CK-12 Foundation
Systems of Linear Equations in Three Variables: Intersecting Planes - No Solution
How many different ways can three planes intersect? The interactive provides three movable planes. Pupils manipulate the planes to determine the number of solutions possible based upon their intersections.
CK-12 Foundation
Checking Solutions to Inequalities: Apples and Bananas Shopping Excursion
Go bananas over a fun interactive! Learners drag a point on a virtual graph of an inequality to see if it is a solution. This helps determine the possible numbers of apples and bananas a shopper can buy with a given amount of money.
Curated OER
Graphing Solutions
In this graphing solutions worksheet, 9th graders solve 13 various types of problems. First, they find the solution of each systems by graphing on the coordinate plane provided. Then, students solve each systems of equations...
Curated OER
Word Problem Solutions
In this word problem solutions worksheet, students solve and complete 5 different problems that include solving various types of word problems. First, they calculate the total cost and cost per students for the table shown. Then,...
Flipped Math
Radical Equations
There might be an extra solution. Pupils discover that the process of solving a radical equation is the same general process of solving any equation. They find out that in some instances, an extraneous solution occurs. Individuals then...
Curated OER
Solving Rational Equations 1
For this Algebra I worksheet, students solve rational equations that may have extraneous solutions. The worksheet is two pages and contains twenty problems. Answer key is provided.
Curated OER
Rational Equations
In this college level mathematics worksheet, students solve rational equations and identify the extraneous solutions. The two page worksheet contains fifty-eight problems. Answers are included.
Inside Mathematics
Two Solutions
Many problems in life have more than one possible solution, and the same is true for advanced mathematics. Scholars solve seven problems that all have at least two solutions. Then three higher-level thinking questions challenge them to...
Charleston School District
Solving Equations with Infinite or No Solutions
Where did all the variables go? Scholars learn how to interpret an equation when they eliminate all variables during the solving process. They interpret the solution as infinite solutions or no solutions.
EngageNY
Solution Sets to Inequalities with Two Variables
What better way to learn graphing inequalities than through discovering your own method! Class members use a discovery approach to finding solutions to inequalities by following steps that lead them through the process and even include...
Curated OER
Integer Solutions to Inequality
When is the last time you assigned your students only one problem? This seemly simple problem requires learners think like a mathematician and reason about how to solve this compound inequality in one variable. More than just using...
Curated OER
How does the solution change?
Four simple equations, each with two variables, try to get at the important question of reasoning about equations. The problem isn't to solve the equations, but to understand the nature of their solutions. These equations address the...
Mathematics Assessment Project
Classifying Solutions to Systems of Equations
Double the fun of solving a linear equation with an activity that asks learners to first compete an assessment task graphing two linear equations to find the common solution. They then complete a card activity solving systems of...
Alabama Learning Exchange
Complex Numbers Solutions
Complex doesn't have to mean harder! Learners experiment with online software to determine the quadratic equations with complex solutions. They use the quadratic formula to solve equations with both real and complex solutions.
Curated OER
How Much Folate?
This task includes scaffolding to support the introduction of the writing and graphing of linear inequalities. Then your geometry learners discover that writing down all possible combinations is not feasible so they are led to use...
Curated OER
Intersecting Graphs
Ninth graders know how to solve a system of linear equations, but what happens when the system involves an exponential function? The instructional slideshow teaches viewers to determine solutions to systems of equations with linear and...
EngageNY
Polynomial, Rational, and Radical Relationships
This assessment pair goes way beyond simple graphing, factoring and solving polynomial equations, really forcing learners to investigate the math ideas behind the calculations. Short and to-the-point questions build on one another,...
EngageNY
Linear Equations in Two Variables
Create tables of solutions of linear equations. A lesson has pupils determine solutions for two-variable equations using tables. The class members graph the points on a coordinate graph.
EngageNY
Writing and Graphing Inequalities in Real-World Problems
Inequalities: when one solution just doesn't suffice. Individuals learn to write inequalities in real-world contexts and graph solution sets on the number line. All inequalities in the instructional activity are of the form x < c or x...
EngageNY
Some Potential Dangers When Solving Equations
Need a less abstract approach to introducing extraneous solutions? This is it! Young mathematicians explore properties used to solve equations and determine which operations maintain the same solutions. They eventually find that squaring...
Curated OER
Nine Exercises Identifying Solution Sets to Systems of Inequalities
In this inequality worksheet, students examine graphs of functions and describe the solution set. Explanations and examples are provided. This one-page interactive, multiple choice, worksheet contains nine problems.
Curated OER
Solving Rational Equations and Checking for Extraneous Solutions
In this solving rational equations activity, students solve twenty rational equations making sure to check for extraneous solutions. The solutions are provided.
Curated OER
Points as solutions
Ninth graders graph linear functions using coordinate points. In this algebra lesson, 9th graders plot points and graph a line. They use the slope intercept form to graph their equation and evaluate points as solution to the function.
Curated OER
Diffusion through Membranes
Students identify diffusion and its processes through experimentation and calculations. They also use a CBL and conductivity probe to measure the conductivity of various solutions and study the effect of concentration gradients on the...
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