Developing Secondary Math Curriculum Thomas Rye Joel E. Ferris High School Spokane, WA For a preview, feel free to read the FAQ on pp 25-26 of your workbook

Developing Secondary Math Developing Secondary Math CurriculumCurriculum

Thomas RyeThomas RyeJoel E. Ferris High SchoolJoel E. Ferris High School

Spokane, WASpokane, WA

For a preview, feel free to read the FAQ on pp 25-26 of your workbook.

Essential QuestionsEssential Questions

What is understanding?What is understanding? How does starting with the end in mind impact How does starting with the end in mind impact

our teaching, as well as student learning?our teaching, as well as student learning? How can Understanding by Design be aligned How can Understanding by Design be aligned

with varying teaching styles and student with varying teaching styles and student populations?populations?

What would we expect to see in classrooms What would we expect to see in classrooms where teaching for understanding is consistent?where teaching for understanding is consistent?


To what extent is there a connection To what extent is there a connection between state standards (national between state standards (national standards) and what is truly standards) and what is truly mathematically important?mathematically important?


In what ways are learning mathematics In what ways are learning mathematics and doing mathematics the same?and doing mathematics the same? How much time do we spend How much time do we spend answering the answering the

questionsquestions?? How much time do we spend How much time do we spend questioning the questioning the

answersanswers??


How can we get students to think and How can we get students to think and communicate mathematically?communicate mathematically? What does it mean to think mathematically?What does it mean to think mathematically? What does the communication of What does the communication of

mathematics look like?mathematics look like?

Setting the StageSetting the Stage

Where do you teach?Where do you teach? Whom do you teach?Whom do you teach? Why are you here?Why are you here?

What is the extent of your knowledge What is the extent of your knowledge regarding Understanding by Design?regarding Understanding by Design?

What is the extent of your experience What is the extent of your experience regarding Understanding by Design?regarding Understanding by Design?


What is the role of mathematics in our What is the role of mathematics in our society?society? ArithmeticArithmetic AlgebraAlgebra GeometryGeometry StatisticsStatistics CalculusCalculus Advanced MathematicsAdvanced Mathematics

Everyday Math?Everyday Math?

The algebra is fun, but was it necessary?


What is mathematics?What is mathematics? What does it mean to do mathematics?What does it mean to do mathematics?

Can students do mathematics?Can students do mathematics?

What does it mean to think What does it mean to think mathematically?mathematically?


So why teach mathematics?So why teach mathematics?

What about mathematics is worth What about mathematics is worth teaching?teaching?

Mathematics is done by a few yet benefits Mathematics is done by a few yet benefits all.all.


What mathematics did you or your colleagues teach this What mathematics did you or your colleagues teach this last year?last year?

What mathematics did your students learn this last year?What mathematics did your students learn this last year?

From your list, mark with a #1, the things they will find From your list, mark with a #1, the things they will find beneficial to them over and over again next year.beneficial to them over and over again next year.

From your list, mark with a #2, the things they will find From your list, mark with a #2, the things they will find beneficial to them over and over again through the next beneficial to them over and over again through the next five to seven years.five to seven years.

From your list, mark with a #3, the things they will find From your list, mark with a #3, the things they will find beneficial to them over and over again through the next beneficial to them over and over again through the next twenty to forty years.twenty to forty years.

What about the book?What about the book?

To what extent is there a connection To what extent is there a connection between your textbook(s) and what is between your textbook(s) and what is mathematically important?mathematically important? Short termShort term Long termLong term

Understanding by DesignUnderstanding by Design

Curriculum framework designed by Jay Curriculum framework designed by Jay McTighe and Grant WigginsMcTighe and Grant Wiggins

A means of developing units of instruction A means of developing units of instruction and curriculum on a larger scaleand curriculum on a larger scale

Understanding by DesignUnderstanding by Design

Stage 1 – What do I want students to Stage 1 – What do I want students to understand?understand?

Stage 2 – How will I know when they Stage 2 – How will I know when they understand?understand?

Stage 3 – How will I get them to Stage 3 – How will I get them to understand?understand?

