mmoran_report3

Michael Moran Report III 1

Instructional Design 7430Summer 2015Report I, II, IIIMichael Moran

Teaching Students the Proper Methods ofAdding and Subtracting Mixed Numbers with Unlike Denominators

Problem Analysis:

In order for students to truly grow in their mathematical skill set, students must be able to properly add and subtract mixed numbers with unlike denominators as these methods will continue to be utilized in future mathematical classroom settings. Students many times will find themselves having issues recalling the proper steps in solving these similar mathematical functions. The students are unable to transfer the knowledge of adding and subtracting mixed numbers without common misconceptions and resulting in incorrect answers. This process is utilized as a building block for future course loads in further education. Common misconceptions surrounding this content includes, but not limited to: adding or subtracting the denominator, adding or subtracting without finding the least common denominator (LCD), and creating improper fractions unsuccessfully through inductive reasoning, not correctly simplifying the answer using greatest common factor (GCF). In response to this problem a solution for solving mixed number functions is to develop the ability to recognize the stature of the function and the correct process of solving. In order for students to solve these functions correctly students must recognize the operation of the function (either addition or subtraction), once the operation is identified the student should then find the least common denominator, create equivalent fractions using their new denominators, and then proceed to use operational skills to solve for a sum or difference.

This problem that students face with adding and subtracting mixed numbers with unlike denominators is common, and one that needs to be addressed for students to be successful in 5th grade and future mathematical classes. Students need to have further experience in manipulating fractions and creating equivalent fractions coming in to the grade level. Allowing students the opportunity to understand entry level operations such as the creation of equivalent fractions, adding and subtracting, using multiples on a consistent basis, and being able to identify the proper mathematical terminology for fractions will better suit the students’ academic achievement. This process begins at the earliest grade levels with correctly identifying a plus or minus sign, and then continues to build on this in 3rd grade. Fractions and proper terminology of a fraction are introduced in 3rd grade, and multiplication facts are fluently addressed in this grade. Another strategy to best suit the students’ academic achievement is the proper educational training of teachers through professional learning and workshops. This would ensure that students are being taught the proper methods and techniques that can be assessed through academic standardized testing data.


Mager & Pipe Gap Analysis

Needs Assessment:

Optimals: In an ideal school setting at Skyview Elementary, the students from 5th grade skill level and up will have and maintain the necessary skill set to perform proper operations to consistently solve adding and subtracting mixed number functions with unlike denominators.

Step 7: What solutions are best?

It is necessary to design instruction to address these skill deficits. This instruction should require students to practice all of the necessary elements of adding and subtracting mixed numbers with unlike denominators using proper strategies and operational rules. This will lead to success in the current grade level and future mathematical environments.

Step 6: Are there other causes? The lack of parental involvement in a student’s academia, the community in which students reside, and the learning environment of the school.

Step 5: Is there a skill deficiency? Yes, there is a skill deficiency. Students are consistently struggling with meeting the standards identified by the state and the federal regulations, leading to higher dropout rates.

Step 4: Are the consequences right-side-up?

Students who do not master this skill may minimize their academic success and may lead to lower socioeconomic demographics in society.

Step 3: Can we apply fast fixes?

No, students need repeated practice and specific instruction is needed to ensure that students can add and subtract mixed numbers with unlike denominators.

Step 2: Is it worth fixing?

Yes, this is a skill set that is necessary to continue to move on in education and is a building block for more advanced mathematical criteria.

Step 1: What is the performance problem?

Students are struggling to properly add and subtract mixed number functions with unlike denominators.


Furthermore, students will have a clear understanding to solve all related operational functions that include fractions. For the benefit of all learners, students would be able to fluently have a clear understanding of multiples and multiplication facts due to the correlation with finding the LCD, students would have a clear understanding of what an equivalent fraction looks like, students will be able to use the Greatest Common Factor (GCF) to simplify the fractions, and also add and subtract fluently with or without regrouping. In an optimal classroom setting, the teacher would be able to identify the students at a mastery rate utilizing proper formative and summative assessments. Further assessments would be considered the state standardized test GA Milestones to check for a mastery performance. As this content has been identified as a key skill set by the Common Core Georgia Performance Standards (CCGPS) and with the mastery of this skill, students would perform at a mastery performance state (2015).

