lisamariesnyder.files.wordpress.com  · Web viewFractions on a Number Line (1 per student) Assessment 1.2 . Exit Ticket (1 per student) Assessment 1.3 Homework (1 per student) Lesson

Lesson Plan

Candidate: Lisa SnyderDate: 3/12/14 Grade: 4th

Lesson Part Activity description/Teacher does Students doFormal/informalAssessment ofPrior Learning orPreassessment(Sequence start)

Pre-Assessment: Comparing FractionsTeacher will administer Pre-assessment on the day before this lesson. This preassessment is designed to measure prior knowledge and is aligned with the central focus and learning target of the learning segment.

Students will complete Pre-Assessment.

Title Lesson 1: Comparing Fractions to BenchmarksStandard (Common Core)

CCSS.Math.Content.4.NF.A.2 Compare two fractions with different numerators and different denominators…by comparing to a benchmark fraction such as 1/2. …justify the conclusions, e.g., by using a visual fraction model.CCSS.Math.Practice.MP5 Use appropriate tools strategically

Central Focus (CF) Compare fractions with different numerators and denominators.Learning Target (LT)

Students will: compare ten fractions to the benchmarks 0, ½, and 1, and

locate the fractions on a number line. use fraction strips and number lines to compare fractions

to the benchmarks 0, ½, and 1.Academic Language to be used:

Review:Compare, Fraction, Number line, “less than”, “greater than”, “closer to”, Denominator, Numerator, Represent, Column, Resource

New:Benchmark

Materials (with specific count)

Assessment 1.1 (1 per student)Sentence strip for student friendly definition of “Benchmark” (1)Student Vocabulary Books (1 per student)Instructional Material 1.1 Comparison language poster (1)Instructional Material 1.2 Fraction sort poster (1 per group) and Fraction cards (1 set of 25 cards per group)Instructional Material 1.3 Fraction Strips (2 per group)Instructional Material 1.4 SMART Board fraction sort activity (1)Instructional Material 1.5 Fractions on a Number Line (1 per student)Assessment 1.2 Exit Ticket(1 per student)Assessment 1.3 Homework (1 per student)

Lesson Part Activity description/Teacher does Students doInstructionInquiryPreviewReview

The teacher will introduce the lesson by showing the learning target written on the board and asking a student to read it. The teacher will then use the Talk Move Repeat, and have several students repeat the Learning Target. The teacher will then ask students to explain it to their partner in their own words, and will then call on 3 students to share with the class what their partner said to them.“Mathematicians, on your desks are pieces of paper that look like this.” Hold up Assessment 1.1 and read it to students. “Your first task today is to think carefully about the learning target and then rate your understanding from 1-5. 1 means I don’t know anything about this topic, 5 means I could teach it to the class”. Teacher will give students 1 minute and then ask students to pass

Students will explain learning target to their partner, in their own words. Students who are chosen will then share with the class.Students will rate their current understanding on a scale from 1-5.

their papers to one person in their group. Teacher will collect papers. “Let’s look at the learning target. Who can tell me what it means when I underline a word?” Who can read the first underlined word for me? We have talked about the word compare before; can somebody tell me what they remember about it? When I ask you to compare in math, what am I asking you to do? Elicit student responses and use talk moves repeat, revoice, and agree or disagree and why. Ask students to take out their Fractions and Decimals vocabulary books. Model adding the word compare to the books, eliciting student ideas for what to use as examples and non-examples. “When we compare things, what kind of language do we use? Can you think of any phrases or words that we use when comparing things?” Elicit student responses and write the phrases on poster paper. Be sure to include phrases such as, “greater than” “less than” “equal to” “closer to” “benchmark”, as well as reviewing the symbols (that they learned in the last unit) for greater than, less than, and equal to. Include sentence starters such as “I think this fraction belongs here because…..” Inform students that you will be listening for their use of the comparison language throughout the lesson. “As the learning target states, today we will be comparing fractions. To start out with, instead of comparing them to each other, we are going to be comparing them to 0, ½, and 1. Why do you think I chose these numbers to compare our fractions to? Are our proper fractions greater than or less than 1? Is this always true? Raise your hand if you think you could find one half of any shape or group. Raise your hand if you think you could find 5 eighths of any shape or group.”The teacher will elicit students’ responses and use all talk moves. Point out that all of our proper fractions fall in between 0 and 1, and that ½ of something is easier to find than any other fraction. Therefore, 0, ½, and 1 are “friendly” numbers that we can compare other fractions to. The teacher will inform students that these friendly numbers, and any other number that we can easily compare something to, is called a benchmark.The teacher will write the word benchmark on a sentence strip on the board and ask a student to read it. “Where have you have heard this word before?” Teacher will elicit students’ prior knowledge of the word benchmark (they take a math benchmark test every few months) before giving a student friendly definition: a benchmark is something that we can compare other things to. Teacher will write definition on sentence strip and leave it on board for student access.“Turn and tell your neighbor what a benchmark is.” Teacher will have 2 students share what their neighbor told them, and will then allow students to ask questions.