The 6 Facets of UnderstandingThe 6 Facets of Understanding(p. 23)(p. 23)

• What does it mean to understand What does it mean to understand mathematics?mathematics?• ExplanationExplanation

• InterpretationInterpretation

• ApplicationApplication

• PerspectivePerspective

• EmpathyEmpathy

• Self-knowledgeSelf-knowledge

Understanding MathematicsUnderstanding Mathematics

Marble MadnessMarble Madness

The continuum of understandingThe continuum of understanding

3 Stages of 3 Stages of Backward DesignBackward Design

Stage One – Identify ResultsStage One – Identify Results

During this session, you will design the During this session, you will design the following for the unit of your choice:following for the unit of your choice: Enduring UnderstandingsEnduring Understandings

What What ““big ideasbig ideas”” do I want kids to remember 40 years do I want kids to remember 40 years from now?from now?

Essential QuestionsEssential Questions What essential question(s) will guide and focus the What essential question(s) will guide and focus the

teaching and learning?teaching and learning? Knowledge and skillsKnowledge and skills

What skills, concepts, and procedures will be needed in What skills, concepts, and procedures will be needed in order for students to understand? order for students to understand?


Examining ContentExamining Content What is important for students to know / be What is important for students to know / be

able to do / understand for 40 able to do / understand for 40 daysdays.. What is important for students to know / be What is important for students to know / be

able to do / understand for 40 able to do / understand for 40 monthsmonths.. What is important for students to know / be What is important for students to know / be

able to do / understand for 40 able to do / understand for 40 yearsyears..

Enduring Understandings

40 days(the test)

40 months(college)

40 years(life)

Facts Worth Familiarity

Concepts/Strategies

Important toKnow/Use

“Big Ideas” WorthUnderstanding



Mathematical Enduring UnderstandingsMathematical Enduring Understandings

40-year learnings in mathematics40-year learnings in mathematics

So, of what ISo, of what I’’ve been teaching the last 15 ve been teaching the last 15 years, what has been of long term use to my years, what has been of long term use to my students?students?


What is one of the most difficult state (or What is one of the most difficult state (or national) standards to teach?national) standards to teach? In what ways is it difficult?In what ways is it difficult? What misunderstandings are common?What misunderstandings are common? In what context do students need to know In what context do students need to know

this?this?

Mathematical UnderstandingsMathematical Understandings

Consider…Consider… what you want your students to take away what you want your students to take away

from your class.from your class.

what you want your students to remember what you want your students to remember about your about your classclass 40 years from now. 40 years from now.

what you want your students to remember what you want your students to remember about about mathematicsmathematics 40 years from now. 40 years from now.

Overarching and Topical Overarching and Topical UnderstandingsUnderstandings

As we consider framing As we consider framing ““Enduring Enduring UnderstandingsUnderstandings”” for our classrooms, it for our classrooms, it helps to keep in mind that there are two helps to keep in mind that there are two types:types: Overarching:Overarching: Broad ideas, transferable to Broad ideas, transferable to

other topics/content areas.other topics/content areas. Topical:Topical: Specific to the unit topic. Specific to the unit topic.

Overarching UnderstandingsOverarching Understandings

At the heart of the disciplineAt the heart of the discipline Run across grade levelsRun across grade levels Many times run across curricular areasMany times run across curricular areas

These may be understandings for your These may be understandings for your entire courseentire course

Try sketching out a few ideas…Try sketching out a few ideas…


Students should…Students should…

see the mathematics in their world.see the mathematics in their world.

think.think.

communicate effectively.communicate effectively.


Mathematics is a useful language for Mathematics is a useful language for symbolically modeling and thus simplifying symbolically modeling and thus simplifying and analyzing our world.and analyzing our world.

Mathematics is a logical and objective Mathematics is a logical and objective means of analyzing and solving problems. means of analyzing and solving problems.

The effective communication of The effective communication of mathematics is essential to its application.mathematics is essential to its application.


What do students think?What do students think?

Math is a method of describing Math is a method of describing relationships between numbers and other relationships between numbers and other measurable quantities.measurable quantities.