Actuals: In reality, there are 32 students, each with their own personal life experiences and learning profile. Each student brings with them a specific learning need and some identified through the Response to Intervention (RTI) process and through the development of an Individual Education Program (IEP), students’ needs are developed through a functionality test and the process of identifying which areas a student must grow in before reaching a mastery level. From a wide range of students that have been identified as students with special needs to gifted education, teachers are faced with developing an individual learning profile to differentiate amongst the group and develop co-efficacy strategies. Through the process of intervention and acceleration based lessons each student is identified by their strengths or weaknesses through formative and summative assessments. Before each unit the class participates in a pre-test to identify which students have the proper schema to excel within this unit. After those students have been identified the educator creates the unit to meet the needs of all the learners.

Discrepancies: There are several discrepancies within the parameters of the instructional content. First, there are several students identified that have a common misconception between the numerator and the denominator. Further, the students have a difficult time identifying the multiples of two numbers (denominators) utilizing multiplication facts. Additionally, students have a difficult time creating an equivalent fraction fluently, without the usage of manipulatives. Also, students have issues with adding or subtracting the mixed numbers with or without regrouping. Furthermore, students are unable to simplify fractions through the use of the procedures using GCF and a factorization tree. Because of this, students will be unable to perform at a proficient minimal level to properly add or subtract mixed number functions.

Goal Statement: Students at Skyview Elementary in the 5th grade level will be able to maintain and fluently perform the operations of mixed number functions and continue knowledge transfer for the years to come.

Instructional Analysis:

The domain of this problem is analysis because it is a well-defined problem with applying rules to determine a solution to the mixed number function. Additionally, for the specific type of learning, this problem is best classified as an intellectual skill.


Goal Analysis:

YES

NO

Subordinate Skill Analysis:

Identify the Proper

Operation of the Mixed Number function.

(Addition or Subtraction)

1

Identify the denominators

of the fractions.

2

Using Multiples find the proper LCD.

3

Create equivalent fractions utilizing the new LCD.

4

M

M

Add or Subtract the Numerator

of our fraction

keeping the common

denominator the same

5

Add or Subtract the

Whole Number of our

Mixed Number Function

6

Simplify the solution of the

Mixed Number Function using the

GCF.

7

Is the solution correct,

after checking

with a peer tutor?

Go to Next problem if applicable.

Return to the beginning step using manipulatives to assist.


A procedural analysis seems most appropriate for this problem. With the procedures being very objective steps cannot be manipulated.

Identify the Proper



1

Recognize that a plus sign (+)

represents addition and a minus sign (-)

represents subtraction.

1.1


of the fractions.

2

The denominator is the bottom number of the fraction bar,

e.g.

½2.1


3

Multiples are the

multiplication facts of a specific

number, e.g. 2: 2, 4, 6, 8

3.1

Create equivalent fractions utilizing the new LCD.

4

Create equivalent

fractions by multiplying

the numerator and

denominator by the same

factor.4.1

Add or Subtract the

Numerator of our fraction keeping the

common denominator

the same.

5

Take each denominator and list out

each denominators

multiples.

3.1.1

Identify and circle the common

multiples of the

denominators.

3.1.2

Locate and identify the

least common multiple

shared by each

denominator.

3.1.3

Add or Subtract

the Whole Number of our Mixed Number

Function.

6

Simplify the

solution of the Mixed Number Function using the

GCF

7

Factors are numbers you can multiply together to get another

number.

7.1

Take the numerator

and denominator and list the

factors.

7.1.1

Identify and circle the common

factors of the numerator

and denominator

7.1.2

Identify the GCF and divide the numerator

and denominator by the GCF.

7.1.3


Entry Level Skills

Recognize that a plus sign (+) represents addition and a minus sign (-) represents subtraction.

A

The denominator is the bottom number of the fraction bar, e.g.

