The typical system of equations or inequalities problem gives the system and asks for the graph of the solution. This task turns the problem around. It gives a solution set and asks for the system that corresponds to it. The purpose of this task is to give students a chance to go beyond the typical problem and make the connections between points in the coordinate plane and solutions to inequalities and equations. Students have to focus on what the graph is showing. When you are describing a region, why does the inequality have to go one way or another? When you pick a point that clearly lies in a region, what has to be true about its coordinates so that it satisfies the associated system of inequalities? |
Population and Food Supply: | In this task students use verbal descriptions to construct and compare linear and exponential functions and to find where the two functions intersect (F-LE.2, F-LE.3, A-REI.11). |
Fishing Adventures 3: | This task is the last in a series of three tasks that use inequalities in the same context at increasing complexity in 6th grade, 7th grade and in HS algebra. Students write and solve inequalities, and represent the solutions graphically. |
Two Squares are Equal: | This classroom task is meant to elicit a variety of different methods of solving a quadratic equation (A-REI.4). Some are straightforward (for example, expanding the square on the right and rearranging the equation so that we can use the quadratic formula); some are simple but clever (reasoning from the fact that x and (2x - 9) have the same square); some use tools (using a graphing calculator to graph the functions f(x) = x^2 and g(x) = (2x-90)^2 and looking for values of x at which the two functions intersect). Some solution methods will work on an arbitrary quadratic equation, while others (such as the last three) may have difficulty or fail if the quadratic equation is not given in a particular form, or if the solutions are not rational numbers. |
Title | Description |
Graph the solution to a system of inequalities.: | This video will demonstrate how to graph the solution to a system of inequalities. |
Introduction to the Coordinate Plane: | In this video, you will learn about Rene Descartes, and how he bridged the gap between algebra and geometry. |
Dependent and independent variables exercise: graphing the equation: | It's helpful to represent an equation on a graph where we plot at least 2 points to show the relationship between the dependent and independent variables. Watch and we'll show you. |
Title | Description |
Graphing Lines 1: | Khan Academy video tutorial on graphing linear equations: "Algebra: Graphing Lines 1" |
Title | Description |
Equation Grapher: | This interactive simulation investigates graphing linear and quadratic equations. Users are given the ability to define and change the coefficients and constants in order to observe resulting changes in the graph(s). |
Title | Description |
Taxi!: | This simple conceptual problem does not require algebraic manipulation, but requires students to articulate the reasoning behind each statement. |
Solution Sets: | The typical system of equations or inequalities problem gives the system and asks for the graph of the solution. This task turns the problem around. It gives a solution set and asks for the system that corresponds to it. The purpose of this task is to give students a chance to go beyond the typical problem and make the connections between points in the coordinate plane and solutions to inequalities and equations. Students have to focus on what the graph is showing. When you are describing a region, why does the inequality have to go one way or another? When you pick a point that clearly lies in a region, what has to be true about its coordinates so that it satisfies the associated system of inequalities? |
Population and Food Supply: | In this task students use verbal descriptions to construct and compare linear and exponential functions and to find where the two functions intersect (F-LE.2, F-LE.3, A-REI.11). |
Fishing Adventures 3: | This task is the last in a series of three tasks that use inequalities in the same context at increasing complexity in 6th grade, 7th grade and in HS algebra. Students write and solve inequalities, and represent the solutions graphically. |
Two Squares are Equal: | This classroom task is meant to elicit a variety of different methods of solving a quadratic equation (A-REI.4). Some are straightforward (for example, expanding the square on the right and rearranging the equation so that we can use the quadratic formula); some are simple but clever (reasoning from the fact that x and (2x - 9) have the same square); some use tools (using a graphing calculator to graph the functions f(x) = x^2 and g(x) = (2x-90)^2 and looking for values of x at which the two functions intersect). Some solution methods will work on an arbitrary quadratic equation, while others (such as the last three) may have difficulty or fail if the quadratic equation is not given in a particular form, or if the solutions are not rational numbers. |
Title | Description |
Graphing Lines 1: | Khan Academy video tutorial on graphing linear equations: "Algebra: Graphing Lines 1" |