Math can give visualization to what cannot Math can give visualization to what cannot be seen.be seen.



Mathematics is something that existed that Mathematics is something that existed that we had to find.we had to find.

Math simplifies our world through Math simplifies our world through determining information hypothetically.determining information hypothetically.



Mathematics opens up universal potential Mathematics opens up universal potential for each human to contribute to our for each human to contribute to our understanding of our world.understanding of our world.

Topical UnderstandingsTopical Understandings

Also big ideas at the heart of the disciplineAlso big ideas at the heart of the discipline Specific to the unitSpecific to the unit Broad enough to transfer beyond the unitBroad enough to transfer beyond the unit Narrow enough to guide the teachingNarrow enough to guide the teaching

Connecting to StandardsConnecting to Standards

Which of the following are enduring Which of the following are enduring understandings?understandings? Understand measurable attributes of objects and the Understand measurable attributes of objects and the

units, systems, and processes of measurement.units, systems, and processes of measurement. Understand patterns, relations, and functions.Understand patterns, relations, and functions. Compare and order fractions, decimals, percents, and Compare and order fractions, decimals, percents, and

numbers written in scientific notation.numbers written in scientific notation. Understand numbers, ways of representing numbers, Understand numbers, ways of representing numbers,

relationships among numbers, and number systems.relationships among numbers, and number systems.

Understanding by Design Understanding by Design TemplatesTemplates

A tool for organizing curricular, A tool for organizing curricular, assessment, and learning plans assessment, and learning plans effectively and efficiently.effectively and efficiently.

The templates embody the first stage of The templates embody the first stage of ““Backward DesignBackward Design””..

Workbook p31, 36-37, 46-51Workbook p31, 36-37, 46-51 1-page template1-page template 3-page template3-page template

MisunderstandingsMisunderstandings

Misunderstandings related to the unit (or Misunderstandings related to the unit (or course) may help identify enduring course) may help identify enduring understandingsunderstandings

Consider…Consider… What is behind the arithmetic mistakes What is behind the arithmetic mistakes

students make?students make? Why is algebraic manipulation difficult for Why is algebraic manipulation difficult for

some (many) students?some (many) students? What causes students to mix up slope?What causes students to mix up slope?

Write UnderstandingsWrite Understandings

Write overarching and topical understandings for Write overarching and topical understandings for your unit (or course)your unit (or course)

Filters to consider…Filters to consider… Is the understanding a big idea at the heart of the Is the understanding a big idea at the heart of the

discipline?discipline? Does the understanding allow for transfer to other Does the understanding allow for transfer to other

topics or fields or to life? (the topics or fields or to life? (the ““so whatso what”” test) test) To what extent does the understanding uncover To what extent does the understanding uncover

common misunderstandings and/or demand common misunderstandings and/or demand ““uncoverageuncoverage””??

A few Examples on page 109A few Examples on page 109

Share UnderstandingsShare Understandings

Share your understandings with the Share your understandings with the people at your tablepeople at your table

Do they pass the filters?Do they pass the filters? P242 (first 2 bullets on stage 1)P242 (first 2 bullets on stage 1)

Sharing with the groupSharing with the group

The Road to Understanding…The Road to Understanding…

How do we get students to engage in the How do we get students to engage in the process of understanding?process of understanding?

Through the process of inquiry, or, as Through the process of inquiry, or, as Understanding by Design puts it, through Understanding by Design puts it, through ““Essential Questions.Essential Questions.””

Types of Essential QuestionsTypes of Essential Questions

OverarchingOverarching

TopicalTopical


Have no one obvious right answerHave no one obvious right answer Framed to provoke/sustain student interestFramed to provoke/sustain student interest Raise important questions across content Raise important questions across content

areasareas Reflect conceptual prioritiesReflect conceptual priorities Recur naturallyRecur naturally

Writing Essential QuestionsWriting Essential Questions

Derived from understandingsDerived from understandings

Written to engage students in discussionWritten to engage students in discussion

Sometimes essential questions lead to Sometimes essential questions lead to additional enduring understandingsadditional enduring understandings


Write some essential questions of your Write some essential questions of your ownown

Keep in mind the filtersKeep in mind the filters No obvious right answerNo obvious right answer EngagingEngaging Raise important other questionsRaise important other questions

Examples on page 98Examples on page 98

Knowledge and SkillsKnowledge and Skills

It is important to consider what key knowledge It is important to consider what key knowledge and skills will be developed during the unit.and skills will be developed during the unit.