½B

Multiples are the multiplication facts of a

specific number, e.g. 2: 2, 4, 6, 8

C

Identify the Proper



1


of the fractions.

2


3

Add and Subtract Mixed Number Functions.


Learner and Context Analysis:

Target Population: This problem that students face with adding and subtracting mixed numbers with unlike denominators is common, and one that needs to be addressed for students to be successful in the 5th grade classroom at Skyview Elementary. Within the specific classroom of 32 students, 3 students were identified on the gifted spectrum, 2 were identified on Tier 3 of the RTI process, 13 students were identified as students with disabilities based on the IEP process, and the rest were Tier 1 students on the RTI process (average range). The students that were determined for the RTI process was based off of AIMSWEB testing quarterly and the student growth model. According to the AIMSWEB testing criteria for a 5th grade student on the Math Computation (M-Comp) students should score at least 13 points on the fall exam and 26 points on the final spring exam to be considered average. Students in mathematics classes also take Math concepts and applications test (M-CAP) where students should score at least 5 points on the fall exam and 12 points by the spring exam to be considered average. Based on the results, almost half of the class is considerably below state average expectations. With this in mind each student’s personal learning profile was thought of when developing the lessons and assessment criteria.

Students at Skyview Elementary are selected by the counselor and administration, as they are each educationally goal driven, for each 5th grade classroom. According to the characteristics of the physical and organizational environment, the classroom has some issues that does not meet the needs of all learners. The classroom has limited technology based on the Title I school setting. There are 4 student computers that have expired learning software which leads to the lack of new mathematical learning methods to be presented to the students and there is no interactive whiteboards within the school to demonstrate mathematical operations to solve mathematical functions. With this in mind each child’s learning profile is not taken into account because of the lack of funding and technological services. Acquiring more technology would improve the classroom setting along with the improvement of student developmental issues within the learning problem analysis. In addition to more technological advances for the classroom, the need for Information Technology (IT) staff would be inherent to ensure the stability of the new interactive technical software. With the current IT staff, it will be necessary for additional training to learn how to apply maintenance and network security to the software. This is to ensure the well-rounded support in all elements so instructors and students will gain the opportunity to exchange learning opportunities. The availability of administrative support is vital to fulfilling educational needs at Skyview Elementary.

Determining the Characteristics of the Target Population: The characteristics of the target population were collected based on a student self-learning analysis utilizing Gardener’s multiple intelligences and the development of a pre-assessment utilized to check for prior knowledge and student understanding of the current content. Each student was given a 13 question pre-assessment on adding and subtracting mixed numbers with unlike denominators. Within this test there were 4 math computation problems, 2 multiple choice questions, 5 word problems, and 2 word problems involving models. The results of the self-learning analysis were tallied for each student on table one and table two consist of the pre-assessment test data.


Self-Learning Analysis Survey (Gardener’s Intelligence Model)Number of Students Determined Intelligences

5 Bodily Kinesthetic8 Interpersonal2 Musical9 Spatial/Visual3 Logical3 Linguistic2 Intrapersonal

Pre-Assessment Results MCC5.NF.1 & MCC5.NF.2

Number Correct (out of 32)

1: Computation 7

2: Computation 6

3: Computation 2

4: Computation 4

5: Multiple Choice 10


7: Problem Solving 3





12: Problem Solving with Model

11


9


Determining the Physical and Organizational Environment:

Information Categories

Data Collection Sources Determined Characteristics

Nature of the Site

Observations Description: This classroom contains 32 student desks, one kidney shaped table for small group, 4 student computers, math vocabulary word wall, multiple factorial graphs, various signs with step-by-step directions for solving mathematical functions, very clean and organized, very welcoming, classroom library with nonfiction and fictional literature (helps with word problem analysis).Constraints: Not enough technology, no interactive white boards, outdated software, too many students in one setting which disables movement about the classroom and limited time with small groups.

