CMS 1St Grade Mathematics Partitioning Lessons

CMS 1st Grade Mathematics Partitioning Lessons

The following lessons were designed around the Common Core State Standard1.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 (non-overlapping) 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 un-shaded 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).

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

Resources:

The Rational Number Project

“Beyond Pizzas and Pies” Julie McNamara, Meghan M. Shaughnessy

New Zealand Council for Educational Research

1st Grade Partitioning Circles and Squares Lesson #1
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. / 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)
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
Additional materials needed: Scissors, crayons / Vocabulary:
One-half,
half of,
equal share,
fair share
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 Lesson #2
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. / 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)
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 / 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.

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 thisgroup 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?”