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1 Jill Rozzi’s Unit Work Sample

US Customary Units and Conversions

LD Resource Room

5th Grade Math

Section I: Topic & Rational: This unit was developed in an attempt to effectively promote student achievement in the area of US Customary Units and Conversions using evidence based teaching strategies. More than half of the students being taught have a specific IEP goal to improve measurement skills-US customary conversions. This unit is on the Long Range Plan as a formal unit to be taught to all of the fifth grade students. South Carolina State Standards for both fourth and fifth grade are also addressed during this unit. The use of measurement is used in many aspects of everyday life: cooking, sports, driving, and much more. This unit will introduce material that relates measurement to their lives and how it can be useful to them. Two unit objectives were created based on SC State Standards and the Long Range Plan unit topics. Each objective was addressed throughout the unit, meaning that the unit was taught to its entirety.

Students: I taught two separate groups of students. One group containing 2 students and the other group containing 3 students. All students receive math resource services for 50 minutes each day, with the exception of one student. After a recent IEP meeting, the team decided that this student would benefit from more time in the general education classroom. This affected my time teaching this student, as he only comes to the resource room 3 days a week.

Section II: Contextual Factors: There are several factors that may affect student learning. Different learning styles, previous performance on units or tasks, health factors, or reoccurring behavior problems are just a few factors that could interfere with student learning. These factors need to be understood and addressed before attempting to effectively teach students. Developing and reading the Long Range Plan helped me to make decisions about strategies and techniques that I should use during the unit in order to effectively teach all students. First, the present level section of the Long Range Plan stated that many of the students in the class had difficulty multiplying two digit numbers and dividing numbers using long division. In an attempt to achieve my unit objective, and help students learn to the best of their abilities, I decided to allow students to use calculators when solving the conversion problems. My goal was to see if students could solve conversion problems accurately; not whether or not they could multiply and divide. The present level summaries also provided information about the student’s current reading levels. Because all of the students receive special education services for reading, I was sure not to make any of the word problems above a third or fourth grade reading level. Again, the goal for the unit was to determine if students can make conversions. Second, the Long Range Plan also showed me that two of the students I would be teaching had Behavior Intervention Plans. I knew that unruly or non-compliant behavior would not allow students to achieve their goals and learn to the best of their ability. I also did not want this type of behavior to affect the learning of other


students in the classroom. Although neither of these students had an effective intervention plan in place, I was able to react to and discuss possible interventions that may be effective for these students. My reaction time was too slow; I ran into behavior problems with these students mid-unit. After much collaboration with my professor and cooperating teacher, a new behavior system was implemented in an attempt to teach and promote acceptable behavior. Third, the long range plan, and the viewing of their individual IEP’s, revealed that all 5 students had an oral administration of content area tests accommodation. I was sure to follow the IEP and read the pre & post test aloud to the students. I did not want this to hinder their performance on the assessments. Fourth, when planning for the unit, I made sure to remember some of the common characteristics of students with learning disabilities. One characteristic of many students with learning disabilities is memory problems. I developed many visual cues and numbered steps to follow to help students learn to convert. I also incorporated physical motions to help them remember that when you go from big to small you multiply and small to big you divide. Finally, the long range plan gave me the opportunity to interview students and begin a positive relationship with each of them. I was able to learn about their hobbies, interests, and favorite and least subjects in school.

Section III: Unit Plan:

Part A: Unit Learning Objectives:

1. By the end of approximately two weeks, when given conversion problems in number sentence, word, or picture format, using US customary units for length, weight, and liquid, students will solve 8/8 problems independently.

2. By the end of approximately two weeks, when given multiple choice questions related to the relationship between units in the US Customary system including length, weight, and liquid, students will choose the correct answer 8/8 times independently.

The first objective is measureable in that students will be choosing the correct answer when solving eight conversion problems using length, weight, and liquid. The second objective is also measureable in that students will be choosing the correct answer when presented with eight different questions related to the relationship between the units of length, weight, and liquid. Both objectives are appropriate for the students because the material, both math concepts and reading concepts, is on their grade level. All of the lessons in the unit were developed to help students achieve both unit objectives. Data was gathered at appropriate intervals to help determine if students were achieving and making progress toward achieving the objectives. These objectives are directly related to the student’s IEP goals and address the following SC State Standards for 4th and 5th grade:

SC State Standards & Indicators:


1. Standard 4-5: The student will demonstrate through the mathematical processes an understanding of elapsed time; conversions within the US Customary System; and accurate, efficient and generlaizable methods of determining area.

2. Indicator 4-5.3 Use equivalencies to convert units of measure within the US Customary System: converting length in inches, feet, yards and mile; converting weight I ounces, pounds, and tons; converting liquid volume in cups, pints, quarts and gallons; and converting time in years, months, weeks, days, hours, minutes and seconds.

