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This lesson provided by:
Author: Valerie Harden
System:Mobile County
School:Dixon Elementary School
Lesson Plan ID: 26362
Title:

Share and Share Alike (Equal Parts)

Overview/Annotation:

This Five E’s AMSTI lesson plan equips students to divide an object into equal parts. A story and interactive whiteboard activity about sharing food demonstrate the idea of equal halves of circles, after which students attempt to half squares and rectangles, and explain their findings to the group.  Finally, children divide paper and electronic pizzas into 3 and 4 equal parts.

This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.

Content Standard(s):
MA2013(K) 18. Correctly name shapes regardless of their orientations or overall size. [K-G2]
MA2013(1) 21. 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. [1-G3]
MA2013(2) 25. Partition a rectangle into rows and columns of same-size squares, and count to find the total number of them. [2-G2]
MA2013(2) 26. Partition circles and rectangles into two, three, or four equal shares; describe the shares using the words halves, thirds, half of, a third of, etc.; and describe the whole as two halves, three thirds, or four fourths. Recognize that equal shares of identical wholes need not have the same shape. [2-G3]
Local/National Standards:

2009 Mathematics ACOS Standards (Kindergarten):

#5  Recognize that a whole object can be divided into parts.

· Distinguishing parts of a whole as equal or not equal

#8  Identify two-dimensional (plane) shapes, including rectangle, square, circle, triangle, hexagon, trapezoid, and rhombus, and three-dimensional (solid) figures, including sphere, cone, and cylinder.

 

National Council of Teachers of Mathematics (NCTM) Principles and Standards for School Mathematics:

Process Standards:

Reasoning and Proof: Select and use various types of reasoning and methods of proof. 

Communication:  Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

Primary Learning Objective(s):

The students will be able to distinguish between equal and unequal parts of shapes, and problem-solve to find ways to divide shapes equally. 

Additional Learning Objective(s):

Students will develop problem solving and collaboration skills as they work together to find ways to equally divide shapes.  They will communicate their reasoning and problem solving strategies. Students will review the names of the plane shapes. 

Approximate Duration of the Lesson: 31 to 60 Minutes
Materials and Equipment:

How Many Ways Can You Cut a Pie? By Jane Belk Moncure

Five brown paper circles, divided (see “preparation”)5”  paper squares (3-4 per child)

4” x 6” paper rectangles (4-5 per child)

Eating Fractions by Bruce McMillan

Small (5”) paper plates (1-2 per child)

The Little Mouse, the Red Ripe Strawberry and the Big Hungry Bear by Don Wood

pattern blocks (included in AMSTI kit)

Observation Checklist (attached)

Technology Resources Needed:

Interactive whiteboard

SMART Notebook Interactive Viewer software 

Computer with LCD projector

Web access

Student computer(s) with web access

Background/Preparation:

 

Make five brown paper circles (about 6”).  Draw thick lines to divide one of them into even halves and four into 2 uneven pieces. Leave one blank.

If you do not already have the SMART notebook software installed, take 5 minutes to download and install the free SMART interactive viewer.  Click on the top “download” button, fill in the required information, then click Run.  Follow the directions in the pop-up window.

 

Procedures/Activities:

Engage:

  1. Engage attention with dialog such as: “Have you ever eaten pie? Does one person ever eat a whole pie by herself?  Let’s see what happens to the pie in this book.”  Read How Many Ways Can You Cut a Pie? By Jane Belk Moncure
  2. Ask: “Have you ever had to share a pizza or a cookie with someone?  Did they ever get a bigger piece than you did?”  Display the blank brown paper circle. “Let’s see if we can cut this “pie” into two pieces so that Frog and Mouse can each have the same amount.”  Cut off a small sector, so that the parts are obviously unequal.  Ask children if the two animals would get the same amount of pie?  How can they tell? Invite volunteers to show the class how they know the two parts are not the same. 
  3. Cut each of the other unevenly divided circles , asking children if the pieces are the same.  Finally, ask a child to show where you should cut.  Cut the circle into equal halves, and fold to show they are the same.  Introduce the word “equal”.
  4. Display the Cutting Cookies Smart board activity (attached). Have a student pull a cookie apart by touching one “half” and sliding it away.  In unison, class says “equal” or “not equal”.  Flip one piece to check (double tap the piece, tap the arrow that appears, choose flip from the pull down menu).  Repeat for other cookies.

Explore:

  1. Explain that now that children are “experts” it is now their job to find ways to divide some other shapes into two equal parts.  Display a square and rectangle and review shape names.
  2. Divide children into pairs.  Give each pair 6-8 squares.  Together they must find a way to cut a square into two equal  Both partners must agree that the parts are equal. parts.
  3. As they work, ask questions such as “How can you tell if your parts are equal?  What strategies did you try?  Can you find another way to make two equal parts?”
  4. Give each pair a supply of rectangles (6-8).  Challenge them to cut these into two equal parts. As they work, ask questions as above. Have them compare the dividing of squares to the dividing of the rectangles.  Ask questions such as “How was it alike?  How was it different?” 

