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Honors Geometry

Honors Geometry. Spring 2012 Ms. Katz. Day 1: January 30 th. Objective: Form and meet study teams. Then work together to build symmetrical designs using the same basic shapes. Seats and Fill out Index Card (questions on next slide)

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Honors Geometry

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  1. Honors Geometry Spring 2012 Ms. Katz

  2. Day 1: January 30th Objective: Form and meet study teams. Then work together to build symmetrical designs using the same basic shapes. • Seats and Fill out Index Card (questions on next slide) • Introduction: Ms. Katz, Books, Syllabus, Homework Record, Expectations • Problems 1-1 and 1-2 • Möbius Strip Demonstration • Conclusion Homework: Have parent/guardian fill out last page of syllabus and sign; Problems 1-3 to 1-7 AND 1-15 to 1-18; Extra credit tissues or hand sanitizer (1)

  3. Respond on Index Card: • When did you take Algebra 1? • Who was your Algebra 1 teacher? • What grade do you think you earned in Algebra 1? • What is one concept/topic from Algebra 1 that Ms. Katz could help you learn better? • What grade would you like to earn in Geometry? (Be realistic) • What sports/clubs are you involved in this Spring? • My e-mail address (for teacher purposes only) is:

  4. Support • www.cpm.org • Resources (including worksheets from class) • Extra support/practice • Parent Guide • Homework Help • www.hotmath.com • All the problems from the book • Homework help and answers • My Webpage on the HHS website • Classwork and Homework Assignments • Worksheets • Extra Resources

  5. Quilts

  6. 1-1: First Resource Page

  7. 1-1: Second Resource Page Write sentence and names around the gap. Cut along dotted line Glue sticks are rewarded when 4 unique symmetrical designs are shown to the teacher.

  8. Day 2: January 31st Objective: Use your spatial visualization skills to investigate reflection. THEN Understand the three rigid transformations (translations, reflections, and rotations) and learn some connections between them. Also, introduce notation for corresponding parts. • Homework Check and Correct (in red) – Collect last page of syllabus • LL – “Graphing an Equation” • Problems 1-47 to 1-53 • Problems 1-59 to 1-62 • LL – “Rigid Transformations” • Conclusion Homework: Problems 1-54 to 1-58 AND 1-63 to 1-67; GET SUPPLIES; Extra credit tissues or hand sanitizer (1)

  9. A Complete Graph y = -2x+5 Create a table of x-values Use the equation to find y-values Complete the graph by scaling and labeling the axes Graph and connect the points from your table. Then label the line. y 10 y = -2x+5 5 x -10 -5 5 10 -5 -10

  10. Day 3: February 1st Objective: Begin to develop an understanding of reflection symmetry. Also, learn how to translate a geometric figure on a coordinate grid. Learn that reflection and reflection symmetry can help unlock relationships within a shape (isosceles triangle). THEN Learn about reflection, rotation, and translation symmetry. Identify which common shapes have each type of symmetry. • Homework Check and Correct (in red) • LL – “Rigid Transformations” • Problems 1-68 to 1-72 • Problems 1-87 to 1-91 • LL – “Slope-Intercept Form” and “Parallel and Perpendicular Lines” • Conclusion Homework: Problems 1-73 to 1-77 AND 1-82 to 1-86; GET SUPPLIES; Extra credit tissues or hand sanitizer

  11. Transformation (pg 34) Transformation: A movement that preserves size and shape Reflection: Mirror image over a line Rotation: Turning about a point clockwise or counter clockwise Translation: Slide in a direction

  12. Everyday Life Situations Here are some situations that occur in everyday life. Each one involves one or more of the basic transformations: reflection, rotation, or translation. State the transformation(s) involved in each case. You look in a mirror as you comb your hair. While repairing your bicycle, you turn it upside down and spin the front tire to make sure it isn’t rubbing against the frame. You move a small statue from one end of a shelf to the other. You flip your scrumptious buckwheat pancakes as you cook them on the griddle. The bus tire spins as the bus moves down the road. You examine footprints made in the sand as you walked on the beach.

  13. Day 4: February 2nd Objective: Learn how to classify shapes by their attributes using Venn diagrams. Also, review geometric vocabulary and concepts, such as number of sides, number of angles, sides of same length, right angle, equilateral, perimeter, edge, and parallel. THEN Continue to study the attributes of shapes as vocabulary is formalized. Become familiar with how to mark diagrams to help communicate attributes of shapes. • Homework Check and Correct (in red) • Finish Problems 1-89 to 1-91 • LL – Several entries • Problems 1-97 to 1-98 • Problems 1-104 to 1-108 • Conclusion Homework: Problems 1-92 to 1-96 AND 1-99 to 1-103; Get Supplies! Chapter 1 Team Test Monday

  14. Symmetry Symmetry: Refers to the ability to perform a transformation without changing the orientation or position of an object Reflection Symmetry: If a shape has reflection symmetry, then it remains unchanged when it is reflected across a line of symmetry. (i.e. “M” or “Y” with a vertical line of reflection) Rotation Symmetry: If a shape has rotation symmetry, then it can be rotated a certain number of degrees (less than 360°) about a point and remain unchanged. Translation Symmetry: If a shape has translation symmetry, then it can be translated and remain unchanged. (i.e. a line)

  15. 1-72 B A A’

  16. Isosceles Triangle Sides: AT LEAST two sides of equal length Base Angles: Have the same measure Height: Perpendicular to the base AND splits the base in half

  17. Reflection across a Side The two shapes MUST meet at a side that has the same length.

  18. Polygons (pg 42) Polygon: A closed figure made up of straight segments. Regular Polygon: The sides are all the same length and its angles have equal measure.

