Fraction Unit by ashrafp


									                 FRACTION DIFFERENTIATED UNIT
*All units must include samples of students’ work.
Name: ____Jodi Adams_______
Grade level: __3rd__                  Subject area: ___Fractions___

Differentiation Strategies used: (Explain, giving lesson #, if applicable.) Most of my
lessons use the process strategy of differentiation. However, lesson 6 includes
both process and content strategies.

Unit Topic: Basic fraction skills
Unit Essential Questions: 1. What do the digits in a fraction represent? 2. When I
compare 2 fractions, how do I know which has a greater value? 3. When are
fractions with two different names equivalent?

Unit Enduring Understandings:
Standards addressed: M3N5: Students will understand the meaning of common
fractions in simple cases and apply them in problem solving situations.

Describe the learners for this activity: A mixed ability 3rd grade classroom
On what basis were these learners chosen for differentiation? Scores on a pretest
Grouping Strategies (Explain, giving lesson #, if applicable): The students will be
grouped based on how they performed on the pretest. I’ll group similar scores
together (21%-40% are high, 20%-10% are average, 9%-0% are low)
Differentiated elements used (check all that apply)
_X_ process _X_ content _X_ product ____learning environment

Description: (Explain what has been differentiated in this unit and how the differentiation
was achieved. Be sure to demonstrate how this activity was different than that for other
students in the classroom or community.) Throughout the unit, process
differentiation is used. In some tiered lessons, the students are grouped based on
levels of mastery shown on the pretest. The activities that each group is assigned
are more or less difficult to complete based on Bloom’s. The low group does a lot
with the guidance of the teacher. At the end of lessons 2, 5, and 7, the students
will complete a Math Learning Log to reflect on his/her learning. These will be
collected and graded using the rubric on the back. A copy is attached.
Describe the activities:
Day 1 Lesson 1 (Whole group)

Activity: Distribute the pre-test to the students. Instruct them to do the very
best that they can, but not to worry if they do not know some of the answers.

Explain to them that a pre-test assesses what they know before we begin a unit –

we haven’t studied any of this material yet. The students will have as much time as

needed to complete the pretest. Using the students’ scores, I will group them

based on mastery. The following chart shows the breakdown of results.

          Group                   Range of scores          Number of Students in
                                     ** out of                  the group
         3: High                 40%-21% correct                    7
       2: Average                20%-10% correct                    8
         1: Low                   9%-0% correct                     3

A copy of the pretest is attached. It is based on 3rd grade standards. It includes

decimals too; however this unit focuses on fractions only. Decimals will be

addressed in a separate unit. These groups are flexible based on need of the

students. No students completely compacted out of the fraction unit.

Reflection: This was not a new strategy for me or my students. They knew what
was expected and the process. However, I have noticed two of my lower level

students rarely complete the entire test, even with extended time. These

students know to try and get as far as they can, but they usually test into the

lower group each time.
Day 2 Lesson 2 (Tiered Lesson & process differentiation)

EQ: What do the digits in a fraction represent?
Activity: I will begin by using the carousel strategy with the whole class. I will
number the students 1-4. The same number groups will begin at a chart in the

room with a specific question. As a group, they will answer the question and after

2 minutes, rotate to the next question. The questions include: 1. What is a

fraction? 2. How can I show ½? 3. When would I use fractions in my everyday

life? 4. What are the two parts of a fraction and what do they tell me? I will

then review the responses to the questions. After, I will break the class into

leveled groups. My high group will complete a math mystery titled “Look Who’s

Talking” together. A copy is attached. It focuses on using fractions and the

knowledge of fractions to solve a mystery. My average group and low group will

stay together to talk about the digits in a fraction and what each means. They will

model the concept of equal groups by folding paper and labeling the numerator and

denominator. I will guide the students to fold paper strips into different equal

groups and we will label the pieces. The average group will break off and practice

the skill by completing text pg. 499 #4-19. The low group will continue to work

with me to practice writing fractions with appropriate numerators and

denominators on white boards. At the end of the lesson, the students will

complete a Math Learning Log to reflect on the lesson and what they have learned.

