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Calculus Concepts Lesson Plan

Learning Objective

Students will develop an understanding of basic calculus concepts, including differentiation and integration, through the use of animated gifs created with Brush Ninja.


  • Computers or tablets with internet access
  • Projector or interactive whiteboard (optional)
  • Paper and pencils for students (optional)



  • Begin the lesson by asking students if they have heard of calculus before. Encourage them to share any prior knowledge they may have.
  • Explain that calculus is a branch of mathematics that deals with change and motion. It helps us understand how things change over time.
  • Introduce the concept of differentiation as finding the rate at which something changes, and integration as finding the accumulation or total amount of something over a period.

Brush Ninja Demonstration

  • Show students how to access and navigate the Brush Ninja website.
  • Provide a brief demonstration on creating simple animations using different shapes and colors.
  • Emphasize that animations can be used to represent change over time, making it a useful tool for understanding calculus concepts.

Differentiation Activity

  • Divide students into pairs or small groups.
  • Assign each group a scenario involving motion or change (e.g., a car accelerating, water filling up in a glass).
  • Instruct students to create an animated gif using Brush Ninja that represents the scenario assigned to them.
  • As they create the animation, encourage students to think about how the object’s position or quantity changes over time.

Group Presentations

  • Have each group present their animated gif to the class.
  • After each presentation, ask other students questions about what they observed in terms of change and motion in the animation.
  • Guide discussions towards identifying key elements related to differentiation, such as speed, direction, or slope.


  • Observe student engagement during activities and discussions.
  • Assess understanding through student participation in group presentations and responses to questions related to differentiation and integration concepts.
  • Evaluate final animated gifs based on accuracy in representing change, motion, differentiation, or integration.


For advanced learners or as an extension activity:

  • Challenge students to create more complex animations that involve multiple objects changing simultaneously.
  • Introduce basic calculus terminology such as limits, derivatives, and definite integrals for higher grade levels.
  • Connect calculus concepts learned through Brush Ninja animations with real-life applications like motion sensors, weather predictions, or growth models.

How to animate with Brush Ninja

This video teaches the basics of using Brush Ninja

More Tutorial Videos →

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Note: The lessons are written with the assumption that teachers will be using them as a starting point, and will be adapting them to suit the needs of their students and curriculum.

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