 Author:
 DAWNE COKER
 Subject:
 Mathematics
 Material Type:
 Activity/Lab, Lesson, Lesson Plan
 Level:
 Lower Primary
 Tags:
 License:
 Creative Commons Attribution
 Language:
 English
 Media Formats:
 Downloadable docs
Education Standards
T4T Partitioning into Halves & Fourths
Overview
This resource is from Tools4NCTeachers.
In this lesson, students explore partitioning shapes into halves and fourths. The lesson could be taught consecutively in one math block or extended over multiple days depending on students’ understanding of the concept of halves and fourths.
Here is a excerpt from this resource. Click the attachment to access the entre, fullyformatted lesson and materials.
Partitioning into Halves and Fourths
In this lesson, students explore partitioning shapes into halves and fourths. The lesson could be taught consecutively in one math block or extended over multiple days depending on students’ understanding of the concept of halves and fourths. 
NC Mathematics Standard:
NC.1.G.3 Partition circles and rectangles into two equal shares.
 Describe the shares as halves and fourths, as half of and fourth of.
 Describe the whole as two of, or four of the shares.
 Describe that decomposing into more equal shares creates smaller shares.
Standards for Mathematical Practice:
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Attend to precision.
Student Outcomes:
 I can show halves and fourths in more than one way.
 I can show that two halves and four fourths must be equal in size.
 I can explain that when a whole rectangle is partitioned into fourths, the shares are
smaller than if the same rectangle was partitioned into halves.
 I can explain the meaning of one half and one fourth.
Math Language:
partition, equal, fair shares, whole, half, halves, fourth, fourths, rectangle
Materials:
 graham crackers (two whole graham crackers per student plus some extras)
 rectangular sheets of paper or sticky notes as alternatives to graham crackers and for the additional activities
 two small paper plates or cut outs per student plus some extras for additional activities
 copies of Exit Ticket
 grid paper for extension
Advance Preparation:
 secure graham crackers (or cut paper rectangles if needed)
 secure small paper plates (or cut paper circles if needed)
 make copies of the Exit Ticket
Launch:
 Introduce the Lesson (35 minutes)
Ask students if they have ever been told by a parent to share a treat, such as a cookie or candy bar, with another person by breaking it in half. Ask if they liked how the other person broke the treat. Why? Ask if they have been the person asked to break the treat in half. Ask them how they partitioned, or broke it. A few may admit they got the larger piece.
Tell students you are going to give them a graham cracker (or piece of paper they can pretend is a candy bar) and you want them to split the treat in half.
Explore:
 Partition Equally Halves (5 minutes)
Pass out graham crackers or paper rectangles (may use sticky notes) to each student. Have them try to partition the rectangle in half. Have additional crackers or paper pieces available for students who realize on their own that they were unsuccessful and want to try again.
Discuss:
 Share Solutions (510 minutes)
Get students’ attention for a wholeclass discussion. Ask them to look at their two pieces and determine if each half is equal. Select a couple of students to share their pieces (at least one who has two equal halves and one who did not break the parts equally). Facilitate a discussion including sharing treats as discussed in Launch.
Ask: How would you feel if you received the smaller piece?
Be sure to explain that two pieces are not considered halves unless they are equal shares.
Ask students: How many halves make one whole?
Have students share their thinking and strategies for how they partitioned.
Ask: What did you do to determine where to break or cut the whole?
Allow several students to share.
Explore:
 Partition Equally – Fourths (5 minutes)
Pass out another graham cracker or paper rectangle and ask all students to partition in half again, perhaps using a strategy just shared. Then have students partition each of the two halves in half again (to create fourths).
Discuss:
 Share Solutions (510 minutes)
Bring students together as a whole group and ask several students to share what they did. Facilitate the discussion with questions as needed to encourage students to determine that they now have four parts and all four parts should be equal. Again draw attention to parts that are not equal, asking students if these would be fourths and why not. Tell them each of the four equal parts is called one fourth.
Ask: How many fourths do I need to make one whole?
Have students compare one fourth and one half. Have them discuss with a partner what happens to the size of the pieces when a whole is partitioned into more parts.
Additional Activities:
 Give students a variety of square and rectangular pieces of paper. They can be different sizes if desired. Ask students to work with partners to partition the squares and rectangles into halves and in fourths in different ways. Ask: How many different ways can you find? Remind students that the parts must be equal to be considered halves and fourths.
Also have students work with circles. Give students two paper plates or cut outs of circles. Have them partition one circle into halves and one circle into fourths. Since the circles can be challenging to partition equally, circulate to ask students questions as students work. Have extra circles on hand for students who realize their pieces are not equal and want to try again.
Evaluation of Student Understanding
Informal Evaluation:
Observe and monitor students as they are partitioning shapes into halves and fourths. Notice if students are:
 partitioning into equal sized pieces
 partitioning into 2 parts for halves
 partitioning into 4 parts for fourths
 realizing there are multiple ways to partition, resulting in different shaped pieces
 determining halves are larger pieces than fourths
 struggling more with circles than squares or rectangles
Formal Evaluation/Exit Ticket:
Give students the exit ticket below to assess their independent knowledge of halves and fourths.

Partition this square into halves.
What part of the rectangle is shaded? _____________________________________________




Meeting the Needs of the Range of Learners
Intervention:
 For students who struggle determining if the parts are equal, break a graham cracker into two parts where one is clearly larger. Ask if it is fair. Allow them to choose the piece they would want and ask why they chose that piece. Explain that halves and fourths are fair shares.
Extension:
 How many different ways can you partition a circle?
 How many different ways can you partition a rectangle?
 If this rectangle is partitioned with two diagonal lines, is each of the four parts equal (show an example)? Note: It will not look equal. After discussing students may use grid paper to model and add the squares to prove that it is equally partitioned into fourths, even though the parts look different.
Possible Misconceptions/Suggestions:
Possible Misconceptions  Suggestions 
When students partition shapes, halves and fourths are not represented as equal parts.
 Partition a few “unfair” examples and relate the shapes to items in the real world. Talk about being the person who would get the larger or smaller piece. Ask: How would you feel? Help students realize that halves and fourths must be equal and relate this to being fair. 
Special Notes:
 First grade students do not use number notation for fractions. Be sure all of your discussion is with the language of half/halves, fourth/fourths, half of, fourth of and not representations showing numerators and denominators ½ and ¼.
 Share that an efficient way to partition fourths is to start with halves and then partition each half into halves again. It is usually easier to make sure all four parts are equal when beginning with halves. This should help students realize that half of a half is one fourth.
 At some point during the lesson, ask students when they see items being partitioned in real life (pizza, pie, or cake cut into pieces; a basketball court with a halfcourt line, etc.)
Name __________________
Exit Ticket
Partition this square into halves.

What part of the rectangle is shaded? _________________________________________________




Name __________________
Exit Ticket
Partition this square into halves.

What part of the rectangle is shaded? ________________________________________________



