pherrington s2.doc

7/29/2019 PHerrington S2.Doc

1/13

Patti Herrington 1

Patti Herrington

FRIT 7430: Instructional Design

Stage 1, Understanding by Design

June 24, 2012


2/13

Patti Herrington 2

UbD Stage 2 Template

Stage 2 Determine Acceptable Evidence

Title of

Unit

Numbers and Operations

FractionsGrade

Level

Fifth (5t )

Stage 1 Identify Desired Results

Students will understand that:

Math (in particular, fractions) plays an important role in our daily lives. Fractions are embedded in multiple content areas of mathematics. Fractions = Division/Ratio Fractions can represent parts of regions, parts of sets, parts of measures, division or ratio. A fraction is not meaningful without knowing what the whole is. Renaming fractions is often the key to comparing them or computing with them. Every

fraction can be renamed in an infinite number of ways. There are multiple models and procedures for comparing and computing with fractions. Operations with fractions have the same meanings as operations with whole numbers, even

though the algorithms differ.

Related Misconceptions:

Numerators and denominators can be added or subtracted. (Do not realize that thedenominator is the size of the fractional part and the numerator is the number of the part.)EX. 1/3 + 2/5 = 3/8

Not finding a common denominator when adding or subtracting fractions with unlikedenominators.

Working with only the whole number or the fractional part of a mixed number. Multiplying on the numerator by numerator and leaving the denominator the same when

multiplying fractions. When multiplying mixed numbers by mixed numbers multiplying the whole numbers and then

the fractions instead of converting the mixed number to an improper fraction. Inversion problems with dividing fractions.

http://www.ernweb.com/public/1237print.cfm
http://www.ernweb.com/public/1237print.cfmhttp://www.ernweb.com/public/1237print.cfmhttp://www.ernweb.com/public/1237print.cfm


3/13

Patti Herrington 3

Essential Questions(copy and paste from Stage 1)

Overarching Questions:

How do fractions play a part in our everyday lives?

Why should I learn about fractions?

Why are fractions such an important part ofmathematics?

How can fractions be modeled, compared, andordered?

Identify real world situations when fractions areused to represent numbers?

Topical Questions:

How do I recognize and name equivalentfractions?

How do I identify fractions as part of a wholeand part of a set?

How to I read and write common fractions?

How can using the greatest common factor helpme write a fraction in simplest form?

How do I add and subtract fractions with likedenominators?

How do I add and subtract fractions with unlikedenominators using the Least Common Multiple?

How do I add and subtract mixed numbers?

How can I multiply fractions?

How do I recognize and rename improperfractions and mixed numbers?

What methods can be used to comparefractions?

How are common denominators used to comparefractions?

How can addition/subtraction of fractions berepresented by objects, pictures, words andnumbers?

How do I identify the inverse relationship whendividing fractions?


4/13

Patti Herrington 4

Stage 2 - Evidence

Performance Task(s)

Performance Activity Culminating Activity (Individual or Group)Facets 1 6 (Explanation, Interpretation, Application, Perspective, Empathy, and Self-Knowledge)

Goal: Students will recognize that fractions are evidenced in many aspects of everyday life andrealize the urgency in learning how to model, compare, and order fractional numbers, as well as,provide evidence of computation through addition, subtraction, multiplication, and division.

Role: Teacher Producer Writer Designer

Audience: Fifth grade students.

Situation: A new student has moved from Atlanta to Brunswick. Our class has just completedour unit on fractions. At his/her old school, the teacher was just beginning to teach the class aboufractions. Your teacher needs your assistance in helping teach this student learn how to makeequivalent fractions, change mixed numbers to improper fractions and improper fraction to mixednumbers, as well as how to add and subtract like and unlike fractions and multiply and dividefractions. In addition you need to help this student understand the urgency in learning to workwith fractions.

