T4T Introduction to Partitioning Shapes
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In this lesson students are introduced to the vocabulary associated with partitioning shapes into equal shares. Students will also explore shapes that are partitioned into halves, thirds, and fourths. Student recording sheets and pictures of anchor charts are included within this lesson.
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Introduction to Partitioning Shapes
In this lesson students are introduced to the vocabulary associated with partitioning shapes into equal shares. Students will also explore shapes that are partitioned into halves, thirds, and fourths.
NC Mathematics Standard:
NC.2.G.3 Partition circles and rectangles into two, three, or four equal shares.
- Describe the shares using the words halves, half of, thirds, third of, fourths, fourth of, quarter of.
- Describe the whole as two halves, three thirds, four fourths.
- Explain that equal shares of identical wholes need not have the same shape.
Standards for Mathematical Practice:
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
7. Look for and make use of structure.
- I understand that partitioning a shape means dividing the whole shape into equal parts..
- I can partition circles and rectangles with two, three, or four equal shares, and describe the shares using correct vocabulary.
whole, half, third, fourth, halves, thirds, fourths, quarters, partition, divide, equal, parts, shares, pieces
- Large chocolate bar (or some other large object that can be divided and captures students’ attention)
- Bags of pre-cut partitioned shapes for the students to sort (see activity sheets)
- Construction paper for students to lay their shapes on when sorting
- Sticky notes and pencils to label the rules for how the shapes were sorted
- Scissors, glue sticks, and math notebook
- Pre-cut partitioned shapes and place them in resealable bags (one bag per student)
- (Additional activity if needed) Copy activity sheets for math notebook (see attached activity sheets)
Launch: 5-10 minutes
- Show the students a large chocolate bar (or some other large item). Call up a student to “share” the item with. Break off a very small part for the student and keep the rest for yourself (be dramatic about this). Hopefully the students will react in some way, if they don’t, ask the child if they are happy with their “share”.
- Ask the class what they notice about the child’s share. Possible responses may include “it isn’t fair”, “it isn’t the same size”, “it isn’t equal”, or “it isn’t even”. It may be helpful to note to students that in mathematics “even” is a characteristic of numbers, so that they may want to use the “equal” or “fair” labels. Record the math vocabulary they use on the board.
- As a class, identify the vocabulary used with partitioning shapes. Make sure the students understand that the most important point is that the shapes are partitioned equally (equal sized pieces). This is a good time to let students know that equally sized pieces do not always look the same even though they will in our examples today. Show or make an anchor chart with the vocabulary.
Explore: 10-15 minutes
- Students will need to work with a math partner. Give each group a bag of pre-cut shapes, sticky notes, and a piece of construction paper. The students will sort their shapes on the construction paper. Give students sticky notes and have them label their rules for how they sorted the shapes. (two parts, circles, etc.)
- Have the partners sort the shapes--don’t give any rules or suggestions. Students may choose to sort by shapes or by number of fractional pieces. Tell the partners they must be able to explain their sort. As the groups are working, ask questions to encourage mathematical thinking:
- What do you notice about the shapes?
- How are your shapes the same? How are they different?
- Why did you sort your shapes that way?
- Is there another way you can sort them?
- Take brief notes on student thinking and responses and sort them as you go to create a progression for your discussion. Misconceptions and “rules” that did not work are just as important as successful sorts and explanations for helping students understand the concept of partitioning. It is often helpful to start with examples of common misconceptions.
Discuss: 10-20 minutes
- Allow groups to share how they sorted their shapes and explain the rule by which the shapes were sorted. Point out the math vocabulary they used that helps to emphasize equal shares.
- Show students a circle and rectangle that are both partitioned into halves. Then repeat with both shapes partitioned in thirds and fourths.
- What is different about these two shapes?
- What is the same about these two shapes?
- Who remembers what word you learned in first grade that names how these shapes are partitioned?
If the discussion doesn’t lead into halves, thirds, and fourths, make sure you also bring those names into the discussion. An important concept to discuss is that two halves equal one whole, three thirds equal one whole, and four fourths equal one whole.
Additional Activities (if needed)
- Students can glue these shapes into their math notebook or on paper underneath the flaps (see activity sheets) identifying how many equal parts the shapes have been partitioned into and then label the number of pieces in each whole.
Evaluation of Student Understanding
Informal Evaluation: Students discuss the partitions and shapes with the teacher or an assistant during math rotations. Are the students able to use the math vocabulary correctly as they put the shapes into their math notebooks? Can they illustrate the vocabulary correctly? Do they demonstrate a good understanding of what it means to partition a shape into equal shares?
Formal Evaluation/Exit Ticket: On a sticky note, write the most important thing to remember when partitioning shapes. Post sticky notes on the board to share tomorrow.
Meeting the Needs of the Range of Learners
Intervention: Allow students to fold or cut shapes along the partitions and prove that the pieces are equal in size. Also, if the students are struggling with focusing on the pieces as opposed to the number of lines, have them number the pieces on each shape. Give students additional shapes to partition.
Extension: Independent assignment to allow students to partition the shapes correctly and to write about partitioning shapes. (See activity sheets)
Students will sort shapes by the name of the shape or the number of lines that partition the shape.
Ask students what else do they notice about the shapes. Is there another way to sort the shapes?
Have them look at the anchor chart created in the lesson.
Students sorted their shapes to match the number of people in the group (we each get three shapes).
Remind students to sort the shapes using a rule that uses math language and can be explained to the other students. What is the same about your shapes? What is different about your shapes? How can comparing the shapes help you to find a rule to sort them by?
Activity Sheet 1--partitioned shapes to cut out
Activity Sheet 2-- more partitioned shapes to cut out
Activity Sheet 3--Flapbook for Sorting Shapes
Activity Sheet 4--Partitioning Circles Extension Activity
Name: Partitioning Shapes
Shade the circles that are partitioned correctly into thirds or fourths.
Explain how you know that those circles are partitioned correctly.
Activity Sheet 5--Partitioning Rectangles Extension Activity
Partition this rectangle into halves.
Partition this rectangle into thirds.
Show two different ways to partition these rectangles into fourths.