July 9th, 2015

Students will learn what fractions represent as they incorporate parts of their friends’ faces into compositions of other objects. Using a variety of grids, they will explore different visual representations of parts of a whole.

### Fraction Mash Activity 2: Put a Face On It

Representing Parts of the Whole: Partitioning Using Grids

### Activity Prompt

Intro: Have you imagined seeing faces in everyday objects like an outlet or a soda can?

What if the face was really there? What if it were your face? In this activity, you will mash up parts of your face with an object you choose.

Add personality to something, create a mysterious picture, and use the Fraction Mash tool to achieve a composition that looks as though it was meant to have your face built into it.

Put A Face On It: In this activity, students will experiment with different grid options and fractional parts to give a face to an otherwise faceless object. To satisfy the challenge, students will create four mashups using the following grid options: columns, rows, pie slices and custom. They can use the same face and object, or change it up for each grid.

### To Do:

Put A Face On It (20 minutes):

Open the app, and select “Make A Mashup.”

Have students choose two pictures to mash up.

For this challenge, a bright face and any object will potentially satisfy the challenge.

• Import from camera roll or take new photos. Pinch to re-size or rotate with attention to how the face image will overlay onto the object.
• Have students make multiple mashups using the following grids: columns, rows, pie slices and custom. Each grid presents its own challenges to create a coherent image.
• Once students have two pictures in place, choose a grid from the options below the two images. Then choose a denominator to start with by swiping the denominator left or right.
• Tap grid sections on either photo to turn the sections on and off. Click combine to see how the mashup looks, save if you’re satisfied, and go back to Create to keep mashing.
• Repeat until you’ve created mashups using columns, rows, pie slices and custom grids.
• Be sure to save your mashups.

### Discussion

Prompt students to describe the mashups they made and what they had to do to achieve certain outcomes. Encourage students to think about how changing the grids and denominators affected their project.

• “As you played with your mashup, were there specific parts of your face that became most important to you desired outcome?” (e.g. Were your eyes more important than your cheeks?)
• “What other objects would you like to use?
• “Why would some objects work better than others?” (Is there something about the fractional parts of those objects that would make a more successful mashup?)
• How does your understanding of fractions help with creating your mashup mashups?

Name: __________________________ Date: _____________

Fraction Mash Quick Intro Activity: Face Mashup

Create some face mashups by taking pictures of you and your friends then experimenting with the fractional components for different mashups.

To Do

1. Take two new pictures, or use pictures from your camera roll. Re-size the pictures by pinching to line up features like eyes and mouths.
2. Start with a denominator of 4. Choose the parts on the left picture that you want to mash up with the unselected parts of the right picture. Select Combine.
3. Go back and forth between creating and combining until you achieve mashups that you’re happy with. Do this three more times for the following denominators: 9, 16, 25.
4. Save your best mashups and prepare to discuss (using mathematical language) what you did to achieve the best effects.

Fraction Mash Quick Intro Activity: Face Mashup

Reflection Questions:

1. As you created mashups and changed the denominator, what did you notice? Did you find a denominator worked best? Why?

2. Try this challenge again with the custom grid and increase the rows and columns to 15 x 15, resulting in 225 for a denominator. How does this affect your ability to create the result that you think works best?

Apps used
Duration: 0-20 mins
Prep: Easy

#### Big Idea

Students will explore and manipulate multiple grid options to slice photos into different shapes.  They will experiment with adding a face to an object (i.e. plants, vehicles, buildings, pets or anything they choose) while noticing that greater denominators offer more parts to play with. Selecting individual pieces of each picture affects the numerator.

NOTE: The concept of the “whole” is important to consider with Fraction Mash.  For the purposes of this app, the “whole” is the picture itself – the image that fits within a frame.  The parts of one picture combine with parts of another picture to make one whole picture: the mashup.

#### Learning Objectives

Students will use different grid options to combat a common misconception where visual models relate to specific fractions (e.g., thirds can only be represented as pie slices).

From this activity, students will be able to:

• Manipulate denominators to increase parts in a whole.

• Recognize how different visual representations can be used to express the same fraction.

Common Core Standards-Math

• CCSS.MATH.CONTENT.3.NF.A.2.A
• CCSS.MATH.CONTENT.3.NF.A.3.A
• CCSS.MATH.CONTENT.3.NF.A.3.B
• CCSS.MATH.CONTENT.3.NF.A.3.D
• CCSS.MATH.CONTENT.4.NF.B.3.B

Mathematical Practices

• MP1
• MP2
• MP4

• Fraction
• Denominator
• Numerator
• Grid
• Whole

#### Device Strategies

Single-device implementation

Create some example mashups ahead of time to share with the class. Have students discuss how they might figure out qualities that result in better mashups. Using an interactive white board or projector, connect an iPad and allow individual students to display their work. Discuss what the class notices about the importance of various fractional parts of faces in relation to the whole.

Multiple-device implementation

This is a perfect activity for 2-4 students per iPad. Have students take turns being the models and the photographer, as well as choosing the objects. This can lead to interesting investigations of fractions that are represented by different grids in the various mashup combinations. Make sure each student completes their own reflection and identifies their part in the collaboration.

#### Tips & Ideas

Discussions of why certain mashups work better than others allows students to share their underlying understandings of fractions in general. These connections help reinforce some of the fractional reasoning introduced here.