September 7th, 2016
 Example of an image with three colors, each making up a fraction of the whole. Students can use Fraction Mash to find the fractions, or, as they will learn in these lessons, Algebra.

#### Introduction

1. Introduce the concept of collage and how fractions are related.  Show examples of geometric collage, and any other art works that you think would be appropriate and helpful for your lesson.

#### To do:

1. Students will use a worksheet that provides instructions and guides them through a course of exploration.  They will be using equations to find exact fractional amounts of each color in a collage.
2. Student questions are included below.
3. Allow set amounts of time for each stage of the worksheet.

#### Sharing

1. With each lesson, spend some time allowing the students to share their work with the class. In this lesson, students can share their collages.

#### Wrapup

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

#### 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.

#### Questions:

1) How did you keep track of the colors in your first mashups? Did you use equations to find any of the fractions? How?

2) Explain how algebra helped you find the fractional components of your classmate’s collages.

3) What did you notice about the difficulty in keeping track of the fractions in your free exploration as your collages got more and more complex? How did you handle that difficulty?

 Another example of 3 colors, with a 4th added in the next image.

 Here you can see that 9/25 of the image is white, so the question: What fractional components are the other 3 colors?

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

#### Big Idea

In this activity students will use Fraction Mash to create collages.  Each collage will be a combination of three colors, each making up a fraction of the whole image.  Thus, the fraction of the image that is blue, plus the fraction that is green, plus the fraction that is purple equals 1.  As students create collages some of the fractional components will be obvious, some will not.  Once students create a collage for which they know the fractional components, they will trade iPads with classmates and find the fractional components of those images.  Finally, students will create their own collage, and keep track of the fractions as they go.

#### 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.