Geometry and Statistics: A Lecture Companion Manual

Unit 1 Geometry Unit
A. Introduction and Standards 
    a. Undefined terms – point, line, plane 
    b. Defined terms – line segment, perpendicular, parallel, ray, angle, vertex, sides 
B. Angles 
    a. Definitions – right, acute, obtuse, straight, reflex, complementary, supplementary, adjacent, vertical, congruent figures, alternate interior, alternate exterior, corresponding 
    b. Paper Folding Activity – Exploring Angle Measures 
    c. Protractors and Compasses Activity 
C. Two-Dimensional Figures – curves, closed, simple, simple closed, convex, nonconvex 
    a. Polygons 
        i. Triangles 
          1. Triangles by angle measures – acute, obtuse, right 
          2. Triangles by side lengths – scalene, isosceles, equilateral    3. Paper Folding Activity 
          4. Pythagorean Theorem 
          5. Triangle Venn Diagram Activity 
        ii. Quadrilaterals 
          1. Quadrilateral Attribute Chart 
          2. Quadrilateral Venn Diagram 
          3. Quadrilateral Geoboard Activity 
       iii. Pattern Block Activity 
b. Ovals and Circles – oval, circle, radius, chord, diameter, tangent, circumference 
c. Circle Activity 
d. Symmetry 
      i. Reflective Symmetry Activity 
      ii. Rotational Symmetry Activity 
      iii. Transformations – translations, reflections, rotations, dilations 
D. Three-Dimensional Solids 
    a. Polyhedrons 
        i. Prisms 
        ii. Pyramids 
    b. Non-polyhedrons 
        i. Cylinder 
        ii. Cones 
        iii. Spheres 
E. Homework Problems 
F. Answer Key

Unit 2 Measurement Unit 
A. Introduction and Standards 
B. Length 
    a. Perimeter/Circumference 
    b. Circle Activity (Revisited) 
C. Area 
    a. Quadrilaterals – rectangle, square, parallelogram 
    b. Triangles – right, isosceles, equilateral, scalene 
    c. Trapezoids 
    d. Circles 
D. Volume 
    a. Polyhedrons 
        i. Prisms – rectangular, square, right triangular, trapezoidal 
        ii. Pyramids, rectangular, square, right triangular, trapezoidal 
    b. Non-polyhedron 
       i. Cylinder 
       ii. Cone 
       iii. Sphere 
E. Total Surface Area 
    a. Rectangular prism 
    b. Right Triangular prism 
    c. Cylinder 
F. Unit conversions 
    a. Square units 
    b. Cube units 
G. Homework Problem
H. Answer Key

Unit 3 Probability Unit
A. Introduction and Standards 
B. Introducing Probability with Simple Games 
    a. Definitions – experiment, outcomes, sample space, probability 
    b. Experimental Probability vs. Theoretical Probability 
        i. Theoretical Probability Examples 
        ii. Probability Properties iii. Experimental Probability Examples 
       1. Flipping a coin example – experimental probability 
       2. Cup experiment – experimental probability 
       3. Racetrack game – experimental probability vs. theoretical probability 
C. Compound events 
      a. Union and Intersection - Venn Diagrams 
      b. Multistage experiments - Tree Diagrams 
          i. Independent 
          ii. Dependent events
D. Counting Techniques 
    a. Counting Principle 
    b. Combinations and Permutations 
    c. Permutation or Combination Activity 
E. Homework Problems 
F. Answer Key

Unit 4 Statistics Unit
A. Introduction and Standards 
B. Types of Data 
    a. Qualitative vs. Quantitative 
    b. Categorical data vs. Numerical (discrete, continuous) 
C. Types of Statistics 
    a. Descriptive statistics vs. Inferential statistics 
    b. Types of Descriptive Statistics 
        i. Position 
           a. Quartile rank 
           b. Percentile rank 
        ii. Central Tendency 
            a. Mean 
            b. Median 
            c. Mode 
        iii. Frequency 
            a. Tallies 
            b. Counts 
            c. Percents/Relative Frequencies 
         iv. Variation/Dispersion 
              a. Range 
              b. Interquartile Range 
              c. Standard deviation v. In-Class Activity 
D. Visualizing data 
     a. Box-and-Whisker plots 
     b. Bar graphs 
     c. Pictographs 
     d. Line graphs 
     e. Line plots 
     f. Stem-and-leaf plots 
     g. Pie graphs 
     h. Histograms 
     i. Scatter Plots 
E. Distributions – skewed left, symmetric, skewed right 
    a. Normal Distributions 
    b. Empirical Rule for Normal Distributions 
    c. In-class Activity 
F. Homework Problems 
G. Answer Key