Introduction to Fractions

Introduction to FractionsA learning experience by: Sarah BerrySpring 2013

Introduction to FractionsA Learning Experience Designed by Sarah BerrySpring 2013

Introduction and BackgroundGrade: 1st GradeNumber of students: 16Time frame: 5 days (1 hour per day)There are 2 students identified as having learning disabilities.

My name is Sarah Berry. I designed this learning experience for a first grade classroom at Smallwood Elementary School located in Amherst, NY. My cooperating teacher is Mrs. DiGiacomo and there are 16 students in the class- 2 of which have identified learning disabilities. The LE took 5days to implement. One hour on each of the 5 days was devoted to math instruction.2

OverviewEnduring Understanding:

Dividing a shape into halves will result in two shares that are equal in size. Likewise, dividing a shape into fourths or quarters will result in four shares which are equal in size.

The understanding students should walk away with from this LE is that when a shape is divided into fractional shares, each share will be equal in size. These pictures demonstrate this concept for the fractions and . 3

OverviewEssential Question:When partitioning a shape into a larger number of equal shares, are there smaller or larger pieces?

Guiding Questions:What do halves look like?What do fourths look like?What does it look like to shade in a quarter of a shape?What does it look like to shade in half of a shape?Which is larger? One half or one fourth?

The essential question which students were to explore was whether dividing a shape into a larger number of shares would result in smaller or larger pieces. In order to guide students thinking, each child worked through questions involving what halves and fourths looked like, what it looks like to shade in or of a shape, and also which fraction was larger- one half or one fourth. Students systematically went through these questions and each students thinking was shaped with the intent of reaching full understanding of the essential question. 4

ObjectivesThe student will be able to:1.0 Draw lines on images of circles and rectangles which divide the shape in half/fourth and color in one-fourth/one-half.2.0 Demonstrate the concept of half/fourth by creating rugs using two or four equal shares which together form a circle/rectangle.

The objectives which were to be achieved throughout this Learning Experience included: students gaining the ability to draw lines to divide circles and rectangles into halves and fourths and to color one portion of these shapes and also to demonstrate the concept of halves and fourths by creating rugs with colored shares of equal sizes. 5

Objectives ContinuedThe student will be able to:3.0 circle figures which accurately represent halves and fourths when given a series of images. 4.0 demonstrate his/her understanding of fractions through answering a series of questions about the fractions and .

Students also were to be able to identify figures that accurately represented halves and fourths by circling them and answer questions about the fractions and in order to demonstrate his/her understanding of these fractions. 6

Student TasksThe students will:Complete a pre-assessmentComplete a series of worksheets whose problems involve dividing/identifying shapes divided into halves and fourths in different ways.Create rugs composed of two/four equal partsComplete a post-assessment

At the start of the LE students completed a pre-assessment which was used as a gauge for students prior knowledge. These results informed my instruction. Throughout the five days of instruction, students completed a series of worksheets with problems involving the division of shapes into halves and fourths and the shading of portions of these. They also created rugs using pieces of colored paper. These rugs represented halves and fourths. Following instruction, students were given a post-assessment to gauge their growth throughout and to asses their knowledge at the close of the learning Experience.7

Common Core Standard: Mathematics (1.G.3)

Standard: 3. Partition circles and rectangles into two and four equal shares, describes 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.

Page Number: 16 (NYS P-12 Common Core Learning Standards for Mathematics) (PDF)

I used the Common Core Mathematic standards. This LE aligns with the grade 1 Geometry standard 3 (which can be found on page 16 of the common core learning standards for mathematics document). This standard deals with the division of circles and rectangles into both two and four equal shares and the ability to describe these shares using specific vocabulary as stated. Also, student should understand that decomposing a shape into more equal shares will create smaller pieces. 8

Assessment Tools

Here you see my post-assessment. On the first page, students are asked to demonstrate their ability to divide a shape into both halves and quarters and also to color in a fractional portion. On the second page, students must demonstrate their knowledge of the second portion of the standard dealing with dividing a shape into more shares. This assessment was read out loud to students. 9

Teacher Exemplar

(I would rather have of a sandwich because I would get a bigger piece.)