Students will raise their hands and share their understanding of the word compare.Students will add the word compare to their vocabulary books and discuss words and phrases that we use when comparing two things.

Students will raise their hands and answer questions.

Students will share their prior knowledge of the word benchmark.

Students will explain to their neighbor their understanding of the word benchmark.

InformalAssessment

“Using a ‘fist of five’, I would like you to show me how well you think you understand what a benchmark is” From the front of the room, the teacher will use this assessment to determine next steps. If the majority of the class shows less than 3 fingers, teacher will explicitly reteach what a benchmark is and how to use it to compare fractions. Teacher will move forward with activities if majority of students hold up 3 or more fingers. Teacher will take note of which students show 0-2 fingers in order to

Students will give a “fist of five” to demonstrate their current understanding.

provide small group instruction in next activity.Teacher will then divide students into prearranged small groups for the practice activity.

Instruction/Practice Activity/(if needed)

“Mathematicians, we are going to do a fraction sort. Each group will receive a poster and a set of fraction cards. The posters have 3 columns; one is labeled 0, one is labeled ½ and the other is labeled 1. What is a word that we could use to describe these three numbers?” Elicit that the numbers are benchmarks. “Your task is to compare your fractions to the benchmarks and decide if each fraction is closer to 0, ½, or 1. When you have decided, you will place that fraction card in the appropriate column. To help you, each group will also get a copy of these fraction strips.” Hold up fraction strips sheet. “The fraction strips sheet represents fractions of different sizes and shows their size in relation to each other.” The teacher will inform students that they will be using their “Contributor” wands, and remind them of the rules of the wands (they must pass them around in a circle, and only the person holding the wand will move a fraction.). Teacher will inform students that when they are finished they may tape down their cards on their poster using the tape that is on each table. Remind students that teacher will be listening for their use of comparison language. “Mathematicians, where could you find help if you forget what a benchmark is? What if you if need help deciding if your fraction is greater than or less than ½? Is there somewhere you could look to help remind you of what words and phrases we use when comparing?” Elicit student responses, being sure that they know they can refer to the benchmark definition on the board, the fraction strips sheet at their desks, and the comparison language prompts on the board and in their vocabulary books. Refer to these as resources. Teacher will distribute materials and allow students to begin their sort, and will then circulate. Teacher will first check in with those students who indicated confusion in the informal assessment, and then the rest of the students.

Students will raise their hands to respond.

Students will raise their hands to identify resources in the classroom.

Students will work in their groups to sort the fractions into the appropriate columns.

InformalAssessment

Teacher will conduct formative assessment to monitor student learning by asking the following questions:

How did you decide which column this fraction went in? Is this fraction greater than or less than one half? How do

you know? How can you use the fraction strips to help you? Which benchmark is this fraction closer to? Do you think it is possible for the same fraction to have two

different names? What is a word we could use to describe those two fractions?

How can you use the denominator to help you decide where to place the fraction? How can you use the numerator?

How close to you think you are to meeting the learning target? What else do you need to do to meet it?

Teacher will use Talk Moves as needed and will ask additional questions to guide students, depending on student needs.

