Mini Work Sample:



Mini Work Sample:

Third grade Introduction to Fractions

Lori Gombart

Northwest Christian College

EDUC 582 Curriculum, Instruction & Assessment

December 14, 2011

Angela Long, PhD

TABLE OF CONTENTS

Section I: Establishing Classroom Climate

Classroom Management Plan ……………………………………………………………..…4

Philosophy of Education ……………………………………………………………….…….7

Section II: Planning for Instruction

Unit Description and Overview………………………………………………………….…..9

Unit Rationale and Essential Questions ………………………………………………….…10

Common curriculum goals …………………………………………………………….……12

ODE Standards, Benchmarks or Foundations ………………………………………….…...14

Bloom’s Taxonomy: Levels of learning targeted………………………………………..….15

Key Facts …………...…………………………………………………………………..…..16

School Demographics…….……………………………………………………………..…..17

Classroom Demographics …………………………………………………...…………..….19

Teacher Road map …………………………………………………………...………..……20

Lesson Plan 1 : M&M’s…………...…………………………………………………..……21

Lesson Plan 2 : Fraction wall…………………………………………………………....….26

Lesson Plan 3 : BIG Number line………………………………………………..……..…..31

Lesson Plan 4 : Pizza…………………………………………………………………..……37

Lesson Plan 5 : Science of fractions……………………………..………………………….42

Section III: Evaluating Student Progress

Description of Pre- and Post-Assessment of the Unit Directly Related to Learning Goals..49

Sample (quantifiable) of pre-assessment and resulting data………………………………..50

Sample (quantifiable) of post-assessment and resulting data……………………………….52

Section V: Exhibiting Professional Behavior

Analysis of Video ………………………………………………………………………..53

Final Self-Evaluation/Diary Reflection…………………………………………………..56

Section VI: Resources/Works Cited

Include all lesson worksheets and handouts for the unit………………………………..58

Lesson 1 Worksheet…………………………………………………………………….59

Lesson 1 Homework: Fraction shapes …………………………………………………61

Lesson 2 Worksheet: KWL chart……………………………………..…………………62

Lesson 2 Worksheet: Blank fraction wall and number line 0 to 1………………………63

Lesson 2 Homework: Blank fraction wall strips ………………………………………64

Lesson 2 Homework: Examples of Number lines…………………………………..…65

Lesson 3 Worksheet…………………………………………………………………...66

Lesson 3 Homework…………………………………………………………………...67

Lesson 4 Worksheet……………………………………………………………….…...68

Lesson 4 Homework…………………………………………………………….…..…69

Lesson 5 Reference Station 1……………………………………………………….…70

Lesson 5 Reference Station 2 …………………………………………………………71

Lesson 5 Reference Station 3 …………………………………………………………72

Lesson 5 Reference Station 4 …………………………………………………………73

Lesson 5 Reference Station 5 …………………………………………………………74

Lesson 5 Reference Station 7 …………………………………………………………75

Lesson 5 Worksheet…………………………………….………………………….….76

Checklist………………………………………………………….………………...….77

Resources………………………………………………………….……………..…….78

Section I: Establishing Classroom Climate

Classroom Management Plan

Setting clear expectations for the rules is a must for students. They need to know what is expected of them to create a safe learning environment. At any age, students can be engaged in conversation about creating a learning environment. This should be done on the first day of school. The simpler the rules are the better because they are easy for kids to remember. At Hucrest Elementary School in Roseburg Oregon, there are three simple rules: be safe, be respectful and be responsible. On the first day of school the students will participate in a brainstorming group discussion of how to achieve these rules. Letting the students create 5 or more ideas under each main heading assists the students in understanding the rules, taking ownership of the classroom environment and promotes achievement towards self-discipline.

Teaching Channel has given me some great ideas for strategies to maintain classroom order. Some strategies to use in the classroom could be creating competition through games to keep order by engaging the students in fun, using proximity to the student to discourage misbehavior, using body language such as a finger to the mouth for being quiet and positive narration such as “I see Jasmine has her desk cleared and ready to go to lunch.”

Managing transitions is a part of classroom management. I liked Ms. Noonan’s (from ) transition plan for “word of the day”. The students take ownership of the classroom by taking turns choosing the word of the day. This technique forces the student to listen to all the instruction before following them. It seems that students get anxious acting on the instructions before they are complete and then miss some of the instructions, which causes further disruption as they the instructions must be repeated for those that didn’t hear them. The idea is that the students cannot move or act on the teacher’s instructions until she says the word of the day. This technique helps the teacher with classroom management while simultaneously expanding the student’s vocabulary.

