FM20.1: Demonstrate understanding of the mathematics involved in an historical event or an area of interest.

FM20.1.b: Collect primary or secondary data (quantitative or qualitative) related to the topic.

Describing Data Using Statistics

FM20.1.c: Assess the accuracy, reliability, and relevance of the primary or secondary data (quantitative/qualitative) collected by:

FM20.1.c.2: identifying and describing the data collection methods

Describing Data Using Statistics

FM20.1.c.4: determining whether or not the data are consistent with information obtained from other sources on the same topic.

Polling: City
Polling: Neighborhood
Populations and Samples

FM20.1.d: Interpret data, using statistical methods if applicable.

Box-and-Whisker Plots

FM20.1.f: Organize and create a presentation (oral, written, multimedia, etc.) of the research findings and conclusions.

Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Stem-and-Leaf Plots

FM20.2: Demonstrate understanding of inductive and deductive reasoning including: analyzing conjectures, analyzing spatial puzzles and games, providing conjectures, solving problems.

FM20.2.g: Analyze an argument for its validity.

Biconditional Statements

FM20.2.h: Identify errors in proofs that lead to incorrect conclusions (e.g., a proof that ends with 2 = 1).

Biconditional Statements
Conditional Statements

FM20.3: Expand and demonstrate understanding of proportional reasoning related to: rates, scale diagrams, scale factor, area, surface area, volume.

FM20.3.a: Identify and describe situations relevant to one?s self, family, or community that involve proportional reasoning.

Beam to Moon (Ratios and Proportions) - Metric
Estimating Population Size
Part-to-part and Part-to-whole Ratios

FM20.3.e: Solve situational questions that require the use of proportional reasoning, including those that involve the isolation of a variable.

Beam to Moon (Ratios and Proportions) - Metric
Estimating Population Size
Part-to-part and Part-to-whole Ratios

FM20.3.g: Explain, using examples, the relationship between the slope of a graph and a rate.

Cat and Mouse (Modeling with Linear Systems) - Metric
Slope

FM20.3.h: Identify and explain the effect of factors within given situations that could influence a particular rate.

Translating and Scaling Functions
Zap It! Game

FM20.3.j: Identify and describe situations relevant to one?s self, family, or community that involve scale diagrams of 2-D shapes and 3-D objects and determine the scale factor for the situations.

Similar Figures

FM20.3.k: Develop, generalize, explain, and apply strategies for solving situational questions based upon scale diagrams of 2-D shapes and 3-D objects, including the determining of scale factors and unknown dimensions.

Similar Figures

FM20.3.l: Draw, with or without the use of technology, a scale diagram of a 2-D shape relevant to self, family, or community to a specified scale factor (enlargement or reduction).

Similar Figures

FM20.3.m: Solve situational problems involving scale diagrams of 2-D shapes and 3-D objects.

Dilations

FM20.3.n: Determine relationships between scale factor and area of 2-D shapes or surface area of 3-D objects; and scale factor, surface area, and volume of 3-D objects.

Dilations

FM20.3.o: Develop, generalize, explain, and apply strategies for determining scale factors, areas, surface areas, or volumes given the scale factor or the ratio of areas, surface areas, or volumes of 2-D shapes and 3-D objects.

Dilations

FM20.3.p: Explain, with justification, the effect of a change in scale factor on the area of a 2-D shape or the surface area or volume of a 3-D object.

Dilations

FM20.3.q: Solve situational questions that involve scale factors, areas, surface areas, and volumes, including ones that require the manipulation of formulas.

Dilations

FM20.4: Demonstrate understanding of properties of angles and triangles including: deriving proofs based on theorems and postulates about congruent triangles, solving problems.

FM20.4.a: Identify and describe situations relevant to self, family, or community that involve parallel lines cut by transversals.

Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Parallel, Intersecting, and Skew Lines

FM20.4.b: Develop, generalize, explain, apply, and prove relationships between pairs of angles formed by transversals and parallel lines, with and without the use of technology.

Constructing Congruent Segments and Angles
Triangle Angle Sum

FM20.4.c: Prove and apply the relationship relating the sum of the angles in a triangle.

Polygon Angle Sum
Triangle Angle Sum

FM20.4.f: Explore and verify whether or not the angles formed by nonparallel lines and transversals create the same angle relationships as those created by parallel lines and transversals.

Constructing Congruent Segments and Angles
Triangle Angle Sum

FM20.4.h: Develop, generalize, explain, and apply strategies for constructing parallel lines.

Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Parallel, Intersecting, and Skew Lines

FM20.5: Demonstrate understanding of the cosine law and sine law (including the ambiguous case).

FM20.5.b: Develop, generalize, explain, and apply strategies for determining angles or side lengths of triangles without a right angle.

Sine, Cosine, and Tangent Ratios

M20.6: Demonstrate an understanding of normal distribution, including standard deviation and z-scores.