Consider two areas as you develop these:Consider two areas as you develop these: Knowledge/skills called for by content standardsKnowledge/skills called for by content standards Knowledge/skills needed by students to be successful Knowledge/skills needed by students to be successful

in reaching desired understandings.in reaching desired understandings.

Declarative KnowledgeDeclarative Knowledge

Facts (dates, names, statistics)Facts (dates, names, statistics) Identify the base, exponent, and coefficient in Identify the base, exponent, and coefficient in

a monomial expression. a monomial expression.

Abstract concepts Abstract concepts See how the base and exponent impact the See how the base and exponent impact the

magnitude of the expression.magnitude of the expression.

Rules and principlesRules and principles Know the rules for exponents.Know the rules for exponents.

Procedural KnowledgeProcedural Knowledge

SkillsSkills Identify “like” monomials. Identify “like” monomials.

Step-by-step proceduresStep-by-step procedures Express numbers using scientific notation.Express numbers using scientific notation.

Complex processesComplex processes Simplify monomial expressions and ratios of Simplify monomial expressions and ratios of

monomial expressions in which the exponents monomial expressions in which the exponents are integers.are integers.

Time to ProduceTime to Produce

Finish up your Stage 1 draftFinish up your Stage 1 draft

Self-Assess your work against the Self-Assess your work against the standards on page 242.standards on page 242.

3 Stages of 3 Stages of Backward DesignBackward Design

Assessment NeedsAssessment Needs

Consider the most appropriate and Consider the most appropriate and efficient way to determine if a student efficient way to determine if a student ““getsgets””…… Enduring UnderstandingsEnduring Understandings KnowledgeKnowledge SkillsSkills

Stage 2 Determine EvidenceStage 2 Determine Evidence

Consider how students might be able to Consider how students might be able to demonstrate their understanding.demonstrate their understanding.

What things will they do?What things will they do? In what formats or settings?In what formats or settings?

Stage 2 Determine EvidenceStage 2 Determine Evidence

During this stage…During this stage… You will outline a performance task for your You will outline a performance task for your

unit.unit. Sketch out a rubric to assess the performance Sketch out a rubric to assess the performance

task.task.

AssessmentAssessment

Consider a unit you recently taught, Consider a unit you recently taught, planned or observed.planned or observed.

What comprised all of the evidence used What comprised all of the evidence used for assessment?for assessment?


Could a student be successful on the Could a student be successful on the assessment package without truly assessment package without truly understanding?understanding?

Could a student truly understand, yet not Could a student truly understand, yet not be able to be successful?be able to be successful?

Stage 2: Determine EvidenceStage 2: Determine Evidence

Determine methods of assessmentDetermine methods of assessment Performance taskPerformance task

ProductsProductsPerformancesPerformances

Other evidenceOther evidenceQuizzes, tests, prompts, work samplesQuizzes, tests, prompts, work samplesObservationsObservationsStudent self-assessmentStudent self-assessment

Assessment MethodsAssessment Methods

Traditional quizzes & tests

Paper/pencilSelected-responseConstructed response

Performance tasks & projects

ComplexOpen endedAuthentic

Facts Worth Familiarity

Concepts/Strategies

Important toKnow/Use

“Big Ideas” Worth

Understanding

For more info see page 142


How can I assess a 40 year understanding How can I assess a 40 year understanding before the end of the semester?before the end of the semester?

Students Students DODO mathematics mathematics

Consider a task analysis from the Consider a task analysis from the Transition Math ProjectTransition Math Project

Rationale for Performance TasksRationale for Performance Tasks

Given the focus on understanding, Given the focus on understanding, a unit or course should be a unit or course should be anchored by performance tasks.anchored by performance tasks.

