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
Number of Solutions for a Triangle
In this solutions for a triangle learning exercise, learners use trigonometric ratios to determine the number of triangles that can be constructed with the given sides and angles. This one-page learning exercise contains 22 problems.
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...
Curated OER
Solving Various Algebraic Equations for Real and Imaginary Roots
In this solving equations worksheet, students solve forty-four algebraic equations for real and imaginary solutions. Types of equations include higher degress polynomials, rational equationals, radical equations, and square roots inside...
Curated OER
Square-Root Functions and Radical Equations
This practice instructional activity includes simple radical equations, and some quadratic equations that can be solved by the square root method. There is good practice here in checking the solutions, and a few graphing problems.
BW Walch
Solving Systems of Linear Equations
Solving systems of equations underpins much of advanced algebra, especially linear algebra. Developing an intuition for the kinds and descriptions of solutions is key for success in those later courses. This intuition is exactly what...
EngageNY
Systems of Equations
What do you get when you cross a circle and a line? One, two, or maybe no solutions! Teach learners to find solutions of quadratic and linear systems. Connect the visual representation of the graph to the abstract algebraic methods.
EngageNY
An Appearance of Complex Numbers 1
Complex solutions are not always simple to find. In the fourth lesson of the unit, the class extends their understanding of complex numbers in order to solve and check the solutions to a rational equation presented in the first lesson....
University of Texas
Complex Numbers
Are complex numbers and binomials similar? This stack of slides provides an introduction to complex numbers and shows how to operate with them. The worked examples show a connection between operating with binomials and operating with...
BW Walch
Creating Linear Equations in One Variable
The example of two travelers meeting somewhere along the road has been a stereotypical joke about algebra as long as algebra has existed. Here in this detailed presentation, this old trope gets a careful and approachable treatment....
Concord Consortium
"Equal" Equations
Different equations, same solution. Scholars first find a system with equations y1 and y2 that have a given solution. They then find a different system with equations y3 and y4 that have the same solution. The ultimate goal is to...
Jesuit High School
Geometry Sample Problems
I'd like to prove that this worksheet has a lot to offer. Seven problems using triangles and parallelograms practice the traditional method of a two-column proof. After the worksheet is some practice problems that show worked out...
NASA
Resolving 3-Plane Traffic Conflicts by Changing Route—Problem Set C
Keep the planes from crashing. Pupils work with three airplanes and change their flight paths to keep them at a safe distance from each other. Individuals work through three problems in the third interactive in a set of six with...
CK-12 Foundation
Linear Systems with Addition and Subtraction: Fill in the Boxes 2
Systematically combine shapes to arrive at one solution. The resource models a system of linear equations using colored shapes. Pupils follow rules to combine circles and squares to add the two equations together, resulting in one...
101 Questions
Nana's Chocolate Milk
Nobody wants to make Nana mad! Help Mr. Meyer fix the chocolate milk he prepared for his Nana using too many scoops of chocolate. Youngsters develop a problem-solving strategy that leads to the solution using ratios and proportions.
Curated OER
Extraneous Solutions
Students find the roots of quadratic equations. In this algebra lesson plan, students solve radical equations and identify the positive and negative roots. They graph and analyze their functions.
Illustrative Mathematics
How Many Solutions?
Determining the number of solutions is an important stepping stone to higher math. In this case, the resource asks algebra pupils to find a second linear equation for a certain solution of a system. When one is asked for a linear...
Curated OER
Estimating Solutions to Word Problems
Learners use estimation to determine the answers to word problems by rounding whole numbers. In this estimation lesson plan, pupils compare and contrast solutions using the best answer.
Curated OER
Estimating Solutions
Finding approximate solutions to word problems allows users to assess the reasonableness of their answers. In a well-paced lesson, the class rounds numbers to estimate the solutions. They explain their thinking and determine if the...
Curated OER
Same solutions?
This activity focuses in on the structure of an equation and how it compares to another. Young algebraists are tasked with grouping together equations that have the same solution by focusing on the transformation of the equations rather...
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