Students will work in their groups to sort the fractions.Students will use comparison language when discussing where to place their fractions.Students will respond to teacher questions and prompts.

Instruction/Practice/Activity (if

Teacher will bring students back together and will ask students to assess their progress towards meeting the learning target with a “fist of five”. Teacher will ask students what they think they need to do in

Students will give a “fist of five” to demonstrate their progress towards

needed) order to meet it. Teacher will display class fraction sort on the SMART Board.“Mathematicians, we are now going to discuss how you sorted your fractions and why you chose to place them in the column that you did. On the board here we have a fraction sort that looks a lot like the one you worked on in your groups. There are three columns, who can tell me what a column is? There is one column for each benchmark, and at the bottom are boxes with the same fractions that you used in your sort. If I call on you, you will come up to the board and use the touchscreen to move a fraction into the column that you and your groups decided it belonged in.”Teacher will draw a name on a popsicle stick to begin the fraction sort, and will have each student choose the next student. Each student will explain their groups reasoning, using the comparison language. Teacher will ask the class if they agree or disagree and why, and students will have the opportunity to revise their thinking if necessary. Students will then use the touchscreen feature to move the fraction into their chosen column. The SMART board activity will reject the fractions placed in the wrong column, providing immediate feedback to students. Teacher will then discuss with class why the fraction was accepted/ rejected.

meeting the learning target.

Students will identify a fraction and explain which column it belongs in and why. The rest of the class will agree or disagree and the selected student will go to the board and use the touchscreen to move their fraction into the chosen column.

InformalAssessment

Teacher will assess that students are using benchmarks to put fractions in the correct column. Teacher will use the same/ similar questions as the previous informal assessment to gauge student learning:

How did you decide which column this fraction went in? How can you use the fraction strips to help you? Do you think it is possible for the same fraction to have two

different names? What is a word we could use to describe those two fractions?

What do you notice about the fractions in the 0 column, the ½ column, the 1 column?

How can you use the denominator to help you decide where to place the fraction? How can you use the numerator?

“One strategy that we can use to figure out which benchmark a fraction is closer to is to compare the numerator and the denominator. We can ask ourselves the following questions:”

What is half of the denominator? What does this tell us? Is the numerator more or less than one half of the

denominator? If it is less, is it closer to zero or to half of the denominator? If it is more, is it closer to one or to half of the

denominator.Discuss with students how they need to take the size of the pieces into consideration; both ½ and ¾ need only one more piece to complete the whole, but ¾ is closer to 1 because its pieces are smaller.

Students will accurately identify which column their fraction belongs in and will explain their reasoning.

Instruction/Practice/Activity (if needed)

“4th graders, we have been using fraction strips in order to help you see how different sized fractions compare to each other, but there are other representations we can use as well. One of those tools or representations is a number line. Who can tell me what a number line is? Where have we seen fractions on a number line in the real world?

Think about our unit on measurement.” Teacher will elicit student responses, and make connections between fractions on a number line and measurement of length. Teacher will then have student helpers distribute number line worksheets and will hold up a copy for students to see. “On your paper are several number lines. Who would like to describe the first line? Are there any numbers on there? What are those numbers telling you? What is a word we can use to describe these numbers? What other information does the number line give you?” The teacher will elicit student responses. “Each of these numbers lines represents a whole that is divided into different sized fractions. To the right of each number line is a list of the fractions that belong on that line. Your task is to label the number line with those fractions, in the correct place.” Teacher will model this on the first number line under the document camera. Teacher will ask students what resources they can use to help them and elicit that they can use their fraction sort poster and their fraction strip sheets. “Remember mathematicians, today our learning target is….. Use the benchmarks you have learned about today, as well as your fraction strips and your fraction sort posters to help you decide where on the number line to place your fractions.” Teacher will circulate as students work individually on their number lines.

Students will share their ideas.

Students will identify classroom resources.

Students will work individually on their number lines.