Product Performance and Purpose: You are to assume the role of the teacher and design abrochure, create a Golg, PowerPoint, or other teacher approved tool to produce an artifact thatdemonstrates, as well as illustrates how to find equivalent fractions, how to work with improperfractions and mixed numbers, how to add and subtract fractions using (like/unlike denominators proper/improper fractions), how to multiply and divide fractions. Remember this tool is to includereal life application and will be used as a tool to help students who are learning about fractions inthe fifth grade.

Standards and Criteria for Success: MCC5.NF.1 MCC5.NF.2 MCC5.NF.5 MCC5.NF.4MCC5.NF.6. MCC5.NF.3 MCC5.NF.7


5/13

Patti Herrington 5

Performance Task(s) Rubric(s)

Assuming the Role of the Teacher(0-1 Points) (2-3 Points) (4-5 Points)

Your

Score

Representation

One to two types ofrepresentations are included.

Examples do not apply to real lifeexperience with fractions.

Most representations are includedthroughout the presentationincluding pictures, numbers, andwords.

Examples apply to real lifeexperiences.

All representations are includedthroughout the presentationincluding pictures, numbers, andwords.

Examples apply to real lifeexperiences.

/5

Communication

Uses limited mathematicalconventions, vocabulary, andterminology with explainingreasoning and procedures.

Uses some mathematicalconventions, vocabulary, andterminology when explainreasoning and procedures.

Uses mathematical conventions,vocabulary, and terminology whenexplaining reasoning andprocedures.

Expresses and organizesmathematical thinking effectively.

/5

Skills

An explanation of some skills wasprovided along with examples.

Skills*making equivalent fractions*changing improper to mixedfractions and mixed fractions toimproper.*adding and subtracting fractionswith like denominators.*adding and subtracting fractionswith unlike denominators.

*multiplying fractions.*dividing fractions.

An explanation of most skills wasprovided along with examples.



An explanation of all skills wasprovided along with examples.



/5

Mechanics

Project has 5 or more math,spelling, or grammatical errors.

Project has 3-4 math, spelling, orgrammatical errors.

Project 0 - math, spelling, orgrammatical errors.

/5

Visual AppealProject is not neat and/ororganized.

Project is relatively neat andorganized.

Project shows creativity and veryneat and organized.

/5

Your Total Score /25


6/13

Patti Herrington 6

Narrative Writing Assessment(0-1 Points) (2-3 Points) (4-5 Points)

Your

Score

Topic andOrganization

Narrative has no topic sentence.

Ideas and opinions are notorganized.

Narrative has a minimallydeveloped topic.

Ideas and opinions are expressedbut not organized.

Narrative has a developed topic.

Ideas and opinions are expressedand organized.

/5

Grammar andPunctuation

Some errors in agreement,number, and/or tense.

Many punctuation and/or caseerrors.

Minor errors in agreement,number, and/or tense.

Minor errors in punctuationand/or case.

No errors in agreement, number,and/or tense.

No punctuation or case errors.

/5

Paragraphs andSentences

Writing has one paragraph or hasdivision but not my content.

Simple sentences used.

Several fragments and/or run onsentences are evident in writing.

Ideas are divided appropriatelyinto paragraphs with limited useof supporting details.

A variety in the length and typeof sentence is used.

Evidence of one fragment or runon sentence is evident in writing.

Ideas are divided appropriatelyinto paragraphs with strong use ofsupporting details.

A variety in the length and type ofsentence is used.

Writing contains no fragments orrun on sentences.

/5

Vocabulary

Some use of key mathematicalterms in narrative. Basic

vocabulary words used.

Uses key mathematical terms innarrative. Ideas in narrative are

minimally expressed. Wordselection is limited.

Uses key mathematical terms innarrative. Ideas in narrative flow

well. Word selection is varied,interesting, and usedappropriately.

/5

Visual AppealHandwriting

Hard to read. Letters not formedwell.

Legible. Letter formed well. Neat. Easy to read. Well-formedletters.

/5



7/13

Patti Herrington 7

Audio/Video Podcast(0-1 Points) (2-3 Points) (4-5 Points)

Your

Score

ScriptThere is little evidence ofplanning. Script is not providedor is weak. Some key vocabularyis uses. Script contains mostlyfactual material and has manygrammatical errors.

