Unit 1 Lesson 4 Vertical Angles Exploration

Part II: Patterns & Observations

Discuss your observations with your partner, including any patterns that you notice.

Without collaborating with your partner, write down any patterns you notice about the angles formed when "Vertical Angles" is shown on the screen. Your answer should be 2-3 complete sentences. Be specific and write enough so that any other person would be able to understand the relationships and patterns you observed from your description. Draw a diagram if you find it helpful.

Part III: Rule

A theorem is a rule written in "if, then" form that can be proven.

Use your explanation from question 2 in part II to write a theorem (rule) about the measurements of vertical angles. Answer this part independently without collaborating. If _______________________________________________________________ ______________________________________________________________, then, __________________________________________________________ _______________________________________________________________

Discuss your theorem with your partner. Then, we will share answers as a group. In the space below, write a revised theorem: If _______________________________________________________________ ______________________________________________________________, then, ___________________________________________________________ _______________________________________________________________

Part IV: Patterns & Observations

Recall your knowledge of supplementary and complementary angles. What relationships do you notice between the sums of the measures of the adjacent angles when “Vertical Angles” is shown on the screen? Include the terms “adjacent angles” and “linear pair” in your description. If you’re not sure what these terms mean, feel free to look them up in the Notability guided notes. Your answer should be 3-4 complete sentences.

Part V: Rule

A theorem is a rule written in "if, then" form that can be proven.

Use your explanation from question 2 in part II to write a theorem (rule) about the measurements of linear pairs. Answer this part independently without collaborating. If _______________________________________________________________ ______________________________________________________________, then, __________________________________________________________ _______________________________________________________________

Discuss your theorem with your partner. Then, we will share answers as a group. In the space below, write a revised theorem: If _______________________________________________________________ ______________________________________________________________, then, ___________________________________________________________ _______________________________________________________________

Part VI: Solving a Problem (Test & Check)

Use the rule you created in question 3 of part III to solve problems.

While creating stairs for a deck, it is important that the support beam on the top of the stairs has the same angle with the rail as the support beam on the bottom of the stairs. The picture below shows the measure of the angle underneath the rail to the right of the support beam. What are the measures of the other three angles around the rail? Show your work.

Use your answer from question 2 and the image below to write equations that can be used to solve for x and y. Remember, equations must have equal signs. Then, solve the equation. Remember to show all of your work! Equation to find x: Solution: Equation to find y: Solution:

Reflection

This reflection is part of your portfolio. Include parts 1 and 2 below.

1. 
   For your reflection, please include your answers from the following parts of this assignment:
   

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  Part I, all 10 cases
  

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  Part II, Question 2
  

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  Part III, Question 3
  

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  Part IV, Question 1
  

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  Part V, Question 2
  

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  Part VI, Questions 2 and 3
  

2. 
   Answer the following question independently and include it in your portfolio. Answer each question using 2-3 complete sentences.:
   

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  How can we use vertical angles to help build structures?
  

• 
  How can you revise the theorem you wrote now that you've used it to solve problems?
  

Rubric

	Below Expectations	Approaching Expectations	Meeting Expectations	Exemplifying Expectations
Knowledge and Understanding 16.9-10.MAT.KU.002 16.9-10.MAT.KU.003	Student shows little to no understanding of vertical angles and other angle pairs. AND Student is unable to write and solve algebraic problem.	Student shows a basic understanding of of vertical angles and other angle pairs. OR Student is able to write and solve algebraic problems.	Student shows a clear understanding of of vertical angles and other angle pairs. AND Student is able to write and solve algebraic problems.
Comments:
Modes of Inquiry 16.9-10.MAT.MI.002 16.9-10.MAT.MI.003 16.9-10.MAT.MI.004	Student is unable to use SPORT method to write a rule AND Student is unable to solve problems using the rule.	Student is unable to use SPORT method to attempt to write a rule OR Student is unable to solve problems using the rule.	Student effectively uses SPORT method to write a rule AND Student is able to solve problems using the rule.
Comments:
Synthesis and Evaluation 16.9-10.MAT.SE.001 16.9-10.MAT.SE.005	Conclusions are not well supported by explanations. AND Student does not make appropriate revisions to their answers.	Conclusions are somewhat supported by explanations. OR Student does not make appropriate revisions to their answers.	Conclusions are well supported by explanations. AND Student makes appropriate revisions to their answers.
Comments:
Communication 16.9-10.MAT.CO.001 16.9-10.MAT.CO.002	Ideas are not communicated clearly. AND Platform/media used were not approved. AND Work is not shown.	Ideas are sometimes communicated clearly. OR Platform/media used were not approved. OR Work is not shown.	Ideas were communicated clearly using proper notation and terminology. AND Approved platform/media used. AND Work is shown.
Comments:
Total

16.9-10.MAT.KU.002 Student demonstrates understanding of the concepts from the algebra branch of mathematics

16.9-10.MAT.KU.003 Student demonstrates understanding of the concepts from the geometry and trigonometry branches of mathematics

16.9-10.MAT.MI.002 Student selects and applies general rules and mathematical problem-solving techniques to solve problems in familiar situations.

16.9-10.MAT.MI.003 Student uses appropriate mathematical concepts and skills to solve problems in unfamiliar situations.

16.9-10.MAT.MI.004 Student discovers patterns as relationships or general rules.

16.9-10.MAT.SE.001 Student draws conclusions consistent with findings.

16.9-10.MAT.SE.005 Student suggests improvements and revisions to methods when necessary.

16.9-10.MAT.CO.001 Student justifies or proves mathematical relationships and general rules.

16.9-10.MAT.CO.002 Student uses appropriate mathematical language and notation in both oral and written explanations.