CMS
1st Grade Mathematics
Partitioning Lessons
The following lessons were designed around the Common Core State Standard 1.G.3 (Partition circles
and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and
quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the
shares. Understand for these examples that decomposing into more equal shares creates smaller shares.)
What is partitioning?
Partitioning involves dividing an object or set of objects into parts. Partitioning into equal-sized (nonoverlapping) parts is an important concept that lies at the heart of understanding fractions, percentages and
decimals. Knowing that shapes, sets and quantities can be partitioned into equal-sized parts, and
understanding the importance of equal-sized partitions is fundamental to recognizing the part-whole
relationship between the numerator and denominator in fractions.
When partitioning, it is important to use a variety of representations of sets, shapes and quantities to ensure
that students are thinking and responding to different issues, not simply memorizing images or procedures to
solve problems. This helps students develop a more robust understanding of what a partition is.
Research shows the following actions may increase the likelihood of
fraction misconceptions later in a student’s career.
 Teaching fraction notation before ample concrete experiences
hinders students’ development of conceptual understanding
 Providing pre-drawn circles and rectangles; shaded and/or unshaded takes away opportunities for students to create a shape and
partition it themselves.
 A student’s conceptual understanding is stronger when they
can partition various shapes (e.g., circles and rectangles) to the
language of “half of”, and “quarter of.”
Frequently Asked Questions:
Why don’t we just use the Pearson Common Core lessons on partitioning
(3.A1-3.A4) ?
- Connecting the language we use when telling time (quarter of, half past,
etc.) is very abstract. Half of an hour is not the same as half of a circle.
Students may want to link what they know about halves and fourths to
work with clocks after they have had experiences partitioning circles and
rectangles.
- The Big Idea in Grade 1 is for students to notice that when we create
more shares, the size of the share gets smaller. Students need work that
allows them fold and cut circles and rectangles, then discuss what
happens when they increase the number of cuts (or folds).
“The BIG idea in 1st grade
is that: Students
understand for these
examples that
decomposing into more
equal shares creates
smaller shares.” North
Carolina Department of
Education, RESA Common
Core presentation
Should students be writing the fractions? Or just saying the names?
- In Grade 1, students should focus on partitioning shapes and using the phrases “half of”, “a fourth of” or “a
quarter of.” Time need not be spent on writing fractions.
- *Additional ideas can be located at
http://elementarymath.cmswiki.wikispaces.net/Partitioning+Circles+and+Squares
Resources:
The Rational Number Project http://www.cehd.umn.edu/rationalnumberproject/default.html
“Beyond Pizzas and Pies” Julie McNamara, Meghan M. Shaughnessy
New Zealand Council for Educational
Researchhttp://arb.nzcer.org.nz/supportmaterials/maths/concept_map_fractions.php
1st Grade
Partitioning Circles and Squares
Lesson #1
Common Core Math Practices
Common Core State Standard:
1.G.3 Partition circles and rectangles into two and four equal shares,
describe the shares using the words halves, fourths, and quarters, and use the
phrases half of, fourth of, and quarter of. Describe the whole as two of, or four
of the shares. Understand for these examples that decomposing into more
equal shares creates smaller shares.
3. Construct viable arguments and
critique the reasoning of others.
5. Use appropriate tools strategically
6. Attend to precision (in
communication)
Materials: You will need enough of the following materials so that your each pair of students
will be able to create one whole sandwich, cookie, plate, and placemat
- White paper squares” bread”
- Round yellow or orange circles “cheese”
- Tan rectangle squares “turkey”
- Brown circles “cookies”
- Construction paper (for placemats)
- Paper plates
Vocabulary:
One-half,
half of,
equal share,
fair share
Additional materials needed: Scissors, crayons
Classroom Routine: Watch a section of the Discovery Education Video: The Number Crew: The Big Slide. The
entire video is 9minutes; however, you can choose to watch a small segment at a time. Segments include: analog vs.
digital clocks, telling time to the hour, half-hour, and quarter hour.
After watching a portion of the video, write a time on the board (to the half hour) and ask students to show it on their
clocks. Examples: 8:00, 8:30, half past 8,
Introduction/ Mini-lesson
 Tell students that for the next few days we are going to explore sharing fairly. Ask, “What does it mean to get
a fair share?” Turn and talk to your partner.
 Hold up a large paper square. Tell students you want to share it with another teacher. Ask them how we
could divide it so we both get a fair share. Students may say fold it, cut it. Explain that sometimes we can fold
to show a fair share, and other times we can cut. Tell students that during workshop today, they will be folding
and cutting paper to show their fair shares.
Workshop
*Note: Students do not need to do the following activities in order. They can start with
a placemat, cookie, etc. and move to the next activity. You may want to provide
students a bag or folder to keep their pieces in as they move around the room.
 Explain to students that they will be going on a “fair share” picnic today. Before
getting students into partner pairs, explain each station:
 Making a sandwich. Tell students they will be making a sandwich with their
partner using: square bread, round yellow cheese, and brown rectangular turkey.
Remind students that they are only making ONE sandwich. Then they should cut
their sandwich so that each partner gets a fair share.
 Half of a plate: Explain to students they will get ONE paper plate. Partners
should fold it into two equal parts. Each partner designs his/her half of the plate.