These will be kept by the student until a later date.

Assessment: Teacher Observation
Reflection: Through my teacher observation, I noticed that despite how they
scored on the pretest, many of my students quickly grasped the concept of writing

fractions and equal groups. It didn’t seem to take as many repetitions to catch on
as I thought. However, my higher group struggled with working together. There

were too many leaders wanting to lead. That caused me to take some of my focus

away from my low group to intervene with the high group. Next time, I might have

them work with a partner instead of a group. I also needed to have a more

“exciting” way for my average group to practice other than the text page. I could

see that they were distracted by some having my attention and others working

with friends.
Day 3    Lesson 3 (Tiered Lesson & process differentiation)

EQ: What do the digits in a fraction represent?
Activity: I will break the class into the ability groups and each will complete a
different activity. We will extend the lesson from the day before and identify and

write fractions of a set. The high and average groups will complete an activity

titled “Bowl of Beans”. Directions are included, but the students will choose 2

fractions. The denominators must be either 2, 3, 4, 6, 10, or 12. They will divide a

piece of paper into 2 equal halves and record one of the chosen fractions at the

top of each half. Using beans, students will create models that show the fractions.

Then write sentences to explain how the model matched the fraction. If time

allows, or the students need to extend, they can complete more than the 2. The

low group will work with me. I will guide them to identify and create fractions of a

set using colored circle manipulatives and white boards.

Assessment: Teacher Observation and check the bean papers
Reflection: This was a fun lesson. Most of my students stayed on task and
interested. I decided at the last minute, and because of the lesson before, to

partner the students from the high and average groups to complete the bean

activity. I let them choose their own partners. That choice, paired with the

interest in the activity, had many students more engaged. The students that

worked with me struggled at first with creating sets to match a given fraction. So

we backtracked and I created the sets. I then asked them to write the matching

fraction. They did well constructing that way. After many examples, I revisited

having them creating the set for a given fraction and it seemed to come easier. I

still have one student that was not as confident with parts of a set, so I will work

with him during morning work time.
Day 4 Lesson 4 (Whole group lesson)

EQ: How do I use fractions in my everyday life?
Activity: I will read The Doorbell Rang by Pat Hutchins. We will discuss what the
denominator would be to represent the cookies from the story. After listening to

the story, small groups (by seating) will get a written problem, real cookie

manipulatives, and paper to create a poster. Examples of the problems are

attached. The focus will be on using what we have learned the last 2 lessons;

naming and writing fractions to match a set and a whole. Students will share the

findings from their posters with the class.

Assessment: Rubric for the poster each group creates (rubric is attached)
Reflection: Cookies, any food for that fact, is a great motivator! The kids were
told if they worked hard and thought about fractions, they’d get to eat their

manipulatives. This encouraged the students to stay focused and work well within

the groups. I had them working with the groups they sit with instead of their

ability group. This allowed for high levels of thinking and modeling to occur at each

group. The students did a good job. I will do this lesson again next year with

fractions! The only thing I would change is to allow for more extension questions

for groups that finish quickly.
Day 5 Lesson 5 (Whole group lesson)

EQ: When are fractions with two different names equivalent?
Activity: We will begin by playing “Hangman”. The key word will be equal. I will
then define what equivalent means by pointing out the word part meaning equal.

Then I will distribute paper to make fraction strips. We will make them together.

I will give them a few minutes to explore the finished strips. Then, I will model

how to use them and how they can show equivalent fractions. I will then have the

students break into small groups (number them 1-5 and group 1’s together and etc)

to answer questions using the paper fraction strips. A copy of the question sheet

is attached. At the end of this lesson, students will revisit their Math Learning

Logs and reflect. They will keep these in their binders.