Performance tasks provide Performance tasks provide evidence that students are able toevidence that students are able to use knowledge in contextuse knowledge in context understand what they knowunderstand what they know

Performance TasksPerformance Tasks

Diverse performancesDiverse performances Differing contextsDiffering contexts EngagingEngaging AuthenticAuthentic


Performance Tasks / PromptsPerformance Tasks / Prompts RelevantRelevant Open-endedOpen-ended AmbiguityAmbiguity Require explorationRequire exploration Demand Demand ““uncoverageuncoverage”” Involve researchInvolve research

Performance TasksPerformance Tasks

Consider which assessments you have done Consider which assessments you have done that might be considered a performance task.that might be considered a performance task.

What were the benefits (both short and long What were the benefits (both short and long term)?term)?

What were the drawbacks (both short and What were the drawbacks (both short and long term)?long term)?

GRASPS (p172)GRASPS (p172)

GGoaloal

RRoleole

AAudienceudience

SSituationituation

PProduct or Performanceroduct or Performance

SStandards for Successtandards for Success

6 Facets of Understanding6 Facets of Understanding

The facets can be used to generate ideas for assessments: Explanation Interpretation Application Perspective Empathy Self-Knowledge

See prompts and ideas on pp. 156-158


Sample TasksSample Tasks

See websiteSee website http://ferrismath.com/teachers/ryehttp://ferrismath.com/teachers/rye

Please steal, modify, and share at will!Please steal, modify, and share at will!


Sample Student WorkSample Student Work

Students are doing mathematicsStudents are doing mathematics Students create professional workStudents create professional work

See work at websiteSee work at website Solar Cooking and pool tablesSolar Cooking and pool tables


Solar Hot Dog CookingSolar Hot Dog Cooking


Elliptical Pool TableElliptical Pool Table


Solar Hot Dog CookingSolar Hot Dog Cooking


Solar SSolar S’’mores!mores!

Performance TaskPerformance Task

Create a performance task for your unit.Create a performance task for your unit. Could a student be successful on the Could a student be successful on the

assessment package without truly assessment package without truly understanding?understanding?

Could a student truly understand, yet not be Could a student truly understand, yet not be able to be successful?able to be successful?

Is the assessment a meaningful and authentic Is the assessment a meaningful and authentic application of the understanding?application of the understanding?

See template pp. 204-206See template pp. 204-206

Grading and RubricsGrading and Rubrics

Create a rubric for assessing/grading your Create a rubric for assessing/grading your performance tasks.performance tasks.

Students self-evaluateStudents self-evaluate Student generated rubricsStudent generated rubrics

DifferentiationDifferentiation Assessing the same understandingsAssessing the same understandings Each student shows improvement in their Each student shows improvement in their

understandingunderstanding

Assessment RubricAssessment Rubric

Rubric ResourcesRubric Resources

Online ResourcesOnline Resources Classic Math RubricClassic Math Rubric NCTM RubricNCTM Rubric RubistarRubistar

Workbook ResourcesWorkbook Resources Generic (p188-9, 193)Generic (p188-9, 193) Template (p191)Template (p191)

Self Review - Stage 2Self Review - Stage 2

CompleteComplete An outline of the performance taskAn outline of the performance task Categories for the RubricCategories for the Rubric Summary of other assessmentsSummary of other assessments Math example of GRASPS on p170Math example of GRASPS on p170


FiltersFilters

Could a student successfully complete the Could a student successfully complete the task without truly understanding?task without truly understanding?

Could a student understand yet not be able to Could a student understand yet not be able to successfully complete the task?successfully complete the task?

Share TasksShare Tasks

Partner with a new group and share:Partner with a new group and share: Targeted enduring understandingTargeted enduring understanding Performance TaskPerformance Task

Discuss:Discuss: To what extent will the performance task allow the To what extent will the performance task allow the

teacher to assess the studentteacher to assess the student’’s level of s level of understanding?understanding?