-make sure to students don’t spend too much time coloring (explain that they can
color
 Half of a placemat: Partners get a rectangular place mat (piece of construction
paper). They decide how to fold their placemat and write their name on their half
of the mat.
 Half of a cookie: Partners choose a cookie (brown circle) and cut it in half.
Once partners have completed the activities at each station, have them sit next to each
other and lay out their Fair Share Picnic.
While waiting for all partners to finish, partners can explore making halves of
rectangles, circles, and squares on the Geoboard.
What to look/listen for:
The discussion portion of
this lesson is the most
important part.
Observe students as they
work so that you can tailor
the discussion to meet the
needs of your students.
As students work, watch for
examples of the following:
-partners who incorrectly fold
or cut the plate or placemat
in half.
-students’ explanations of
how they divided up their
object.
Discussion
When all students have finished setting out their “picnic” tell students they are going to go on a gallery walk. Tell
students, “As you walk, see what kinds of ways your classmates divided up their shapes.” This will allow students to
see multiple representations of halves, as well as get a look at non-examples.
If there are incorrect examples, students may say things like, “This one isn’t right/fair/etc.” Stop students and ask for
clarification. “What do you mean?” Why isn’t this one fair?” What do the rest of you think? If students agree each
partner would NOT get half, ask students, “What could these partners do to fix it?” Allow students to change their
representation if needed.
After discussing non-examples and incorrect examples, ask students to orally explain how they determined how to cut
their objects in half. Make sure you have a few students talk and share their strategies.
***VIP! You will need to save these representations for tomorrow’s lesson!
1st Grade
Partitioning Circles and Squares
Common Core State Standard:
1.G.3 Partition circles and rectangles into two and four equal shares, describe
the shares using the words halves, fourths, and quarters, and use the phrases
half of, fourth of, and quarter of. Describe the whole as two of, or four of the
shares. Understand for these examples that decomposing into more equal
shares creates smaller shares.
Materials: You will need enough of the following materials so that your each
group of 4 students will be able to create one whole sandwich, cookie, plate,
and placemat.
- White paper squares” bread”
- Round yellow or orange circles
“cheese”
- Tan rectangle squares “turkey”
- Brown circles “cookies”
- Construction paper (for placemats)
- Paper plates
Additional materials needed: Scissors, crayons
Lesson #2
Common Core Math Practices
3. Construct viable arguments and
critique the reasoning of others.
5. Use appropriate tools strategically
6. Attend to precision (in
communication)
Vocabulary:
One-half,
half of,
equal share,
fair share
One-fourth,
fourth of
Quarter of
Classroom Routine: Watch a section of the Discovery Education Video: The Number Crew: The Big Slide.
Then, ask students to show what time we go to lunch, etc. Be sure the times you choose are to the hour and half-hour.
Introduction
 Ask students to recall how they shared their “picnic” yesterday.
 Tell them today we are going to do the picnic again, but this time with groups of four.
 Ask, “What do you think might happen?” Have students turn and talk to their partner to respond.
 At this point, you may want to show students a representation of a square and ask them to generate ideas on how to
cut or fold it so everyone in the group would have a fair share. However, if you think your students are able, you could
just have students move to workshop.
Workshop
*Note: Students do not need to do the following activities in order. They can start with a
placemat, cookie, etc. and move to the next activity. You may want to provide students a bag
or folder to keep their pieces in as they move around the room.
 Explain to students that they will travel in groups of four to create their “fair share picnic”.
You may want to explain each station before asking students to move:
 Making a sandwich. Tell students they will be making a sandwich with their group using:
square bread, round yellow cheese, and brown rectangular turkey. Remind students that
they are only making ONE sandwich. Then they should cut their sandwich so that each
student in the group gets a fair share.
 A fourth of a plate: Explain to groups they will get ONE paper plate. Partners should
fold it into four equal parts. Each student in the group designs his/her fourth of the plate.
-make sure to students don’t spend too much time coloring (explain that they can color
 A fourth of a placemat: Groups get a 1 rectangular place mat (piece of construction
paper). They decide how to fold their placemat and write their name on their fourth of the
mat.
 Half of a cookie: Groups choose a cookie (brown circle) and cut it into fourths.
Once groups of 4 have completed the activities at each station, have them sit next to each
other and lay out their Fair Share Picnic.
While waiting for all groups to finish, students can explore making halves of rectangles, circles,
and squares on the Geoboard.
What to look/listen
for:
The discussion portion
of this lesson is the
most important part.
Observe students as
they work so that you
will be able to tailor the
discussion to meet the
needs of your students.
As students work,
watch for examples of
the following:
-groups who incorrectly
fold or cut the plate or
placemat in fourths.
-students who notice
that the pieces are
smaller than yesterday.
Discussion
When all students have finished setting out their “picnic” ask students to go on a gallery walk. This will allow students to
see multiple representations of fourths, as well as get a look at non-examples. Students may say things like, “This one
isn’t right/fair/etc.” Stop students and ask for clarification. “What do you mean?” Why isn’t this one fair?” What do the
rest of you think? If students agree each student in the group would NOT get one fourth, ask students, “What could this
group do to fix it?” Allow groups to change their representation if needed.
Bring a few samples from yesterday to the discussion. Ask, “how was sharing today different from the day before?”
“What do you notice about the pieces? What do you notice about the size of the pieces?”
“Compare the size of a fourth to a half, what do you notice?”