3. Standard 5-5: The student will demonstrate through the mathematical processes an understanding of the units and systems of measurement and the application of tools and formulas to determine measurements.

Part B: Assessment Plan: A pre-assessment was necessary to determine where to begin instruction. The results from the pre-assessment also provided specific information about the student’s strengths and needs relative to the unit topic. After instruction began, I needed a way to determine if my instruction was effective, so I created several different types of formative assessments. After all lessons were taught, and the unit objectives were taught to their entirety, a summative post-assessment was given to measure student progress and to see if progress was made towards achieving the unit objectives. All formative and summative assessments were teacher developed. The pre-post-assessment was a paper and pencil assessment.

Accommodations: All five students had an accommodation on their IEP to have any content area test orally read to them. I was sure to abide by the IEP and read all assessments aloud to all students. The students also had an IEP accommodation stating that they should be tested in a small group setting. I only had two groups of students; one group with two students and one group with three students.

Assessment before the unit: I developed a paper and pencil pre-assessment that helped me determine where to begin instruction. The pre-assessment directly related to both unit objectives. Page one of the pre-assessment correlated to objective number 1; students solved eight conversion problem using measurements in the US Customary System. Page two of the assessment correlated directly with the second unit objective; students answered questions about the relationship between the different units of measurement. Based on the results from this pre-assessment I was better able to guide my lessons and prepare for the unit. Below is a copy of the pre-assessment given to all students prior to instruction.


What Do I Know About Measurement? Page 1

Directions: Circle or write the best answer. Leave question blank if you don’t know.

1. 5 feet =_______inches

a) 60 inchesb) 45 inchesc) 17 inches

2. 1 yard is equivalent to

3 feet.How many feet are in 5 yards? ___________

3. 24 inches = ______________feet

4. My dog weighs 50 pounds. If there are 16 ounces in 1 pound, how many ounces does he weigh?

a) 900 ouncesb) 800 ounces

5. 1 ton = 2,000 pounds

3 tons=________ pounds

6. An elephant weighs 2 tons. If there are 2,000 pounds in 1 ton, how many pounds does

he weight?

a) 8,000 poundsb) 2,000 poundsc) 4,000 pounds

7. There are 8 pints in 1 gallon.

How many pints are in 5 gallons? ________________

8. 5 gallons =__________quarts


Pretest Applications Page 2

This is basic knowledge that students must have before having a clear understanding of in order to achieve the unit objective.

This will be a verbal and hands on assessment.

I will ask students to measure:

1. Inches: Use of a ruler: measure your pencil and tell me how many inches it is long. a. What is longer? An inch or a foot?

2. Feet: Use of a ruler or yard stick: measure the desk and tell me how many feet tall it is.a. What is longer? A foot or a yard?

3. Yards: Use of a yard stick: measure this table and tell me how many yards it is long.a. What is the shortest unit of length measurement? Inches or feet

I will ask students:

1. Would you weigh yourself using ounces, pounds, or tons?2. Which weighs more? A pound or an ounce? 3. Do you think a golf ball weighs 6 ounces or 6 pounds?

I will ask students:

1. If you were really thirsty, would you rather have 1 fluid ounce of water or 1 cup of water?2. Which has more volume? A pint or a gallon?


Assessments used during unit: After instruction began, I needed a way to evaluate student performance. Formative assessments were given to my students during each lesson to determine the effectiveness of my instruction. I used a variety of formative assessments during the lesson, depending on the skills I wanted to assess. To assess student’s understanding of unit objective number 1, converting between units of measurement, students were asked to complete conversion problems independently either on a paper and pencil worksheet or through a computer activity where they recorded their answers. These paper and pencil assessments were scored and as a review at the beginning of the next lesson, we discussed each problem again. Depending on the results for these assessments, instruction either continued or a re-teach lesson was implemented. To assess student’s understanding of unit objective number 2, determining the relationship between different units of measurement, I used a teacher checklist/documentation data sheet to document which students identified each unit of measurement. Instruction did not move on until all students were able to physically and verbally identify each unit of measurement with 100% accuracy. I have attached an example of the reporting and documenting sheet that I used during lesson #4 to determine if students were gaining the knowledge about the relationship between gallons, quarts, pints, and cups. I used this sheet to help me decide if I should continue on with instruction or spend more time teaching the units of liquid measurement. I also attached a copy of an assessment that students took after learning about and practicing the steps to solving a conversion problem.


Reporting and Documenting Understanding of Liquid Measurement: gallons, quarts, pints, cupsMonitor Progress During Lesson #4

1. By the end of the 50 minute lesson, given 4 unlabeled containers: gallon, quart, pint, and cup, students will say the name of each container with 100% accuracy.

a. Verbal: Did the student SAY the correct name when I pointed to the container?

