Build confidence in proofs by proving a known property. Pupils explore two approaches to proving base angles of isosceles triangles are congruent: transformations and SAS. They then apply their understanding of the proof to more complex...

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...

Explore properties of addition as they relate to matrices. Using graphical representations of vector matrices, scholars test the commutative and associative properties of addition. They determine if the properties are consistent for...

Keep it on the chains. Pupils work through the steps in the chain rule using the interactive as a guide. Learners identify the two composed functions and their associated derivatives from a set of choices. They continue on to build the...

Estimating a square root is as easy as evaluating a linear equation. Using the derivative of the square root function, pupils calculate an estimation of square roots. Class members determine the equation of the tangent line at the value...

Direct substitution fails. Now what? The seventh of eight videos in Unit 4 - Contextual Applications looks at L'Hopital's rule. Scholars learn to take the derivative of both the numerator and denominator of a function when substitution...

How do you find the measure of an arc? Learners first review relationships between central and inscribed angles. They then investigate the relationship between these angles and their intercepted arcs to extend the Inscribed Angle Theorem...

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...

Collaborative groups utilize their knowledge of parent functions and transformations to determine the equations associated with graphs. The graph is then related to the scenario it represents. 

Matrix multiplication can seem random to pupils. Here's a instructional activity that uses a real-life example situation to reinforce the purpose of matrix multiplication. Learners discover how to multiply matrices and relate the process...

Examine the usefulness of matrices when solving linear systems of higher dimensions. The instructional activity asks learners to write and solve systems of linear equations in four and five variables. Using matrices, pupils solve the...

An addition table supports third graders as they learn strategies to improve their math fluency. When finding sums greater than ten, students are taught how to first make a ten and then add on the rest. A similar method is also...

Teaching young mathematicians about collecting and analyzing data allows for a variety of fun and engaging activities. Here, children observe the weather every day for a month, recording their observations in the form of a bar graph....

Grow an equation for the exponential graph. Given a graph of an exponential function, class members write the equation of the function provided. The graph labels two points on the graph: the y-intercept and the point where x is one.

Learn the stories a formula holds. An interesting lesson takes a unique approach to teach how to use formulas. Beginning with a formula, learners predict what the variables stand for and then use the formula to make calculations and tell...

Peek behind the curtain. Using a helpful resource, teachers and pupils see the way concepts appear on the AP® Calculus exam. Scholars use the questions to prepare for their own exams, gaining quality practice before test day. Questions...

Get a free peek into a calculus exam. Released free-response items from the AP® Calculus AB exam provide teachers and pupils examples of how topics may appear. The six questions cover topics such as growth rates, volumes of rotations,...

How would those items score? The resource provides pupils an opportunity to answer actual free-response questions and determine their scores. Items from the AP® Calculus AB exam from the 2008 administration demonstrate how topics appear...

Take a second look. Form B of the AP® Calculus BC free-response questions allow pupils and teachers to see another set of items. The six questions expand the set of items from the 2011 free-response questions. Form B items include a...

If members of your class wonder where they can use the math they learn in middle school, let them discover the answer. Learners apply geometry concepts of scale and measure to calculate the costs of framing a house addition.

Win the war of the worlds! Scholars solve a variety of problems related to an alien invasion. They determine where spaceships have landed on a coordinate map, devise a plan to avoid the aliens, observe the aliens, and break a code to...

Double the dog ears, double the fun. Five problems provide increasing challenges with non-linear growth. Topics include dog ears, family trees and population data, and geometric patterns.  

The world is full of patterns. Help learners quantify those patterns with mathematical representations. The first Algebra instructional activity in a compilation of four uses a series of activities to build the concept of patterns using...

Practice, assess, or review mathematicians' skills with this integer worksheet addressing order of operations using positive and negative integers, and solving equations in which letters stand for numbers.