Math 3 Quarter 4 Overview


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1 Math 3 Quarter 4 Overview EO5 Rational Functions 13% EO6 Circles & Circular Functions 25% EO7 Inverse Functions 25% EO8 Normal Distribution 12% Q4 Final 10% EO5 Opp #1 Fri, Mar 24th Thu, Mar 23rd ML EO5 Level 3 Mastery Reform Due Tue, Apr 11th EO6 Opp #1 Tue, Apr 25 ML EO6 Level 3 Mastery Reform Due Tue, May 9th EO7 Opp #1 Wed, May 10th ML EO7 Level 3 Mastery Reform Due Wed, May 17th EO8 Opp #1 Thu, May18th Level 2 Opp #2 Q4 Final Tue Wed, May EO5 Opp #2 Thu, Apr B211 EO6 Opp #2 Thu, May 11th EO7 Opp #2 Fri May 19th in Class Inv 3 p374 #5 7, STM, CYU, EQ 533 Practice Worksheet Inv 4 p376 #1, 4 7, STM, CYU, EQ 534 Practice Worksheet Level 2: #8 p382, #9 p382, #10 p382, #11, p383, #23 p385, #25 p386 Level 3: #26 p386, #29 p387 Due Wednesday Level 4: #20 p385, #27 p387, #28 p387, #30 p388 Choose 4 EO5 MC Quiz Wed, Mar 22nd EO5 Review, p1 2 Thu, Mar 23rd ML EO5 Opp #1 Fri, Mar 24th EO5 Review, p3 4 EO6 INTRO Worksheet Sign Analysis UPDATE with examples of rational expressions Arc Length & Sector Area Operations with RATIONAL FUNCTIONS.....is just like operations with fractions 1
2 Tangents to a Circle 612 Chords, Arcs, & Central Angles 613 Angles Inscribed in a Circle OYO p408 OYO #21, 22. Choose 2: #1, Write 1 PROOF: 12, 13, 19. #4a, 4b, 4c, 14a, Choose 1: #2, 24 14b, 26 Circle Vocabulary Circle Theorems about Tangents Circle Theorems about Cords, Arcs, & Central Angles Choose 2: #3, 5, 6, 7, 15, 20, 25 Circle Theorems about Inscribed Angles Add the CYU on p400 as your example! Finish by Thursday EO6 Quiz #1 Mon, Apr 10th EO6 Quiz #2 Fri, Apr 21st EO6 Opp #1 Tue, Apr 25th ML EO6 Quiz #1 Mon, Apr 10th 10th (PSAT) & 11th (SAT) 9th (PARCC) No school for 9th & 12th No school for 10th, 11th & 12th EO6 Quiz #2 Fri, Apr 21st EO6 Opp #1 Tue, Apr 25th ML 2
3 Today we start Unit 6! p395 Activity #1 p396 read & p397 Think About This Situation Draw a picture & answer the questions for a, b, and d. a. b. d. O P The longest chord is... The longer the chord... The shorter the chord... 3
4 o P r P P l P o r The longest chord is... The longer the chord... The shorter the chord... Why does nobody talk to a circle? Because there is no point! 4
5 DEFINE TOOLKIT 61: Circle Vocabulary 1. Arc 2. Arc Length 3. Bisect 4. Central Angle 5. Chord 6. Circle 7. Circle: Area 8. Circle: Circumference 9. Circle: Longest Chord 10. Circumscribed 11. Diameter 12. Exterior Point 13. Inscribed 14. Inscribed Angle 15. Interior Point 16. Line 17. Line Segments 18. Major Arc 19. Minor Arc 20. Measure Notation m 21. Perpendicular Lines 22. Perpendicular Bisector 23. Radius 24. Secant 25. Sector 26. Sector Area 27. Tangent & Point of Tangency Sentence Description Diagram Notation Note: List these terms in your Toolkit with a couple of lines in between. Complete the definitions as you work through Unit 6 Lesson 1. #6 What is this? What do you know about it? #23 #8 O is the center O Circle The set of all points in a plane that are a given distance from a given point (center). Circles are named by their center. Radius A segment with one endpoint on the center of a circle and the other endpoint on the perimeter of the circle. Circumference The length of the perimeter of a circle, i.e., the distance around a circle. 5
6 #11 Diameter A chord that passes through the center of the circle. The longest chord of a circle. The diameter of a given circle is twice the length of its radius. #5 Chord A segment that joins two points on the circumference of a circle. *A diameter is a special kind of chord 6
7 #13 #10 Inscribed vs. Circumscribed The circle is inscribed inside the triangle. The circle is circumscribed outside the triangle. #24 Secant A line that contains a chord of a circle 7