  19. Line: Slope-Intercept Form (pg 47) y-intercept Slope y = mx + b Slope: Growth or rate of change. y-intercept: Starting point on the y-axis. (0,b)

  20. Slope-Intercept Form You can go backwards if necessary! Next, use rise over run to plot new points First plot the y-intercept on the y-axis Now connect the points with a line!

  21. Parallel Lines (pg 47) Parallel lines do not intersect. Parallel lines have the same slope. For example: and

  22. Perpendicular Lines (pg 47) Perpendicular lines intersect at a right angle. Slopes of perpendicular lines are opposite reciprocals (opposite signs and flipped). For example: and

  23. Venn Diagram #1: Has two or more siblings #2: Speaks at least two languages

  24. Venn Diagrams (pg 42) Condition #1 Condition #2 Satisfies condition 2 only A B C Satisfies condition 1 only Satisfies neither condition Satisfies both conditions D

  25. Problem 1-98(a) #1: Has at least one pair of parallel sides #2: Has at least two sides of equal length

  26. Problem 1-98(a)

  27. Problem 1-98(b)

  28. Problem 1-98(c)

  29. Describing a Shape

  30. Shape Toolkit

  31. Shape Toolkit

  32. Day 5: February 3rd Objective: Continue to study the attributes of shapes as vocabulary is formalized. Become familiar with how to mark diagrams to help communicate attributes of shapes. THEN Develop an intuitive understanding of probability, and apply simple probability using the shapes in the Shape Bucket. • Homework Check and Correct (in red) • Wrap-Up Problems 1-107 to 1-108 • Problems 1-115 to 1-119 • Closure Problems CL1-126 to 1-134 [Choose problems you need to work on as individuals] • Conclusion Homework: Problems 1-110 to 1-114 AND 1-121 to 1-125; Supplies! Chapter 1 Team Test Monday

  33. Probability (pg 60) Probability: a measure of the likelihood that an event will occur at random. Example: What is the probability of selecting a heart from a deck of cards?

  34. Shape Bucket

  35. Day 6: February 6th Objective: Assess Chapter 1 in a team setting. THEN Learn how to name angles, and learn the three main relationships for angle measures, namely supplementary, complementary, and congruent. Also, discover a property of vertical angles. • Homework Check and Correct (in red) • Chapter 1 Team Test (≤ 45 minutes) • Start Problems 2-1 to 2-7 • Conclusion Homework: Problems 2-8 to 2-12 Chapter 1 Individual Test Friday

  36. 2-2 A C’ C B B’

  37. Day 7: February 7th Objective: Learn how to name angles, and learn the three main relationships for angle measures, namely supplementary, complementary, and congruent. Also, discover a property of vertical angles. THEN Use our understanding of translation to determine that when a transversal intersects parallel lines, a relationship exists between corresponding angles. Also, continue to practice using angle relationships to solve for unknown angles. • Homework Check and Correct (in red) • Finish Problems 2-1 to 2-7 • Problems 2-13 to 2-17 • Start Problems 2-23 to 2-28 • Conclusion Homework: Problems 2-18 to 2-22 AND 2-29 to 2-33 Chapter 1 Individual Test – Is Thursday okay instead?

  38. Notation for Angles Name or If there is only one angle at the vertex, you can also name the angle using the vertex: Incorrect: F E D Measure Correct: Incorrect: Y ? ? W X Z

  39. Angle Relationships (pg 76) 30° x° 60° y° x° + y° = 90° 70° 110° x° y° x° + y° = 180° x° 85° y° x° = y° 85° Complementary Angles: Two angles that have measures that add up to 90°. Supplementary Angles: Two angles that have measures that add up to 180°. Example: Straight angle Congruent Angles: Two angles that have measures that are equal. Example: Vertical angles

  40. Marcos’ Tile Pattern How can you create a tile pattern with a single parallelogram?

  41. Marcos’ Tile Pattern Are opposite angles of a parallelogram congruent? Pick one parallelogram on your paper. Use color to show which angles have equal measure. If two measures are not equal, make sure they are different colors.

  42. Marcos’ Tile Pattern What does this mean in terms of the angles in our pattern? Color all angles that must be equal the same color.

  43. Marcos’ Tile Pattern Are any lines parallel in the pattern? Mark all lines on your diagram with the same number of arrows to show which lines are parallel.

  44. Marcos’ Tile Pattern J a b M L c d w x N P y z K Use the following diagram to help answer question 2-15.

  45. Why Parallel Lines? 53° x

  46. 2-16 X X

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