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!

leg

leg

hypotenusea

b

c

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 = C2

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 ProblemSolution

• 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

B

20 miles

A 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

2 2 2a b c 2 2 220 45 x

2400 2025 x 22425 x

22425 x

x 2425x 49.24

In the accompanying diagram, triangle A is similar to triangle B. Find the value of n.

8

6 3

n + 2

C

Rigor/Relevance Framework

Remember…REAL

WORLD

THOUGHT PROVOKING

TEACHERWORKS

STUDENTWORKS

STUDENT THINKS

STUDENT THINKSAND WORKS

LOW HIGH

LOW

HIGH

A B

C D

RIGOR/RELEVANCE FRAMEWORK

RIGOR

RELEVANCE

Work in groups to place each card in its appropriate quadrant.

SolutionsQuadrant A Acquisition

16. 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.

Quadrant 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.

Quadrant 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.

Quadrant 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.

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 risk-taker.

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 Framewor

k

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

Awareness 1

Comprehension 2

Application 3

1

Knowledge in one discipline

2

Apply knowledge in one discipline

A

Acquisition

Students gather and store bits of knowledge/information and are expected to remember or understand this acquired knowledge.

Low-level Knowledge

A Quadrant

• name• label• define• select• identify• list• memorize• recite• locate• record

• definition• worksheet• list• quiz• test• workbook• true-false• reproduction• recitation

Verbs Products

Awareness 1

Comprehension 2

Application 3

B

Application

3

Apply knowledge across disciplines

4

Apply to real-world predictable situation

5

Apply to real-world unpredictable situation

Students use acquired knowledge to solve problems, design solutions, and complete work.

High-level Application

B Quadrant

• apply• sequence• demonstrate• interview• construct• solve• calculate• dramatize• interpret• illustrate

• scrapbook• summary• interpretation• collection• annotation• explanation• solution• demonstration• outline

Verbs Products

Application 3

Analysis 4

Synthesis 5

Evaluation 6

1

Knowledge in one discipline

2

Apply knowledge in one discipline

C

Assimilation

Students extend and refine their knowledge so that they can use it automatically and routinely to analyze and solve problems and create solutions.

High-level Knowledge

C Quadrant

• sequence• annotate• examine• report• criticize• paraphrase• calculate• expand• summarize• classify• diagram

Verbs Products

•essay•abstract•blueprint•inventory•report•plan•chart•questionnaire•classification•diagram•discussion•collection•annotation

3

Apply knowledge across disciplines

4

Apply to real-world predictable situation

5

Apply to real-world unpredictable situation

Application 3

Analysis 4

Synthesis 5

Evaluation 6

D

Adaptation

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.

High-level ApplicationHigh-level Knowledge

D Quadrant

• evaluate• validate• justify• rate• referee• infer• rank• dramatize• argue• conclude

• evaluation• newspaper• estimation• trial• editorial• radio program• play• collage• machine• adaptation• poem• debate• new game• invention

Verbs Products

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 - 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.

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

50

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

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?