Compatibility with

instructional needs

Observations Description: Instruction is delivered daily to 32 students on a 90 minute block schedule within the 180 day academic calendar, small groups enable student growth through one on one or smaller interactive groups, clean learning environments spark learning interest, vocabulary word wall improves dialogue amongst the students and in response with involvement and interactions, classroom library improves reading ability and conceptual learning.Constraints: Teachers don’t have time to collaborate as much as is needed, county has been slow in replacing needed equipment/interactive technology within the classroom, large class sizes based off of limited faculty, furlough days limiting planning amongst teachers.

Site compatibility

for learner needs

Observations Description: Students love interactive lessons that involve games and manipulatives and the learning environment which promotes active learning and creativity. Constraints: Limited interactive technology and the limited space for games and interactions with peers.

Objectives:

Terminal Objectives: In the classroom, when given multiple examples, instructions on strategies of operational procedures (CN), students will be able to successfully add and subtract mixed numbers with unlike denominators (B). Students will be able to perform operational procedures to solve functions of mixed numbers on a consistent basis at a 70% accuracy rate according to the Common Core Georgia Performance Standards (CR).


Subordinate Skills Subordinate Objectives for Main Step1. Identify the Proper Operation of the Mixed Number function. (Addition or Subtraction)

1.1 Students are given a function that will include either an addition or subtraction sign (CN), students will need to determine the operation of the sign (B). Students will be considered successful if they identify the proper operational sign (CR).

2. Identify the denominators of the fractions.

2.1 Students will be given a mathematical function (CN), students will identify the bottom number of the fraction as the denominator (B). Students will be considered successful if they correctly identify the proper number as the denominator (CR).

3. Using multiples find the proper LCD.

3.1 Students are given multiples of the denominators (CN), students will expand the multiples of the two denominators (B). Students will be considered successful if they correctly identify the common multiples and the least common denominator (CR).

4. Create equivalent fractions utilizing the new LCD.

4.1. Students given the proper least common denominator (CN), students will create equivalent fractions using manipulatives and write out the steps of multiplying the denominator by the same factor (B). Students will be considered successful if they create an equivalent fraction with common denominators (CR).

5. Add or Subtract the numerator of our fraction keeping the common denominator the same.

5.1 With the proper equivalent fractions determined (CN), students will add or subtract the numerators of the fractions while keeping the common denominator the same (B). Students will be considered successful if they add or subtract their numerators properly (CR).

6. Add or Subtract the Whole Number of our Mixed Number Function.

6.1 With the proper equivalent fractions determined (CN), students will add or subtract the whole number of the mixed number fraction while keeping the common denominator the same (B). Students will be considered successful if they add or subtract their whole numbers properly (CR).

7. Simplify the solution of the Mixed Number Function using the GCF

7.1 With the problem solved correctly (CN), the student will simplify the fraction to its simplest form using the greatest common factor method (B). Students will be considered successful if they conduct their answer simplest form.

Cognitive Subordinate Objective Domain: 3, 5, 6, 7Attitudinal Subordinate Objective Domain: 1 and 2Psychomotor Subordinate Objective Domain: 4


Assessment:

We would assess the psychomotor subordinate skill of creating the equivalent fractions utilizing the new least common denominator (LCD). The assessments that we would use to determine the success rate of this skill would be through observation and one-on-one conferencing utilizing the proper techniques and strategies of manipulatives. Through this observation the students would be given two fractions with unlike denominators and the students would properly identify the LCD using multiples and then correctly circling the lowest of the common multiples. The students will then use fractional manipulatives to check their equivalent fractions. While walking and around and informally observing we could ask simple questions to check for understanding of the concept. E.g. “Jennifer, how did you identify your denominators? How did you determine those multiples?”

In this instructional design unit, we plan on using many different types of assessments. We plan on using written responses, observation, and a quick formative assessment through conferencing. We would observe the students utilization of the fractional manipulatives and then conference with students to have verbal responses on step-by-step conceptual reasoning to find the least common denominator. As a way of assessing students’ understanding of the concept concerning least common denominator, it is appropriate to have a checklist that we will utilize to check for student understanding. By doing the formative assessment we will gain more insight into the student reasoning and cognitive process in solving for least common denominator. This will allow us to reiterate to those students who have not grasped the concept of properly finding the least common denominator between two mixed number fractions. This formative assessment will be a gateway to build small groups based on conceptual understanding. Those students who have mastered the concept will be accelerated and moved on to further steps and the students who were identified as having little conceptual understanding will be working with the instructors in a smaller group setting to provide more instruction.

