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,...

Demonstrate linear and quadratic functions through contextual modeling. Young mathematicians explore both types of functions by analyzing their key features. They then relate these key features to the contextual relationship the function...

Start the exploration of trigonometry off right! Pupils build on their understanding of similarity in this lesson that introduces the three trigonometric ratios. They first learn to identify opposite and adjacent...

Breaking the law in math doesn't get you jail time, but it does get you a wrong answer! After developing the Law of Sines and Cosines in lesson 33 of 36, the resource asks learners to apply the laws to different situations. Pupils must...

Guide your class through the intricacies of solving compound inequalities with a resource that compares solutions of an equation, less than inequality, and greater than inequality. Once pupils understand the differences, the...

Should matrices be allowed to commute when they are being multiplied? Learners analyze this question to determine if the commutative property applies to matrices. They connect their exploration to transformations, vectors, and complex...

Learn through constructions! Learners examine a translation using constructions and define the translation using a vector. Pupils then construct parallel lines to determine the location of a translated image and use the vector as a guide.

Is that drawn to scale? Capture the artistry of geometry using the ratio method to create dilations. Mathematicians use a center and ratio to create a scaled drawing. They then use a ruler and protractor to verify measurements. 

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

It's time for your young artists to shine! Learners examine images to determine possible similarity transformations. They then provide a sequence of transformations that map one image to the next, or give an explanation why it is...

Learn similarity through a transformations lens! Individuals examine the effects of transformations and analyze the properties of similarity, and conclude that any image that can be created through transformations is similar. The...

Playing with mathematics can invoke curiosity and excitement. As pupils construct triangles with given criteria, they determine the necessary requirements to support similarity. After determining the criteria, they practice...

Not all triangles are right! Pupils learn to tackle non-right triangles using the Law of Sines and Law of Cosines. After using the two laws, they then apply them to word problems. 

Lead a discussion on the similarities between the properties of area and the properties of volume. Using upper and lower approximations, pupils arrive at the formula for the volume of a general cylinder. 

What is the relationship between a hemisphere, a cone, and a cylinder? Using Cavalieri's Principle, the class determines that the sum of the volume of a hemisphere and a cone with the same radius and height equals the volume of a...

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....

What do you do when factoring doesn't work? Learners complete the square when faced with quadratic expression that don't factor traditionally. They then use factoring by grouping to solve polynomial equations.

Don't allow those polynomial functions to misbehave! Understand the end behavior of a polynomial function based on the degree and leading coefficient. Learners examine the patterns of even and odd degree polynomials and apply them to...

Pupils learn to solve square root equations and rationalize denominators. Problems include those with extraneous solutions. 

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. 

Turn your class upside down as they explore the reciprocal functions. Scholars use the unit circle to develop the definition of the secant and cosecant functions. They analyze the domain, range, and end behavior of each function.

Don't give your classes the third degree. Use radians instead! While working with degrees, learners find that they are not efficient and explore radians as an alternative. They convert between the two measures and use radians with the...

Build a solid understanding of trigonometric transformations through exploration. Learners work in teams to analyze the effects of different algebraic components on the graph of a sine function. 

Without data, all you are is another person with an opinion. Show learners the power of statistics and probability in making conclusions and predictions. Using two-way frequency tables, learners determine independence by analyzing...