Students will create a series of combinations of images and generate a family tree with visual representations of the resulting fractions.

*Analyzing Fractions while Combining and Recombining Mashups*

**Family Tree** (20 minutes)

Family Tree Student Sheets

iPad with Fraction Mash app

Wifi access for sharing mashups

**Intro:** Have you ever seen the funny photographs where faces get combined to create a mashup? (Display examples like these: http://aplus.com/a/celebrity-face-mashups.)

In this activity, you will create mashups of faces and then combine (or remix) your mashups. Combining and recombining is the Fraction Mash process of creating a family tree.

Family Tree: Using four individual faces, pair them into two sets of grandparents. With set 1, create a single mashup using vertical bars and 10ths and represent both grandparents equally (i.e. 5/10 and 5/10). With set 2, create another mashup with vertical bars and 5/10ths. The mashups from set 1 and set 2 represent the parental generation. Finally, mashup the parents in five ways of your choosing and follow steps to analyze the fractional components related to the parents and grandparents.

**Family Tree Challenge** (20 minutes):

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

- Have students choose four grandparents for the family tree. They could be students in the class, famous people with photos from the Internet, or people you would like your students to work with for this activity.
- Import from camera roll or take new pictures. Focusing on overlaying features like eyes and mouth helps line up images for cohesive outcomes.
- Have students create mashups with the two sets of grandparents using vertical bars and tenths. Each grandparent will be represented equally, 5/10 and 5/10.
- Once the first two mashups are complete, students now have the parental generation to work with. Have students mash up the two parents in five different ways. That is, have them use different grids, denominators, etc. The parents do not need to be represented equally but remember that no child comes 100 percent from one parent.
- Have students analyze the family tree using the student sheets.
- Repeat if desired with different grandparents, and different grids, denominators, numbers of children, etc.

Prompt students to describe the mashups they made and what they had to do to achieve certain outcomes. Encourage students to think about how many combinations were possible at the parent and child level of the family tree. Also, what fraction of each grandparent is each child?

Ask students:

- As you mashed up the parents and children, how did fractions play a role?
- When you mashed up the children, did some grids work better than others?

Create more extensive family trees using people from different contexts. For example, students could use their own grandparents, or comic book heroes, etc. The more they care about their relationship to the people they are mashing, the more they will be interested to dig into the math involved.

OR:

Many other Fraction Mash activities invite students to mashup animals, faces and even objects. That same sort of creativity could go into creating a family tree. Perhaps a starting set of grandparents could be a giraffe and a penguin with another set being a car and a flower. Students can follow the same steps to explore these relationships but with even wackier images.

OR:

Expand the parameters of the grids and denominators to your liking, or to the level of your students. Perhaps start by mashing up grandparents with a 100ths grid to set up a much more complex family tree. Ask your students to create a larger family tree, bringing in many more faces and stories for each family.

Follow steps to create a representation of a family tree and then explore the fraction relationships involved between children, parents and grandparents.

**To Do:**

1. Choose two sets of grandparents and call them set 1 and set 2. You can take pictures of yourself and classmates or use images from the Internet or camera roll that are imported into the Fraction Mash app.

2. Using Fraction Mash, line up grandparents in set 1 and choose the vertical bar grid. Then swipe the denominator to 10. Make a mashup with 5/10 of each grandparent represented. The more precise your mashup is, the more fun your results will be. Save the mashup to the camera roll and repeat with grandparents in set 2.

3. The two mashups you made are now the parents in your family tree. Bring the two parents into Fraction Mash and line them up side by side.

4. Create five new mashups from these two parents. Each of these mashups will represent their children. For the children, choose any grid and denominator that you want. The parents do not need to be represented equally, but they should be represented at least somewhat as no child comes from any parent 100 percent. Be sure to save each child with the grid.

5. Once you have the five children, answer the reflection questions.

Fraction Mash Activity 5: Family Tree

**Reflection Questions:**

1. What are the names of your family members?

2. Examine the fractional components of each child and fill in the table below. (Note: Another way to think about these fractions is in terms of ratios. For example, the ratio of Parts of Child 1 from Grandparent 1 to Total Parts is the fraction in the first grid of the table.)

Children (Add Child’s name) | What fraction of Grandparent 1? | What fraction of Grandparent 2? | What fraction of Grandparent 3? | What fraction of Grandparent 4? |

Child 1_______ | ||||

Child 2_______ | ||||

Child 3_______ | ||||

Child 4_______ | ||||

Child 5_______ |

2. What is the sum across each row for Child 1–5? Why?

3. When you look at the children, use fractions to describe which grandparents they resemble the most. Do any of the children visually resemble a grandparent more even though the fractional makeup isn’t the greatest? Why?

4. How did the different grids affect the creation of your family tree?

5. How would you attempt to figure out how many combinations of parents and children there could be from the two sets of grandparents?