In schools the status quo persists! ???? Why Rigor and Relevance ???? • Changing Nature of Work --‐- Technology • Global Competition --‐- It’s 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 Engagement Rigor/Relevance Framework The Pythagorean Theorem Objective- To solve problems involving the Pythagorean Theorem. For Right Triangles Only! hypotenuse leg a c b leg Now 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? • So 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 The 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 = C 2 B Ladder Problem A 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? B Ladder Problem Solution • First draw a diagram that shows the sides of the right triangle. • Label the sides: – Ladder is 25 m – Distance from house is 7 m • Use a2 + b2 = c2 to solve for the missing side. Distance from house: 7 meters A car drives 20 miles due east and then 45 miles due south. To the nearest hundredth of a mile, how far is the car from its starting point? a b c 2 20 miles x 2 2 20 45 x 2 400 2025 x 2 45 miles 2 2 2425 x 2 2425 x x 2425 x 4 9 .2 4 2 C In the accompanying diagram, triangle A is similar to triangle B. Find the value of n. n+2 8 6 3 Remember… Rigor/Relevance Framework R E A L THOUGHT PROVOKING W O R L D RIGOR/RELEVANCE FRAMEWORK C R I G O R STUDENT THINKS HIGH A LOW D STUDENT THINKS AND WORKS B TEACHER WORKS LOW STUDENT WORKS HIGH RELEVANCE Work in groups to place each card in its appropriate quadrant. Solutions 16. 27. 3. 24. 17. 22. 12. 10. Quadrant A Acquisition Distinguish rational from irrational numbers. Simplify, factor, and compute polynomials. Solve and graph linear equations. Create and solve factorial expressions for permutation problems. Compute numbers with scientific notation. Predict the probability of events using ratios. Bisect line segments and angles. Provide examples to illustrate properties of real numbers. 11. 15. 2. 6. 21. 25. 9. Quadrant B Application Draw Venn diagrams to represent a set of real conditions, e.g., common characteristics of students in class. Find length of line segments without measuring. Take measurements using calipers and micrometers. Calculate measurement error in real observations. Calculate frequency of vibration of various piano strings. Calculate medical dosages for different weight animals. Plot changes in temperature at different altitudes from a NASA space flight. 19. 28. 20. 13. 4. 26. 18. Quadrant C Assimilation Solve interdisciplinary problems with signed numbers, such as molecules with a charge of protons and electrons. Identify congruence of shapes from expressions and truth statements. Complete Euclidean proofs in geometry. Construct truth tables as a shorthand method for discussing logical sentences. Analyze factors in difference between theoretical empirical probability. Select best measures of central tendency to support a particular point of view. Solve quadratic equations and linear inequalities. 1. 5. 7. 8. 14. 29. 23. Quadrant D Adaptation Determine types of measurements/calculations involved in designing everyday items. Make calculations of electrical load of appliances based on usage in homes in the community. Examine the different elements, visual effects, and features found in a computer game and use mathematics to design some of these elements. Create formulas to predict changes in stock market values. Design support posts of different materials and size to handle stress load in a building. Develop a sampling plan for a public opinion poll. Design a roller coaster ride. Draw a Pig – On 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 If 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. Facing 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. With many details, you are analytical, cautious, and distrustful. With few details, you are emotional and naive, you care little for details and are a risktaker. With 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. The size of the ears indicates how good a listener you are. The bigger the better. And 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. Rigor/ Relevance Framework Teaching for Rigor and Relevance • We don’t have to teach in all four quadrants, just know they exist! – Elective teachers usually flow A-B-D – Academic teachers usually flow A-C-D • We need to know that all levels of rigor and relevance exist, and that there are appropriate times for each. Where do you teach? • Look at the verbs and products • Think about some of your “favorite” or “best” lessons and decide where you already have strengths in teaching Students gather and store bits of knowledge/information and are expected to remember or understand this acquired knowledge. Application 3 A Comprehension Awareness Acquisition 2 1 Low-level Knowledge 1 2 Knowledge in one discipline Apply knowledge in one discipline A Quadrant Verbs • • • • • • • • • • name label define select identify list memorize recite locate record • • • • • • • • • Products definition worksheet list quiz test workbook true-false reproduction recitation Students use acquired knowledge to solve problems, design solutions, and complete work. Application 3 B Comprehension Awareness Application 2 1 High-level Application 3 4 5 Apply knowledge across disciplines Apply to realworld predictable situation Apply to realworld unpredictable situation B Quadrant Verbs • • • • • • • • • • apply sequence demonstrate interview construct solve calculate dramatize interpret illustrate Products • • • • • • • • • scrapbook summary interpretation collection annotation explanation solution demonstration outline Students extend and refine their knowledge so that they can use it automatically and routinely to analyze and solve problems and create solutions. Evaluation Synthesis 6 C 5 Analysis 4 Application 3 Assimilation High-level Knowledge 1 2 Knowledge in one discipline Apply knowledge in one discipline C Quadrant Verbs • • • • • • • • • • • sequence annotate examine report criticize paraphrase calculate expand summarize classify diagram Products •essay •abstract •blueprint •inventory •report •plan •chart •questionnaire •classification •diagram •discussion •collection •annotation Students 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. Evaluation 6 D Synthesis 5 Analysis 4 Application Adaptation High-level Knowledge High-level Application 3 3 4 5 Apply knowledge across disciplines Apply to real-Apply to realworld world predictable unpredictable situation situation D Quadrant Verbs • • • • • • • • • • evaluate validate justify rate referee infer rank dramatize argue conclude Products • • • • • • • • • • • • • • evaluation newspaper estimation trial editorial radio program play collage machine adaptation poem debate new game invention Where do you teach? • Look at the verbs and products • Think about some of your “favorite” or “best” lessons and decide where you already have strengths in teaching • Look at the Instructional Strategies list to find strategies that are stronger for the quadrants you don’t reach as much Instructional 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 Handbook Quad D Moments • Teaching 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 Moment” • An easy way to move your students to Quad D is to have them teach each other Key Elements of Quad D • Anchor in the Standards • Backward Design – Begin with the end (a performance task) in mind • Align instruction and assessment • Keep lessons Student –Centered • Rigor and Relevance is naturally differentiated *It takes a year to make Quadrant D a habit* Math - Elementary C D Find values in number sentences when represented by unknowns. Develop formula for determining large quantity without counting, (e.g. beans in a jar.) A B Memorize multiplication tables. Collect outside temperatures for several days and make a graph of results. As 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. Share Your Performance Tasks Where to begin with RR • • • • • • • • Don’t Forget Why and Relationships Analyze one of your tests Analyze the state test Think about the level of questions you ask students Identify and share a Quadrant D lesson Use strategies with high rigor/relevance Consider Standards in groups Create a Quadrant D performance for a unit 50 50 Next Steps • Remember this is mental model/way of thinking, NOT A PROGRAM • Successful Practices Network and Gold Seal Lessons Final Questions • On your note card, write down any lessons for which you would like help developing a Quadrant D Activity. • Questions?