July 13th, 2015

In this activity, students graft part of one animalâ€™s body to a part of another animalâ€™s body, creating a new hybrid creature. This activity explicitly asks students to re-define their previous definition of a â€śwhole.â€ť

### Fraction Mash Activity 4: Paraffe, Pandaphant, Pengorse

Analyzing Fractions and Redefining a Whole

### Expected Activity Time

Paraffe, Pandaphant, Pengorse (20 minutes)

### Materials and Prep

• Paraffe, Pandaphant, Pengorse Student Sheets
• iPad with Fraction Mash app
• Wifi access for sharing mashups

### Activity Prompt

Intro: Have you ever seen the funny photographs where two animals get combined to create a mashup? (Display examples like these: https://twitter.com/animalmashups.) In this activity, you will create your own hybrid creature and explore its fractional makeup.

Paraffe, Pandaphant, Pengorse: Combine two animals with Fraction Mash, and then follow steps to redefine the whole and explore the fractional makeup of your creations.

### What To Do

Paraffe, Pandaphant, Pengorse (20 minutes):

Open the app, and select â€śMake A Mashup.â€ť

• Students will start by choosing which two animals to mashup â€“ import from camera roll or take new pictures. What will fit well together for cohesive outcomes?
• Help students get oriented with tapping parts on the grid to turn them on and off. They can click Combine to see how the mashup looks, and go back to Create to continue perfecting their mashup.
• Have students start with the square grid option using 5 x 5. Count how many squares the hybrid animal is on. If theÂ animal is just barely in a square part, do not count it. Be consistent. This total will be the redefined â€śwhole.â€ť Then count the number of parts that make up each animal. An example is shown: Of the 25 squares, about 12 have the animal on them, two are penguin for 2/12 and 10 are horse for 10/12.
• Now have students change to a custom grid, increase the denominator, and count how many are the whole hybrid animal and how many are of each animal that went into the mashup.
• Repeat this until there are four different grid examinations.
• Have students compare the fractions across the different grids and denominators, and notice that the fractional makeup should remain about the same.
• Have students address some reasons for inconsistencies in their reflection.

### Fraction Mash Activity 4: Paraffe, Pandaphant, Pengorse

Mash two pictures into a hybrid creature, manipulate the denominator, and choose the grid parts to keep and leave out of your final creation.

To Do:

1. Use photos from your camera roll or take two new ones. Resize the pictures by pinching and zooming to create your new hybrid creature. Click Combine to see how well your mashup works, and if itâ€™s not quite right, go back to Create to make improvements. When youâ€™re satisfied with your mashup, click Create and save to camera roll.

1. Go back to Create import the mashup animal that you just made. On the right, import or snap a photo of a solid bright color. Now, as you work with your mashup, you will be ignoring the brightly colored parts and concentrating on the parts of the grid that make up your animal. (Notice the example pictured above.)

1. Fraction Mash gives you a grid overlay that defines the whole as the entire picture. But now, you are going to redefine the whole by counting the number of squares that your mashed up hybrid creature takes up onscreen.

1. Start by using the Squares grid option and swipe the denominator to 25ths. Count how many parts (i.e. squares) your animal takes up. If there are only tiny parts of the animal in a grid, then do not count it.
1. Count how many squares one of the animals takes up and then how many the other takes up. Notice that those two numbers should now add up to 1 (your new â€śwholeâ€ť). For example, 2/12 + 10/12 = 12/12. Save the picture with the grid to your camera role.

1. Repeat the process three more times using custom grids and denominators. Use the denominator of 100 and two more that are greater than 100. Make note of the fractional makeup each time and save your mashups with the grids turned on.

1. Answer the reflection questions on the following student sheet.

### Reflection Questions

1. What was the fraction makeup of your hybrid creature in the 5 x 5 square grid? What was the fraction makeup in each of the following grids and denominators that you tried? Fill in the table below to help keep track of your fractional analysis as you redefined the whole each time.

 Animal Name: How many grid parts did your animal cover in total? How many grid parts did one of the animals take up?Animal 1: _______________ How many grid parts did the other animal take up?Animal 2: _______________ 25ths and squares (5 x 5 square grid) 2nd grid and 100ths 3rd grid and denominator of _____ 4th grid and denominator of ______
1. Compare the number of grid parts of each animal over the total for each mashup that you created. For example, (# penguin parts / total parts) for each mashup you did.
1. Are the fractions pretty close to equivalent? If so, explain why. If the fractions are far from equivalent or if there are small differences, give some reasons for the disparity.
1. Based on what you found above, what are the ratios of animal 1 to animal 2? What is that ratio of each animal to the whole? (Optional: How do these ratios affect the fictional behavior of your animal?)

### App Features You Will Use

 In Create Mode, you will use: Â 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. Â Import or take a new picture. (Visible when you choose to take a new photo.) Turn the grid on/off. (Visible when you choose to take a new photo) View a semi-transparent overlay of the other picture. Â 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: View the equation that expresses the sum of the mashup. Â Turn on/off an effect that blends images.

1. […] activity was adapted from Paraffe, Pandaphant, Pengorse and may be referenced for more […]

Apps used
Duration: 0-20 mins
Prep: Easy

#### Big Idea

In this activity, students combine animals to form whacky, hybrid creatures and explore the fractional parts by changing denominators. Up until this point, Fraction Mash has defined the â€śwholeâ€ť as the picture itself â€“ the image that fits in a frame. However, in this activity students will redefine their â€śwholeâ€ť by focusing only on the grid parts that their hybrid takes up. This redefined, new â€śwholeâ€ť will be specific to each hybrid mashup. For example, if a hybrid â€śparaffeâ€ť takes up 65 parts within an 8 x 25 grid, one may consider it to be 15/65 parrot and 50/65 giraffe. Students will then modify the grid and/or change the denominator to notice if fractional parts of the hybrid are equivalent to that which were originally observed.

#### Learning Objectives

Students will engage with the very concept of a fraction as they define and redefine the whole.

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.
• Evaluate rational numbers as represented on the number line.

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

CCSS.MATH.CONTENT.6.RP.A.1

CCSS.MATH.CONTENT.7.RP.A.2

Mathematical Practices

MP1

MP2

MP4

• Fraction
• Denominator
• Numerator
• Grid
• Whole

#### Device Strategies

Single-device implementation

Using an interactive white board or projector, share a premade hybrid creature with the class. Define the new â€śwholeâ€ť together, choose individuals to assist with changing the grid and/or denominator, and analyze the fractions as a class.

Multiple-device implementation

This is a perfect activity for groups of two to four students. Have students collaborate to make a hybrid creature and then all take their turn at defining the â€śwhole.â€ť Does everyone agree? Then have students take turns manipulating the grid and/or changing the denominator. Have students discuss whether or not they arrived at equivalent fractions for each animal part. Subtle differences give rise to great opportunities for discussion.

Tip and Tricks: Discussions of why certain animal 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.

#### Tips & Ideas

Discussions of why certain animal 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.