Here is a resource where algebra learners show their understanding of a system of equations involving a circle and a line. Once graphed, learners see two points of intersection, one where the ordered pair is read, and a second where...

Here is a coin problem where the algebra learner determines the pair of linear equations needed to solve the system. Whether the equations are taken from a table, or your scholars recognize the format of a coin problem, it is an...

It's time to show off what they learned! The final lesson in the series is a review learning exercise on the topics learned throughout the unit. Scholars solve systems of equations using graphic and algebraic methods, solve system-based...

What do your young geniuses really know? Assess the procedural knowledge of your pupils at the same time as their higher-level thinking with an assessment that identifies their depth of knowledge. Topics include solving...

Here is a resource that helps your algebra learners understand the connection between the graph of two lines, the equations of lines, and the solutions and intersecting points of lines. It would make a great assessment question, but can...

Starting a year of Algebra I? This mighty packet practices all of the major topics with different ranges of difficulty. Standards include everything from linear to quadratic to rational expressions. Use it in a...

Round and round and round we go. Given a diagram of three circles, two of which share a point with the third circle, learners identify the radius of each circle. Doing so requires setting up and solving a system of equations based on the...

In this integrated algebra worksheet, learners solve problems involving systems of equations, quadratic equations, inequalities, surface area, and radicals. This 28-page worksheet contains 39 multi-step problems.

What an impressive task it is to make dental impressions! Pupils learn how dentists use proportional reasoning, unit conversions, and systems of equations to estimate the materials needed to make stone models of dental impressions....

Learners find the common point of a linear and quadratic system given a graph of the system. Then they find a specific point located only on the parabola.

Drawing from a scenario of the history of the penny, learners write and solve a system of linear equations from a context.

In this integrated algebra learning exercise, students answer 39 questions in preparation for the Regents High School Examination. Students solve problems about various topics in algebra and algebra II, including quadratics, systems of...

Here is a real-world application for systems of equations. When is it better to pay an enrollment fee and lower daily rate, and when is it better to pay the regular price? The local swim center is having a special offer, reductions in...

If at first you cannot graph, substitute. The lesson introduces the substitution method as a way to solve linear systems if the point of intersection is hard to determine from a graph. The 28th installment of a 33-part series finishes...

Use 2x2 matrices to move along a line. The second day of a two-day lesson is the 28th installment in a 32-part unit. Pupils work together to create and solve systems of equations that will map a transformation to a given...

What's in a triangle? Just 180 degrees worth of angles! Young learners use given angle relationships in a triangle to write an algebraic representation. Using a system of equations, they simplify the equation to a linear representation.

Determine the better deal. Pupils write the equation for the cost of printing tickets from different printers. They compare the costs graphically and algebraicaly to determine which printer has the best deal based upon the quantity of...

Here is a fun project. Sammy observes a chipmunk and a squirrel to see how many holes each needs in order to stash the same number of acorns.  Scholars could find the answer algebraically or create a table to analyze the...

Number towers use addition or multiplication to ensure each level is equal. While this is common in factoring, it is often not used with algebraic equations. Solving these six questions relies on problem solving skills and being able to...

Learners must think critically about the graphical and algebraic forms of a system of linear equations in order to come up with their own system when given a point that is the solution to the system.

Challenge the class to utilize their knowledge of linear and quadratic functions to determine the intersection of the parent quadratic graph and linear proportional graphs. Using the pattern for the solutions, individuals develop a...

In this assessment task, learners determine whether a crown with given information is composed of pure gold. The task expects algebraic and numerical solution methods, so unlike Archimedes, no bathtub is necessary.

There are many ways to correlate coffee to life, but in this case a learning exercise looks at the price of two different sizes of coffee. It requires interpreting a graph with two unknown variables, in this case the price, and...

Mathematical reasoning and linear systems are two of the strategies used to solve this number puzzle. Your learners will enjoy the challenge and the variety of ways to approach this challenge.