Assessment Examples:

Attitudinal: For this objective, I would have the students respond with a check mark to determine the proper operational function of addition or subtraction within the mixed number with unlike denominators. The students will be given three operational problems.

Problem: Addition Subtraction

1. 2 31

+ 1 43

2. 6 43

– 1 85

3. 3 21

– 1 51


Cognitive: For the cognitive skills of adding and subtracting mixed numbers with like denominators, I would conduct an assessment that includes 3 basic adding and subtracting mixed number fractions. This will be based off the assumption that students have the entry level skill of adding and subtracting mastered.

1. 214 + 1

24

2. 418 + 4

58

3. 3512 - 1

212

Psychomotor: During our informal observation that leads into one-on-one student conferencing, we can now determine and assess through our student check list, whether the student has grasped the concept through correctly using fractional manipulatives to find equivalent fractions. Given three fractions students will correctly create equivalent fractions using the fractional manipulatives.

E.g. 18 =

216

1. 31

=

2. 85

=


3. 43

=

Instructional Strategy:

In order to prepare the students for the terminal objective we will provide multiple examples and instructions on strategies of operational procedures so the students will be inherent to successfully add and subtract mixed numbers with unlike denominators. Students will be able to perform operational procedures to solve functions of mixed numbers on a consistent basis at a 70% accuracy rate according to the base objectives of the Common Core Georgia Performance Standards. The first pre-instructional activity that we would conduct is a pre-assessment on the process of adding or subtracting mixed numbers with unlike denominators. This pre-assessment will allow us to collect data and build compatible small groups with likeness of strengths and weaknesses. The small groups in more detail will, based on the pre-assessment performance, either be working on remediation and learning the fundamental skills to add or subtract mixed numbers with unlike denominators, or working on accelerated leveled functions involving mixed numbers. Groups will be constantly shifting throughout the weekly lessons, as it will be contingent on formative and summative assessment performances by the students. Groups will also be multi-dimensional as the groups will not be primarily homogeneous, but heterogeneous. Homogeneous groups will be formed based off of similar achievement level determined through the pre-assessment and formative assessments throughout the week. The formative assessments will determine throughout the week which subordinate skills are being mastered and which skills still need more practice. When students are grouped homogeneously they will be grouped by which students have mastered the skill and which students need more practice and remediation. The purpose of the heterogeneous grouping will allow students to work with other students that have either mastered the skill and the students that have not mastered the skills. This structure is set in place to incorporate gifted learners with students of less comprehensive ability, which will allow students the opportunity to work with each other and learn problem solving skills, team work, and create availability. It also creates an environment of checks and balances among the students. In addition, this grouping will create opportunity for the teacher to actively interact around the room asking questions that can check for student understanding. The ideal pre- and post-assessment is located below as it will be used at the beginning of the unit and the end to utilized comparative data between the results of the pre- and post-assessment. This will allow the teacher to determine academic growth of success or lack thereof and comprehensive issues regarding adding/subtracting mixed numbers.


Summative Assessment: Adding/Subtracting with Mixed Numbers

Student Name: ________________________

Pre-Post TestFind the Sum. Write your answer in simplest form.

1. 2 31

+ 1 43

2. 4 87

+ 4 31

Subtract to find the difference. Write your answer in simplest form.

3. 3 21

– 1 51

4. 6 43

– 1 85

5. During his first vet visit, Pedro’s puppy weighed 6 81

pounds. On his second visit, he

weighed 9 161

pounds. How much weight did he gain between visits?

A. 2 1615

B. 3 161

C. 3 1615

6. Jill walked 8 81

miles to a park and then 7 43

miles home. How many miles did she walk in all?

A. 15 87

B. 15 124

C. 15 161

7. John had 4 81

of pizzas for his birthday party. Elizabeth and her friends ate 3 41

of the pizza. How much pizza was left over?


