Time for pupils to use their imagination! Learners examine the relationship between a system with no real solution and its graph. They then verify their discoveries with algebra. 

Quadratic solutions come in all shapes and sizes, so help your classes find the right one! Learners use the quadratic formula to find solutions for quadratic equations. Solutions vary from one, two, and complex. 

Discover the relationship between tangent lines and the tangent function. Class members develop the idea of the tangent function using the unit circle. They create tables of values and explore the domain, range, and end behavior of...

I got a different answer, are they both correct? While working through modeling problems interpreting graphs, the question of precision is brought into the discussion. Problems are presented in which a precise answer is needed and...

0/0 doesn't equal 0! Begin this lesson by allowing the class to explore the concept of dividing by zero. The introduction allows for discovery and provides meaningful examples of dividing by zero. This understanding leads to solving...

Doubling a network or combining two networks is quick and easy when utilizing matrices. Learners continue the network example in the second lesson of this series. They practice adding, subtracting, and multiplying matrices by a scalar...

Teach how graphic designers can use mathematics to represent three-dimensional movement on a two-dimensional television surface. Pupils use matrices, vectors, and transformations to model rotational movement. Their exploration involves...

How can matrices help us solve linear systems? Learners explore this question as they apply their understanding of transformation matrices to linear systems. They discover the inverse matrix and use it to solve the matrix equation...

Build an understanding of the powers of 10. Pupils investigate the results of raising 10 to positive and negative powers. They relate this understanding to the magnitude these powers represent in this seventh lesson of 15.

They appear to be different, yet they are the same line. Part 24 out of 33 lessons provides a theorem about the relationships of coefficients of equivalent linear equations. Pupils use the theorem to determine whether two equations are...

Teach cube roots by building on an understanding of square roots. The third installment of a 25-part series asks learners to solve simple quadratic and cubic equations using roots. Scholars compare square roots and cube roots throughout...

Explore the patterns of fractions that produce finite and infinite decimals. The sixth lesson of the series asks learners to determine a similar feature of fractions that produce finite decimals. Using the patterns, pupils create...

How do you fit a tape measure around the Earth? No need if you know a little geometry! Pupils begin by extending their understanding of the Side Splitter Theorem to a transversal cut by parallel lines. Once they identify the...

Examine the various rigid transformations and recognize sequences of these transformations. The lesson asks learners to perform sequences of rotations, reflections, and translations. Individuals also describe a sequence that results in...

Angles and triangles: they're all connected. Uncover the connections between angles in triangles. Scholars learn how to find both exterior and interior angle measures in triangles. The lesson emphasizes the vocabulary related to these...

Explore the process of simplifying square roots through an analysis of perfect squares. The fourth instructional activity of 25 expects individuals to find the perfect square factors in each radicand as a means of simplifying. The...

Are you searching for a purpose for geometric constructions? Use an engaging approach to explore dilations. Scholars create dilations using a construction method of their choice. As they build their constructed dilation, they...

Applying a learned technique to a new type of problem is an important skill in mathematics. The lesson asks scholars to apply their understanding to analyze dilations of different figures. They make conjectures and conclusions to...

Ancient Egyptians sure knew their trigonometry! Pupils learn how the pyramid architects applied right triangle trigonometry. When comparing the Pythagorean theorem to the trigonometric ratios, they learn an important connection that...

Use everything you know about quadratic equations to solve polynomial equations! Learners apply the Zero Product Property to factor and solve polynomial equations. They make a direct connection to methods they have used with quadratic...

Five out of four people have trouble with fractions! After comparing simplifying fractions to simplifying rational expressions, pupils use the same principles to multiply and divide rational expressions. 

What do fractions and rational expressions have in common? Everything! Learners use common denominators to solve rational equations. Problems advance from simple to more complex, allowing pupils to fully understand the material before...

How hard can it be to split something in half? Learners investigate how previously learned concepts from angle bisectors can be used to develop ways to construct perpendicular bisectors. The resource also covers constructing a...

Investigate the application of vector transformations applied to linear systems. Individuals use vectors to transform a linear system translating the solution to the origin. They apply their understanding of vectors, matrices,...