This is my teacher exemplar for what I would expect on this assessment in order to gain a score of 6 out of 6. 10

Student Work- Distinguished

This is an example of student work which was at the distinguished level. This student correctly divided and colored the shapes and also identified as larger than . 11

Student Work- Distinguished

Total Score: 6/6 ATTRIBUTESCOREHalf Circle1Quarter Circle1Circle one-half1Circle one-fourth1Short Response2

Based on the rubric, this student gained full credit for all attributes and received a score of 6/6. 12

Student Work- Proficient

( by cus it you wit)

This is an example of student work at the proficient level. This student accurately divided and colored the shapes and also identified as preferable to . However, he/she struggled with explaining the reasoning behind this. 13

Student Work- ProficientATTRIBUTESCOREHalf Circle1Quarter Circle1Circle one-half1Circle one-fourth1Short Response1.5 Total Score: 5.5/6

This students received full credit on the first four attributes, and partial credit on the short response attribute. Overall, he/she received a 5.5/6.14

Student Work- Developing

This is the example of a student who is at the developing level. He/she correctly divided and colored the shapes, however struggled in demonstrating his/her understanding that dividing a shape into more equal shares will result in smaller shares. 15

Student Work- Developing Total Score: 5/6 ATTRIBUTESCOREHalf Circle1Quarter Circle1Circle one-half1Circle one-fourth1Short Response1

This student received full credit for the first 4 attributes and only half credit for the short response attribute. 16

Student DataQuestion Number# of students with correct answerPre-TestPost-Test1151627163151647145------156------14

Overall, the class showed growth throughout the Learning experience. On every question in the assessment, students showed improvement between the pre-assessment and the post-assessment. The post-assessment included two additional questions not included in the pre-assessment. A majority of the students did get these questions correct by the end of the Learning Experience. 17

Student Data

Question numberNumber of Students with correct answerPost-TestPre-Test X X

This graph demonstrates students growth over the course of the LE. 18

ModificationsStudents sit on the perimeter of the rug for direct instruction.

Students have work checked, are given suggestions, and then they fix the assignment until it is 100% correct.

Students work close to special education teacher.

During all instruction, I had students sitting on an area rug on the floor. Students were to sit on the perimeter of the rug (leaving the center open). This allowed for me to use manipulatives which all students were able to see. I also could easily see all students and thus limit any behavior problems or distractions.

Something unique to this learning experience is the procedure for independent work. As students complete their work, they brought the assignment to me and had me look it over. I then made suggestions and corrections and the student would return to their desk and make any changes necessary. This procedure offered a built in learning experience for students. They had to work through every problem until they had an answer which was 100% CORRECT.

Those students with identified learning disabilities were seated at the front of the room by the special education teacher. This allowed for more immediate supervision of independent work and also allowed for directions to be read out loud as needed in hopes to avoid any confusion with the assignments.

19

ReflectionId like to thank Dr. Arnold and my peer review group- Katie A., Kara K., Amanda K., Nicole E., Kelly K., and Melanie- for all the amazing feedback on this learning experience!

As a result of my review I found it important to provide students with tangible examples of the rugs which they would be making. I also recognized the benefit of modeling the checklist which was to be used with my post-assessment. By doing this, I could be sure students knew how to use the checklist appropriately.

I owe a big thank you for the success of this LE to my professor, Dr. Arnold and also my peer review group. Each member of this group had a great deal of feedback to give me and allowed me to really develop and expand this learning experience.

Some of the things I decided to improve as a result of my peer review include providing students with tangible examples of the rugs they were making and modeling the self checklist to the students to ensure they understood how to use it effectively.

20

Contact InformationSarah Berry

sberry@daemen.edu

If you have any questions or wish to contact me, I can be reached through email using the address sberry@daemen.edu. 21