Here is an example of what the final collection of ways to apply the three simple rules:

Mrs. Gombart’s Classroom Rules

Follow School rules: Be safe, Be respectful and Be Responsible.

Ask the students, what are some Ways to be Safe?

Keep hands and feet to self

Walk calmly and quietly while you are in the school building

Follow school rules

Wash hands after using restroom

Ask the students, what are some Ways to be Respectful?

Keep hands and feet to self

Raise your hand when you have a question or want to participate

Do your best

Follow direction the first time

Respect rights and property of others

Be positive (no putdowns)

Accept differences

Be an active listener

Ask the students, what are some Ways to be Responsible? (What are the student’s responsibilities)

Be prepared

Be an active listener

Let the teacher teach

Arrive on time

Stay on task

Put your name on your papers ASAP

Ask questions (Only dumb question is the one not asked)

Discipline yourself so the teacher doesn’t have to

Be a part of the solution, not the problem

Build a cooperative community

Keep food or drinks in your backpack

Consequences procedures for breaking the rules?

If you break a classroom rule:

1. Name is written on the board – 1st warning

2. One check by their name – 2nd warning

3. Two checks by their name – 3rd warning

4. Three checks by their name – Sent to the office

*Names will be erased with appropriate behavior as expected above.

Philosophy of Education

Education in my classroom will comprise of three essential values; the knowledge that can be built on and manipulated, a safe environment that allows all individuals to thrive and a teacher willing to match the teaching style with the learning style of the student. In addition the teacher must have high expectations for the students and be aware of the unseen forces that affect a student’s ability to learn.

Education, in its primal sense, is about obtaining basic skills. These skills include obtaining concrete knowledge such as reading, writing and arithmetic to communicate. Once a person knows how to read and write then their imagination can do the rest to create our world. Going to school is a foundation for getting the skills of knowledge and how to apply and manipulate the knowledge to explore our planet through science, art, music, language, world travel, and affect our planet by creating a thriving and safe community.

How can the learner feel safe to explore their thoughts and ideas? The teacher can promote a safe environment for learning by encouraging questions. Welcoming questions, the teacher often learns as much as the student. Normalizing error during group discussions where asking questions and giving incorrect answers are part of the learning process, allows students to feel comfortable while participating in learning. The only dumb question is the one not asked and classroom also learns from wrong and right answers.

Students learn best when they feel liked, appreciated and valued by the teacher. By finding the good in every student, the teacher instills confidence and nurtures a love for education. Connection between the student, teacher and class is at the heart of engaging students to want to go to school and learn. Each student has something to offer the learning process. Celebrating uniqueness has its own reward. It gives the student permission to be their unique self; appreciated by everyone.

The teacher must be flexible, experienced and willing to apply an assortment of teaching skills within a classroom of many different learners. Each day will begin with clear expectations for the day and feedback will be specific and promote positive growth. Each lesson planned will have a variety of techniques that appeal to the variety of learners. This flexibility must also take into consideration the unseen factors of education in the diversity of learners such as race, socio-economic status and family values to support opportunity for self-expression, personal growth and a desire to learn in the classroom and for a lifetime. Education is freedom

Section II: Planning for Instruction

Unit Description and Overview

Before third grade, students only know numbers as whole. This unit on fractions has the main purpose to develop students understanding of fractions also as numbers.

The Common Core Standards (CCS) adopted by Oregon are designed to prepare students to go to college and have careers by mastering higher order thinking skills through opportunities to speak, listen, cooperate, think, analyze, reflect, and apply to real life (Teaching Channel). In the real world any math problem will have multiple ways to arrive at the answer. During these opportunities students may even learn by making mistakes while practicing these skills. The CCS focuses on fewer topics in greater depth. This unit on fractions is designed the same way. Building on previous knowledge, learning new knowledge and then being able to apply it in the future is the goal with this unit. Using real life examples is another goal of CCS and another goal of this unit. Math becomes sensible and worthwhile when students can apply it to their world.

Instructional strategies used in these five lessons will encourage learning such as finding more than one way to get an answer through use of appropriate strategy, modeling mathematics, practicing precision and opportunities to explain their thinking.

Looking at the CCS provides the foundation of what to teach. The teacher then chooses how to accomplish these standards. Applying knowledge from the real world is essential to keep the students engaged in learning. Woven into these lessons are opportunities to work with props such as candy, clocks and measuring sticks. Alternating between dyads and group discussion will allow scaffolding learning to take place.

