July 13th, 2015

In this introductory activity, students break two pictures into fractional parts and combine them
to make a mashup. They will learn the core tools of Fraction Mash while exploring
denominators and numerators.

Fraction Mash Activity 1: Quick Intro: Face Mashup

Exploring Numerators and Denominators in Fractions

0 screenshot

Fraction-Mash-Face-Mashup-Example

Activity Prompt

Intro: Have you ever seen funny photographs where faces are combined to create a mashup?(Display examples like these: http://aplus.com/a/celebrity-face-mashups) In this activity, you will create some face mashups by taking pictures of you and your friends then experimenting with the fractional components for different mashups. Face Mashup Challenge: Make 4 mashups using the same two faces, yours and a friend’s. Start with the simple denominator of 4, and then create three more mashups using 9, 16 and 25.

To Do:

Face Mashup Challenge (20 minutes):
Have students open the app, and select ‚ÄúMake A Mashup.‚ÄĚ To start, students need to choose two pictures to mash, adjusting them so that the eyes and mouths line up for the best mashups.

  • 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.
  • Have students experiment with choosing parts and selecting Combine to check to see if their photos line up. In Create mode, have students make four mashups with the same two pictures, moving from simple to more complex:
  • Have students set the denominator to 4 and create a mashup. Then save the mashup to the camera roll by selecting the send icon on upper right part of the screen.
  • Repeat using denominators 9, 16 and 25, and make sure they save each mashup.

 

Discussion Prompt

students to describe their mashups and the decisions they made. Encourage students to think about howchanging the denominator affected their mashups.

Ask:

  • How¬†did¬†Fraction¬†Mash¬†help¬†you¬†create¬†your¬†most¬†satisfying¬†mashup?
  • What¬†denominator¬†did¬†it¬†use?
  • Which¬†denominators¬†gave¬†you¬†the¬†most¬†satisfying¬†effects?¬†Why?

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

  • ‚ÄúThe¬†larger¬†denominator¬†gives¬†me¬†more¬†parts,¬†but¬†they‚Äôre¬†smaller.‚ÄĚ
  • ‚Äú1/2¬†is¬†a¬†larger¬†part¬†than¬†1/9¬†so‚Ķ‚ÄĚ
  • ‚ÄúAll¬†the¬†denominators¬†we¬†used¬†were¬†square¬†numbers.¬†They¬†used¬†the¬†same¬†number¬†of¬†pieces¬†across¬†as¬†up¬†and¬†down.‚ÄĚ
  • Other¬†statements¬†about¬†ways¬†in¬†which¬†increasing¬†or¬†decreasing¬†denominators¬†helped¬†to¬†achieve¬†the¬†result¬†they¬†were¬†after.

Fraction Mash Quick Intro Activity:

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

Fraction-Mash-Example-face-mashup

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.
  1. 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.
  1. 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.
  1. 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?
  1. 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?

 

App Features You Will Use

In Create Mode, you will use:
fm1 Swipe right to increase or left to decrease the numerators and denominators. This controls how many parts are in your mashup and how big they are.
 fm2 Import or take a new picture.
 fm3 (Visible when you choose to take a new photo) Turn the grid on/off.
 fm4 (Visible when you choose to take a new photo) View a semi-transparent overlay of the other picture.
fm5 Change grid options to slice the picture the way you want. Custom allows you to choose how many parts as the number of rows times the number of columns.
In Combine Mode, you can use:
fm6 View the equation that expresses the sum of the mashup.
fm7 Turn on/off an effect that blends images.

 

 

Comments

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Big Idea

Each grid has an associated numerator and denominator. The numerator shows how many pieces of the picture are selected. The denominator controls how many parts the picture is partitioned into. As students aim to create their favorite mashups, they notice and attend to the visual impacts different fractional parts offer.

NOTE: The concept of the ‚Äúwhole‚ÄĚ is important to consider with Fraction Mash. For the purposes of this app, the ‚Äúwhole‚ÄĚ is the picture itself ‚Äď 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:

  • Change denominators to increase or decrease the number of parts that make up a whole.
  • Recognize that larger denominators yield more parts that are smaller in size.
  • Use fraction language to discuss their pictures and compare the effects.

Standards Addressed

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

Vocabulary

  • Fraction
  • Denominator
  • Numerator
  • Grid
  • Whole

Device Strategies

Single-device implementation

Bring student volunteers up to the front of the classroom to pose and be the first faces used in the activity. Challenge the class to visualize mashups with many and fewer parts. Have students discuss how they might figure out the fractional parts of the whole that would result in better mashups. Share examples via your interactive white board or projector and discuss what students notice about the importance of various fractional parts of faces in relation to the whole.

 

Multiple-device implementation

Because this activity elicits collaboration, it is a perfect activity for students to work 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 of themselves in mashups.

 

Tips and Tricks: Discuss why certain mashups work better than others and allow students to share their underlying understandings of fractions in general. These connections help reinforce some of the fractional reasoning introduced here.

Tips & Ideas

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