July 9th, 2015

Students create a mashup, hiding parts of their friendâ€™s face within another image, and pose the question: What is the greatest fraction of a personâ€™s face that can be revealed before figuring out who it is? What is the smallest fraction that can remain hidden so it is still recognizable? In comparing different mashups, students explore which fractional quantities are larger, smaller or equivalent.

Comparing Fractional Quantities and Equivalent Fractions

Expected Activity Time Hidden Face Challenge (20 minutes)

### Materials and Prep

• Hidden Face Challenge Student Sheets
• iPad with Fraction Mash app
• Wifi access for sharing mashups

### Activity Prompt

Intro: Do you ever see faces hidden in objects? In this activity, you will hide your face in an object in two ways: 1) trying to show as much of your face as possible yet still be hidden, and, 2) show as little of your face as possible yet your classmates can still tell itâ€™s you in the picture.

Hidden Face Challenge: Create two images, one in which you are trying to show as much of your face without being recognizable to the class, and another where you are trying to show as little of your face as possible while still being recognizable.

What To Do

Hidden Face Challenge (20 minutes):

Have students open the app, and select â€śMake A Mashup.â€ť To start, students need to choose two pictures to mash, one of an object and one of themselves.

• Students can import from the camera roll or take new pictures.
• Suggest that students turn on the Overlay feature while taking a new photo to help them line up their shot.
• To adjust individual photos in the frames, students can use two fingers to zoom or rotate. Encourage students to think about where they want to place the face on/in the object and:
• Decide whether they are trying to show as much of their face but still be hidden or as little of their face but still be recognizable.
• Experiment with choosing parts and selecting Combine to check to see how the mashups look.
• As they work, have students save their mashups.
• Once saved, anonymously post their images to the online project space or send them to you (the teacher) so you can share them with the class.
• Have students rate which ones show the greatest fractional parts of the whole to least for each challenge. Pick winners.

### Discussion

Prompt students to share the mashups they made and what they had to do to achieve the effects they wanted. Ask students:

• Which mashups have the fewest fractional parts of the whole? The most?
• What grids seem most effective in revealing or hiding someone?
• How do the pictures with unlike denominators compare?
• As you created your mashups, did you notice any parts of your face that was highly important to achieving the effect?

Examples of language and discourse to listen for as students engage with Fraction Mash:

• â€śThe larger denominator gives me more pieces, but theyâ€™re smaller.â€ť
• â€śThe face sections are about the same as the object sections, yet the face still seems hidden because â€¦â€ť
• â€ś1/2 is a larger piece than 1/9 so â€¦â€ť
• Statements about comparative fractional quantities and ways in which increasing or decreasing denominators helped to achieve the result they were after.

### Extensions and Inquiring Further

Examine what fraction of the whole image their different facial parts are. The faces can be resized by zooming. How does this affect the fractions of each part (eyes, nose, etc.)? Is the eye 1/8 of the face? 1/10? etc.

Apps used
Duration: 0-20 mins
Prep: Easy

#### Big Idea

How much of your face can be hidden in such a way that you are still recognizable to your peers? How much can be revealed without someone figuring out and that itâ€™s you? In this activity, the question of â€śhow muchâ€ť is answered in terms of fractional quantities of the whole picture. Students will use differentÂ grids to partition their pictures and select which parts of their faces to reveal. In sharing and comparing their final mashups, students will figure out what fractional parts of the faces are represented in their mashups and which fractional quantities are larger, smaller, or equivalent. For example, if one student used 4/16 of their face in their picture and another student used 1/4 of their face in their picture, who wins the challenge? Both since both are equivalentâ€”1/4 of the whole.

NOTE: The concept of the â€śwholeâ€ť is important to consider with Fraction Mash. For the purposes of this app, the â€śwholeâ€ť is the picture itself â€“ 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 denominators, numerators, and various grid options to solve problems built around real world images. From this activity, students will be able to:

• Increase or decrease denominators to affect the number of parts in the whole.
• Compare fractions â€“ greater, less than, equal to.
• Use grid overlays to partition the whole into fractional parts of different types.

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:Â Make sense of problems and persevere in solving them.
• MP2:Â Reason abstractly and quantitatively.
• MP4:Â Model with mathematics.

#### Vocabulary

• Fraction
• Equivalent Fractions
• Denominator
• Numerator
• Grid
• Whole

#### Device Strategies

Single-device implementation

Create a set of mashups before class in which you hide faces of either popular (to your students) celebrities or students in the class in objects as shown in the example. Using an interactive white board or projector, talk through the fraction of the entire image that is â€śface partsâ€ť in comparison to the rest of the image. Discuss features of images, in terms of fractions, that allow faces to be successfully hidden. Then work as a class to create some new Hidden Face mashups.

Multiple-device implementation

This activity works well with students working in pairs. Have students take turns being the models and the photographer. This can lead to interesting investigations of fractions that have to do with the differing combinations for mashups.

#### Tips & Ideas

To facilitate a fair challenge, have students send their mashups to you anonymously so the class is unaware who is in the photo mashups. Also encourage students to use object photos or people that blend best with their friend so they are unrecognizable. If you feel some students will be more recognizable than others regardless of fractional parts selected, you can offer students four preselected photographs that everyone has to mashup for the challenge.