Unit rationale and essential questions

Third grade students will build on their knowledge that they received in second grade and their familiarity of telling time, using money and a tactile experience of dividing clay into parts of the whole. Although fractions are an aspect of everyday life, students may not realize how often they must apply fractions in their life. Using a clock to express time in fractions, money in fractions, foods like pizza, brownies and apples will demonstrate the relevance of fractions to their lives and their community. We will explore fractions in a science laboratory in lesson five so students can rationalize the limits of fractions.

I plan to make fractions fun and easy to understand by involving many opportunities to learn hands on. Students will divide clay into parts and change their shapes without changing their fraction. Using real life examples of candy, paper pizzas, fractions walls and science experiments through out the lessons will assist the students to integrate the concepts of fractions as parts rather than size or shape, after all, fractions come in all shapes and sizes.

Since elementary students need lots of opportunity to practice concrete skills, they will be given demonstrations on the overhead, handouts to follow along with, work in dyads and small groups while exploring and interacting with the clocks, money and clay, food and science. There will be a variety of ways to explore fractions such as hands on, drawing visual representations of circle, rectangular and array fractions and analyzing some fractions experiments.

This lesson is primarily focused on introducing the student to recognize a fraction when written, to use oral language and read a fraction and practice it in many forms on worksheets, videos, songs and kinesthetically.

To achieve the skills and knowledge of the learning objectives the students will discuss fractions found in their world with clocks, money, shapes made of clay, paper pizzas and science experiments. Students will meet standards of understanding a fraction as 1/b and a/b as part of the whole. They will integrate their understanding of a fraction based on its parts and not its size. This knowledge will be the foundation for further lessons. Students will make the connections between their visual drawings of fractions and the parts of a number line from 0 to 1. They will also be able to demonstrate why fractions can be equal, larger than or smaller than another fraction.

Unit Essential Questions

1. What is a fraction?

2. What is the number of parts called and does it go on the bottom or top?

3. What is the entire number of possible parts and does it go on the top or bottom?

4. What if no parts are missing, then, what is it called?

5. How can a fraction be represented with numbers and diagrams?

6. Does size matter in a fraction?

7. Which fraction is more?

8. If the divided parts were a different shape how would we write, and read them?

9. What is a number line?

10. How do you make a whole number into a fraction?

Common curriculum goals

The following goals for this unit are derived from the Common Core State Standards for Mathematics .

The primary goal of third grad introduction to fractions is to develop understanding of fractions as numbers.

The students will first understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

Second, students will understand a fraction as a number on the number line; represent fractions on a number line diagram. Students will represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. Students will represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

Thirdly, students will explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Students will understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. Students will recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Students will explain why the fractions are equivalent, e.g., by using a visual fraction model. Students will explain whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. Students will compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Students will record the results of comparisons with the symbols.

ODE Standards, Benchmarks or Foundations

The following benchmarks and standards are taken from . In benchmark 3.1 Number and Operations, students will develop an understanding of fractions and fraction equivalence. In benchmark 3.1.1, students will represent common fractions (e.g., halves, thirds, fourths, tenths) as equal parts of a whole, parts of a set, or points or distances on a number line. In benchmark3.1.2, students will recognize and demonstrate that sizes of fractional parts are relative to the size of the whole. In benchmark 3.1.3, students will use fractions to represent numbers that are equal to, less than, or greater than one. In benchmark 3.1.4, students will solve problems that involve comparing and ordering fractions by using models, benchmarks (0, Ω, 1), or common numerators or denominators. In benchmark 3.1.5, students will identify equivalent fractions using models, including the number line. In benchmark 3.1.6, students will add common fractions with like denominators.

Bloom’s Taxonomy: Levels of learning targeted

There are three domains for learning according to Bloom’s Taxonomy: Cognitive (knowledge), Affective (attitude) and Psychomotor (skills). Within the cognitive domain learning is organized into a hierarchy from the simplest to complex (Bloom’s Taxonomy of Learning Domains). This hierarchy begins with Knowledge or remembering and answering questions. This unit will cover all 6 levels of the hierarchy. This lesson will have several vocabulary words answering the question “what are fractions?” Students will need to recall this information in future lessons that build on the first lesson. Students will demonstrate their Understanding/Comprehension of their understanding of fractions by organizing fractions from small to large and comparing the sizes of fractions on a number line. Students will illustrate understanding of fractions in visual diagrams circles, rectangles and array’s. Students will be Applying their skills of fractions in writing their own story problem in their “My book about fractions”. Students will be analyzing the information collected in their science journals to answer the question of, ”When comparing fractions, why is the comparison only valid when they refer to the same whole?” Students will evaluate their thinking process about fractions in answering group discussion in answering questions such as, “ Based on what you know, how would you explain why 1/4 is bigger than 1/8th?” Students will synthesize/create when they answer the question “ what theory can you formulate about the size of fractions 1/b as b gets bigger?

