Calculus 12 - Curriculum Document
Calculus 12 - Outcomes At-a-Glance
Calculus 12 - Pacing Guide - This pacing guide replaces the previous yearly plan. It has been updated to reflect removed outcomes and provide flexibility for responsive instruction.
Calculus 12 - Desmos Activity Collection - A collection of online student Desmos activities organized by unit.
B1 calculate and interpret average and instantaneous rate of change
B2 calculate limits for function values and apply the properties with and without technology
C1 identify the intervals upon with a given function is continuous and understand the meaning of a continuous function
B3 remove removable discontinuities by extending or modifying a function
B4 apply the properties of algebraic combinations and composites of continuous functions
A1 apply, understand, and explain average and instantaneous rates of change and extend these concepts to secant line and tangent line slopes
C2 understand the development of the slope of a tangent line from the slope of a secant line
C3 find the equations of the tangent and normal lines at a given point
Additional Resources and Activities for Unit 1
An Introduction to Limits - Hand out a quarter sheet of card stock to each student and ask them to draw and cut out an curvy amoeba shape (you can give it a face and a name if you'd like). Trace this shape onto 1.5 cm graph paper and count squares to estimate the area of this shape. Repeat the process on 1.25 cm, 1 cm, 0.75 cm and 0.5 cm graph paper. Graph these values and talk about what would happen if you continued to repeat this process. This process is called a limit and is used for lots of math. You might discuss Archimedes' estimate of the value of pi using the area of polygons and the idea of limits.
An Intuitive Introduction to Limits - Some nice ideas here for a discussion of what limits are before jumping into calculations.
WOBD Limits #1, Limits #2 and Limits #3 - Which One Doesn't Belong prompts for discussions on limits. from Caitlyn Gironda
Tutorials from the Calculus Phobe (W. Michael Kelly) - A playlist of videos about limits. These used to exist at flash videos but have been converted to YouTube.
Chapter 1, Lesson 1: What Is a Limit?
Chapter 1, Lesson 2: When Does a Limit Exist?
Chapter 1, Lesson 3: How do you evaluate limits?
Calculus - The limit of a function - A YouTube video describing the limit of a function.
Walking Limits - Create a large function on the floor with painters tape. Use this function to discuss limits with two students walking toward each other from both sides. From Caitlyn Gironda.
Limits and Continuity Desmos Activity - In this activity, students consider left and right limits—as well as function values—in order to develop an informal and introductory understanding of continuity.
Graphing Piecewise Functions and Identifying Discontinuities - Students graph several piecewise defined functions. After they are graphed, students identify the location and types of discontinuities.
Limit Graph Sketching Activity - Students create a function that satisfies a number of limit statements. As each statement is revealed, students edit their graph to include additional details.
Evaluating Limits Secret Message Activity - Students work in small groups to solve problems which create a key. This key can then be used to decipher a secret message.
What is a tangent? - Students may have seen the word tanget in relation to the tangent line to a circle or the tangent ratio. In Calculus they will think about tangent as an instantaneous rate of change. How are all these concepts related. What is a good definition for tangent in Calculus? These slides will work through these questions.
WODB - Started your Calculus class with this "Which One Doesn't Belong" image then referred back to it for what is a critical point, local min/max, Rolle's Theorem. Shared by Luke Walsh.
The Intermediate Value Theorem Desmos Activity - A blog post describing a Desmos activity to have students consider the Intermediate Value Theorem. Four graphs where areas around the x-axis where interesting things are going on are obscured. Ask the same three questions of each one. Behind which circle(s) must there be roots for this function? Behind which circles might there be roots? and Behind which circles is it impossible for there to be roots?
Average Rate of Change Question Stack - *Updated June 2025* Students lay out all of the question stack cards individually with the answer sides facing up. Students choose one card to flip over. Students work out the problem on the card they have just flipped over. When they have decided on an answer, they check the “answer bank” to see if their answer is there. If the answer is in the answer bank, this card is flipped over to reveal a new question. This process repeats until the last question is flipped over.
Introducing Tangents with a Car Speedometer - Using a video of a car trip to determine the average speed of the trip. How does this speed relate the the instantaneous speed of the car.