8. A cake recipe calls for 1 87

cups of water, 1 43

cups of milk, and 2 cups of sugar. How much liquid is used for the cake recipe?

9. Kat had 2 53

bag of carrots. She gave 43

of a bag of carrots to her sister. Which shows how many bags of carrots Kat had left?

10. Erika walked 2518

miles before lunch and 5041

miles after lunch. How far did she walk in all?

11. Ellen has 53

of an orange. She gives 41

of the orange to her brother. Which shows how much of the orange Ellen has left?

12. Using the model below how much of the cake was eaten? Create an equation and solve?

13.

If the two separate models above were added together, what would be the total? Create an equation and solve?


Subordinate Objective Strategy: After conducting this pre-assessment the groups will be formed to start working on intervention strategies to reach the terminal objective. In order to prepare the students for the terminal objective we will provide multiple examples and instructions on strategies of operational procedures so the students will be inherent to successfully add and subtract mixed numbers with unlike denominators. Students will be able to perform operational procedures to solve functions of mixed numbers on a consistent basis at a 70% accuracy rate according to the base objectives of the Common Core Georgia Performance Standards. All students have certain areas in which they did not meet standard performance, but did meet standard performance in the major subordinate objectives 3.1 and 4.1. The subordinate objective 3.1 states that students will be considered successful if they correctly identify the common multiples and the least common denominator when they are given multiples of the denominators and the students expand the multiples of the two denominators correctly. The subordinate objective 4.1 states that students that are given the proper least common denominator will create equivalent fractions using manipulatives and write out the steps of multiplying the denominator by the same factor. They are considered successful if they create an equivalent fraction with common denominators. Both of these subordinate objectives have strong correlation to each other and both are foundational building blocks for the terminal objective. The most frequent issue that is noted in the academic year is the failure to apply finding the LCD when adding or subtracting mixed numbers with unlike denominators. Students consistently add the numerators together regardless if the denominator is not the same, or they add both numerators and both denominators. These two subordinate objectives will be highlighted immediately when starting the process of teaching adding and subtracting mixed numbers with unlike denominators. To present this information we would utilize math manipulatives such as fraction bars and fraction pies where students are able to create equivalent fractions by using these manipulatives. Allowing the students the opportunity to primarily focus on creating equivalent fractions prior to adding or subtracting fractions will provide students the background knowledge. This process will hopefully alleviate common misconceptions surrounding fractions with unlike denominators.


Further practices with the subordinate objective consist of us giving each student a set of fraction pies as shown in the picture above. This will create the instructional activity for students to manipulate and create the equivalent fractions. This practice utilizing psychomotor skills will allow them the opportunity to see and touch fractions, while gaining realization the importance of having common denominators. First, the teacher will give them a few fractions to create equivalent fractions, and then the students will work with a partner(s) and create equivalent fractions for one another. The students will be separated into groups of four and one student will give a fraction and the other three will then create an equivalent fraction. Each group will be heterogeneously, as stated, so that each group will have a high level comprehensive student that can check and balance other students work, and assist on a compatible level with any student that maybe struggling. The teachers will circulate the classroom and check for comprehensive understanding. By actively placing this instructional strategy in motion it will allow an opportunity for a greater correlation between subordinate objectives and terminal objective.

Terminal Objective and Subordinate Objectives Evaluation Follow-Through: To help solidify the students’ comprehensive level of the subordinate objectives, and grow towards successfully meeting the terminal objective, the students will complete a “ticket out the door system.” The students will receive two sticky notes and will answer given reflective questions from the instructor based on how they felt about the lesson, and operational procedures based on the lesson of add and subtract mixed numbers with unlike denominators. On the first sticky note given the students must write at least 1-2 sentences explaining how they feel about the lesson that was taught that day. Once they record their reflection they will then place the sticky notes on a picture of a red light, with each light representing a general feeling, in order to gain access to the exit of the classroom. The answers to the teachers reflective questions creates an opportunity for the instructor to understand student understanding on today’s lesson and their confidence on the terminal objective and subordinate objectives by placing the reflection on one area of the stop-light. Allowing students the opportunity to reflect privately will provide the teachers with feedback on what areas need to still be worked on and which skills the teachers can move on. These reflective sticky notes will also allow the teacher to build small groups the next day. On the second sticky note students will answer two questions involving the operational procedures of finding the LCD and creating equivalent fractions. These sticky notes will also provide clarity to determine between the students who comprehend the material in regards to the subordinate skills and which students need more help on the subordinate skill sets in order to master the terminal objective.


