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

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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
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 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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#### Formative Assessments

 Name Description Writing Absolute Value Inequalities Students are asked to write absolute value inequalities to represent the relationship among values described in word problems. Writing Absolute Value Equations Students are asked to solve a set of absolute value equations. Solving Absolute Value Inequalities Students are asked to solve a set of absolute value inequalities. Solving Absolute Value Equations Students are asked to solve a set of absolute value equations. Quilts Students are asked to write and solve an equation that models a given problem. Follow Me Students are asked to write and solve an equation that models an exponential relationship between two variables. State Fair Students are asked to write and solve an equation that models a given problem. Music Club Students are given a real world context and asked to model the situation by writing and then solving a multistep inequality.

#### 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.

#### Perspectives Video: Professional/Enthusiast

 Name Description Gear Heads and Gear Ratios Have a need for speed? Get out your spreadsheet! Race car drivers use algebraic formulas and spreadsheets to optimize car performance.

#### 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 Learn how to evaluate an expression with variables using a technique called substitution (or "plugging in"). Evaluating an algebraic expression in a word problem In this example of evaluating expressions, we're dusting off some geometry. On top of that, it's a word problem. We're seeing how different concepts in math are layered on top of each other to create more interesting and complex problems to solve. 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.

#### Unit/Lesson Sequence

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:

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#### 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.

#### 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.

 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.