A script was written for thepodcast performance. Languageused is good and some use ofkey vocabulary is included.Script contains factual materialand has a few grammaticalerrors.

A well written script was writtenfor the podcast performance.Language used is interesting anduses key vocabulary. Scriptcontains factual material and hasno grammatical errors.

/5

DeliveryThe podcast appearsunrehearsed, the enunciation ismuddled and not clear and therecitation lacks expression andenthusiasm

The podcast is rehearsed, theenunciation is sometimes clearand intelligible, and there is someexpression andenthusiasm in the recitation.

The podcast is rehearsed anddelivered smoothly, theenunciation is clear andintelligible, and there isexpression and enthusiasm in therecitation.

/5

Audio/TechnicalThe volume is poor for bothmusic and voice, there isconsiderable background andother distracting noise, andthere are several technicalglitches.

The volume is good forboth music and voice,there is little background or otherdistracting noise, andthere are no technicalglitches.

The volume is good forboth music and voice,there is no backgroundor other distractingnoise, and there are notechnical glitches.

/5

Group WorkThe group functioned fairly well,with most members contributing,sharing and supporting theothers effort. They weresometimes on task.

The group functioned well, withall members contributing, sharingand supporting the others effort.They were almost always ontask.

The group functioned exceptionallywell, with all memberscontributing, sharing andsupporting the others effort. Theywere always on task.

/5

Your Total Score /20Adapted from Rayburn Elementary School Podcast Rubrics


8/13

Patti Herrington 8

Expository Writing Assessment(0-1 Points) (2-3 Points) (4-5 Points)

Your

Score

ResponseStudent attempted to answerquestion(s).

Written explanation did notsupport knowledge of content.

Visual explanation did notsupport knowledge of content.

Student answered question(s).

Written explanationdemonstrated minimal knowledgeof content.

Visual explanation demonstratedminimal knowledge of content.

Student answered question(s).

Written explanation demonstratedcomplete knowledge of content.

Visual explanation demonstratedcomplete knowledge of content.

/5

Grammar andPunctuation

Some errors in agreement,number, and/or tense.

Many punctuation and/or caseerrors.

Minor errors in agreement,number, and/or tense.

Minor errors in punctuationand/or case.

No errors in agreement, number,and/or tense.

No punctuation or case errors.

/5

Vocabulary

Minimal use of key mathematicalterminology is used inexplanation.

Limited use of key mathematicalterminology is used inexplanation.

Exclusive use of key mathematicalterminology is used in explanation.

/5

Visual AppealHandwriting

Appearance of paper is verymessy. Writing is hard to read.

Appearance of paper issomewhat messy. Writing islegible.

Appearance of paper is neat.Writing is easy to read. Well-formed numbers and letters. /5



9/13

Patti Herrington 9

Other Evidence(e.g. tests, quizzes, work samples, observations)

Interactive Journals

Facet 6 (Self-Knowledge)

Standard Questions

1. In what ways did your knowledge about fractions change today?2. What applications did you find useful for use with fractions?3. What surprised or disappointed you today?4. What do you still wonder about?5. What else do you want me (the teacher) to know?

Culminating Writing AssessmentFacet 4 (Perspective)

Personal Narrative (using interactive math journals) - Using your math journal you are to write a personal narrative of

your learning experiences with fractions. Things you may want to include are: What you knew about fractions beforethe fraction unit began; things you did not know; what was easy; what was difficult; what frustrated you the most;where you stand at the end of this unit (have learned everything or still need help on some areas).

Expository WritingFacet 1 (Explanation)

Equivalent Fractions:How can you use multiplication or division to find equivalent fractions? Using the fraction 4/8 write an equivalent

fraction using multiplication and an equivalent fraction using division.Improper Fraction Mixed Numbers:

Explain how to write two and one-fourth as an improper fraction?How can you write any improper fraction as a mixenumber? (In addition to your writing, provide an example.)