Instructional Materials

Pre-Instructional Activity:In the pre-instructional activity that we would conduct is a pre-assessment on the process of adding or subtracting mixed numbers with unlike denominators. This pre-assessment will allow us to collect data and build compatible small groups with likeness of strengths and weaknesses. The small groups in more detail are based on the pre-assessment performance, and the students will either be working on remediation and learning the fundamental skills to add or subtract mixed numbers with unlike denominators, or working on accelerated leveled functions involving mixed numbers. Once, the pre-assessment has been given and the students have been divided into their respected groups based off the pre-assessment data, we will then conduct an open floor questionnaire about common misconceptions. Allowing the students this opportunity will provide students with a voice in the classroom and allow them to discuss what they might have common with another student in the classroom setting. The students will then feel more connected to the lesson and less distant from the curriculum. Providing our students with a chance for input will also provide character building and a level playing field with their fellow classmates. The teachers will take a step back and allow the students the opportunity to discuss the content amongst each other with little teacher voice.

Presentation Strategies and Activities:For the majority of our presentation to the students we would conduct whole group instruction to address common misconceptions that were recognized by the students’ pre-assessment discussion. Following the whole group instruction would be the small group delivery to address each subordinate skill. The subordinate skills as mentioned earlier will be addressed through psychomotor, attitudinal, and cognitive domains. The small group instruction will allow us the opportunity to work with a maximum number of 8 students and as little as one-on-one conversations. Students will be allowed to use math manipulatives such as the fraction pie charts, fraction bars, and fraction pattern blocks to have tangible applications. These materials will be found on multiple learning resource sites that are approved from the Board of Education and school district. Using the domains correlating with each subordinate and the proper materials will clear up and benefit students from having reoccurring misconceptions of fractions. Below is a representation of how we would conduct fraction by fraction correlations which correlates with subordinate skill 4.1.


Materials: Flowchart for materials used in the Instructional Curriculum:

Session One ActivitiesSession Two Activities

1. Administer pre-assessment test.

2. Collect data from pre-assessment and utilize to build small groups.

3. Open floor pre-assessment discussion.

1. Address the misconceptions that each group identified during the open forum.

2. Conduct steps 1-4 of the subordinate skill chart.

3. Students in small groups will use the fractional manipulatives to practice correlating fractions and creating equivalent fractions.

4. Students will only focus on subordinates 1-4 until mastered. (When students master a skill the groups will vary and be flexible.)

Session Three Activities

1. Review subordinate skills 1-4 and check for student understanding.

2. Conduct steps 5-6 of the subordinate skills chart.

3. Students will focus on adding or subtracting the fractional parts and whole numbers with or without regrouping.

4. Students will only focus on subordinates 1-6 until mastered. (When students master a skill the groups will vary and be flexible.)

Session Four Activities


2. Conduct step 7 of the subordinate skill chart.

3. Students in small groups will use the fractional manipulatives to practice simplifying fractions.

4. Students will focus on subordinate skills 1-7 until post-assessment activity.Session Five Activities


Formative Evaluation:

Post-Assessment Results MCC5.NF.1 & MCC5.NF.2

Number Correct (out of 32)

1: Computation 28

2: Computation 30

3: Computation 27

4: Computation 29









30


31

Based on data collected through the student summative assessments given at the end of the unit, continued observations and formative assessments recorded daily throughout the classroom setting, interviews with students conducted at the end of the unit, our findings indicate that students’ understanding of adding and subtracting mixed numbers with unlike denominators has improved drastically based off the post-assessment results recorded above. The students scored alarmingly well when using models and computation, and students scored average to above average with problem solving skill sets. The data displayed proves that problem solving can also be correlated to students that read below grade level. As a classroom of 32 students and 13 students identified with special disabilities reading below grade level, places these students at a disadvantage when applying their new found math skills with reading comprehension. The results are also correlated to the strengths of the instructor and their usage for math manipulatives and tangible applications.