Key Facts

Fractions are part of the unit whole.

Fractions can be less than one unit whole, or greater than a unit whole.

Whole numbers can be written as fractions.

Fractions can be compared to each other such as >, =, or , =, or , =, or , =, or , =, or 1/6

|1 |2 |

|1 |2 |3 |

| 4 |5 |6 |

|1/2 |> |1/6 |

|2/4 | |2/6 |

|1/3 | |3/3 |

|8/8 | |2/2 |

|1/4 | |3/4 |

|2/3 | |1/6 |

|1/8 | |2/8 |

|5/10 | |1/2 |

|3/2 | |6/4 |

|1/5 | |3/5 |

|1/9 | |9/9 |

|3/3 | |1 |

Station 7 Reference guide

If you could only have one slice of pizza where one slice equals 1/4, choosing from the mini, small, medium or large, which one would you want? Explain why in words and visual images?”

How to measure a pizza or it’s box

The diameter of a circle is the same distance of a box. Use your ruler to measure the four boxes.

Use your graph paper to draw the boxes. Make one graph square equal to one inch.

Make a table in your Science Journal to collect the information on pizza size

|Pizza |mini |small |med |Lrg |

|Diameter in inches | | | | |

Lesson 5 Homework

Students will write up their observations and make a nice book about fractions as well as finish handouts from previous lessons.

Check list for Introduction to fractions

❑ I understand that a fractions is a number

❑ I recall the definition of a Numerator

❑ I recall the definition of a Denominator

❑ I know how to compare fractions and their equivalence

❑ I know how to represent common fractions (e.g., halves, thirds, fourths, tenths) as equal parts of a whole

❑ I know how to represent common fractions as parts of a set, or points or distances on a number line.

❑ I recognize and demonstrate that sizes of fractional parts are relative to the size of the whole.

❑ I use fractions to represent numbers that are equal to, less than, or greater than one.

❑ I solve problems that involve comparing and ordering fractions by using models, benchmarks (0, Ω, 1), or common numerators or denominators.

❑ I identify equivalent fractions using models, including the number line.

Resources

Blooms Taxonomy of Learning Domains (June 1999) Retrieved 12-4-11 from

.

Common Core Standards: Elementary School (09-12-2011) Video from Teaching Channel dot org. Retrieved 12-3-2011 from .

Common Core State Standards for Mathematics retrieved from Oregon department of Education

website at .

Retrieved 11-29-11 from .

Gallery Walk (12-7-2011) Video from Teaching Channel dot org. Retrieved 12-11-11 from

Gardner’s multiple intelligences pie graph: Use when considering differentiation and how to make subject matter engaging. Retrieved 11-27-2011 from

[pic]

KWL Chart. Retrieved 11-14-2011 from Alabama learning exchange from

Mathdrills(dot)com Retrieved 11-19-11 from . Use for homework, assessments images, etc.

Mathwire(dot)com for activities for fractions. Fraction line up. Retrieved from 12-7-11 .

Ms. Noonan: Managing transitions (07-28-2011) Video from Teaching Channel dot org. Retrieved 11-30-2011 from .

ODE searchable standards. Retrieved 11-26-2011 from .

Super teachers worksheets dot com (n. d.) Colorful-fractions-circles.pdf retrieved from .

Templates used in education for teachers Retrieved 12-7-11 from

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[pic]

This is a picture of two whole oranges as a fraction:

There are 2 whole units. The numerator is 2.

The unit of orange is NOT divided; the unit is whole.

The denominator of a whole unit is 1.

2 whole units is written

[pic]

This is a picture of ONE orange cut into eight pieces when all the pieces are still present as a fraction:

The 1 unit of orange is cut into 8 slices.

The denominator is 8 because the unit is divided into 8 pieces.

There are 8 pieces present, so the numerator is 8.

Written as a fraction this one sliced orange with all the pieces present is written as

[pic]

This is a picture of two whole oranges as a fraction:

There are 2 whole units. The numerator is 2.

The unit of orange is NOT divided; the unit is whole.

The denominator of a whole unit is 1.

2 whole units is written

[pic]

This is a picture of one cake cut into 8 pieces.

The Denominator is 8 because it is cut into 8 pieces.

The Numerator is 8 because all the pieces are present.

This is the cake written as a fraction:

8

8

This is a picture of two pans of cake.

There are 2 whole units.

The numerator is 2.

The pans are NOT divided, therefore the denominator is ONE.

Fractions of whole numbers are written

2

1

1

2

1

2

1

6

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