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### Course: Pixar in a Box > Unit 5

Lesson 1: Building crowds- Start here!
- Introduction to combinatorics
- 1. Counting with tables
- Tabela de combinações
- 2. Robot combinations
- Robot combinations
- 3. Tree challenge
- 4. Counting with trees
- Árvore de combinações
- 5. Casting challenge
- Desafio de combinação
- Getting to know Fran Kalal
- Hands-on activity

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# Hands-on activity

# Dinosaur Combinatorics

**This is a hands on activity designed to follow the first lesson**. It asks students to design and build a

*certain number*dinosaur parts in order to create a crowd of a

*given size*.

It's most appropriate for grades 5-7 and can be completed within an hour.

# Supply List

- Sheets of paper for cutting out parts
- Markers (or any other drawing medium)
- Glue (for character assembly)
- Presentation boards (optional)

# Activity flow

## Step 0: Homework (~40 min)

In advance of this activity you should go through the first lesson at your own pace.

## Step 1: Introduce problem (~5 min)

Pixar is working on an upcoming movie which requires large crowds of dinosaurs. Each dinosaur should be made out of

**exactly 5 parts**: head, body, arm pair, leg pair & tail.The director has requested enough parts so that

**exactly 1000**different dinosaurs can be made. No more, no less. Remember, a dinosaur is said to be**different**if*at least*one body part is different.If you create too many parts it will be seen as wasteful and costly. You should be able to solve this problem with

**less than 25 parts**total.## Step 2: Group discussion (~5 min)

Work through these warmup questions as a group using tree diagrams:

- If you have 3 different heads, 3 different tails and 2 different bodies how many different dinosaurs could you make?
- If you have 3 different heads, 2 different tails, 1 body and 2 different pairs of arms how many different dinosaurs could you make?

## Step 3: Break up into groups

This activity makes sense in groups of 2-4.

## Step 4: Math challenge (~10 min)

First you should do the math and work out how many of each dinosaur part you will make. There are multiple solutions as long as they use

**all 5 kinds of parts**.Remember, to save money you need to

*minimize*the number of parts you build. Everyone should be able to do this with less than 25 parts. Who can do it with the**fewest parts**?## Step 5: Design challenge (~20min)

Now you can build your dino parts using the quantities determined in the previous step. You can do this with paper, markers and scissors (or any other materials).

## Step 6: Conclusion (time permitting)

- Can you prove that you can make 1000 different dinosaurs with the parts you've designed.
- Which group had the fewest number of parts?
- Combine your
**favorite parts**to make two of your own dinosaurs. Be sure to give them names, diets and a backstory!

# Bonus questions

- What is the absolute minimum number of parts needed to create 1000 different dinosaurs?
- What if we needed exactly 1200 different dinosaurs?
- Remember Pixar automates this so the characters can quickly be created. Pixar also designs and redesigns so things look great. What would you do to improve your work if you took what you have and redesigned?

# Common Core State Standards

*By participating in this activity, you acknowledge that similar characters may be independently created and you agree to waive any claims against Pixar or Khan Academy for any similarities between the images you produce and independently created characters.*