Adding/Subtracting Like Fractions:

How do you add or subtract like fractions? Is the sum of 1/4 + 2/4 less than or greater than 1? Explain.Adding/Subtracting Unlike Fractions:What must you do first before adding or subtracting unlike fractions? How can you find a common denominator for tw

unlike fractions?Multiplying Fractions:How do you multiply two fractions? Provide an example. How can you use multiplication to multiply a whole numberby a fraction? Provide an example.Dividing Fractions:How can you write a fraction as a division problem? Provide an example. How can you divide a whole number by afraction?Provide an example.

Other Performance Assessments

Audio/Video Podcasts Vocabulary and Think A-LoudsFacet 3 and 5 (Application and Empathy)

Using vocabulary and skills learned, you and your group will create audio/video podcast(s) that demonstrates yourknowledge of a specific content area of fractions. You will select a target group of learners (struggling, average,

advanced, English Learners, etc.) and create an audio/video podcast that will be placed on classroom webpage.


10/13

Patti Herrington 10

Fraction Story of CollageFacet 2 (Interpretation)Create a fraction story or collage (with/without technology) at shows various examples of using fractions in your daily

life. Suggestions for use of technology might include using:www.mixbook.com;http://littlebirdtales.com; or

www.glogster.com.
http://www.mixbook.com/http://www.mixbook.com/http://www.mixbook.com/http://littlebirdtales.com/http://littlebirdtales.com/http://littlebirdtales.com/http://www.glogster.com/http://www.glogster.com/http://www.glogster.com/http://littlebirdtales.com/http://www.mixbook.com/


11/13

Patti Herrington 11

Student and Teacher Self-Assessment and Reflection

Interactive JournalsFacet 2 (Interpretation)

Standard Questions (Student)1. In what ways did your knowledge about fractions change today?2. What applications did you find useful for use with fractions?3. What surprised or disappointed you today?4. What do you still wonder about?5. What else do you want me (the teacher) to know?

Standard Questions (Teacher)

1. Did the lesson go according to plan?2. Were the students engaged in the presentation and use of materials?3. Were the students attentive?4. Was the flow of the lesson appropriate?5. After review of observations, formative assessments, and/or review of interactive journals are the students

learning?

Problem Solving Rating ScaleFacet 4 (Perspective)

1 3 5_________________________________________

I do not understand I can explainthe problem this problem

1 3 5_________________________________________

I cannot recognize I can recognize

the important and the important andunimportant parts unimportant partsof this problem. of this problem.

1 3 5_________________________________________

I do not know I can solve thewhere to start. problem and explain

my solution.

1 3 5_________________________________________

This was a This was an

difficult problem easy problem.


12/13

Patti Herrington 12

Lesson UnderstandingFacet 6 (Self-Knowledge)

thumbs up thumbs ok thumbs down


13/13

Patti Herrington 13

UbD Stage 2 Scoring Rubric

(0 Point) (1-2 Points) (3 Points)Your

Score

1. Assessments are notrepresentative of

different facets of

understanding.

Assessments appear to

utilize some facets to build

assessments for

understanding.

Utilizes the six facets to

build assessments for

understanding.

Assessments clearly

identify the correlating

facet.

Assessments demonstratecongruency among goals

/3

2. Performance task(s)are not authentic

Designs performance task,

which requires learners to

exhibit understanding

through authentic

performance tasks.

Designs authentic

performance task(s)

Task(s) in alignmentwith

goals and standards/3

3. Does not providescoring rubric for

the performance

task(s)

Designs appropriate

criterion-based scoring

rubric to evaluate learner

performance task(s)

Designs a scoring rubric that

includes distinct traits of

understanding and

successful performance /34. Selection ofassessment formats

is limited.

Includes at least two

different formats of

assessment.

Includes a variety (at least 3

types) of appropriate

assessment formats within

the unit to provide

additional evidence of

learning

/3

5. Fails to provideopportunities for

learners to self-

assess.

Provides opportunities for

learners to self-assess.

Self-assessments clearly

used as feedback and

reflection for students and

teachers, as well as for

evaluation.

/3


pherrington s2.doc

Documents