How do you build a polygon from an inequality? An engaging lesson challenges pupils to do just that. Building from the previous lesson in this series, learners write systems of inequalities to model rectangles, triangles, and even...

Systems of parallel lines have no solution. Pupils work examples to discover that lines with the same slope and different y-intercepts are parallel. The 27th segment of 33 uses this discovery to develop a proof, and the class determines...

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...

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...

Prove theorems through an analysis. Learners find the midpoint of each side of a triangle, draw the medians, and find the centroid. They then examine the location of the centroid on each median discovering there is a 1:2 relationship....

You say that perpendicular bisectors intersect at a point? I concur! Learners investigate points of concurrencies, specifically, circumcenters and incenters, by constructing perpendicular and angle bisectors of various triangles.

Prove that an equation in slope-intercept form names only one line. At the beginning, the teacher leads the class through a proof that there is only one line passing through a given point with a given slope using contradiction. The 19th...

The process of elimination really works! Use elimination when substitution isn't doing the job. The 29th segment in a series of 33 introduces the elimination method to solving linear systems. Pupils work several exercises to grasp the...

Horses need exercise, too. Scholars create linear equations to model the perimeter of exercise fields for horses. They finish by solving their equations for the length and width of the fields.

What's so special about tangents? Learners first explore how if a circle is tangent to both rays of an angle, then its center is on the angle bisector. They then complete a set of exercises designed to explore further properties and...

What was the property again? Tired of hearing this from your pupils? Use this table to organize properties studied and as a reference tool for individuals. Learners apply each property in the third column of the table to ensure their...

Get hands on with solving systems of equations graphically. A solid lesson plan uses guided practice to show how to solve systems of linear equations. It allows time for sharing ideas and provides a printable matching activity...

Solving systems by substitution can be a challenging topic in algebra I. Here is a lesson that builds on students' understanding of intercepts to begin the process of substitution, and all work is reinforced graphically to build...

Describing a line using an algebraic equation is an essential skill in mathematics. The previous lesson in the series challenged learners to determine if segments are perpendicular with a formula. Now they use the formula to...

If we stack up all the cross sections of a figure, does it create the figure? Pupils make the connection between the complete set of cross sections and the solid. They then view videos in order to see how 3D printers use Cavalerie's...

Can you solve an equation graphically? Absolutely! This Algebra II instructional activity makes the connection between solving an absolute value equation and graphing two functions. Graphing absolute value functions is presented through...

In statistics, probability rules—literally! Learners use their previous knowledge and explore a set of rules for conditional probability, independent probability, and complements. Given different scenarios, they must determine what type...

Gaining practice in translating a verbal description into a diagram and then an equation is the real point of this similar triangles exercise. Once the diagram is drawn, multiple methods are provided to reach the conclusion. An effective...

Young mathematicians identify different cases of intersecting secant lines. They then investigate the case where secant lines meet inside a circle.

There are many equations Algebra I students are not ready to solve. Graphing to solve gives them a strategy to use when they are unsure of an algebraic approach to solve the problem. The lesson exposes learners to a wide variety of...

Mirror, mirror on the wall, which is the fairest resource of them all? Individuals write and solve one-step equations for problems about angle measurement, including those involving mirrors. Both mathematical and real-world problems are...

Apply, apply, apply! A measurement activity applies a number of concepts to help learn a new construction. Scholars learn to divide a segment into n equal parts using a method that uses the Side Splitter Theorem and a method...

It doesn't matter whether secant lines intersect inside or outside the circle, right? Scholars extend concepts from the previous lesson to investigate angles created by secant lines that intersect at a point exterior to the circle....

In the first installment of a 21-part module, scholars build on previous understandings of probability to develop the multiplication rule for independent and dependent events. They use the rule to solve contextual problems.