Explain:

  1. Gather the children once again in a central location.  Have each pair bring with them the shapes they successfully divided into equal halves.
  2. Begin with the squares.  Have one pair display the halves they brought to the rug.  Use questions such as the following to encourage children to communicate their reasoning and problem solving skills:  How do you know they are equal?  Show us how you and your partner figured it out.  Does everyone agree?  (If the parts are not actually equal, prompt other children to explain why) Did anyone figure it out a different way?  Can you show us? Raise your hand if you cut your square the same way they did.  Did anyone cut it a different way?  Show us.  How can you tell the parts are equal?  How many ways can we cut a square into two equal parts?  As students explain their thinking encourage them to use math vocabulary such as parts, halves, divide and equal.  Make sure student understand these concepts. 
  3. Repeat this dialogue for the rectangles.

 Extend:

  1. If time permits, read The Little Mouse, the Red Ripe Strawberry and the Big Hungry Bear by Don Wood, and discuss whether the strawberry is cut into equal parts. If it had been cut horizontally would the parts be equal? Display this Symmetry Website on the interactive board, and click the first two shapes to see them cut into equal halves.  Ask children to predict where each shape will be “cut” before clicking it.
  2. Extend the learning to include 3-4 equal parts. Read Eating Fractions by Bruce McMillan.  Challenge children to cut squares and rectangles into 3 or 4 equal parts.  Discuss as above.
  3. Have children color small paper plates to resemble pizzas.  Ask children who need a challenge to cut their “pizzas” into three equal parts, those who need extra practice to make two parts, and the rest to make four.
  4. Use this web book I Want My Half to practice dividing objects into 2-5 equal parts.
  5. For an extra challenge, remove the tan rhombi from the pattern blocks and put the remaining blocks in a center.  Ask students to figure out which pattern blocks are equal parts of which other ones (example, a red trapezoid block can be divided into three green triangle blocks).

Evaluate:

While circulating during the explore phase, observing students’ work and listening to their explanations, use the Observation Checklist (attached) or anecdotal records to note students’ level of mastery.  Use the rubric below to assign a score to each student.

4 -- Student found more than one way to equally divide each shape.

3 -- Student found one way to divide each shape, and clearly understands the difference between equal and unequal parts.

2 – Student divided one shape equally and the other unequally, OR divided the shapes almost equally.

1 – Student cannot distinguish between evenly and unevenly divided shapes


Attachments:**Some files will display in a new window. Others will prompt you to download. CuttingCookies.notebook
ObservationChecklist.doc
Assessment Strategies:

While circulating during the explore phase, observing students’ work and listening to their explanations, use the Observation Checklist (attached) or anecdotal records to note students’ level of mastery.  Use this rubric to assign a score to each student.

4 -- Student found more than one way to equally divide each shape.

3 -- Student found one way to divide each shape, and clearly understands the difference between equal and unequal parts.

2 – Student divided one shape equally and the other unequally, OR divided the shapes almost equally.

1 – Student cannot distinguish between evenly and unevenly divided shapes

Extension:

  1. Extend the learning to include 3-4 equal parts. Read Eating Fractions by Bruce McMillan.  Challenge children to cut squares and rectangles into 3 or 4 equal parts.  Discuss as above.
  2. Have children color small paper plates to resemble pizzas.  Ask children who need a challenge to cut their “pizzas” into three equal parts, those who need extra practice to make two parts, and the rest to make four.
  3. Use this web book I Want My Half to practice dividing objects into 2-5 equal parts.
  4. For an extra challenge, remove the tan rhombi from the pattern blocks and put the remaining blocks in a center.  Ask students to figure out which pattern blocks are equal parts of which other ones (example, a red trapezoid block can be divided into three green triangle blocks).
Remediation:

Students who need extra practice can view this Fabulous Fractions web book.  The first two-thirds of the book deal with equal halves.

 

This Pizza Party learning game can be used to reinforce the idea of equal parts. Children count the number of people who need to share the pizza and watch as the pizza splits into that many equal pieces. 

Each area below is a direct link to general teaching strategies/classroom accommodations for students with identified learning and/or behavior problems such as: reading or math performance below grade level; test or classroom assignments/quizzes at a failing level; failure to complete assignments independently; difficulty with short-term memory, abstract concepts, staying on task, or following directions; poor peer interaction or temper tantrums, and other learning or behavior problems.

Presentation of Material Environment
Time Demands Materials
Attention Using Groups and Peers
Assisting the Reluctant Starter Dealing with Inappropriate Behavior

Be sure to check the student's IEP for specific accommodations.
Variations Submitted by ALEX Users:
Alabama Virtual Library
Alabama Virtual Library

Hosted by Alabama Supercomputer Authority
The University of Alabama at Birmingham
The University of Alabama at Birmingham
The Malone Family Foundation
The Malone Family Foundation
Thinkfinity
Thinkfinity
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