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GPS Geometry

GPS Geometry. a crash course . UNIT 1: Geometry Gallery. Previously Math 1- Units 3 and 6 The biggest unit Vocab heavy. Unit 1: Geometry Gallery STANDARDS. TOPIC 1- Logical Equivalence (M1- 4.3) Use conjecture, inductive reasoning, deductive reasoning, counter examples and indirect proof

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GPS Geometry

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  1. GPS Geometry a crash course 

  2. UNIT 1: Geometry Gallery • Previously Math 1- Units 3 and 6 • The biggest unit • Vocab heavy

  3. Unit 1: Geometry GallerySTANDARDS TOPIC 1- Logical Equivalence (M1- 4.3) • Use conjecture, inductive reasoning, deductive reasoning, counter examples and indirect proof • Understand and use the relationships among a statement and its converse, inverse and contrapositive

  4. Unit 1: Geometry GallerySTANDARDS TOPIC 2- Angles (M1 – 5.7,5.5, 5.6) out of order • Determine the sum of interior and exterior angles in a polygon • Understand and use the triangle inequality, the side-angle inequality, and the exterior- angle inequality

  5. Unit 1: Geometry GallerySTANDARDS TOPIC 3- Proofs (triangles and quadrilaterals) (M1-4.5,4.6,4.8-4.10) split up by congruence, bad order (M1-5.8-5.12) • Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL) • Understand, use and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid and kite

  6. Unit 1: Geometry GallerySTANDARDS TOPIC 4- Points of Concurrency (M1- 5.2-5.4 bad order) • Find and Use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.

  7. POST TEST Differentiation Strategies • VOCAB VOCABVOCAB • 4 card notecards • Word walls • Taboo • Vocab Books • Walk around flash-cards • Proof Notecards • Highlighters • MAPA CICO • Color Code Conditional Statements

  8. Differentiation Strategies • Algebra Skills • Set- up THEN solving • Interior/exterior formulas

  9. UNIT 2: Coordinate Geometry • Previously Math 1- Unit 6 • Algebra heavy

  10. Unit 2: Coordinate GeometrySTANDARDS TOPIC 1- Distance, Midpoint and the Pythagorean Theorem (M1- 4.1) • Determine the distance between two points • Determine the midpoint of a segment • Determine the distance between a point and a line

  11. Unit 2: Coordinate GeometrySTANDARDS TOPIC 2- Geometry Application M1- {5.2-5.4} triangle segments {5.9, 5.11,5.12} quadrilaterals • Understand the distance formula as an application of the Pythagorean theorem • Use the coordinate plane to investigate properties and verify conjectures related to triangles and quadrilaterals.

  12. y y y y x x x x

  13. POST TEST Differentiation Strategies • Formulas (use xxyy not x1x2 y1y2) • GRAPH PAPER! • Slope • Rulers • Checklist for quadrilaterals

  14. UNIT 3: Statistics • Previously Math 2- Unit 4 • Obviously- nothing to do with geometry but here it is anyway! • A lot of repeated concepts from GPS Algebra’s unit on statistics

  15. Unit 3: StatisticsSTANDARDS TOPIC 1- Measures of Spread • Understand and calculate the means and standard deviations of sets of data • Use means and standards deviations to compare data sets • Compare the means and standard deviations of random samples with the corresponding population parameters, including those population parameters for normal distributions. Observe that the different sample means vary from one sample to the next. Observe tat the distribution of the sample means has less variability than the population distribution.

  16. Unit 3: StatisticsSTANDARDS TOPIC 2- Data Collection/ Representing Populations • Pose a questions and collect sample data from at least two different populations

  17. POST TEST Differentiation Strategies • Pop-Up distribution • Z-scores • Review of boxplots

  18. UNIT 4: Right Triangle Trigonometry • Previously Math 2- Unit 2

  19. Unit 4: Right Triangle Trigonometry STANDARDS TOPIC 1- Special Right Triangles (M2-5.1) Similar Triangles are NOT in the book! • Determine the lengths of sides of 30º-60º-90º triangles • Determine the lengths of sides of 45º-45º-90º triangles • Discover the relationship of the trigonometric ratios for similar triangles

  20. Unit 4: Right Triangle Trigonometry STANDARDS TOPIC 2- Trigonometric ratios (M2-5.2-5.4) • Solve application problems using the trigonometric ratios • Explain the relationship between trigonometric ratios of complementary angles

  21. UNIT 5: Circle and Spheres • Previously Math 2- Unit 3 • Vocab heavy • 2nd largest unit

  22. POST TEST Differentiation Strategies • Foldables • “I have” “I need” • “Does it make sense” • Drawing a picture- where is your shadow • HIGHLIGHTERS! • Word Problems • Rationalizing the denominator

  23. Unit 5: Circles and SpheresSTANDARDS TOPIC 1- Circles (M2- 6.1-6.8) • Understand and use properties of chords, tangents and secants as an application of triangle similarity • Understand and use properties of central, inscribed and related angles • Use the properties of circle to solve problems involving the length of an arc and the area of a sector • Justify measurements and relationships in circle using geometric and algebraic properties

  24. Unit 5: Circles and SpheresSTANDARDS TOPIC 2- Spheres (M2- 6.9) • Use and apply surface area and volume of a sphere • Determine the effect on surface area and volume of changing the radius or diameter of a sphere

  25. POST TEST Differentiation Strategies • VOCAB VOCABVOCAB • Foldables • Vocab book (WITH PROBLEMS) • Where is the semi-circle • Angles are always smaller than arcs • “Does it make sense” • Sectors/Arc Length- Ratio • Spheres foldable- finding radius

  26. UNIT 6: Exponential and Inverses • Previously Math 2- Unit 5 • Again, not Geometry related (oh well…)

  27. Unit 6: Exponential and InversesSTANDARDS TOPIC 1- Inverses • Discuss the characteristics of functions and their inverses, including one-to-ones, domain and range • Determine the inverses of linear, quadratic and power functions and functions of the form f(x)=a/x, including the use of restricted domains • Explore the graphs of functions and their inverses • Use composition to verify that functions are inverses of each other

  28. Unit 6: Exponential and InversesSTANDARDS TOPIC 2- Exponential functions • Extended properties of exponents to include all integer exponents • Investigate and explain characteristics of exponential functions, including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rates of change and end behavior • Graph functions as transformations of f(x)=a(x) • Solve simple exponential equations and inequalities analytically, graphically and by using appropriate technology • Understand and use basic exponential functions as models of real phenomena

  29. Unit 6: Exponential and InversesSTANDARDS TOPIC 3- Geometric Sequences • Understand and recognize geometric sequences as exponential functions with domains that are whole numbers • Interpret the constant ratio in a geometric sequence as the base of the associated exponential function

  30. POST TEST Differentiation Strategies • All the ways to write domain  • Exponent chart rules • Highlight parts of the exponential • Algebra skills

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