Your young physicists analyze the forms of four equivalent exponential expressions representing an amount of a radioactive material in a substance. They show how each expression is equivalent to the others and what aspects of the decay...

Challenge the class to determine the equation of a line. The 21st part in a 33-part series begins with a proof that every line is a graph of a linear equation. Pupils use that information to find the slope-intercept form of the...

Your business executives choose which of three equivalent forms of a quadratic equation is the most useful for finding various pieces of information in this task centered on a company's profits.

Pupils calculate the equation of a quadratic in vertex form from a specific graph and determine an equation that would fit the description of a parabola. The final question determines the individuals' understanding of the signs of the...

Where does the line of rotation need to be to get a cone? Pupils respond to three questions involving rotating a right triangle about different lines. The scholars describe the solid created along with providing details about its...

A problem set explores how an international crisis could affect the economic health of Canada using authentic materials from College Board. Other questions ask learners to create and evaluate supply and demand curves and examine factors...

Learners must think critically about the graphical and algebraic forms of a system of linear equations in order to come up with their own system when given a point that is the solution to the system.

Math scholars investigate the cost of living in Hong Kong compared to Chicago but must first convert the different types of currency. They then choose a type of graph to compare different spending categories and finish the activity by...

Collaborative learners will see the geometric addition of functions by graphing the sum of two graphed curves on the same coordinate plane. This task then naturally flows into giving learners the algebraic representation of the curves...

Pupils rewrite expressions in equivalent forms to identify key features. They use the vertex and factored forms of quadratic expressions to identify the extrema and intercepts. To finish the installment of the Claim 1 Item Slide Show...

Daily routines not only help to manage classrooms, they can also provide students with rich opportunities for learning. This activity supports young learners in developing their number sense by counting up the school days on a class...

To know what is on the test would be great. The six free-response question from the second form of the 2008 AP® Statistics gives pupils an insight into the format and general content of the exam. Each question requires the test...

The government catches a firm in the act of polluting. What will happen to the company's profits? Learners consider the question and others using authentic College Board materials. Other problem sets examine wages and labor and price...

Investigate the relationship between the slope-intercept form and the slope of the graph. The lesson plan leads an investigation of the slope-intercept equation of a line and its slope. Pupils realize the slope is the same as the...

Develop another way to find the equation of a line. The lesson introduces the procedure to find the equation of a line given two points on the line. Pupils determine the two points from the graph of the line.

It's time to show off what they learned! The final lesson in the series is a review activity on the topics learned throughout the unit. Scholars solve systems of equations using graphic and algebraic methods, solve system-based word...

Instead of the typical quadratic questioning, explore the function and look at the three different ways a parabola can be written. The main task is when given several clues, young mathematicians must write an equation that matches the...

One, two, or zero solutions—quadratic systems have a variety of solution possibilities. Using the parent function and the standard form of the function, learners describe the values of a, b, and c that produce each solution type. They...

Does complex number multiplication have the class spinning? Here's a resource that helps pupils explore and discover the geometric effect of multiplying complex numbers. In the 14th installment in the 32-part unit groups look at the unit...

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...

Prove the Law of Sines two ways. The ninth segment in a series of 16 introduces the Law of Sines to help the class find lengths of sides in oblique triangles. Pupils develop a proof of the Law of Sines by drawing an altitude and a second...

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...

Learners analyze the difference between the slope intercept and standard forms of a line in this task. Given two general points using letters they explore linear functions and linear equations.

The equations look different, but their graphs are the same. How can that be? This activity leads your mathematicians in an exploration of three different forms of the same quadratic function. After comparing the equations, their graphs,...