ClosureAssessment ofStudent Voice

When there are ten minutes remaining in the lesson, teacher will bring the current activity to a close. “Students, those of you who are not finished with your number lines will have the opportunity to do as a part of tonight’s homework. Let’s review todays lesson:

What is a benchmark? What are some words and phrases we use when comparing

something to a benchmark? How can we use benchmarks to compare fractions?” Why do we use benchmarks? What are some tools we used today to help us compare

fractions?Teacher will then distribute the exit ticket which allows students to assess and demonstrate their learning

Students will participate in closing discussion.

Students will complete exit ticket before leaving for lunch.

Formal Assessment orPostassessment(Sequence end)

[The section for formal postassessment ends the lesson sequence and does not need to be shown on preceding lessons.]

Formal Postassessment will be given at the end of the learning segment.

edTPA Training Prompts

Context for Learning1. In what type of school do you teach?The school where I teach is an urban school with approximately 490 students. 87% of the students receive free or reduced price meals, 10% receive special education services and 62% of students are transitional bilingual. The school population is very diverse, with 37% of the students identifying as Asian, 17% as Black, 32% as Hispanic/Latino, 10% as White, and the remainder identifying with more than one race. The school also has a large immigrant and refugee population, with some students having never received any formal education before enrolling. In order to meet the needs of such a diverse student population, the school has programs in place for identifying and addressing academic, social, and personal needs. There is a before school program named Zero Hour, where students can receive tutoring that is tailored to their needs, a social worker is a permanent member of the staff and, along with the community outreach team, provides services for the students and families personal needs. The school also has an Interventions program, where for 30 minutes a day teachers and para-educators provide intensive instruction in the areas that students are struggling in.2. Describe special features of the classroom setting.Over half of the class receives Interventions in mathematics, during which they receive intensive specialized instruction from para-educators. 3. Describe district, school, or cooperating teacher requirements or expectations that affect teaching.I am expected to use the curriculum Math Expressions Common Core, by Houghton Mifflin Harcourt, for math instruction. The pacing guide is determined by the fourth grade faculty and the school’s math specialist and I am expected to follow it as much as possible. Standardized benchmark tests are given at various points in the year, and the pacing guide allows us to make sure that our students are ready for these assessments.4. What is the name of the course? What is its length? What is the schedule?The course is mathematics and it is taught for 70 minutes every day.5. Is there any ability grouping?There is no tracking at the school where I teach and students are not grouped by ability for mathematics. All students are present during mathematics. This means that there is a wide range of ability levels in the classroom and when lesson planning I must take each of these individual needs into consideration.6. Identify textbooks and other instructional programs used during instruction.The school at which I teach uses the Math Expressions Common Core curriculum, by Houghton Mifflin Harcourt, published in 2013, and the assessment guides and student activity books that go with it. In addition, the curriculum is supplemented by a series of Response to Intervention lessons for struggling students.7. Describe other resources, such as dry boards or laptops, used during instruction.The classroom in which I teach has a SMART Board, a white board, and easel which are often used and a math bulletin board where important vocabulary, posters, and other related math visuals are displayed. The curriculum comes with a selection of manipulatives, primarily base ten blocks and fractions strips, and the school has a math resource room with many more manipulatives that can be incorporated into our lessons. We also have a selection of mathematics based children’s literature. My mentor teacher and I use a variety of online resources for graphic organizers and example problems, and we also create

our own using the computers in the classroom. The classroom has 30 Chromebook laptops for student use although they will not be utilized for this lesson.8. What is the grade level composition? How many males and females?The students of this class are in 4th grade, with ten males and fifteen females.9. Summarize the composition of students needing support, such as English Language Learners, gifted, students with IEPs or 504s, struggling readers, underperforming students. Identify each student’s accommodation, modification, or method of support.Two students have IEP’s for Specific Learning Disability, but only one of them qualifies for special instruction in mathematics. The specific accommodations required are: chunking of material, read materials to student, preferential seating and behavior monitoring, immediate feedback, reduce length of assignments, use manipulatives and graphic organizers.Although the second student does not receive special mathematics instruction, her IEP accommodations do apply to mathematics and are as follows: extra response time, oral instead of written responses when appropriate, frequent checks of understanding, read materials to student, group with higher ability students. Student also receives ELL instruction. Fifteen students in the class receive ELL instruction, and the remainder of the class has tested out of the ELL program. The students receiving ELL instruction currently require materials to be read to them, vocabulary to be explained, graphic organizers, visuals, and shortened assignments. One student in the class has ADHD with a 504 pending. This student is gifted in mathematics; however he frequently has days when he cannot function independently.