J Gallon: Y N Pint: Y N Fluid Ounce: Y NCup: Y N Quart: Y N

H Gallon: Y N Pint: Y N Fluid Ounce: Y NCup: Y N Quart: Y N

K Gallon: Y N Pint: Y N Fluid Ounce: Y NCup: Y N Quart: Y N

D Gallon: Y N Pint: Y N Fluid Ounce: Y NCup: Y N Quart: Y N

A Gallon: Y N Pint: Y N Fluid Ounce: Y NCup: Y N Quart: Y N

2. By the end of the 50 minute lesson, when the teacher says: gallon, quart, pint, and cup, students will point to the corresponding container with 100% accuracy.

b. Physical: Did the student POINT to correct container when I said its name?

J Gallon: Y N Pint: Y N Fluid Ounce: Y NCup: Y N Quart: Y N

H Gallon: Y N Pint: Y N Fluid Ounce: Y NCup: Y N Quart: Y N

K Gallon: Y N Pint: Y N Fluid Ounce: Y NCup: Y N Quart: Y N

D Gallon: Y N Pint: Y N Fluid Ounce: Y NCup: Y N Quart: Y N

A Gallon: Y N Pint: Y N Fluid Ounce: Y NCup: Y N Quart: Y N

3. By the end of the 50 minute lesson, given a sheet of paper with the big gallon on it, students will draw a picture of the Gallon Man including quarts, pints and cups with 100% accuracy.

c. Did the student independently draw the Gallon Man after tracing?

J: Y N H: Y NK: Y N D: Y NA: Y N


Lesson #2 Assessment

Directions: Circle or write the best answer.

1. 18 yards=___________feet

a. 54 feet

b. 48 feet

c. 6 feet

2. 24 inches=___________feet

a. 48 feet

b. 5 feet

c. 2 feet

3. 24 feet=___________yards

a. 9 yards

b. 8 yards

c. 36 yards

4. 2 miles=___________yards

a. 4,567 yards

b. 1,760 yards

c. 3, 520 yards

5. 1 foot= 12 inches

56 feet=__________inches


Assessments used after unit: At the end of the unit, students were given the post-assessment. The post assessment was the same test as the pre-assessments, except for how students expressed their knowledge on the second page, relative to objective number 2. On the pre-assessment, students were to write their knowledge based on the manipulatives that I had. On the post-assessment, students answered the same eight questions in a multiple choice format. Again, both pages of the summative assessment correlate with the both unit objectives. Data was gathered to determine if students made progress in comparison to their pre-assessment results. Using the same test for both the pre and post assessment allowed me to see direct improvement over time.

Part C: Results of the Pre-Assessment : After administering the pre-assessment, I counted the number of items that each student correctly answered and divided it by the total number of questions to determine the percent correct for each student. This baseline data will help determine the student’s current level of understanding relative to US Customary Units and Conversions.

A B C D E0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

81%

38%44% 44%

38%

Overall Pre-Assessment Results

Student

Perc

ent C

orre

ct

The base line data above indicated that students had a vague understanding of US Customary Units prior to instruction. The average score on the pre-assessment, combining all five student’s scores, was 49% correct. Student’s scores ranged from 38% correct up to 81% correct. It was clear that in order for students to achieve their IEP goals and my unit objectives, effective and explicit instruction was necessary for all students.


A B C D E0%

10%20%30%40%50%60%70%80%90%

100%

63%

0% 2% 0% 0%

100%

75% 75%

88%

75%

Pre-Assessment Results Relative to Unit Ob-jectives

Objective #1: ConversionsObjective #2 Unit Relationship

Students

Perc

ent C

orre

ct

The graph above depicted individual student performance relative to both unit objectives. The baseline data revealed that all students scored much higher when asked about the relationship between the different units of measurement (red bar) compared to their performance on the conversion problems (blue bar). When planning my unit, the results from the pre-assessment showed me that the majority of instruction needed to focus on teaching students simple and clear steps to solving conversion problems. From the results of the pre-assessment it was clear that I should begin instruction without skipping any skills or concepts. Looking at the individual answers from students in both groups, two out of three students in the afternoon group scored 100% correct on the understanding weight section of the assessment. From the results, I decided to combine the understanding weight and converting weight lesson. I decided this would be effective because students would have already been introduced to and practiced solving conversion problems in the previous lesson and if their pre-assessment results revealed that they already knew about the relationship between ounces, pounds, and tons, then there would be no reason to spend a whole lesson covering material they already mastered. A formative assessment would determine if the lesson would continue onto solving weight conversions or if I should continue to teach about the relationship between ounces, pounds, and tons.

