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.
MathMatize Polls - These polls can be used to have class conversation around multiple choice and fill in the blank questions around derivatives. This site was created by a Canadian university professor.
A2 demonstrate an understanding of the definition of the derivative
C4 Demonstrate an understanding of the connection between the graphs of f, and f ʹ
B5 find where a function is not differentiable and distinguish between corners, cusps, discontinuities, and vertical tangents
B6 derive, apply, and explain power, sum, difference, product and quotient rules
B7 apply the chain rule to composite functions
B8 use derivatives to analyze and solve problems involving rates of change
B9 apply the rules for differentiating the six trigonometric functions
A3 demonstrate an understanding of implicit differentiation and identify situations that require implicit differentiation
B10 (optional) apply the rules for differentiating the six inverse trigonometric functions
B11 calculate and apply derivatives of exponential and logarithmic functions
B12 (optional) apply Newton’s method to approximate zeros of a function
B13 estimate the change in a function using differentials and apply them to real world situations
B14 solve and interpret related rate problems
Additional Resources and Activities for Unit 2 - Definition of Derivative and Basic Derivative Rules (Constant Multiple rule, sum and difference rule, power rule, product rule, quotient rule, chain rule)
Introducing Calculus Activities - A number of rich tasks for introducing calculus concepts design at the University of Cambridge.
Which One Doesn't Belong (WODB) Graph #1 and #2 - You can use the problems to discuss continuity and differentiability.
How Steep is this Hill? Desmos Activity - This activity is meant to be an introductory activity for Calculus. It tries to draw out several ideas. 1) that if you zoom into any curve enough it can be approximated by a straight line, 2) to approximate the slope of a curve we can use a straight line and 3) to calculate the slope of that line at any point, we should choose two points on the curve that are very close to each other. Ideally, I envision giving this to students as a homework piece to warm them up for the main lesson on slopes of secants and tangents.
Sketchy Derivatives Desmos Activity - In this activity, students respond to a variety of graph-sketching prompts to demonstrate (and deepen) their understanding of the graphs of derivatives. This activity is designed for students with at least some experience in sketching derivatives.
Power Rule Apartment Escape - Students move from room to room (hyperlinked slides in a Google Slide presentation) to escape the apartment by answering Power Rule questions (similar to a choose your own adventure novel). A student recording sheet and teacher instructions are included.
Power Rule Tarsia Puzzle - Students cut out pieces of a puzzle and connect functions to their derivatives by using the power rule. Solution
Derivatives Power Rule Open Middle Question - Directions: Using the numbers 1 through 9 (without repeating), fill in the boxes to create a function such that at x = 2, the derivative (at that point) is closest to the value of 449. You could easily change the target value or follow up with a question where the coefficient of x is a fraction. from Gregory L. Taylor
SSDD Quotient Rule - "Same Surface, Different Deep" Structure math problems. Four quotient rule problems that look similar but require different strategies to solve.
Derivative Matching Cards - Students are give a set of cards with the graph of either a linear, quadratic or cubic function on them. Their job is to pair up the graphs of the functions with the graphs of the derivatives. There are a total of 12 functions with 12 derivatives. Solution. There is a Desmos Card Sort Activity that was inspired by this activity.
Derivatives Spiders - A series of six "spiders" of increasing difficulty to practice basic derivative rules. from Alan Lutwyche.
Derivative Rules Add 'Em Up Activity - This is a self-checking activity. These are google slides that can be printed or posted electronically. A series of four sets of questions. Students work in small groups to answer each set. If they correctly complete the set, they move on to the next set.
Why is it Called the Chain Rule? video - A description of the chain rule using visuals relating to gear ratios.
Chain Rule Challenge - Students find the derivatives of trig functions that are nested inside each other requiring the chain rule.
Derivative Donuts - Students work in a team of 4. Each student is given 4 "domino" cards and work to make a loop with them. Students are challenged to do this activity silently. This was inspired by the NRICH "Doughnut Percents" activity (and this activity makes a good warm-up prior to working with derivatives).
Additional Resources and Activities for Unit 2 - More Derivative Rules (trigonometric derivatives, e^x and ln(x), implicit differentiation)
Establishing the Derivatives of sin x, cos x & tan x video - Discovering the rules for trig derivatives from Eddie Woo.
WODB Implicit Differentiation - A "Which One Doesn't Belong?" discussion prompt to spark a discussion about implicit differentiation.
Implicit Differentiation Sorting Activity - Students sort cards showing the steps of several implicit differentiation problems.
A fun way to Estimate the value of e - Generate 64 random integers from 1 to 64 and put snap cubes on the squares of the chessboard to represent those numbers. How many of the squares end up with no cube on them? The ratio of 64 to empty squares is approximately e.
Additional Resources and Activities for Unit 2 - Related Rates
Observing Related Rates Stations Activity - Students take observations of related rates in action at three different stations (inflating balloons, cars at an intersection and a sliding ladder). They measure and record their observations on a recording sheet. Students can them determine the related rates equation and compare their observed rates with rates calculated from an equation.
Related Rates, Yet Another Redux - Some great ideas on introducing related rates. A nice worksheet with the context of balloons. Start class by asking for a volunteer to blow up balloons. Tape an empty balloon, a balloon with one breath, with two breaths, etc to the whiteboard. Then the class has a discussion about what they could measure about the balloons and what changed with each balloon. This five minute start to class will hopefully reinforce the main idea. If we change one thing (number of breaths), many other things can change (volume, radius, etc) at different rates.
Create Your Own - Ask students to work in pairs to create their own original related rates problem. The problem should include an illustration and a correct solution.
Unit 2 Cumulative Review
Derivative Rules Scavenger Hunts - Two scavenger hunts on derivative rules, a basic set (power, product, quotient, chain rules) and a more challenging set (implicit, trig, exponent, log rules). Teacher can post both sets of questions and students can select the one they want to review. Some students might start on the basic set and move on to the more challenging set if they finish early. Students can use a recording sheet for their work.
Writing Tangent Line Equations Drag & Drop - Given a variety of functions, students find the derivative at a point to find the equation of the tangent line through that point. from Girl Math