Task 1: Planning1. Central Focusa1. Describe the central focus and purpose for the content you will teach in this learning segment.The central focus for this lesson is comparing fractions with different numerators and denominators. This is the second in a series of 6 lessons addressing this central focus. In the first lesson students compared fractions with like numerators or denominators. In this lesson they will work towards comparing fractions with different numerators and denominators by first learning how to compare fractions to benchmarks. Students will then learn to use number lines to compare fractions, a tool that is previewed at the end of this lesson, before moving towards comparing fractions by creating common denominators. a2. Explain how the learning target is measurable, includes a verb (language function), and a few subject specific vocabulary words.The learning target is measurable since it gives a specific number of fractions to be compared to a benchmark in order for the target to be considered met. The language function of the learning target/ lesson is compare, which is integrated into all parts of the lesson. Subject specific vocabulary words are compare, fraction, benchmark, and number line. a3. Explain how the learning target is worded so that students can self-assess their progress toward meeting it.The learning target explicitly states the tasks that students must complete in order to meet it. Students will self-assess their progress by determining how many more fractions they must compare, and whether or not they have successfully placed the fractions on a number line.b. How is the learning target related to the central focus? How are the learning targets unified by the central focus?

The learning target is directly related to the central focus by asking students to compare fractions.c. Explain how your plans build on each other to help students learn. How do learning targets add knowledge or skills from one lesson to the next?This lesson builds on the previous lesson by continuing the focus on comparing fractions and giving students additional tools for doing so. The following lessons will build on this lesson by giving students other tools for comparing fractions.d. How and when will you give students opportunities to express their understanding of the learning targets and why they are important to learn?Students will be given several opportunities to express their understanding of the learning targets, at the beginning, middle, and end of the lesson. They will be asked to describe the learning target in their own words, and to self-assess their current knowledge of the central focus of the lesson in writing, in the beginning. During the activities they will be asked to verbally assess their progress toward the learning target and to evaluate what they need to do in order to meet it. At the end of the lesson they will be asked what they did to meet the learning target.2. Knowledge of Students to Inform Teachinga. Prior learning, prerequisite skills, and understanding: What do students know, what can they do, and what are they learning to do?This lesson falls in the third week of a unit on fractions. Students understand basic fraction concepts, such as the concept that fractions are equal parts of a whole, and know the words numerator and denominator and what they represent. They have extensively studied unit fractions. Students are proficient at performing addition, subtraction, and multiplication with fractions with like denominators or numerators, and can compare fractions with like numerators and denominators. In this and the following lessons, students are learning to compare fractions with unlike numerators and denominators. The unit preceding this was a measurement unit in which students learned about measures of length, mass, volume, time, and temperature. Their study of units of length will assist them in understanding fractions on a number line.b. Personal/cultural/community assets related to the central focus—What do you know about your students’ everyday experiences, cultural backgrounds and practices, and interests?Most of the students come from low socioeconomic backgrounds, many come from immigrant families who have recently immigrated to the United States, and a few have recently come from refugee camps in Somalia, Myanmar, and Nepal. The students come from a variety of cultural backgrounds and speak a range of languages at home. Three of my students are Muslim females who are reluctant to speak up in class due to their upbringing, but will participate in small group activities. All of the students are interested in technology and are engaged by any lesson that involves the use of the technology available in the classroom. 3. Supporting Students’ Learninga. Explain how your understanding of your students’ prior learning and personal/cultural/community assets (from prompts 2a–b above) guided your choice or adaptation of learning tasks and materials.Since my students come from such a wide range of backgrounds, I chose activities that would provide a shared experience in order to avoid relying on background knowledge that they may not have. The fraction sort was chosen as an activity since it is something that all students can participate in regardless of prior knowledge. Even those students in their first year of formal schooling can participate in the activity by using the provided fraction strips to aid their decisions. The whole-class fraction sort was chosen in order to engage the students’ love of technology. Every student has the opportunity to

