1. DATE Learning Target 1B: 1B I can prove the Law of Sines. I can explain when to apply the laws for oblique triangles, and explain the ambiguous case. Mathematical Language is the vehicle for communicating thoughts, ideas, and conclusions

2. What question would you ask ……?

3. Given the task, What is your first question? Task Prove the Law of Sines Actions Analyze Alone Create a Plan together Monitor your thinking

4. Law of Sines

5. Used for acute and oblique triangles when: AASASA

6. Proof of Law of Sines (Acute Triangle)

7. Proof of Law of Sines (Oblique Triangle)

8. Goal Problems for LT 1B RoutineRecall & Reproduction Annotate work with Questions? Clarifications? Sally has a kite flying at the end of 1750 feet of string at an angle of 75 degrees with the ground. An observer notes that the angle formed by the kite and the flier is 102 degrees. How far is the kite from the observer? Given: Alpha=80 degrees C=16 Beta=34 degrees Solve the triangle

9. Active Practice GRASP Based on your qualitative goal evidence, decide on your short-term goal for LT 1B Choose where you want to start practice Find a partner who has a similar goal Start collaboration by talking through goal problems questions and clarifications Questions to drive collaboration & COMMUNICATION: What exactly are you doing? Can you describe it precisely? Why are you doing it? How does it fit into the solution?

10. Practice Insights Annotate your “work” (qualitative data) against the work sample: Identify areas of confusion Identify areas of strength Analyze reasoning Write down questions Notes based on student questions and my analysis of work during active practice

11. Non-Routine Goal Problem NEXT STEPS?

12. Law of Sines E. Explain Ambiguous Case

13. Law of Sines (SSA)-Ambiguous Case When given the measures of two sides and a non-included angle one of the following will be true:

14. Law of Sines (SSA)-Ambiguous Case No triangle exists Angle A is acute  a <h Angle A is obtuse  a < b or a = b

15. Law of Sines (SSA)-Ambiguous Case One triangle exists Angle A is acute  a > b or a = b Angle A is acute  a = h Angle A is obtuse  a > b

16. Law of Sines (SSA)-Ambiguous Case Two triangles exist Angle A is acute  h< a < b

17. Goal Problems (Try again) Routine Recall & Reproduction Use the Rubric to analyze your current level Kathy is taking a walk along a straight road. She decides to leave the road, so she walks on a path that makes an angle of 35 degrees with the road. After walking for 450 meters, she turns 75 degrees and heads back towards the road. How far does Kathy need to walk on her current path to get back to the road?

18. Non-Routine Goal Problem NEXT STEPS?

19. Analyze your Goal Problems Evidence Annotate your “work” (qualitative data) against the work sample: Identify areas of confusion Identify areas of strength Analyze reasoning Write down questions Align quantitative data: GRASP Academic and effort rubric data Next choice for learning? Take Action Seek answers to questions

20. Non-Routine Problem Lola rolls a ball on the ground at an angle of 23 degrees to the right of her dog Buttons. If the ball rolls a total distance of 48 feet, and she is standing 30 feet away, how far will buttons have to run to retrieve the ball?

21. Law of Cosines

22. Used for acute and oblique triangles when: SAS SSS

23. Alternate Goal Problems (Just in case ) Recall & Reproduction Find the height of the mountain. Routine For the initial 90 miles of a flight, the pilot heads 8 degree off course in order to avoid a storm. The pilot then changes direction to head toward the destination for the remainder of the flight, making 157 degree angle to the first flight course. Determine the total distance of the flight.

24. Given the task, What is your first question? Task Find the formula for area for the triangle below Actions Analyze Alone Create a Plan together Monitor your thinking

25. Area of Triangles -SAS

26. Reflecting on my learning 1). What did I learn mathematically this week? Explain 2). What did I learn about using assessments to level up in my learning 3). Next steps