2. Conduct step 7 of the subordinate skill chart.

3. Students in small groups will use the fractional manipulatives to practice simplifying fractions.

4. Students will focus on subordinate skills 1-7 until post-assessment activity.Session Five Activities


Based on interviews with the student population in this particular classroom, students expressed a new found appreciation for fractions and thoroughly enjoyed the lessons with manipulatives. The two instructors both participated in the interview process by dividing the group of students in two. Each instructor conducted one-on-one interviews at the end of the unit in the conference room. Interview questions are designed to provide tangible evidence of student growth within this terminal objective. Below is the list of questions that the interviewers asked the interviewees. Interview results indicated that all students seemed to agree that having manipulatives made the learning easier and more tangible to apply to each math function. Most students also agreed that problems that required regrouping caused more frustration and conceptual thinking. Even with the usage of manipulatives subtracting mixed numbers with re-grouping was the hardest concept to master.

1. Based on the post-test results are you pleased with your grade? Why?

2. Based on the post-test results, what questions do you feel you need to continue working on? Why?

3. Based on the post-test results, what skills of solving mixed number fractions with unlike denominators by adding and/or subtracting do you feel like you have mastered? Why?

4. If you were to teach this unit, which skills of solving mixed number fractions with unlike denominators by adding and/or subtracting do you feel would require more attention or less attention, and why?

5. Based on the post-test which process was easier for you, using manipulatives, or using computation with just paper and pencil? Why?

Revision:In the future, we hope to continue instructional strategies due to the ever changing diversity in population and cultural academic strengths and weaknesses. In addition to the instructional delivery we would like to include more technology through the implementation of the educational grants and secondary educational funding to advance the learning styles and portfolios of the Board of Education. As our professional learning continues to grow through the years of teaching and becoming involved professional organizations, we will improve not only our instructional methods but the institutions vision and goals. Continuing with growth and professionals and advancement in classroom settings our instructional delivery and instructional units will continue improve and flourish.

Based off the formative and summative assessments we feel that word problems need to be at the forefront and placing a major emphasis on identifying key words and practicing more with these types of problems. We will also use the student observations and recorded interviews to help focus on the skills that they felt needed more attentions such as regrouping with mixed numbers and less time on basic computation problems. The interview process helped shed some light on what common misconceptions the students had and what the teacher needed to work on


in the future. We also agreed that a pre-test interview would also be helpful since each group is different and has different needs.


References

Georgia Department of Education (2015). CCGPS Frameworks Teacher Edition Mathematics

Grade 5 Unit Four: Adding, Subtracting, Multiplying, and Dividing Fractions. Retrieved

from: https://www.georgiastandards.org/Common-Core/Common%20Core

%20Frameworks/CCGPS_Math_5_Unit4Framework.pdf

Learning Games for Kids (2015). Fractions/Pie Charts. Retrieved July 6, 2015:

http://www.learninggamesforkids.com/graphic-organizers/math-graphic-organizers/

fractionpie-chart-graphic-organizers.html

Learning Resources (2015). Wooden Pattern Blocks. Retrieved July 6, 2015:

http://www.learningresources.com/product/wooden+pattern+blocks.do

MathPlayground (2014). Math Manipulatives. Retrieved July 6, 2015:

http://www.mathplayground.com/Fraction_bars.html

http://www.mathplayground.com/Fraction_bars.html

http://www.learningresources.com/product/wooden+pattern+blocks.do

http://www.learninggamesforkids.com/graphic-organizers/math-graphic-organizers/fractionpie-chart-graphic-organizers.html

http://www.learninggamesforkids.com/graphic-organizers/math-graphic-organizers/fractionpie-chart-graphic-organizers.html

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