September 7th, 2016
 This is a sample Fraction Mash screenshot showing one step in the process to Minecraft your face.  As students tap grids on and off they are playing with fractions.

#### Introduction

The block faces of Minecraft (aka Minecraft Aesthetics)

 Minecraft faces are made up of blocks of colors that look like large pixels.  In a world of realistic graphics in video games, many have been surprised by the popularity of the low resolution graphics in Minecraft.  Students will generally be familiar with the game, and will enjoy the challenge to both Minecraft themselves while exploring the math of their “pixels” as they arrange and rearrange colors.

#### What you need to get started

A set of iPads with the Fraction Mash app

#### Time Needed

Depending on how much time you want to spend on this project, anywhere from 1 class period (if students are already familiar with Fraction Mash) to 3 class periods.

#### Collaboration and Group Work

These lessons are designed for students to work individually, in pairs, or in groups.  Each student should do all the work on their own sheets, and the iPad should be shared across group members as equally as possible.

We suggest that groups be no larger than four students.  Four or more students in a group will require extra attention to make sure that every group member is contributing equally.

#### Introduction

1. Discuss and/or review the “fractional boxy style” of Minecraft.  Show some pictures as examples, point out how a small fraction of in the right place looks like an eye, and consider briefly mentioning that the human brain is extremely skillful at facial recognition.
2. Consider creating some space in your classroom for their printed Minecraft faces, and let them know before the activity that you will be doing this.

#### To do

1. The student sheets guide students through the process of creating their Minecraft faces.
2. Students are going to need a sampling of “Minecraft colors.”  You can provide the sample colors to the camera rolls on their iPad via the web, or by taking pictures of the colors.

 A few color samples from Minecraft.

1. Part 1 is a simple face to get started, limited to 2 colors and the selfie pic, and keeping the denominator at 25.
2. Part 2 opens up to more creativity, denominators, colors, and provides a chart for students to keep track of each iteration.
3. After each part, students will answer a few questions, included below.
4. Circulate the room and check for understanding, help students as needed.

#### Sharing

1. With each lesson, spend some time allowing the students to share their work with the class. In this lesson, students can share difficulties they might be having as well as successes in balancing colors with their photo, keeping track of the fractional components, etc.
2. You might also invite students to continue thinking about the idea that small fractions of faces, objects, buildings, etc. are the essential details that our minds focus on to recognize what and who they are.

#### Wrapup

If necessary, have students label their iPads so they will be able to return to them for the next lessons.

#### Questions

1. What fraction of your first Minecraft face is Color 1? Color 2? Your face? Express this is a single equation.
2. As you look around at your classmates images, and they look at yours, are you able to recognize each other?  What are the distinct characteristics that make faces recognizable?
3. What fraction of your final Minecraft face is not using your selfie pic?
4. What fraction of your final Minecraft face would you estimate to be the essential pieces so that one of your classmates could recognize you?  Which parts are those?
5. In Minecraft, the zombies are green and easily recognized.  What fractions of colors in a Minecraft face would make it hard to know if a character wa
6. Solve the following three problems.

a)

b)

c)

7) Choose one of the problems above and explain how it could be represented by a picture made with Fraction Mash?  (Hint: It could involve a re-mix.)

8) How is the image you described in #6 like the images you made in this activity?

 Below are several sample screens that show how students will save images, import them to Fraction Mash to create re-mixes of the mashups.  This series of remixes leads to the final design of a face that resembles a Minecraft face.

 Step 3 in a remix.  The reason students might do remixes in this situation is to warp the face slightly, so that key facial features line up in the grid the way they want them to. Notice that the eyes are further apart, and the mouth is lower from the nose than in the original pic on the right.

 Now we see the green grid with eyes, nose, and mouth, and students can explore the fractions of their facial parts in the overall grid.

 Lastly, the all important additional decorative details.  But of course, more opportunities also to think about the fractional makeup of each part of the whole.

 The final student example, Minecraft Your Face!!!

#### Extend the lesson with Volumize

 Volumize is another app from NYSCI that allows students to build with basic geometric solids in an introductory 3D modeling environment.  Below see some sample screenshots, notice that the images from this lesson can be used as skins on the Volumize model, built on top of a screenshot from Minecraft.

Apps used
Duration: 40-60 mins
Challenge Level: Intermediate
Prep: Easy

#### Big Idea

In this activity students will use Fraction Mash to create images of their faces in the style of Minecraft.  Once they have their basic designs, they will be guided through a series of questions to make changes and express each new face as an algebraic expression.

#### Learning Objectives

From this activity, students will be able to:

• Create visual models of fractions and then recreate the models using different grids and denominators.
• Visualize and analyze equivalent rational numbers that have different denominators.
• Use a series of sums of fractions represented by visual models to create collages that will deepen their understanding of order of operations and fractions in general.

#### Device Strategies

If necessary, have students label their iPads so they will be able to return to them for the next lessons.

These lessons are designed for students to work individually, in pairs, or in groups.  Each student should do all the work on their own sheets, and the iPad should be shared across group members as equally as possible.
We suggest that groups be no larger than four students.  Four or more students in a group will require extra attention to make sure that every group member is contributing equally.