Part D: Instructional Plan:

Strategies, Activities, Materials, and Resources used:


I used a variety of teaching strategies, activities, materials, and resources that helped me effectively accomplish the unit objectives. First, for all lessons I was sure to only cover content on student’s current ability level and necessary to achieve the unit objectives. The baseline data helped me determine which topics and skills needed to be covered in more depth: solving conversion problems. Second, when teaching the steps to solving conversion problems, I used strategy instruction. Strategy instruction follows a simple outline of presentation, in which teachers model the skill, use a variety of guided practice activities for students to practice the skill, and then allow students to practice the skill independently. I followed this instructional sequence each time the students converted between units. Third, I developed a handout including the steps for solving a conversion problem and an example. This was developed in an attempt to accommodate to the common characteristic of students with learning disabilities, memory problems. Another strategy used to help students decide if they should multiply or divide was a physical prompt in which students used their arms to model if the problem went from big to small, multiply or small to big, divide. Finally, during all guided practice activities and/or independent work I provided the students with corrective feedback. If students were incorrectly completing a task, I intervened and told them what they were doing wrong and how to fix it.

For the lessons in which students learned about the relationship between different units of measurement, I used a lot of hands on manipulatives and activities. These hands on activities involved students measuring items using different manipulatives; such as rulers, yard sticks, gallons, quarts, pints, cups, ounces, pounds, etc. in order to record measurements of length, weight, and liquid. Students also had to apply their knowledge of the relationship between the different units to measure real life, situational items: their long jumps and height, ingredients in a smoothie, and the weight of items using ounces and pounds. For all activities, I used the model-lead-test instructional strategy, in which I thoroughly modeled the skill and allowed students to practice before they were expected to complete them independently. I also used a variety of guided practice activities so that students had multiple opportunities to practice the skills.

Technology was also a large part of instruction and guided practice activities. I created an interactive PowerPoint to introduce the steps to solving conversion problems. Students were involved in the lesson because they were able to go up to computer or board and select the correct answer. The PowerPoint also provided them with corrective feedback. For example, if they chose the incorrect answer they were directed to a slide that took them through the steps to correctly solving the problem. A BookBuilder was also used during the lesson as another way for students to practice solving conversion problems. Finally, the BuildingBlocks interactive computer CD was used during the unit. The CD


had interactive games involving measurement, often used as a supplemental or guided practice activity.

I used various resources in order to develop a thorough and effective unit. First, the South Carolina State Standards helped me to outline the topics to be covered during the unit. The South Carolina Department of Education website supplied me with the list of standards and a support document that clearly outlined the skills to be learned in order to achieve the objectives and indicators. Second, my cooperating teacher supplied me with ideas to help develop effective lessons. If I had any questions or concerns about anything, she talked me through it so that I was able to devise a plan. Third, my university supervisor supplied me with effective corrective feedback after being observed. Behavioral and instructional techniques were revised after receiving helpful feedback about my current performance. Fourth, as stated, my long range plan served as a beneficial resource throughout the development of the unit. Specific student needs, IEP accommodations, interests, and prior work performance were found on the long range plan and helped me design effective and relatable lessons. The long range plan also informed me about any contextual factors that should be addressed before or during the unit.

Primary Sources of Content:

The SC Department of Education website was one of the primary sources of content that I used when developing this unit. This website supplied me with what all 5th grade students in South Carolina need to know about US Customary Units of Measurement. Also, my cooperating teacher provided me with information and tips about what she had taught in previous years to help guide my teaching. Various teacher websites provided me with different instructional strategies and materials. The National Math Advisory Panel website provided me with the Gallon Man picture and the idea to have students measure their long jump and height. Finally, a teacher blog gave me the idea to use the physical prompt to help students decide if they should multiply or divide when solving conversion problems.

Instructional Strategies Used:

One of the most effective, evidence based teaching strategies, proven to be effective when teaching students with learning disabilities is following the Model-Lead-Test sequence of instruction. In each lesson, I first modeled the skill using verbal mental modeling to clearly explain my thought process. I was sure to say only the necessary information needed to solve the problems, using vocabulary on their ability level. After I thoroughly modeled the skill, students practiced the skill with me. Guided practice activities would then take place where students practiced the skill through the use of a


game, physical movements, short stories, independent practice cards, white boards, or BookBuilder and interactive PPTs. Staying in the ‘lead’ phase of Model-Lead-Test, until students can independently complete the skill with accuracy, is essential to ensure students are practicing the skills correctly. To make sure students are practicing the skills correctly, corrective feedback was supplied to students. I clearly pointed out what the student was doing wrong, and then I modeled the steps to solve that problem. Students would then try the skill again. Verbal praise was also provided to students on a regular basis. After students practiced the skill, received feedback, and completed it with independence, students are then tested to see if they can accuracy complete the skills with complete independence.

Teaching simple facts or facts that are memorized were taught in isolation and discrimination. In isolation, I showed the object, stated its name and characteristic, and then asked the students to repeat exactly what I said. After all students stated the name and characteristic of each item, I tested students to see if they were able to discriminate between the new objects and previously learned objects. For example, in lesson #4, I set up all four units of liquid measurement, gallon, quart, pint, and cup and then reviewed the name of each. I then turned each object around, so the names were not displayed to students, and as I pointed to each object, they chorally responded with the name. We practiced this using choral response and then I tested them individually. Again, presenting information using isolation and discrimination is an evidence based teaching strategy proven to be effective when teaching students with learning disabilities.

I also used hands-on activities to help students apply their knowledge. I tried to incorporate activities that related related to real life situations; such applying the skills to cooking, sports, or measuring height and weight at the doctors. For example, in lesson number 4, after teaching the gallon, quart, pint, and cup in isolation and discrimination and measuring water in each of the containers, we applied the knowledge of measuring liquid to make a smoothie. Relating learning to real life experiences helps to make learning fun and engaging for most students.

Each of the instructional strategies listed above have been proven to be effective when teaching students with learning disabilities. Finding strategies that engage and motivate students to learn will help achieve any objective. I incorporated strategies to accommodate to the needs and characteristics of students with learning such as hand outs, visual prompts, short stories and physical prompts. There were also many strategies that I used to help engage and motive learning, while practicing crucial skills necessary to achieving the unit objectives, such as: relating information to real life, telling short stories, using games and technology, using physical movements and hands on manipulatives to visualize and perceive information. I also incorporated the use of direct and explicit instruction which has been proven to be effective when working with


students with learning disabilities. All of the instructional strategies used throughout the lesson were selected in an attempt to supply students with information and knowledge in order to achieve the unit objectives.

Lesson Plans:

After reading the SC State Standards and listing the skills that students must possess in order to achieve the objectives, I created a unit outline. I decided to teach one lesson for each length, weight, and liquid measurement in which students gained an understanding of the relationship between the units in each. For example, in order for students to solve length conversion problems, students must be able to decide which unit of the conversion problem is larger. In order to do this, students need to be familiar with the relationship between all units. To help student gain this understanding I taught an ‘understanding lesson’ before we converted units.

Lesson # 1 was titled, “How Long? Understanding Length: inches, feet, yards, and miles.” I created the lesson objectives, which directly relate both unit objectives. Ultimately, I wanted students to be able to choose the longest and shortest unit when given an option of two, using inches, feet, yards, and miles. In order to do this, I decided to first introduce the four length units in isolation and then see if they were able to distinguish between them in a discrimination activity. After students visually and auditory were introduced to each unit of measurement, I modeled how to measure different items around the room using mental modeling and allowing students to practice measuring items after I measured them. After each student practiced measuring with each tool of measurement-tape measure, ruler, and yard stick, I passed out the “Measure It” activity sheet. I verbally explained that we would estimate the length of each together and they would write the estimations in the first box. After estimations, I explained that they would be using the tools of measurement to measure the items and write it in the actual length box. I assisted measuring at each station. Once all students measured all four items, students circled the longest length to practice finding the longest or biggest measurement. Students then cut up their four boxes and place them in order from longest to shortest, using the actual length measurements. Then we placed all of the student’s measurements in order from greatest to least together. Students then made a list on the board listing different things that could be measured in inches, feet, yards, and miles. Finally, students independently completed the Length sheet; independently applying their knowledge to complete an activity on their own.

Lesson #2 was titled, “Converting Length.” This was the lesson that I introduced the steps to solve conversion problems. I developed a lesson objective where students would independently convert one step conversions between inches and feet, inches and yards, feet and yards, and yards and miles using multiplication and division with the use of a


calculator. I taught a brief mini-lesson on how to properly use a calculator to solve multiplication and division problems. First, I opened with a brief review from yesterday. Then I opened up the interactive PPT. I introduced the word conversion and then our goal in solving conversion problems. I used the Model-Lead-Test sequences of instruction, first modeling the steps to solve a conversion problem through mental modeling. Then the interactive PPT had students solving many problems with the use of written and verbal prompts. Students would write their work and answer on the board using their own mental modeling during the guided practice stage. These slides provided prompts which gradually faded throughout the PPT guided practice stage. After multiple opportunities to practice with and without prompts, the PPT then had multiple problems in which students solved problems on their white boards and selected an answer on the PPT. The PPT supplied students with a reinforcing prompt if they chose the correct answer, or a visual prompt to solving the problem if they selected the wrong answer. After several conversion problems, I wanted to see students independently converting problems. So, I created a BINGO game in which students were presented with a problem and marked the answer on the BINGO board. This was an engaging way to have students practice conversion problems. Finally, after much corrective feedback and multiple opportunities to practice, students answered 5 conversion problems independently.

Lesson #4 was titled, “Understanding Liquid Measurement: gallons, quarts, pints, and cups.” On day #3, I implemented a new behavioral plan in which students graded their own behavior and I graded their behavior at 10 minute intervals. The new plan was a result of a lack of consistency of consequences and an ineffective previous behavior plan. After creating three lesson objectives, students reviewed the steps to converting problems and the relationship between the units of length and weight. I introduced each of the units of liquid measurement in isolation and then had students discriminate between them. I reported their progress on the “Reporting and Documenting Student Progress” sheet. This sheet guided my instruction. If all students did not discriminate with 100% accuracy, I would re-teach each item in isolation. Students then were introduced to the gallon man and how he could be used to help remember the relationship between gallons, quarts, pints, and cups. I told the gallon man story to help students remember the steps to draw the gallon man. After much tracing, students independently drew the gallon man. I reported progress on the same documentation sheet. Students then used the gallon man to answer questions. This was to help me determine if students were able to use and understand the gallon man. We then modeled the equivalences based on the gallon man, using the gallons, quarts, pints, and cups to transfer water between each. Finally, students applied their knowledge to measure ingredients to make smoothies.

Lesson #5, “Converting Liquid” involved students converting between the four units of liquid measurement. Students were presented with a review of the units of liquid


measurement. We practiced drawing the gallon man and telling the gallon man story. Students were given the “Understanding Liquid” assessment at the beginning of the lesson. This would help me determine what the students remembered and if I needed to re-teach any material. We reviewed the steps in converting problems and then I used the Model-Lead-Test instructional strategy to solve conversion word problems. We then completed the same instructional procedure to solve several horizontal conversion problems together. As a guided practice activity, students were supplied with 7 half sheets of paper, all of different color to solve on their own. When they were finished we went over the problems together. Students checked their work with the answer cards and solved any problems they missed. We then played a “Flip It” activity, in which students were presented with a conversion problem, either word problem or horizontal problem, and they solved it on their white boards. When I said, “Flip It,” students would then reveal their answers.

Section IV: Analysis of Student Learning:

Strategies Used to Monitor Student Progress:

I used many strategies to monitor student progress and achievement throughout the unit. Assessing and analyzing student performance helped me to guide instruction and measure student progress. I used informal and formal assessments during the unit to evaluate student performance. I developed all assessments, making sure that they directly correlated with the lesson objectives and in turn correlated with the unit objectives. All assessments were maximally free from bias and deemed valid and reliable results. The assessments were given at appropriate intervals in which I could determine if instruction should continue on or if a re-teach lesson was necessary in order for students to achieve objectives.

One specific strategy that I used during the many lessons to monitor progress was teacher questioning. Throughout the guided practice activities I would ask students questions to help them explain what they were doing or why. The type of questioning ranged from responses being ‘yes’ or ‘no’ to providing an explanation of their work. The use of questioning allowed me to guide my instruction based on the needs of the students. Another strategy that I used to monitor student progress was choral response. I had students verbally announce answers. I also had students provide answers using white boards. Students would flip their board to show their answer when I said, “Flip It.” A single prompt or cue to let students know when to produce the answer proved to work the best. I also reported student progress by documenting their actions and progress on a “Reporting and Documenting” sheet. This served as a checklist to see which students were able to complete skills directly after they were taught, as well as the next day to see if students retained the information. Also, the guided practice activities often provided me with data to determine if students have mastered the skill taught that day. Depending on the results from the guided practice activity, either in a written format or an activity format, I would


re-teach the lesson, spend more time in the Model phase, or continue on with the lesson. Finally, each lesson contained some type of formative assessment either at the end of the lesson or at the beginning of the next lesson to assess student performance relative to achieving the the lesson’s objective.

Decisions Made Based on Formative Assessment Results:

I had to use the results from the formative assessments to guide instruction. One of the biggest decisions that I made was adding a short review lesson at the beginning of the Lesson #3 because one group of students chose to misbehave and act up during Lesson #2 and missed instructional time. At the beginning of lesson #3, I brought the interactive PPT out and reviewed the steps to converting a problem. Students were compliant and engaged. They solved the guided practice problems as I provided feedback when necessary. I also decided to add a short mini-lesson on solving word problems. Because students had many opportunities to practice solving horizontal conversion problems, when a word conversion problem came up in guided practice, students asked questions and I ended up solving the problems with them. I decided to create a five question word problem page. We solved the problems together and I really emphasized that we solve these problems just like we solve the horizontal problems. This issue was probably my fault, in that I did not include much instruction on how to solve the word problems before I asked them to solve them during guided practice activities. Finally, looking at the results from the formative evaluation from lesson #3, the weight lesson, I decided to do a small re-teach lesson at the beginning of lesson #4. I looked at the data from the evaluation and determined that students were having difficulty converting weight. During the next lesson, I spent about 15 minutes repeating the activities done in lesson #3. I also spent more time modeling and solving problems. I decided to hand out the ‘steps to solving conversion problems’ handout again. We reviewed the steps and then engaged in approximately 10 conversion problems using the white boards.

Pre- & Post- Assessment Results:

At the end of the unit, students were given the post-assessment. The students were only assessed on content and skills that they were taught throughout the unit. As stated the average score on the pre-assessment was 49% correct. The average score on the post-assessment was 83% correct. The scores increased dramatically. The post-assessment data reflects the scores for all five students, but student D missed the last day of the unit as well as four days after that because of an illness. Student D was not able to take the post-test until a week after the instruction. This many have skewed his results slightly. Although no one scored 100% correct, like the objective indicated, significant progress and improvement was made for each student.


