The struggle is real! In differential calculus, we used the limit of the slopes of secant lines to define the slope of a tangent line. So, it’s only fitting that limits are also the foundation of integral calculus. After approximating area by rectangles, we discover that area can also be defined by the limit of a Riemann Sum. Students begin by… View Post

## 4 Big Theorems About Polynomials

Algebra 2 is filled with so many rich topics and concepts to be discovered. I want to take a look at Polynomial Functions today. We establish vocabulary terms and review factoring methods from Algebra 1, then it’s time to explore end-behavior, multiple roots and function behavior, relative extrema, and theorems about polynomials. But first, our students need some new computational… View Post

## Keep Calm and Use L’Hospital’s Rule

In the last of three posts on Teaching Limits, let’s explore the use of L’Hôpital’s Rule for those who teach Calculus. When Pre-Calculus students use direct substitution that results in 0/0, they know the next step should be to apply one of the algebraic techniques. When Calculus students have studied derivatives, they can explore this new technique as an application… View Post

## More Thoughts on Teaching Limits

In my previous post, 3 Tips Before Teaching Limits, we set the stage for helping our Pre-Calculus students prepare for their journey into the world of Calculus. You can read those helpful hints HERE. Let’s dig into the methods for teaching and finding limits. Introduce the definition of a limit and explain that intuitively, when we say “as x approaches… View Post

## 3 Tips Before Teaching Limits

As the second semester begins, do you think about how well your Pre-Calculus students understand functions from a Calculus perspective? By now they have explored piecewise functions, asymptotes, extrema, continuity, boundedness, and have been exposed to some limit notation. Soon it will be time to enter the world of Calculus with a study of Limits and Continuity. As teachers, we… View Post

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