Standard #: MAFS.912.A-CED.1.1 (Archived Standard)


This document was generated on CPALMS - www.cpalms.org



Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational, absolute, and exponential functions.


General Information

Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Algebra: Creating Equations
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
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes

Test Item Specifications

    Also assesses:
    MAFS.912.A-REI.2.3 
    MAFS.912.A-CED.1.4

    Assessment Limits :
    In items that require the student to write an equation, equations are limited to exponential functions with one translation, linear functions, or quadratic functions. 

    Items may include equations or inequalities that contain variables on both sides. 

    Items may include compound inequalities. 

    In items that require the student to write an exponential function given ordered pairs, at least one pair of consecutive values must be given.

    In items that require the student to write or solve an inequality, variables are restricted to an exponent of one. 

    Items that involve formulas should not include overused contexts such as Fahrenheit/Celsius or three-dimensional geometry formulas. 

    In items that require the student to solve literal equations and formulas, a linear term should be the term of interest.

    Items should not require more than four procedural steps to isolate the variable of interest. 

    Items may require the student to recognize equivalent expressions but may not require a student to perform an algebraic operation outside the context of Algebra 1.

    Calculator :

    Neutral

    Clarification :

    Students will write an equation in one variable that represents a real world context. 

    Students will write an inequality in one variable that represents a real-world context. 

    Students will solve a linear equation. 

    Students will solve a linear inequality. 

    Students will solve multi-variable formulas or literal equations for a specific variable. 

    Students will solve formulas and equations with coefficients represented by letters.

    Stimulus Attributes :
    Items assessing A-CED.1.1 and A-CED.1.4 must be placed in real-world context. 

    Items assessing REI.2.3 do not have to be in a real-world context.

    Response Attributes :
    Items assessing REI.2.3 should not require the student to write the equation. 

    Items may require the student to choose an appropriate level of accuracy. 

    Items may require the student to choose and interpret units. 

    For A-CED.1.1 and A-CED.1.4, items may require the student to apply the basic modeling cycle.



Sample Test Items (1)

Test Item # Question Difficulty Type
Sample Item 1

The table shows a company's income and expenses over the last 7 days.

The company found that its weekly income and expenses were approximately the same from week to week.

A. Select the correct definition of the variable x.

B. Drag terms to the boxes and symbols to the circles to create an equation that can be solved to approximate the number of weeks it will take for the company's income to be $10,000 more than its expenses.

N/A GRID: Graphic Response Item Display


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Related Resources

Formative Assessments

Name Description
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Writing Absolute Value Equations

Students are asked to solve a set of absolute value equations.

Solving Absolute Value Inequalities

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Solving Absolute Value Equations

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Follow Me

Students are asked to write and solve an equation that models an exponential relationship between two variables.

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Music Club

Students are given a real world context and asked to model the situation by writing and then solving a multistep inequality.

Lesson Plans

Name Description
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Students will reaffirm their knowledge about linear equations. Will be able to apply the concept to real life situations.

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CollegeReview.com

This is a model-eliciting activity where students have been asked by a new website, CollegeReview.com, to come up with a system to rank various colleges based on five categories; tuition cost, social life, athletics, education, city population and starting salary upon graduation.

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.

My Candles are MELTING!

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Piles of Paper

Piles of Paper is a student activity that demonstrates linear and exponential growth using heights of flat and folded paper. Data tables are created and then algebraic models are developed. Real world types of linear and exponential growth are also introduced.

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Original Student Tutorials

Name Description
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Learn how to solve and graph one variable inequalities, including compound inequalities, in part 1 of this interactive tutorial series.

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Perspectives Video: Professional/Enthusiast

Name Description
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Problem-Solving Tasks

Name Description
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 mathematical practice standard MP4 (Model with mathematics), and crucial as the system has an integer solution for both situations, that is, whether or not we include the dollar on the floor in the cash box or not.

Sum of Angles in a Polygon

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Harvesting the Fields

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Basketball

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Throwing a Ball

Students manipulate a given equation to find specified information.

Paying the Rent

Students solve problems tracking the balance of a checking account used only to pay rent. This simple conceptual task focuses on what it means for a number to be a solution to an equation, rather than on the process of solving equations.

Buying a Car

Students extrapolate the list price of a car given a total amount paid in states with different tax rates. The emphasis in this task is not on complex solution procedures. Rather, the progression of equations, from two that involve different values of the sales tax, to one that involves the sales tax as a parameter, is designed to foster the habit of looking for regularity in solution procedures, so that students don't approach every equation as a new problem but learn to notice familiar types.

Planes and Wheat

In this resource, students refer to given information which defines 5 variables in the context of real world government expenses. They are then asked to write equations based upon specific known values for some of the variables. The emphasis is on setting up, rather than solving, the equations.

Teaching Idea

Name Description
Translating Word Problems into Equations This site shows students how to translate word problems into equations. It gives seven steps, from reading the problem carefully to checking the solution, to creating equations. The lesson moves on to a few simple exercises in which a natural language sentence is translated to an algebraic equation. It then moves on to more elaborate word problems which require students to identify the important data and follows the given seven steps to create and solve the equation. The more complex questions draw on student understanding of geometric formulae. There are six questions at the end for students to test their new knowledge of how to create and solve equations.