participate in this activity. The final activity of locating fractions on a number line is required by the curriculum, and the fraction sort gives each student the ability to be successful in this activity. Student prior learning of units of measurement will also assist them in understanding fractions on a number line.b. Describe and justify why your instructional strategies and planned supports are appropriate for the whole class and students with similar or specific learning needs.The lesson begins with a whole-class discussion of the comparison language that students need to know in order to be successful. This whole-class discussion was chosen since all students needed to receive the same information. I then move from whole-class discussion to small group activities in order for every student to have the opportunity to engage with the materials and to contribute to a low-stress small group discussion. The “contributor” wands that I will provide ensure that students all take turns so that no one student dominates the conversation or activity. With the variety of personal and academic backgrounds present in my classroom, a shared experience such as that provided by this activity is necessary in order to provide every student with the tools needed to succeed in the lesson. I then chose to transition back to whole-class discussion in order for every student to share their understanding, to address misconceptions, and to provide feedback through the SMART Board activity. The SMART Board activity was also chosen to keep students engaged in this whole-class discussion. The fractions sort and the SMART Board activity provide both visuals and manipulatives in order to support ELL and IEP students. The final activity of constructing a number line also provides a strong visual for these students. c. How will students identify resources to support their progress toward the learning targets?Students will be asked throughout the lesson to verbally identify resources that could be used to help them. They will also be asked to name which resources they utilized in their exit ticket. d. Describe common preconceptions (based on prior learning and experiences) within your content focus and how you will identify and address them.Common preconceptions are that fractions with greater denominators are greater fractions, and that if you only need to add one more unit fraction to get to 1, then that fraction is closer to 1 (For example, ½ must be closer to 1 than 6/8, since you only need to add one unit fraction to ½ but you need to add 2 unit fractions to 6/8). The first misconception has been explicitly addressed in the previous lesson and will be addressed again in the whole class discussion. The second misconception will be explicitly addressed first if/when it comes up in small groups, and then during the whole class fraction sort. Students will be asked to consider not just the numerator when deciding where the fraction lies, but also the relationship between the numerator and the denominator, and we will revisit the idea that the numerator and denominator together make up a fraction and they are not to be considered separate numbers. 4. Supporting Development through Languagea. Language function: What verb appears in your learning target that represents the language function?The verb that represents the language function in this lesson is compare. b. Language demand: What learning activities or products will student write, speak, or do to represent the language demand and an opportunity to practice the language function?Students will participate in a whole-class shared writing activity to produce the Comparison Language poster. This poster will identify the words, phrases and symbols used when comparing things in mathematics. Each of the activities of the lesson involves actively comparing fractions to benchmarks. c. Additional language demand: How will students practice content vocabulary words shown in the learning targets? Students will be explicitly asked to use the comparison language throughout the activities of the lesson.