The graph above, “Class Average Pre-Assessment vs Post-Assessment,” depicts the overall gains that the students made from the pre-assessment to the post-assessment. The average rose from 49% to 83%. This is a large improvement. A class average score of 83% is a great improvement from 49%, but the objective was not achieved. Students did not complete the assessment with 100% accuracy. There are several reasons why this could have occurred, but more instruction or practice is necessary in order to achieve the objective.

A B C D E0%

10%20%30%40%50%60%70%80%90%

100%81%

38%44% 44%

38%

94%88%

75% 75%81%

Pre- and Post- Assessment Results

Pre-AssessmentPost-Assessment

Student

Perc

ent C

orre

ct

The graph above provides a clear overview of individual student performance on the pre-assessment and the post-assessment. All five students showed growth after a unit of instruction. Most students gained an average of 31% or more on the post assessment score. The graph clearly shows improvement for every student.

Pre-Assessment Average Post- Assessment Average0%

10%20%30%40%50%60%70%80%90%

100%

0.49

0.83

Class AveragePre- Assessment VS Post-Assessment

Assessment

Perc

ent C

orre

ct


Item Analysis and Range of Assessment Results:

I completed a brief item analysis of the student responses in order to assess the quality of the test as a whole. On the conversions part of the assessment, page 1, there was no single item that all four students answered incorrectly. Although, two out of the four students answered number 7 incorrectly. This item was a liquid conversion problem but rather than it being a word problem or a horizontal problem, the question was asked in a way that students had to write their own conversion problem. Looking at the student’s work, the two students who missed problem 7 did not attempt to re-write the problem out in a horizontal sentence. The two students in the afternoon group did write it out in a horizontal sentences, like I taught them in class, and they both provided the correct answer. This makes me wonder if my instruction of answering this type of problem was less effective for the two students in the morning group.

Subgroup Data Results:

B E0%

10%20%30%40%50%60%70%80%90%

100%

38% 38%

88%81%

Pre- & Post- Results from Students in Morn-ing Group

Pre-AssessmentPost-Assessment

Students in Morning Group

Perc

ent C

orre

ct

The graph above depicts the student performance data on the pre- & post-assessment for the two students who received instruction in the morning group. I chose to present and compare their scores because both students were present for every lesson and participated in every activity. Looking at the graph, both students showed great numerical gains. The average of both students’ pre-assessment scores was 38% correct. After much instruction and practice, the average of these two student’s post-test scores was 85% correct. An overall increase of 47% correct, almost doubling their pre-assessment scores. As stated, both students in this group incorrectly answered number 7. This error was probably because of my lack of instruction and/or lack of guided


practice problems set up in this particular format. Instruction on how to solve this type of problem was provided to them, but it may not have been effective.

Individual Graph: Student B:

Pre-Assessment Post-Assessment0%

10%20%30%40%50%60%70%80%90%

100%

0.38

0.88

Pre- and Post- Assessment Results: Student B

Assessment

Perc

ent C

orre

ct

The graph above depicts the performance of one student whole received instruction during the morning group with one other student. It is clear that performance improved. Looking the answers that this student provided on the post-assessment, he missed one question for each objective. He missed the poorly formatted question, number 7. He also incorrectly chose that he would rather drink 1 fluid ounce then 1 cup of water if he was really thirsty.


Individual Graph: Student C

Pre-Assessment Post-Assessment0%

10%20%30%40%50%60%70%80%90%

100%

0.44

0.750000000000001

Pre- and Post- Assessment Results Student C

Assessment

Perc

ent C

orre

ct

The above graph depicts the performance of student C. This student received instruction during the afternoon group, with two other students. During my time teaching this group, this student’s amount of time receiving math services decreased. The week I started teaching my unit was the first week that this student started to come to resource only 3 days a week for math instruction. This lack of instruction hindered Student C’s performance on the post-test. This student missed lesson #3, ‘understanding and converting weight.’ The questions on the post-assessment revealed that he had this knowledge without my instruction because he correctly answered 8/8 multiple choice questions about the relationship between weight, length, and liquid. This student also missed instruction when I taught lesson # 5, ‘converting liquid.’ During this lesson, students were provided with many opportunities to practice converting problems, in both horizontal and word problem format. Looking at results from Student C’s post-assessment, he missed 3/8 conversion problems. This student needed constant prompting and verbal cues to stay on task while completing this assessment. Because I was orally administering the post-assessment to all three students, Student C was able to stay on task for the majority of assessment. Overall, even with missing two days of instruction, Student C still made drastic improvements. His scores ranged from 44% correct to 75% correct. He improved 31% from the pre-assessment to the post-assessment.