Assessment: Teacher Observation
Reflection: The students really liked making their own manipulatives that they
could use in any number of ways. We began by using them together to show

equivalent fractions. My high kids got this quickly and began doing more on their

own. During my lesson, the ELMO projector was in my classroom from a lesson my

student teacher taught, so I decided to use it too. What a GREAT tool to use to

model how some manipulatives worked. I was able to move the paper pieces around

on the overhead, and the kids could see it on the board through the LCD projector.

Very cool… I want one of my very own. Anyway, after breaking the kids into groups

and giving each the question, they quickly got to work. That was reassuring.

However, I had one student who didn’t want to share his thinking with his group

members and tried to hide his manipulatives. He said he felt like they were

cheating. The lesson went well. Next time though, I could tier my groups and give

them all more than one question to work on.
Day 6 Lesson 6 (Tiered Lesson) (process and content differentiation)

EQ: When are fractions with two different names equivalent?
Activity: I will break the students off into the leveled groups. The high group will
work with a partner from within that group. They will choose a “Fraction Fairy

Tale” (see attached). These stories include 4-5 story problems that use fractions.

I will take a grade for these activities. The average group will complete a see-saw

worksheet on their own. This worksheet will allow the kids to practice identifying

equivalent fractions. They will be asked to use the fraction strips that they made

from the day before, if needed. A grade will be taken from the activity. The low

group will work with me at the back table. I will continue to model what equivalent

fractions are by using a balance scale and weighted fractions. The students will

each take a turn to try and balance the scale to make them equal.

Assessment: The high and average groups will receive a percentage grade based on
the work done. The low group will receive a participation grade using teacher


Reflection: This lesson was observed by Tori Sinco. It started off with a quick
review of equivalent fractions and directions. All the students were engaged and

working hard to solve their problems. The fairy tales were too easy for my high

kids and didn’t require them to think as hard as I thought it would. Next time, I

will require them to also write their own and share with another group. The middle

group did a great job of making the seesaws balance. I even liked the feedback

the students gave me on the reflection piece. The low group still struggled a bit

with equivalent fractions, even using the balance scale. I’m going to need to pull

them some more to work. I did have one student that didn’t do well on the seesaw

activity. He clearly still didn’t grasp equivalent fractions, so I will move him to my

low group for the next activity.
Day 7 Lesson 7 (Tiered Lesson) (Process differentiation)

EQ: When I compare two fractions, how do I know which has a greater value?
Activity: I will start off whole group using a flipchart that introduces adding and
subtracting fractions with like denominators. Afterwards, I will break the class

into their ability groups. The high group will be making cubes independently. They

will be writing 6 story problems, one on each side (3 adding and 3 subtracting) and

also include an answer sheet. They will have an example to look at. The average

group will complete an activity called “Pizza Party” in their small group. See the

attached directions for the activity. The low group will work with me using

fraction stacks. We will use these to model how to add and subtract fractions

with like denominators. They will record our models on a separate piece of paper.

At the end of the lesson, the students will revisit the Math Learning Logs one last

time. They will reflect on what they learned. I will collect these to grade using

the rubric on the back of the log.

Assessment: Teacher Observation (Participation grade)
Reflection: After teaching this lesson, I reflected on a few things…
First, I think that the students like being broken into groups and doing different

tasks, as long as they are meaningful. However, they want to work with a partner a

lot, which doesn’t always let me know what they know, on their own. Or, sometimes,

working with someone cause more off task behavior than on task. That is what I

observed with my higher students who were supposed to be writing addition and

subtraction story problems. Initially, I expected them to work independently on

the activity. A few asked if they could work on it with a partner and I said “yes”.

This caused some not to work to their full potential. However, working with my

lower students allowed them more direct instruction which allowed them to become

more successful and grasp the concept better. Overall, it wasn’t a bad lesson.
Day 8 Lesson 8 (5 days to complete) (Whole group) (Process differentiation)

EQ: none
Activity: The class will be given a choice board to complete. I will expect the high
group to complete 3 activities (one from each skill area) over the 5 days. While

the average group should complete 2 activities and the low group should complete

at least one (and not the free choice). The Choice board is attached.

Assessment: The students will be assigned a participation grade on completing the
required assignments.

