Math · Grades 11 to 12

Calculus SEL activities

36 ready to use activities that teach Calculus content and build one Social and Emotional Learning (SEL) skill, about 20 minutes each.

Limits and Continuity

• What Changes, and How Fast? Self-awareness · Week 1Average rate of change on smaller and smaller intervals, and noticing how confident each step feels.
• Getting Closer: Limits from Graphs and Tables Self-management · Week 2Reading limits and one sided limits from tables and graphs, with a pause and check plan.
• Limits with Algebra Relationship skills · Week 3Choosing substitution, factoring, or rationalizing to find limits, with kind and specific partner feedback.
• Squeeze and Infinity Social awareness · Week 4The squeeze theorem, infinite limits, and limits at infinity, comparing a classmate's method with your own.
• Continuity and the Intermediate Value Theorem Responsible decision-making · Week 5Checking continuity, fixing removable discontinuities, and deciding when the Intermediate Value Theorem applies.

Differentiation: Definition and Basic Rules

• The Derivative as a Limit Self-awareness · Week 6From average to instantaneous rate of change, finding the derivative as a limit and noticing which steps feel strong.
• Smooth or Sharp? Differentiability Social awareness · Week 7Estimating derivatives and seeing where a graph is smooth, cornered, or too steep, by looking from both sides.
• Power Rule and Friends Self-management · Week 8Fast derivative rules, with a pause and check routine that catches careless slips.
• Product and Quotient Rules Relationship skills · Week 9Product and quotient rules in a group with clear roles and kind, specific feedback.

Differentiation: Composite, Implicit, and Inverse Functions

• The Chain Rule Self-management · Week 10Taking derivatives of functions inside functions, one layer at a time, without skipping steps.
• Implicit Differentiation Self-awareness · Week 11Finding slopes on curves like circles, and noticing where my own mistakes tend to happen.
• Inverse Functions and Their Derivatives Responsible decision-making · Week 12Choosing between the inverse derivative rule and inverse trig formulas, and explaining the choice.
• Choosing the Right Rule Responsible decision-making · Week 13Reading how a function is built before choosing a derivative rule.

Contextual Applications of Differentiation

• Motion: Position, Velocity, Acceleration Social awareness · Week 14Reading the signs of velocity and acceleration to tell a motion story.
• Related Rates Relationship skills · Week 15Linking rates of change through 1 equation, as a team.
• Close Enough? Local Linear Approximation Responsible decision-making · Week 16Using a tangent line to estimate and deciding whether to trust it.
• L'Hospital's Rule Self-management · Week 17Pausing to check the form, then persisting when a limit first gives 0/0.

Analytical Applications of Differentiation

• The Mean Value Theorem Self-awareness · Week 18Checking conditions before claiming a theorem applies, and knowing how sure you are.
• Finding Extreme Values Responsible decision-making · Week 19Critical points, sign charts, and choosing the right test to find local and absolute extreme values.
• Concavity and the Second Derivative Social awareness · Week 20Concavity, points of inflection, and seeing a classmate's method as another valid view.
• Connecting f, f', and f'' Graphs Relationship skills · Week 21Reading a graph of f' to tell what f and f'' are doing, and talking through disagreements kindly.
• Optimization Responsible decision-making · Week 22Setting up and solving optimization problems, and deciding as a group how to justify the answer.

Integration and Accumulation of Change

• Accumulation: Area Under a Rate Self-awareness · Week 23Estimating total change from a rate table with Riemann and trapezoidal sums, and noticing how sure we feel.
• From Riemann Sums to the Definite Integral Self-management · Week 24Writing Riemann sums in summation notation, seeing the definite integral as a limit, and staying steady with new notation.
• The Fundamental Theorem of Calculus Social awareness · Week 25The Fundamental Theorem links derivatives and integrals; seeing a classmate's reasoning from their side.
• Antiderivatives and Indefinite Integrals Self-management · Week 26Finding antiderivatives with a calm check step, so small slips get caught before they spread.
• u-Substitution Relationship skills · Week 27u-substitution as a team, where each role speaks up clearly and passes the work on.
• Choosing an Integration Strategy Responsible decision-making · Week 28Choosing an integration technique on purpose, by looking at structure before acting.

Differential Equations

• Slope Fields Self-awareness · Week 29Reading slope fields and comparing a first guess with what the slopes show.
• Separation of Variables Social awareness · Week 30Separating variables to find particular solutions while noticing how a partner sees the same problem.
• Exponential Growth and Decay Responsible decision-making · Week 31When a quantity changes at a rate proportional to its size, dy/dt = ky leads to y = y0 e^(kt), and the given facts decide which model fits.

Applications of Integration

• Average Value and Accumulation in Context Self-management · Week 32A definite integral can give an average value, a displacement, a total distance, or an amount in a tank, and pausing to ask which one is wanted keeps the work on track.
• Area Between Curves Relationship skills · Week 33Area between curves is the integral of top minus bottom, or right minus left, and a group that checks each step together catches the sign errors.
• Volumes: Cross Sections and Disks Social awareness · Week 34The same base region can build different solids, and each classmate's picture of a slice helps everyone see how volume is a sum of cross sections.

AP Exam Review and Reflection

• Free Response Practice: Show Your Reasoning Self-management · Week 35On a free response question, a correct answer earns full credit only with a clear justification, and a calm routine helps students write it under time pressure.
• Looking Back: My Calculus Year Self-awareness · Week 36One function can show all 4 big ideas of calculus: limits, change, analysis of functions, and accumulation, and naming where you grew builds self-awareness.

RoseThread Connect activities are drafted with the help of AI and shaped by educators. Students never have to share anything personal. Our five SEL skills are informed by CASEL's SEL Framework; RoseThread Learning is not affiliated with or endorsed by CASEL. AP and Advanced Placement are trademarks of the College Board, which was not involved in making and does not endorse RoseThread Connect.