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In schools the status quo persists!Tracy1???? Why Rigor and Relevance ????

Changing Nature of Work -- Technology Global Competition -- Its a Flat World Conceptual Age -- Requires Whole Brain Thinkers Youth Have Changed -- Digital Natives Next Generation Assessments Increased Accountability for Learning Multiple Achievement Gaps Poor Student EngagementTracy2

Rigor/Relevance FrameworkTracy3The Pythagorean Theorem

Tracy4Objective- To solve problems involving the Pythagorean Theorem.For Right Triangles Only!legleghypotenuseabcTracy5Now draw diagonal lines across the blue rectangles, making four smaller blue triangles. Call those lines C. Do you see that you have made four blue right triangles, whose sides are A, B, and C?

Tracy6So now you have one square with area AxA (the big yellow one) and one square with area BxB (the little green one) and two rectangles with area AxB (the light blue ones). So the area of the whole square is (A+B) x (A+B) or the area is (AxA) + 2(AxB) + (BxB). Or you might say that(A+B)2 = A2 + 2AB + B2

Tracy7The area of all four triangles together is the same as the two blue rectangles you made them from, so that is 2AB. The area of the pink square in the middle is CxC or C2. And the area of the whole big square is, as we have already seen, A2 + 2AB + B2 So A2 + 2AB + B2 = 2AB + C2 We can subtract 2AB from both sides, so that gives (ta da!)

A2 + B2 = C2Tracy8

Tracy9Ladder ProblemA ladder leans against a second-story window of a house. If the ladder is 25 meters long, and the base of the ladder is 7 meters from the house, how high is the window?

BTracy10Ladder ProblemSolutionFirst draw a diagram that shows the sides of the right triangle.Label the sides: Ladder is 25 mDistance from house is 7 mUse a2 + b2 = c2 to solve for the missing side.Distance from house: 7 metersBTracy1120 milesA car drives 20 miles due east and then 45 milesdue south. To the nearest hundredth of a mile, how far is the car from its starting point?45 milesx

Tracy12In the accompanying diagram, triangle A is similar to triangle B. Find the value of n.863n + 2CTracy13

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Rigor/Relevance FrameworkRememberREAL

WORLD

THOUGHT PROVOKINGAmber17TEACHERWORKSSTUDENTWORKSSTUDENT THINKSSTUDENT THINKSAND WORKSLOWHIGHLOWHIGHABCDRIGOR/RELEVANCE FRAMEWORKRIGORRELEVANCEAmber18Work in groups to place each card in its appropriate quadrant.Amber19SolutionsQuadrant A Acquisition16.Distinguish rational from irrational numbers.27.Simplify, factor, and compute polynomials.3.Solve and graph linear equations.24.Create and solve factorial expressions for permutation problems.17.Compute numbers with scientific notation.22.Predict the probability of events using ratios.12.Bisect line segments and angles.10.Provide examples to illustrate properties of real numbers.

Amber20Quadrant B Application11.Draw Venn diagrams to represent a set of real conditions, e.g., common characteristics of students in class.15.Find length of line segments without measuring.2.Take measurements using calipers and micrometers.6.Calculate measurement error in real observations.21.Calculate frequency of vibration of various piano strings.25.Calculate medical dosages for different weight animals.9.Plot changes in temperature at different altitudes from a NASA space flight.Amber21Quadrant C Assimilation19.Solve interdisciplinary problems with signed numbers, such as molecules with a charge of protons and electrons.28.Identify congruence of shapes from expressions and truth statements.20.Complete Euclidean proofs in geometry.13.Construct truth tables as a shorthand method for discussing logical sentences.4.Analyze factors in difference between theoretical empirical probability.26.Select best measures of central tendency to support a particular point of view.18.Solve quadratic equations and linear inequalities.

Amber22Quadrant D Adaptation1.Determine types of measurements/calculations involved in designing everyday items.5. Make calculations of electrical load of appliances based on usage in homes in the community.7. Examine the different elements, visual effects, and features found in a computer game and use mathematics to design some of these elements.8. Create formulas to predict changes in stock market values.14. Design support posts of different materials and size to handle stress load in a building.29. Develop a sampling plan for a public opinion poll.23. Design a roller coaster ride.Amber23Draw a PigOn a blank piece of paper draw a pig. Do not to look at your neighbor's pig. It must be animal variety, any size any shape

Rob24If the pig is drawn:

Toward the top of the paper, you are positive and optimistic. Toward the middle, you are a realist. Toward the bottom, you are pessimistic, and have a tendency to behave negatively.

Rob25Facing left, you believe in tradition, are friendly, and remember dates (birthdays, etc.)Facing right, you are innovative and active, but don't have a strong sense of family, nor do you remember dates.Facing front (looking at you), you are direct, enjoy playing devil's advocate and neither fear nor avoid discussions.Rob26With many details, you are analytical, cautious, and distrustful.With few details, you are emotional and naive, you care little for details and are a risk-taker.Rob27With less than 4 legs showing, you are insecure or are living through a period of major change.With 4 legs showing, you are secure, stubborn, and stick to your ideals.