8 #27.O Tangent A line in the plane of a circle that intersects the circle in exactly ONE point, the line is tangent to the circle. l. Y Point of Tangency The point of intersection is called the point of tangency. In the diagram, O is the center Y is the point of tangency on line l #1 Arc A portion of an entire circle. It can be measured by its length or by its degrees. 8
9 Central Angle An angle whose vertex is at the center of the circle. A x x A central angle is equal in degrees to the measure of its intercepted arc. A is the center of the circle Practice... What is the value of x??? 112 x x 160 Inscribed Angle An angle whose vertex is on the perimeter of the circle. An inscribed angle is equal to half its intercepted arc. x 2x Practice... What is the value of x??? x x 88 9
10 p397 Essential Questions What are important properties of tangents to a circle and how can they be verified? Mathematicians will be able to... Language Objective...write two theorems about tangents to a circle using the terms perpendicular, point of tangency, exterior point, and congruent. Activities #1, 2ab, 3, 5, STM, CYU, EQ Choose 3 + Review = 7 OYOs On Your Own p408 Level 2: #13 p412, #19 p415 Level 3: #1 p408, #2 p408 (proof), #24 p415 Level 4: #12 p411 Review: p417 #30, p418 #32, 33, 34 10
11 More about Tangents... Draw a radius from to the point of tangency. Does it look like anything special? p398. O l. Y If a radius is perpendicular to a line at a point where the line intersects the circle, then the line is tangent to the circle at that point. 11
12 Answer (1) (2) (3) (4) (5) (6) 12
13 What's the perimeter of this triangle? 4 inches 1 inch 4 inches 13
14 Remember this? Language Objective Mathematicians will be able to......write two properties of tangents to a circle using the terms perpendicular, point of tangency, exterior point, and congruent. Can you do it? TOOLKIT 611: Circle Theorems about Tangents 1. A line tangent to a circle is perpendicular to the radius at the point of tangency. 2. Tangent segments drawn to a circle from the same exterior point are congruent. Point of Tangency 14
15 Remember this? Essential Questions What are important properties of tangents to a circle and how can they be verified? Can you write a sophisticated response that shows a deep understanding of the mathematical concept? Activity #2 15
16 EO6 Toolkits TOOLKIT: Arc Length & Sector Area 1. Arc Length: A portion of the circumference. The Greek letter Theta is the angle of interest 2. Sector Area: A portion of the circle's area. 16
17 DEFINE TOOLKIT 61: Circle Vocabulary 1. Arc 2. Arc Length 3. Bisect 4. Central Angle 5. Chord 6. Circle 7. Circle: Area 8. Circle: Circumference 9. Circle: Longest Chord 10. Circumscribed 11. Diameter 12. Exterior Point 13. Inscribed 14. Inscribed Angle 15. Interior Point 16. Line 17. Line Segments 18. Major Arc 19. Minor Arc 20. Measure Notation m 21. Perpendicular Lines 22. Perpendicular Bisector 23. Radius 24. Secant 25. Sector 26. Sector Area 27. Tangent & Point of Tangency Sentence Description Diagram Notation Note: List these terms in your Toolkit with a couple of lines in between. Complete the definitions as you work through Unit 6 Lesson 1. TOOLKIT 611: Circle Theorems about Tangents 1. A line tangent to a circle is perpendicular to the radius at the point of tangency. p400 #2a,b Point of Tangency 2. Tangent segments drawn to a p400 #5c circle from the same exterior point are congruent. s Add the CYU on p400 as your example! 17
18 Attachments M3 211 Organizer.docx M3 311 Parallel Lines & Transversal Foldable.pdf SelectorTools.exe For each of the triangles below.docx M3 513 Organizer ANSWERS.pdf M3 531 Fractions ANSWERS.pdf M3 531 Fractions Worksheet.pdf
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