Domain: Geometry
Standard Code: 1.G.3
Author Name: Suzie Golden and Lorie Singer
Title of Task: Framing Fractions/Picture Pie
Adapted from: Smith, Margaret Schwan, Victoria Bill, and Elizabeth K. Hughes. “Thinking Through a Lesson Protocol: Successfully Implementing High-Level Tasks.”
Mathematics Teaching in the Middle School 14 (October 2008): 132-138.
PART 1: SELECTING AND SETTING UP A MATHEMATICAL TASK
*partition circles and rectangles into 2 and 4 equal shares
What are your mathematical goals for
*describe the whole as two of or four of the share
the lesson? (i.e., what do you want
Students to know and understand about *decomposing a shape into more equal shares creates smaller shares
*During a mini lesson after launch or during debriefing(half, halves, fourth, fourths, quarter, quarters,
mathematics as a result of this lesson?)
half of, a fourth of, and a quarter of)
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What are your expectations for
students as they work on and
complete this task?
What resources or tools will
students have to use in their
work that will give them
entry into, and help them
reason through, the task?
How will the students work—
Independently, in small groups, or
in pairs—to explore this task?
How will students record and
report their work?
Expectations:
*Be on task
*Work independently or in small groups
*Glue or draw their product in their math journal and explain their thinking
*Report their work during debriefing
Resources:
Circles: i.e. die cuts, paper plates, coffee filters, tortillas, etc.
Rectangles: i.e. die cuts, sentence strips, construction paper, candy bar, etc
Math Journal
Pencils/crayons
Glue
Scissors
Optional- a frame to glue in their products
For Extension Lessons:
Picture Pie by Ed Emberly
Die cuts of circles (wholes, halves, fourths, and I have used eighths) or circles that have lines
representing the different fractions to help them cut in a straight line)
How will you introduce students to the
activity so as to provide access to all
Students while maintaining the
cognitive demands of the task?
*This is an exploratory task without teaching fraction vocabulary or modeling prior to the task.
Picture Pie
Launch 1: You are having a friend over for a play date. After playing for a while, you and your friend
get hungry. Your mom gives you a cherry pie to share with your friend. You and your friend are very
hungry and want to eat the whole pie. How will you cut the pie into two equal parts to make it fair?
Give student a circle (i.e. die cuts, paper plates, coffee filters, tortillas, etc.) to act as their pie. Students
will then cut their pie and discuss with a partner if it is fair. Debrief as a class before the next launch.
Launch 2: Surprise! Another date! You are having 3 friends over for a play date. After playing for a
while, you and your friends are starving. Your mom gives you a cherry pie to share with your friends.
You and your friends are very hungry and want to eat the whole pie. How will you cut the pie into
equal parts to make it fair for you and your friends? Give student a circle (i.e. die cuts, paper plates,
coffee filters, tortillas, etc.) to act as their pie. Students will then cut their pie and discuss with a
partner if it is fair. Debrief as a class before the next launch.
Framing Fractions
Launch 1: You are playing at your friend’s house. Your friend has a candy jar but there is only one
candy bar left. How will you cut the whole candy bar into equal parts to make it fair for you and your
friend? Give student a rectangle (i.e. die cuts, sentence strips, construction paper, candy bar, etc.) to
act as their candy bar. Students will then cut their “candy bar” and discuss with a partner if it is fair.
Debrief as a class before the next launch.
Launch 2: You are playing at your friend’s house. Your friend has a candy jar but there is only one
candy bar left. Their mom says you have to share it with your friend’s little brother and sister. How
will you cut the whole candy bar into equal parts to make it fair for you, your friend, and the little
brother and sister? Give student a rectangle (i.e. die cuts, sentence strips, construction paper, candy
bar, etc.) to act as their candy bar. Students will then cut their “candy bar” and discuss with a partner if
it is fair. Debrief as a class before the next launch.
*Now a class lesson could be used to teach the vocabulary (half, halves, fourth, fourths, quarter,
quarters, half of, a fourth of, and a quarter of)
PART 2: SUPPORTING STUDENTS’ EXPLORATION OF THE TASK
As students work independently or in
*Optional: Bring a small group back for struggling students.
small groups, what questions will you
Getting Started Questions:
ask to—
*What is your plan?
 help a group get started or make
*What is fair/equal?
progress on the task?
 focus students’ thinking on the
Focus Questions:
key mathematical ideas in the
*Show me your thinking?
task?
 assess students’ understanding of *How many do you have?
key mathematical ideas, problem- *Does everyone have a piece?
*Is there another way?
solving strategies, or the
*Would pick that piece?
representations?
 advance students’ understanding
Assessing Questions:
Of the mathematical ideas?
*Will you explain that to me?
*How are you sure that is fair?
*What does fair/equal mean?
*Can you draw it?
Advanced Questions:
*What if X number of friends left? How will it change?
*What if X number of friends joined? How will it change?
*Is their another way to cut it to share it equally? (rectangle)
How will you ensure that students
remain engaged in the task?
 What assistance will you give or
what questions will you ask a
student (or group) who becomes
quickly frustrated and requests
more direction and guidance is
solving the task?
 What will you do if a student (or
group) finishes the task almost
Immediately? How will you
extend the task so as to provide
additional challenge?
Assistance:
*Can you fold it to show a fair share?
*Teacher folds and students cut.
Extension:
*Ask the advanced question above and provide another manipulative.
*Picture Pie Project: Show and discuss book. Give the students die cuts of whole circles and
circles cut into halves, fourths, eighths. Have the students determine what fraction each shape is.
Have the students label their shapes using the words (whole, half, fourth, eighth) or the number
notation (1, ½, 1/4, 1/8). Then the students will make a picture using all or some of their shapes.
After they have glued their shapes on to the Framing Fractions paper, have the students then write
how many of each fraction they used. They may draw a few straight lines to complete their
picture.
Example:
See last attached page. (sorry if my dotted line font doesn’t show up on your computer)
PART 3: SHARING AND DISCUSSING THE TASK
After each launch, invite the students you have selected to come up and share their solutions.
How will you orchestrate the class
Using the document camera to present the strategies they used to solve the task. Use the
discussion so that you accomplish your
questions below to guide the discussion.
mathematical goals?
 Which solution paths do you want
Specific Questions:
to have shared during the
class discussion? In what order will *What do you notice?
*Why is that equal?
the solutions be presented? Why?
*Can you explain your thinking?
 What specific questions will you ask
*Would you rather have a half or a fourth? (after the last launch)
so that students will—
1. make sense of the
What will you hear or see:
mathematical ideas that you
*language for fair and equal
want them to learn?
*equal parts
2. expand on, debate, and question
*accurate work (product or drawing)
the solutions being shared?
*Students will be sharing their work with partners and class.
3. make connections among the
different strategies that are
presented?
4. look for patterns?
5. begin to form generalizations?
What will you see or hear that lets you
know that all students in the class
understand the mathematical ideas that
you intended for them to learn?
Framing Fractions
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Framing Fractions
I used 1 whole circle, 1 half of a circle, 2 fourths of a circle,
and 5 eighths of a circle.