How to create and find prompts for studentsHow to create and find prompts for students Extending problemsExtending problems

Numerical, graphical, and algebraic representationsNumerical, graphical, and algebraic representations Take away the detailsTake away the details

Web resourcesWeb resources Mathforum.orgMathforum.org www.nctm.orgwww.nctm.org Archives.math.utk.eduArchives.math.utk.edu Connecticut CurriculumConnecticut Curriculum

Student Selected TasksStudent Selected Tasks

Create a test and complete it or trade with Create a test and complete it or trade with someone else that chose thissomeone else that chose this

Make a dictionary / glossary to explain & include Make a dictionary / glossary to explain & include examplesexamples

Create a gameCreate a game Write a chapter for a bookWrite a chapter for a book Create a story problem for each conceptCreate a story problem for each concept Make an audio tape (back with written work)Make an audio tape (back with written work) Take the chapter test and choose at least 2 Take the chapter test and choose at least 2

problems to explain in writing and show more problems to explain in writing and show more than one way to do than one way to do

ResultsResults

Students no longer ask why we learn Students no longer ask why we learn mathematicsmathematics

Students gain appreciation for the Students gain appreciation for the mathematics all around themmathematics all around them

Students begin doing mathematics (true Students begin doing mathematics (true problem solving)problem solving)

Students clearly communicate Students clearly communicate sophisticated mathematical ideassophisticated mathematical ideas

ResultsResults

““It was such a joy having you for pre-It was such a joy having you for pre-calculus. Although I may have whined a lot calculus. Although I may have whined a lot about an overwhelming workload (and about an overwhelming workload (and there there waswas a lot!) I have never felt so a lot!) I have never felt so engaged as I did in your class. You not engaged as I did in your class. You not only taught each lesson with passion and only taught each lesson with passion and exuberance, but you took care in showing exuberance, but you took care in showing the relevance in each section.the relevance in each section.”” ~Katya ~Katya

ResultsResults Your wit and "funny" jokes made class entertaining Your wit and "funny" jokes made class entertaining

and fun, and your big picture ideas and teaching and fun, and your big picture ideas and teaching strategies made your class an amazing learning strategies made your class an amazing learning environment. Even as much as people struggled with environment. Even as much as people struggled with the applications, and complained that "other kids the applications, and complained that "other kids didn't have to do them", you stuck to them and they didn't have to do them", you stuck to them and they helped so much. I have always had a love for math, helped so much. I have always had a love for math, because it just makes sense to me. But you made because it just makes sense to me. But you made math not only enjoyable, but applicable to life. That math not only enjoyable, but applicable to life. That has made all the difference to me, and many other has made all the difference to me, and many other students. By this level, many teachers would just say students. By this level, many teachers would just say "you're never going to need to use this, but...." and "you're never going to need to use this, but...." and instantly lose the attention of the students. However, instantly lose the attention of the students. However, you didn't take that path of teaching…you didn't take that path of teaching…”” ~Devon ~Devon

3 Stages of Backward Design

Stage 3: Planning LearningStage 3: Planning Learning

When planning learning activities and When planning learning activities and lessons, consider the following question: lessons, consider the following question:

““Can students be engaged but not Can students be engaged but not learning?”learning?”

Stage 3: Planning LearningStage 3: Planning Learning

A Colleague once shared, “My students A Colleague once shared, “My students are always learning.”are always learning.”

I agreedI agreed

Intentional PlanningIntentional Planning

Is the day-to-day work Is the day-to-day work alwaysalways guiding guiding students toward the understandings?students toward the understandings?

Teacher freedom / teaching stylesTeacher freedom / teaching styles

W.H.E.R.E.T.O.W.H.E.R.E.T.O.

What will students do to What will students do to know know wherewhere they have they have come from, come from, wherewhere they are, they are, and and wherewhere they are going in they are going in the unit?the unit?

Provides purposeProvides purpose


What will students do that What will students do that hookshooks their attention, holds their attention, holds their interest, and engages their interest, and engages their best efforts throughout their best efforts throughout the unit?the unit?

Counterintuitive ProblemsCounterintuitive Problems


What will students do that allows them to explore the big ideas and essential questions that guide the unit?

What instruction is needed to equip the students for their final performance?


