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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.
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Also assesses:
- 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.
MAFS.912.A-REI.2.3
MAFS.912.A-CED.1.4
- Test Item #: Sample Item 1
- Question:
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.
- Difficulty: N/A
- Type: GRID: Graphic Response Item Display
Related Courses
Related Access Points
Related Resources
Formative Assessments
Lesson Plans
Original Student Tutorials
Perspectives Video: Professional/Enthusiast
Problem-Solving Tasks
Teaching Idea
Tutorials
Unit/Lesson Sequence
Video/Audio/Animations
STEM Lessons - Model Eliciting Activity
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.
MFAS Formative Assessments
Students are asked to write and solve an equation that models an exponential relationship between two variables.
Students are given a real world context and asked to model the situation by writing and then solving a multistep inequality.
Students are asked to solve a set of absolute value inequalities.
Students are asked to write absolute value inequalities to represent the relationship among values described in word problems.
Original Student Tutorials Mathematics - Grades 9-12
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.
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.
Learn how to solve rational linear and quadratic equations using cross multiplication in this interactive tutorial.
Write linear inequalities for different money situations in this interactive tutorial.
Student Resources
Original Student Tutorials
Learn how to solve rational linear and quadratic equations using cross multiplication in this interactive tutorial.
Type: Original Student Tutorial
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.
Type: Original Student Tutorial
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.
Type: Original Student Tutorial
Write linear inequalities for different money situations in this interactive tutorial.
Type: Original Student Tutorial
Problem-Solving Tasks
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.
Type: Problem-Solving Task
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.
Type: Problem-Solving Task
Students manipulate a given equation to find specified information.
Type: Problem-Solving Task
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.
Type: Problem-Solving Task
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.
Type: Problem-Solving Task
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.
Type: Problem-Solving Task
Tutorials
Learn how to evaluate an expression with variables using a technique called substitution (or "plugging in").
Type: Tutorial
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.
Type: Tutorial
This lecture shows how algebra is used to solve problems involving mixtures of solutions of different concentrations.
Type: Tutorial
Video/Audio/Animations
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.
Type: Video/Audio/Animation
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?
Type: Video/Audio/Animation
This Khan Academy video tutorial introduces averages and algebra problems involving averages.
Type: Video/Audio/Animation
Parent Resources
Problem-Solving Tasks
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.
Type: Problem-Solving Task
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°.
Type: Problem-Solving Task
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.
Type: Problem-Solving Task
Students manipulate a given equation to find specified information.
Type: Problem-Solving Task
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.
Type: Problem-Solving Task
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.
Type: Problem-Solving Task
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.
Type: Problem-Solving Task
Video/Audio/Animation
This Khan Academy video tutorial introduces averages and algebra problems involving averages.
Type: Video/Audio/Animation