Reflection: Not so good… It could have been better. I should have tiered the
choice boards and had the same expectations of completing 3 activities. Some of

my high students felt like they didn’t get pushed and my low kids got too pushed.

Although, they did enjoy the tasks once they got started. I also didn’t allow for as

much time to complete their activities as originally planned due to my student

teacher needing to take over. With that being said, I had 4 students not turn in

the finished activity, however it was my lower students. I also used a premade

choice board… why recreate the wheel? I would have tweaked some of the lessons

a bit in order to better match what we had done in class. Next time…
Day 13 Lesson 9 (4 days to complete) (Whole class) (product differentiation)

EQ: How do I use fractions in my everyday life?
Activity: The class will be given some choices to create a final product using their
mastered fraction skills. I have tried to limit the choices, but wanted to include

multiple intelligences within the choices. The students will be able to create a

board game using fraction skills, write and illustrate a story that includes at least

3 basic fractions, 2 adding situations, and 2 subtraction situations. Design a poster

to teach a second grader about fractions including all the skills we’ve discussed,

complete a WebQuest (for my high group only) on fractions, or write a song or

poem to help learn important fraction vocabulary and skills. The direction sheet

that would be given to the student is attached.

Assessment: Rubric
Reflection: The students were really excited to get started on this project!! I
was interested when I gave them choice, how many wanted to use technology. Due

to limited number of computers in the classroom, I had to only let 5 students

complete the WebQuest activity. I only had one student choose the song/poem, 6

choose to make board games, and 6 choose to create a poster to teach second

graders. A few of them got to share their posters with a second grader from Mrs.

Beal’s class (authentic audience). I also set out the board games during one day or

centers and indoor recess. They were excited to play the games. That was an eye

opener for some who didn’t do as good a job on the games they created. It was

realized when someone went to play it. Giving the rubric to the students and going

over what an “A” would look like was helpful to many, especially my high students!

They knew what they had to do to reach their goal. I will definitely do this

culminating activity again. Next time, to make it even more rigorous, I would have
a few more choices including a more creative one by using a SCAMPER activity and

the fraction skills.
Day 17 Lesson 10 (Whole group)

EQ: none
Activity: The students will take the post test, which is the same as the pretest
except with the decimal questions deleted (decimals is the next mini unit). I will

ask the students to do their best and take their time. I will allow students to

move around the room to comfortable spot where they will be able to work.

Assessment: Graded tests and look for gains
Methods & Materials for the Gifted
Teacher: Jodi Adams       Date __2/13/09____
Content Area: Math: fractions      Grade Level: 3rd
Focus of the unit:
The focus of the unit was basic fraction skills. Students should be able to write,
identify, compare, order, add and subtract fractions with like denominators.

What activities did you include that demonstrate higher level thinking? (critical and/or creative
thinking) I had the students reflecting on what they were learning throughout the
unit. I tried to ask a lot of “why” questions and would ask them to prove there
thinking/answers to me. My culminating activities encouraged them to be creative
thinkers in how they showed what they learned. The choice board from lesson 8
also allowed for higher level thinking because it had them applying what they could

How would you describe/judge the students’ engagement in learning during the unit?
The students were highly engaged throughout the unit. Students who were getting
meaningful work were pleased to do it, and do it well. I did find that during some
lessons, a few students had to change ability groups. Either they performed
better on the pretest, or during the course of the lesson, didn’t master the
content. So the groups were very flexible. I felt like this was a better way to get
to my students’ needs even more.

Did the students perform as you had expected? Explain. I wasn’t sure what to expect. The
students seemed to take away a lot from the unit and most did perform as
expected. However, a few students had to be moved around with in my leveled
groups due to not grasping concepts as readily as I thought. Many students
commented on how they liked the activities and the choices, especially the
culminating activity.

If you teach this unit in the future, what would you change or add to make improvements?
√ Attach work samples from student(s) and any handouts provided to students.
√ Attach pretest
√ Attach copies of instructions, handouts, and worksheets
��Attach observation reports

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