What will students do that What will students do that causes them to causes them to reflectreflect, , rethinkrethink, or “dig deeper” into , or “dig deeper” into the unit’s core the unit’s core understandings?understandings?

How will the students be How will the students be afforded opportunities to afforded opportunities to reviserevise and and refinerefine their work? their work?


How will students How will students exhibitexhibit their understandings their understandings through final products and through final products and performance?performance?

How will they How will they evaluateevaluate their their own learning for strengths own learning for strengths and weaknesses?and weaknesses?


How will the learning be How will the learning be tailoredtailored to student needs? to student needs?

In what ways will the In what ways will the instruction be instruction be differentiated?differentiated?


How will the learning be How will the learning be sequenced and sequenced and organizedorganized??

Misunderstandings AgainMisunderstandings Again

Common misunderstandings or Common misunderstandings or misconceptions can also help you design misconceptions can also help you design the learning experiences that will lead the learning experiences that will lead students to understanding.students to understanding.

Misunderstandings and HooksMisunderstandings and Hooks

Creating ThinkingCreating Thinking

When he drives 40 mph Mr. Earl E. Bird When he drives 40 mph Mr. Earl E. Bird arrives to work 3 minutes late. When he arrives to work 3 minutes late. When he drives 60 mph Mr. Earl E. Bird arrives to drives 60 mph Mr. Earl E. Bird arrives to work 3 minutes early. How fast should he work 3 minutes early. How fast should he drive to arrive precisely on time?drive to arrive precisely on time? Explore numerically, graphically, algebraicallyExplore numerically, graphically, algebraically Generalize the solutionGeneralize the solution Students discuss extraneous informationStudents discuss extraneous information

Taken from Taken from The Mathematics TeacherThe Mathematics Teacher

Stage 3Stage 3

Map out a rough draft of stage 3Map out a rough draft of stage 3 Be sure to include at least one idea from each Be sure to include at least one idea from each

of WHERETOof WHERETO Self-Assess vs. the standards on p242.Self-Assess vs. the standards on p242.

The Understanding by Design The Understanding by Design ClassroomClassroom

What does an Understanding by Design What does an Understanding by Design classroom look like?classroom look like? Students always know why they are doing Students always know why they are doing

what they are doing.what they are doing. Students are engaged and always know what Students are engaged and always know what

they are working toward.they are working toward. Any given day…Any given day…

See pp 268-269 in workbookSee pp 268-269 in workbook

Online ResourceOnline Resource

Understanding by Design ExchangeUnderstanding by Design Exchange

www.ubdexchange.orgwww.ubdexchange.org

Searching for units, understandings, Searching for units, understandings, questions, tasksquestions, tasks

Writing unitsWriting units Receiving expert and peer feedbackReceiving expert and peer feedback


What is understanding?What is understanding? How does starting with the end in mind impact How does starting with the end in mind impact

our teaching, as well as student learning?our teaching, as well as student learning? How can Understanding by Design be aligned How can Understanding by Design be aligned

with varying teaching styles and student with varying teaching styles and student populations?populations?

What would we expect to see in classrooms What would we expect to see in classrooms where teaching for understanding is consistent?where teaching for understanding is consistent?


To what extent is there a connection To what extent is there a connection between state standards, national between state standards, national standards and what is truly mathematically standards and what is truly mathematically important?important?

In what ways are learning mathematics In what ways are learning mathematics and doing mathematics the same?and doing mathematics the same?

How can we get students to think and How can we get students to think and communicate mathematically?communicate mathematically?

Where do you go from here?Where do you go from here?

Teaching the unitTeaching the unit Reflecting and revisingReflecting and revising

Peer reviewPeer review Examining student workExamining student work

Collaborative planningCollaborative planning Observing classroomsObserving classrooms

Contact InformationContact Information Tom Rye [email protected] Rye [email protected] http://ferrismath.com/teachers/Rye/resources.htmhttp://ferrismath.com/teachers/Rye/resources.htm

Documents

Developing Secondary Math Curriculum Thomas Rye Joel E. Ferris High School Spokane, WA For a preview, feel free to read the FAQ on pp 25-26 of your workbook