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Level 2 Geometry

Level 2 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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Level 2 Geometry

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  1. Level 2 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 1-17 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 • “Try This!” Algebra Review (x2) • LL – “Graphing an Equation” • Problems 1-48 to 1-51, 1-53 • Problems 1-59 to 1-61 • 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. Try This! Algebra Review Complete the table below for y = -2x+5 Write a rule relating x and y for the table below. y = 3x+4

  10. 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

  11. Try This! Algebra Review Solve the following Equation for x and check your answer: 6x + 3 – 10 = x + 47 + 2x

  12. Solving Linear Equations (pg 19) Simplify each side: Combine like terms Keep the equation balanced: Anything added or taken away from one side, must also be added or taken away from the other Move the x-terms to one side of the equations: Isolate the letters on one side Undo operations: Remember that addition and subtraction are opposites AND division and multiplication are opposites

  13. Day 3: February 1st Objective: Understand the three rigid transformations (translations, reflections, and rotations) and learn some connections between them. Also, introduce notation for corresponding parts. THEN 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). • Homework Check and Correct (in red) • Try This! • Problems 1-59 to 1-61 • LL – “Rigid Transformations” • Problems 1-68 to 1-72 • Start Problems 1-87 to 1-89 (Notes if time) Homework: Problems 1-73 to 1-77 AND 1-82, 85, 86; GET SUPPLIES; Extra credit tissues or hand sanitizer

  14. Try This! February 1st The distance along a straight road is measured as shown in the diagram below. If the distance between towns A and C is 67 miles, find the following: The value of x. The distance between A and B. 5x – 2 2x + 6 A B C

  15. 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

  16. 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.

  17. Day 4: February 2nd 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) • Finish Problems 1-70 to 1-72 • LL – Notes • Problems 1-87 to 1-89 • LL – Notes • Start Problem 1-97 if time Homework: Problems 1-92 to 1-96 AND 1-100; GET SUPPLIES; Extra credit tissues or hand sanitizer

  18. 1-71 Reflections • Lines that connect corresponding points are ___________ to the line of reflection. • The line of reflection ______ each of the segments connecting a point and its image. perpendicular bisects

  19. 1-72 B A A’

  20. 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

  21. 1-72 Isosceles Triangles • Two sides are _____ . • The ____ angles are equal. • The line of reflection ______ the base. equal base bisects

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

  23. 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.

  24. 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)

  25. Slope-Intercept Form You can go backwards if you need! 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!

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

  27. 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

  28. Day 5: February 3rd 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) • Wrap-Up Problem 1-89 • LL – Notes • Problem 1-98 • Problems 1-104 to 1-107 Homework: Problems 1-101 to 1-103 AND 1-110 to 1-114; SUPPLIES; Chapter 1 Team Test Monday

  29. 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)

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

  31. 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

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

  33. Problem 1-98(a)

  34. Problem 1-98(b)

  35. Problem 1-98(c)

  36. Describing a Shape

  37. Shape Toolkit

  38. Shape Toolkit

  39. Day 6: February 6th Objective: Assess Chapter 1 in a team setting. THEN Develop an intuitive understanding of probability, and apply simple probability using the shapes in the Shape Bucket. • Homework Check and Correct (in red) • Try This! Algebra Review • Chapter 1 Team Test • Problems 1-115, 116, 119 Homework: Problems 1-121 to 1-125 AND CL1-126 to 1-129; Chapter 1 Individual Test Friday

  40. Try This! February 6th 1. 2. Solve the following equations for x:

  41. 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?

  42. Day 7: February 7th Objective: Develop an intuitive understanding of probability, and apply simple probability using the shapes in the Shape Bucket. 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) • Try This! Algebra Review • Problems 1-116, 119 • Problems 2-1 to 2-7 Homework: Problems CL1-130 to 1-134 AND 2-8 to 2-11; Chapter 1 Individual Test Friday

  43. Shape Bucket

  44. 2-2 A C’ C B B’

  45. 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

  46. Angle Relationships (pg 76) 30° x° 60° y° x° + y° = 90° 70° 110° x° y° x° + y° = 180° x° 85° y° x° = y° 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 85°

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