September 7th, 2016
 This is a Fraction Mash screenshot showing one iteration in the process of creating the personality collage.  The student chose “running” as a characteristic that makes up 2/25 of his personality.  The final result is a self-portrait collage, and an algebraic expression that describe the student and their varied interests and personality traits.

#### What are infographics?

 Infographics are visual images, such as a chart or diagram, that represent information or data. Pie charts, like the one pictured, are a great way to introduce students to the idea of infographics because they clearly visualize data (even if that data is estimated fractional makeup of someone’s personality).    If “Funny” gets reduced, how does that affect the rest of the infographic?  Will “Charming” increase?  Will a new category be needed? Students will get to make these personality choices as they familiarize themselves with creating and interpreting infographics.

#### Self portraits

 Artists have been creating self-portraits since the beginning of painting as an art form.  How artists choose to represent themselves can be an expression revealing aspects of their personality.   In this collage example, the artist might be expressing that she lives in a city, rides bicycles, and loves the color pink. Ask students what details they might include in their own self portrait.

#### 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 infographics, fractions and self portraits.  There are lots of great examples of infographics online.
2. Plan to display all the self portraits somehow, either on your web site, or print them and post around the room.

#### To do

1. The lesson guides students through creating a self portrait collage, and provides some questions (included below) that gets them tinkering with the fractions.
2. Circulate the room and check for understanding, help students as needed.

#### Sharing

1. Spend some time allowing the students to share their work with the class. In this lesson, students can share difficulties and successes they might be having with the fractions.
2. You might also invite students to continue thinking about how these categories have changed over the years, and will change in the years ahead.

#### Wrapup

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

#### Part 1

1) Write the equation with fractions whose sum is 1/1, or you.

2) Did any pieces of your original selfie show in your final collage?  What fraction?

3) Reduce your largest fraction and add that amount to one of the other pieces.  What’s your new equation?

#### Part 2

4) How many pieces of you are there in your final collage?

5) What is the equation of all your parts?

6) If you were to make yet another collage, but with characteristics of the kind of person you want to become, what would that equation be?

7) Solve the following three problems.

a)

b)

c)

6) 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.)

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

 Sample image of a personality collage made in Fraction Mash

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

#### Big Idea

In this activity, students will use Fraction Mash to create an infographic that breaks down the components of their personality. Are they witty? Sarcastic? Funny? It will be up to students to create the pie chart or infographic of their choosing to represent the fractions of themselves that make up their whole self.  Then, they will prompted through a series of questions inviting them to tinker with the math.  For example: If you decide to reduce your style game by a third, which part of you gets the boost?  Students will express the parts that make up the whole as an algebraic expression. The result is a class set of self portraits, each with a set of algebraic expressions that mathematically describe all the pieces.

#### 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.