d. What learning activities enable students to practice using symbols or abstract representations of information (syntax), if these are part of the lesson?Symbols and syntax are not part of this lesson but were addressed in the previous lesson and will be again addressed in the next. Students will write comparison statements using the symbols for greater than, less than, and equal to. e. How is discussion (discourse) structured in activities?During whole class discussion the teacher acts as a guide and uses talk moves to encourage discourse. f. What other writing or speaking activities enable students to practice vocabulary and the verb shown in the learning target?Additional activities will be introduced in following lessons. 5. Monitoring Student Learninga. Describe how your planned formal and informal assessments will provide direct evidence for you and your students to monitor learning.Students will take a preassessment that allows me to analyze what they already know. A postassessment including the questions from the preassessment plus additional qualitative questions will be given at the end of the learning segment. In this lesson, the students will be asked to self-assess their knowledge of the topic at the beginning and end of the lesson, so that both students and I can see how they think their own learning is progressing. An exit ticket will provide both quantitative and qualitative data to be used formatively to guide the next day’s instruction, and to provide a summative assessment of student learning. Student homework will also be scored and formally assessed as evidence of the days learning. Informal assessments include teacher observations, including observing students use of academic language, assessing whether students are sorting fractions accurately, and student self-assessments through the use of “fist of 5”. Students’ self-assessments and teacher observations will used to give additional or modified instruction and one-on-one support. b. Explain how the design or adaptation of your planned assessments allow students with specific needs to demonstrate their learning.Students with IEP’s and ELL students will have the directions for formal assessments read and explained to them. Each of the formal assessments include subjective questions requiring written responses, and ELL and IEP students will be permitted to verbally answer these questions. IEP students will be given the same assessments as the rest of the class but with adjusted assessment criteria. c. Describe when and where you will elicit student voice (oral or written) during instruction to raise awareness in both you and the students of where students are relative to the learning targets.Students will verbally explain the learning target to each other, and share their explanations with the class, at the beginning of the lesson, and will be asked to rate their understanding of the topic in writing. Throughout small group activities I will ask students to assess their progress towards the target and to consider what they need to do in order to meet it. At the end of the lesson the student will once again be asked to assess their progress towards the target both verbally and in writing. d. What tools and strategies will students use to monitor their own learning process during the learning segment?Students will use their fraction sort posters and number line worksheets to evaluate whether they met the target.6. Analysis of Student WorkStudent fraction sorts were varied, with all students able to place unit fractions and fractions equivalent to whole numbers in the correct locations. Most groups were able to place fractions equivalent to one

half in the correct column. Students struggled most with fractions that were between one half and one. Different groups developed different strategies for comparing these fractions, with all groups at least touching on the idea that they could find out how many more unit fractions were needed to get to one and to then compare this difference. Student performance on the number line was also varied. Each number line was pre-divided, but when asked to place fractions of different sizes on the same line, most students were able to only place the fractions corresponding to the tick marks. When asked to place thirds and sixths on a line that was divided into sixths, most students struggled to place the thirds but were able to accurately place the sixths. Student performance on the homework was consistently strong, with the majority of students getting at least 12 out of 16 questions correct. The four students who did not perform as well are all lower-level English Language Learners and this tells me that their problem is likely language based and that I need to give some explicit instruction to help them understand the symbols and academic language.7. Student Use of FeedbackStudents will be asked to provide written answers to prompts in order to evaluate their performance after feedback has been given. Students will be encouraged to correct and resubmit their work. 8. Language UseFor this lesson, students use of language was primarily oral. They participated in a shared writing experience, where the teacher recorded their responses in order to create the Comparison Language poster. Students were also asked to use the comparison language as they participated in small group and whole class discussions. In the following lessons students will be asked to respond to prompts in writing which will provide evidence of their language use. Research:My lessons have been designed to provide shared experiences that do not draw on background knowledge from outside the classroom that my students may not have. This strategy is supported by Banks & Banks in their 2010 work Multicultural Education. One of Banks’ Dimensions of Multicultural Education is Equity Pedagogy; a way of modifying teaching so that students of all cultural, racial, and social-class backgrounds can achieve academically (Banks & Banks, 22). The fraction sort activity that my students will participate in provides a shared experience that students can draw upon in future lessons involving the comparison of fractions. The introduction of number lines as a tool for comparing fractions is supported by the work of Van de Walle, Karp, and Bay-Williams, in their 2013 work Elementary and Middle School Mathematics. According to this work, linear models, such as fraction strips, Cuisenaire rods and number lines, are effective tools for teaching fractions, with the number line being particularly effective for use in comparing fractions (Van de Walle et al, 294). Number lines allow students to make connections to their prior learning of units of measurement, as well as allowing them to construct a model with which they can compare the relative sizes of fractions (Van de Walle et al, 294).

References:Banks, J. A., & Banks, C. A. (2010). Multicultural education: issues and perspectives (2nd ed.). Boston:

Allyn and Bacon.Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school

mathematics: teaching developmentally (5th ed.). Boston: Allyn and Bacon.

Instructional Material 1.2: Fraction sort poster (cards not pictured)

Instructional Material 1.4: SMART Board Interactive Fraction Sort

Student work: Group A completed fraction sort poster

Student work: Completed Class fraction sort: