Proving triangles are similar is often an exercise in applying one of the many theorems young geometers memorize, like the AA similarity criteria. But proving that the criteria themselves are valid from basic principles is a great...

Can you follow a composition of transformations, or better yet construct them? Young mathematicians analyze the composition of dilations, examining both the scale factor and centers of dilations. They discover relationships for both...

Combine transformations and triangle congruence in a single lesson. Scholars learn to view congruent triangles as a rigid transformation. Using triangle congruence criteria, learners identify congruent triangles and the rigid...

How do you prepare class members for the analytical thinking they will need in the real world? An assessment requires the higher order thinking they need to be successful. The module focuses on the concept of rigid transformations...

Does Newton's Law of Cooling have anything to do with apples? Scholars apply Newton's Law of Cooling to solve problems in the 29th installment of a 35-part module. Now that they have knowledge of logarithms, they can determine the decay...

Introducing ... the Transmographer. Young mathematicians investigate translations, reflections, and rotations. The applet lets users perform transformations on triangles, squares, and parallelograms.

Young mathematicians first graph a series of quadratic equations, and then investigate how various parts of the equation change the graph of the function in a predictable way.

Assess pupil understanding of the relationship between matrices, vectors, linear transformations, and parametric equations. Questions range from recall to more complex levels of thinking. Problems represent topics learned throughout the...

Breaking the rules is one thing, proving it is another! Learners expand on their previous understanding of congruence and apply a mathematical definition to transformations. They perform and identify a sequence of transformations and use...

Introduce translations as transformations that move figures in horizontal and vertical distances with a video that shows how to translate the figures. A second video covers how to determine the translation that has occurred. Pupils...

Model real-life structures with mathematics. A project-based lesson presents a problem situation requiring classes to develop a function to model the St. Louis Arch and the Rainbow Bridge in Arizona. They create their models by...

Model geometric concepts through a hands-on approach. Learners apply similar triangle relationships to solve for an unknown side length. Before they find the solution, they describe the transformation to help identify corresponding sides.

Shift the function and transform the key features of the graph. By translating the graph of the rational function, class members find out how the key features alter. Pupils determine the domain, range, asymptotes, and intervals of...

Searching for a detailed lesson to assist in describing rotations while keeping the class attentive? Individuals manipulate rotations in this application-based lesson depending on each parameter. They construct models depending on the...

How do you know if a pair of triangles are congruent? Use the lesson to help class members become comfortable identifying the congruence criteria. They begin with an exploration of ASA and SSS criteria through transformations and...

Take a unique approach to study the graphing of trigonometric functions. Young scholars consider two sine functions and write three functions that will lie between the two given. They use a graphing utility to assist in their explorations.

Reflections are the geometric mirror. Pupils explore this concept as they discover the properties of reflections. They focus on the coordinates of the reflections and look for patterns. This is the third lesson in a seven-part series.

Picture this—the class creates pictures using functions. Here, learners build functions to model specific graphic criteria. They use their knowledge of parent functions and transformations to create the perfect function. 

How do you graph a quadratic function efficiently? Explore graphing quadratic functions by writing in intercept form with a lesson that makes a strong connection to the symmetry of the graph and its key features before individuals write...

Take some intellectual fun and apply it to the concept of multiplying expressions together. A guide models how to break two numbers into an area model to multiply together in pieces similar to FOILing. The rest of the puzzles consist of...

Don't just go through the steps to solve an algebraic equation, show learners how to balance an equation with visual models. The packet introduces the idea of mobile balances to reinforce the idea that both sides must match to make the...

It's more than just numbers on a line, its an organizational, mental math machine to help learners understand the value of numbers. The tool is handy when introducing positive and negative integers to see their values and...

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

Young mathematicians dive into the number line to discover decimals and how the numbers infinitely get smaller in between. They click the zoom button a few times and learn that the number line doesn't just stop at integers. Includes...