Formative Grades:

For each lesson I evaluated student performance toward the lesson objective. The objectives for each lesson can be found on the actual lesson plans attached. This graph shows the student’s grades, percentage correct, on the performance evaluations. These grades helped me guide instruction. The actual evaluation papers or activities were collected, scored, and returned to students the previous day. We went over each question in detail after students independently completed the evaluation. I included some formative assessments that provided me with actual data on student performance. For several lessons, informal observation and hands on assessments were used to help determine and guide instruction.

The chart above shows the data gathered from independent formative evaluations from several of the unit lessons. It is obvious that the students did not perform as well on lesson #3 in comparison to some of the other lessons. Based on the data from the formative evaluation of after the instruction in lesson #3, a re-teach lesson was implemented at the beginning of lesson #4.

Student Grades:

At the end of the unit, I scored the post-assessments using a percent correct method. I divided the number of items the student got correct by the total number of items on the test. Each student also had several numerical progress monitoring grades. My teacher has all of the student’s grades, both formative and summative, and will be including the summative post assessment score to be calculated in to get an average for progress reports. She will count this score just like any of the other curriculum based assessments that she gives in her class. For each unit, the resource teacher either creates a summative assessment or selects one from a curriculum. These curriculum based assessment scores are also averaged in with various progress monitoring probes to get an average, which is their progress report or report card grade. Grades are provided to the student’s general education teacher. Depending on how much time the student spends in the general education classroom, receiving math services, the general education grades will be

Student: #1: Understanding

Length

#2: Length

Conversions

#3: Understanding and Converting

Weight

#4: Understanding & Drawing Gallon

ManA 100% 100% 88% 100%B 92% 100% 77% 100%C (left early) 0% 55% 100%D 78% 100% 77% 100%E 100% 80% 100% 100%


averaged in with the grades from curriculum based assessments and curriculum based measurement probes from the special education room.

Section V: Reflection and Self Assessment:

Overall, I think all students improved drastically. Each student made improvements from the pre-assessment to the post-assessment and showed progress along the way. The class average scores from the pre-assessment to post-assessment showed growth as well. Students were showing progress on the formative evaluations along the way. If their performance proved to be less than 100% on the formative evaluations and/or teacher checklists, a small review/mini-lesson was implemented at the beginning of the next day. After the review/re-teach mini-lesson I should have given the students another independent evaluation to determine if the extra instruction was beneficial. Instead, I modeled skills and then we practiced re-working the evaluation.

One problem that I encountered during the lesson was my ineffective behavior management techniques. At one point I was unable to get the students under control and the students were not gaining the knowledge to achieve the unit objectives. After much collaboration with both my cooperating teacher and my university professor, a new behavior management plan was implemented the very next day. I spent several minutes discussing the new system with the students. We also spent time providing examples and non-examples of the 5th grade behavior. Overall I think the new system was effective. The students responded very well and seemed to enjoy grading their own behavior. The first day that my teacher started teaching the 5th grade group again, she told me that the students asked where the behavior sheets were. Another student asked me if they could take their behavior charts home to get signed. My cooperating teacher said she was going to start using the system for the third, fourth, and fifth grade students.

I think that my use of evidence based teaching strategies such as progress monitoring, response cards, direct instruction, gradual release of physical and verbal prompts, and several other techniques helped students gain the knowledge to achieve the objectives. My performance using these strategies helped students perform and achieve throughout the unit.

Overall, I think I did a good job teaching the students about US Customary Conversions, but there are several things that I would do differently if I were to teach this unit again. First, looking at the pre/post assessment, I would change the format of several of the questions to make them a little less confusing. For example, the picture that I used in number 2 is confusing and this could be why all five students missed that question on the pre-assessment. In an attempt to help students understand this question, I had students copy the horizontal conversion question onto their paper. I did not want students to get frustrated or confused on the assessment. Reflecting on my teaching during the unit, I would also give these five students a short personal informational quiz to see what types of rewards they like or their favorite activities in the resource room. This would help me create rewards and consequences that are actually meaningful to them. For


example, during the unit I told students that if they earn 3 dots during the lesson then we could play BINGO. Well, BINGO may not be a reward for everyone so this was not very effective. I now know that response cards are most effective when students are provided with a cue to let them know when to show their answer. During several activities, students were solving problems on their white boards and I would have them check their answers with my white board. Several students would get upset if I called on them and another person answered. After talking with my professor I tried a technique where students only flipped their boards when I said, ‘flip it.’ Then they would check their answer with mine and I did not have to call on any one particular student. Finally, if I were to teach this unit to these students again, I would spend more time correcting the errors that students made on the formative assessments. Although we went over them as a class on the following day, I’m not sure that students received the detailed and explicit instruction they needed to understand why they missed the problems. If I had more time I would have tried to work more 1-1 with students who were having difficulties converting problems while other students practiced skills. More direct, 1-1 instruction to correct these errors may have helped to make more connections.

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