Rob28The size of the ears indicates how good a listener you are.The bigger the better. Rob29And last but not least . . the longer the pig's tail you have drawn, the more satisfied you are with the quality of your sex life.

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Rigor/Relevance FrameworkEmma31Teaching for Rigor and RelevanceWe dont have to teach in all four quadrants, just know they exist! Elective teachers usually flow A-B-DAcademic teachers usually flow A-C-DWe need to know that all levels of rigor and relevance exist, and that there are appropriate times for each.

Emma32Where do you teach?Look at the verbs and productsThink about some of your favorite or best lessons and decide where you already have strengths in teaching

Emma33Awareness 1 Comprehension 2Application 31Knowledge in one discipline2Apply knowledge in one disciplineAAcquisitionStudents gather and store bits of knowledge/information and are expected to remember or understand this acquired knowledge.Low-level KnowledgeEmma34A Quadrant

namelabeldefineselectidentifylistmemorizerecitelocaterecord definitionworksheetlistquiztestworkbooktrue-falsereproductionrecitationVerbsProductsEmma35Awareness 1 Comprehension 2Application 3BApplication3Apply knowledge across disciplines4Apply to real-world predictable situation5Apply to real-world unpredictable situationStudents use acquired knowledge to solve problems, design solutions, and complete work. High-level ApplicationEmma36B Quadrant

applysequencedemonstrateinterviewconstructsolvecalculatedramatizeinterpretillustrate scrapbooksummaryinterpretationcollectionannotationexplanationsolutiondemonstrationoutlineVerbsProductsEmma37Application 3Analysis 4Synthesis 5Evaluation 61Knowledge in one discipline2Apply knowledge in one disciplineCAssimilationStudents extend and refine their knowledge so that they can use it automatically and routinely to analyze and solve problems and create solutions.High-level KnowledgeEmma38C Quadrant

sequenceannotateexaminereportcriticizeparaphrasecalculateexpandsummarizeclassifydiagramVerbsProductsessayabstractblueprintinventoryreportplanchartquestionnaireclassificationdiagramdiscussioncollectionannotationEmma393Apply knowledge across disciplines4Apply to real-world predictable situation5Apply to real-world unpredictable situationApplication 3Analysis 4Synthesis 5Evaluation 6DAdaptationStudents think in complex ways and apply acquired knowledge and skills, even when confronted with perplexing unknowns, to find creative solutions and take action that further develops their skills and knowledge.High-level ApplicationHigh-level KnowledgeEmma40D Quadrantevaluatevalidatejustifyraterefereeinferrankdramatizeargueconclude evaluationnewspaperestimationtrialeditorialradio programplaycollagemachineadaptationpoemdebatenew gameinventionVerbsProductsEmma41Where do you teach?Look at the verbs and productsThink about some of your favorite or best lessons and decide where you already have strengths in teachingLook at the Instructional Strategies list to find strategies that are stronger for the quadrants you dont reach as much

Emma42Instructional Strategies The appropriateness of a particular instructional strategy in a given situation can be determined by matching the characteristics of the strategy, the learner, and what needs to be learned.

Rigor and Relevance HandbookEmma43Quad D MomentsTeaching in Quadrant D with high rigor and relevance does not have to mean large projects that take long periods of time.Adapt what you already do by adding a short D MomentAn easy way to move your students to Quad D is to have them teach each otherEmma44Key Elements of Quad DAnchor in the StandardsBackward Design Begin with the end (a performance task) in mindAlign instruction and assessmentKeep lessons Student CenteredRigor and Relevance is naturally differentiated

*It takes a year to make Quadrant D a habit*

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Emma46Math - ElementaryC

Find values in number sentences when represented by unknowns.

D

Develop formula for determining large quantity without counting, (e.g. beans in a jar.)

A

Memorize multiplication tables.

B

Collect outside temperatures for several days and make a graph of results.

Rob47As a group, write down a Quadrant A activity.Pass the card to the next group.Write down a Quadrant B task, building on the Quadrant A question your group received.Pass the card to the next group.Write down a Quadrant C task, building on the Quadrant A & B tasks your group received.Pass the card to the next group.Write down a Quadrant D task, building on the Quadrant A, B & C tasks you received.

Rob48Share Your Performance TasksRob4950Where to begin with RRDont Forget Why and RelationshipsAnalyze one of your testsAnalyze the state testThink about the level of questions you ask studentsIdentify and share a Quadrant D lessonUse strategies with high rigor/relevanceConsider Standards in groupsCreate a Quadrant D performance for a unit50Tracy50Next StepsRemember this is mental model/way of thinking, NOT A PROGRAMSuccessful Practices Network and Gold Seal Lessons

Tracy51Final QuestionsOn your note card, write down any lessons for which you would like help developing a Quadrant D Activity.Questions?

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