DATELearning 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

What question would you ask ……?

Given the task,What is your first question?

Task

Prove the Law of Sines

Actions

• Analyze Alone• Create a Plan together

• Monitor your thinking

Law of Sines

Law of Sines

Used for acute and oblique triangles when:

AAS ASA

Proof of Law of Sines (Acute Triangle)

Proof of Law of Sines (Oblique Triangle)

Goal Problems for LT 1B

Routine Recall & 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 degreesC=16Beta=34 degrees

Solve the triangle

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?

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

Non-Routine Goal Problem

NEXT STEPS?

Law of Sines• E. Explain Ambiguous Case

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:

Law of Sines (SSA)-Ambiguous Case• No triangle exists

• Angle A is acute a <h

• Angle A is obtuse a < b or a = b

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

Law of Sines (SSA)-Ambiguous Case

Two triangles exist• Angle A is acute h< a < b

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?

Non-Routine Goal Problem

NEXT STEPS?

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

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?   

Law of Cosines

Law of Cosines• Used for acute and oblique triangles when:

SAS SSS

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.

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

Area of Triangles -SAS

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