# Educator's guide

*Pixar in a Box* is designed to help students answer an age old question: "Why do I need to learn this stuff?" Our answer is found in a series of interactive lessons that demonstrate that the very same concepts that they learn in school are used to make movies at Pixar.

## Lesson design

Each topic in

*Pixar in a Box*breaks down into two lessons:#### Lesson One focuses on a design challenge at Pixar.

Each topic begins with a design-focused lesson that doesn't require any math concepts beyond the elementary level. We hope people of all ages try these lessons. The goal of the first lesson of each topic is to get students solving problems with interactive tools, while exposing the connections to mathematics, science and computer science.

#### Lesson Two is more focused on technical concepts.

Each topic then goes into a second lesson that dives deeper into the concepts introduced in Lesson One. For each lesson, we’ve identified the appropriate grade level and prerequisites.

## Find your lesson

Below is summary of each lesson, listed by recommended grade(s). We’ve added a list of key concepts for each lesson to help you find connection points. We recommend completing the first lesson in each topic before moving on to the second lesson. On average, our lessons take approximately 45-60 minutes to complete.

### Grades 5-6

In this lesson, students will use animation tools to bring a ball to life. Along the way, they’ll learn some basic principles of animation.

**Math**: Slope-Intercept form of a line**Math**: Introduction to curves

Students can explore how water, fire and smoke effects are created using millions of tiny particles.

**Math**: Analyze shapes in 2D**Science**: Introduction to problem modeling**Science**: Gravity & viscosity

In this lesson, students will learn about the geometry of dinosaur scales. They’ll make their own skin model using something called a Voronoi partition.

**Math**: Midpoints**Math**: Introduction to random distributions

Discover one of Pixar's key modeling technologies: subdivision surfaces. This lesson introduces the split and average operations used to make smooth surfaces. It takes 40-50 minutes to complete.

**Math**: Midpoints**Math**: Manipulating shapes in 2D and 3D

Students will learn about the basics of rendering and practice some ray tracing and shading. This lesson takes 35-40 minutes to complete.

**Math**: Analyze shapes in 3D space**Science**: Reflection & refraction

Students will explore how swarms of robots were created for

*WALL-E*using combinatorics. They will then use combinations to create their own cast of robots. This lesson introduces the counting principle using tree diagrams and takes 30-45 minutes to complete.**Math**: Combinations**Math**: Counting principle using tree diagrams

In this lesson, students will discover how to create parabolic arcs by weaving together straight lines. Plus, there's a hands-on activity at the end!

**Math**: Midpoints**Math**: Introduction to curves

In this topic, students will explore how characters are brought to life using simple controls. They will learn to use geometric transformations to make a lamp jump.

**Math**: geometric transformations

In this lesson, students will learn how cameras function and how they are used to achieve various artistic effects. This lesson takes 45-60 minutes to complete.

**Math**: Ratios**Math**: Analyze diagrams in two dimensions Science: Refraction

### Grades 7-8

In this lesson, students will be given a scene from the Pixar Art Department to build. They'll explore how the operations of translation, rotation and scaling are used to position objects. This lesson takes 50-60 minutes to complete.

**Math**: Geometric transformations**Math**: Plotting points on 2D coordinate plane

This lesson explores how randomness is used to generate organic looking patterns for things like dinosaur skin.

**Math**: thinking about problems in 1D, 2D & 3D**Math**: Introduction to random distributions

In this lesson, students will build a simple snowman model using JavaScript. Students can then extend the model to create their own character in the final project.

**Computer Science**: Variables, arrays & objects (JavaScript)

Students will explore how to calculate a weighted average of three points and connect this to the subdivision operation from Lesson One. This lesson takes 35-50 minutes to complete.

**Math**: Solving algebraic equations with more than one variable**Math**: Weighted average of three points (2D coordinate plane)

This lesson explores how regions in Pixar’s scenes are blurred to create depth of field, and explains the geometry that makes this process work. This lesson takes 50-60 minutes to complete.

**Math**: Similar Triangles**Math**: Plotting in the 2D coordinate plane**Math**: Negative exponents**Math**: Solving systems of equations**Science**: Refraction

### Grades 9-12

How do computers draw particle systems for us? In this lesson, students will explore the physics behind the scenes that makes it all work.

**Math**: Vector addition and subtraction**Math**: Solve linear equations by substitution**Science**: Position, velocity and acceleration curves**Science**: Newton’s second law (f=ma)

In this lesson students construct snakes using permutations and develop a powerful counting tool: the binomial coefficient. This lesson takes 45-60 minutes to complete.

**Math**: Permutations**Math**: Binomial coefficient

This lesson begins with linear interpolation and builds to Bezier curves using de Castiljau's algorithm. It's great to try after a student has finished the Environment Modeling topic.

**Math**: Polynomial equations**Math**: Linear interpolation

This lesson will push students to derive the rotation formulas they used in the previous “Sets and Staging” lesson. This lesson takes 35-45 minutes to complete.

**Math**: Trigonometry (ratios)**Math**: Trigonometry (rotation formula)

Students will discover how computers efficiently draw millions of parabolas using DeCastlejau's algorithm. This lesson introduces weighted averages of two points, leading to parametric curves.

**Math**: Weighted averages**Math**: Ratios and proportions**Math**: Solving systems of linear equations**Math**: Parabolas

Students can explore the most fundamental calculation that a ray tracer does: line-plane intersection in 2D and 3D. This lesson involves solving systems of equations and takes at least 60 minutes to complete.

**Math**: Solving systems of equations with 4 unknowns

# Hands-on activities

We've created hands-on activities to extend our introductory lessons. You'll find these at the bottom of lessons under "hands-on activities". Here are links to take you directly to our activities:

- Learn hand drawn animation in this three-part activity.
- Appropriate for
**all ages**

- Apply combinations to create a crowd of dinosaurs using a small number of parts.
- Appropriate for
**grades 5 to 8**

- Use string art construction to weave parabolic curves by hand.
- Appropriate for
**all ages**