Tutorials

Name Description
How to evaluate an expression with variables

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Unit/Lesson Sequence

Name Description
Sample Algebra 1 Curriculum Plan Using CMAP

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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.

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Video/Audio/Animations

Name Description
Solving Mixture Problems with Linear Equations

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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?

Averages

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Student Resources

Original Student Tutorials

Name Description
Solving Rational Equations: Cross Multiplying:

Learn how to solve rational linear and quadratic equations using cross multiplication in this interactive tutorial.

Solving Inequalities and Graphing Solutions Part 2:

Learn how to solve and graph compound inequalities and determine if solutions are viable in part 2 of this interactive tutorial series.

Click HERE to open Part 1.

Solving Inequalities and Graphing Solutions: Part 1:

Learn how to solve and graph one variable inequalities, including compound inequalities, in part 1 of this interactive tutorial series.

Click HERE to open Part 2.

Writing Inequalities with Money, Money, Money:

Write linear inequalities for different money situations in this interactive tutorial.

Problem-Solving Tasks

Name Description
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 mathematical practice standard MP4 (Model with mathematics), and crucial as the system has an integer solution for both situations, that is, whether or not we include the dollar on the floor in the cash box or not.

Harvesting the Fields:

This is a challenging task, suitable for extended work, and reaching into a deep understanding of units. Students are given a scenario and asked to determine the number of people required to complete the amount of work in the time described. The task requires students to exhibit , Make sense of problems and persevere in solving them. An algebraic solution is possible but complicated; a numerical solution is both simpler and more sophisticated, requiring skilled use of units and quantitative reasoning. Thus the task aligns with either MAFS.912.A-CED.1.1 or MAFS.912.N-Q.1.1, depending on the approach.

Throwing a Ball:

Students manipulate a given equation to find specified information.

Paying the Rent:

Students solve problems tracking the balance of a checking account used only to pay rent. This simple conceptual task focuses on what it means for a number to be a solution to an equation, rather than on the process of solving equations.

Buying a Car:

Students extrapolate the list price of a car given a total amount paid in states with different tax rates. The emphasis in this task is not on complex solution procedures. Rather, the progression of equations, from two that involve different values of the sales tax, to one that involves the sales tax as a parameter, is designed to foster the habit of looking for regularity in solution procedures, so that students don't approach every equation as a new problem but learn to notice familiar types.

Planes and Wheat:

In this resource, students refer to given information which defines 5 variables in the context of real world government expenses. They are then asked to write equations based upon specific known values for some of the variables. The emphasis is on setting up, rather than solving, the equations.

Tutorials

Name Description
How to evaluate an expression with variables:

Learn how to evaluate an expression with variables using a technique called substitution (or "plugging in").

What is a variable?:

Our focus here is understanding that a variable is just a letter or symbol (usually a lower case letter) that can represent different values in an expression. We got this. Just watch.

Calculating Mixtures of Solutions:

This lecture shows how algebra is used to solve problems involving mixtures of solutions of different concentrations.

Video/Audio/Animations

Name Description
Solving Mixture Problems with Linear Equations:

Mixture problems can involve mixtures of things other than liquids. This video shows how Algebra can be used to solve problems involving mixtures of different types of items.

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?

Averages:

This Khan Academy video tutorial introduces averages and algebra problems involving averages.



Parent Resources

Problem-Solving Tasks

Name Description
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 mathematical practice standard MP4 (Model with mathematics), and crucial as the system has an integer solution for both situations, that is, whether or not we include the dollar on the floor in the cash box or not.

Sum of Angles in a Polygon:

This problem provides students with an opportunity to discover algebraic structure in a geometric context. More specifically, the student will need to divide up the given polygons into triangles and then use the fact that the sum of the angles in each triangle is 180°.

Harvesting the Fields:

This is a challenging task, suitable for extended work, and reaching into a deep understanding of units. Students are given a scenario and asked to determine the number of people required to complete the amount of work in the time described. The task requires students to exhibit , Make sense of problems and persevere in solving them. An algebraic solution is possible but complicated; a numerical solution is both simpler and more sophisticated, requiring skilled use of units and quantitative reasoning. Thus the task aligns with either MAFS.912.A-CED.1.1 or MAFS.912.N-Q.1.1, depending on the approach.

Throwing a Ball:

Students manipulate a given equation to find specified information.

Paying the Rent:

Students solve problems tracking the balance of a checking account used only to pay rent. This simple conceptual task focuses on what it means for a number to be a solution to an equation, rather than on the process of solving equations.

Buying a Car:

Students extrapolate the list price of a car given a total amount paid in states with different tax rates. The emphasis in this task is not on complex solution procedures. Rather, the progression of equations, from two that involve different values of the sales tax, to one that involves the sales tax as a parameter, is designed to foster the habit of looking for regularity in solution procedures, so that students don't approach every equation as a new problem but learn to notice familiar types.

Planes and Wheat:

In this resource, students refer to given information which defines 5 variables in the context of real world government expenses. They are then asked to write equations based upon specific known values for some of the variables. The emphasis is on setting up, rather than solving, the equations.

Video/Audio/Animation

Name Description
Averages:

This Khan Academy video tutorial introduces averages and algebra problems involving averages.



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