M20.6.a: Identify situations relevant to self, family, or community in which standard deviation and the normal distribution are used and explain the meaning and relevance of each.

Polling: City
Real-Time Histogram

M20.6.b: Explain the meaning and purpose of the properties of a normal curve, including mean, median, mode, standard deviation, symmetry, and area under the curve.

Polling: City
Populations and Samples
Real-Time Histogram
Sight vs. Sound Reactions

M20.6.c: Calculate, using technology, the population standard deviation of a data set.

Polling: City

M20.6.d: Critique the statement ?Every set of data will correspond to a normal distribution?.

Polling: City

M20.6.e: Analyze a data set to determine if it approximates a normal distribution.

Polling: City
Populations and Samples
Real-Time Histogram
Sight vs. Sound Reactions

M20.6.f: Compare the properties of two or more normally distributed data sets and explain what the comparison tells you about the situations that the sets represent.

Polling: City
Populations and Samples

M20.6.g: Explain, using examples that represent multiple perspectives, the application of standard deviation for making decisions in situations such as warranties, insurance, or opinion polls.

Polling: City
Real-Time Histogram

FM20.7: Demonstrate understanding of the interpretation of statistical data, including: confidence intervals, confidence levels, margin of error.

FM20.7.a: Identify and explain the significance of the confidence interval, margin of error, or confidence level stated with respect to statistical data relevant to self, family, or community.

Polling: City

FM20.7.b: Explain how confidence levels, margins of error, and confidence intervals can be impacted by the size of the random sample used.

Polling: City
Polling: Neighborhood

FM20.7.c: Make inferences and decisions with justification about a population from sample data using confidence intervals.

Polling: City

FM20.7.d: Provide and critique examples from print or electronic media in which confidence intervals and confidence levels are used to support a particular position.

Polling: City

FM20.7.e: Support a position or decision relevant to self, family, or community by analyzing statistical data, as well as considering other factors.

Polling: City
Real-Time Histogram

FM20.8: Demonstrate understanding of systems of linear inequalities in two variables.

FM20.8.a: Identify situations relevant to self, family, or community which could be described using a system of linear inequalities in two variables.

Linear Programming
Systems of Linear Inequalities (Slope-intercept form)

FM20.8.b: Develop, generalize, explain, and apply strategies for graphing and solving systems of linear inequalities, including justification of the choice of solid or broken lines.

Linear Programming
Systems of Linear Inequalities (Slope-intercept form)

FM20.8.e: Write a system of linear inequalities for a given graph.

Linear Programming
Systems of Linear Inequalities (Slope-intercept form)

FM20.8.f: Match optimization questions and the graphs of sets of linear inequalities.

Linear Programming

FM20.8.g: Apply knowledge of graphing of systems of linear inequalities and linear programming to solve optimization questions.

Linear Programming

FM20.9: Demonstrate an understanding of the characteristics of quadratic functions of the form y = a(x - p)² + q , including: vertex, intercepts, domain and range, axis of symmetry.

FM20.9.a: Identify situations and objects relevant to self, family, or community which could be described using a quadratic function.

Addition and Subtraction of Functions
Quadratics in Polynomial Form

FM20.9.b: Develop, generalize, explain, and apply strategies for determining the intercepts of the graph of a quadratic function, including factoring, graphing (with or without the use of technology), and use of the quadratic formula.

Exponential Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic
Zap It! Game

FM20.9.c: Conjecture and verify a relationship among the roots of an equation, the zeros of the corresponding function, and the x-intercepts of the graph of the function.

Polynomials and Linear Factors
Roots of a Quadratic

FM20.9.d: Explain, using examples, why the graph of a quadratic function may have zero, one, or two x-intercepts.

Exponential Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic
Zap It! Game

FM20.9.f: Develop, generalize, explain, and apply strategies (with or without the use of technology) to determine the coordinates of the vertex of the graph of a quadratic function.

Quadratics in Polynomial Form
Quadratics in Vertex Form

FM20.9.g: Develop, generalize, explain, and apply a strategy for determining the equation of the axis of symmetry of the graph of a quadratic function when given the x-intercepts of the graph.

Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic

FM20.9.h: Develop, generalize, explain, and apply strategies for determining the coordinates of the vertex of the graph of a quadratic function and for determining if the vertex is a maximum or a minimum.

Quadratics in Factored Form
Quadratics in Vertex Form
Zap It! Game

FM20.9.i: Generalize about and explain the effects on the graph of a quadratic function when the values for a, p, and q are changed.

Exponential Functions
Translating and Scaling Functions
Zap It! Game

FM20.9.l: Develop, generalize, explain, and apply strategies for sketching the graph of a quadratic function.

Addition and Subtraction of Functions
Exponential Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic
Translating and Scaling Functions
Zap It! Game

FM20.9.m: Solve situational questions involving the characteristics and graphs of quadratic functions.

Addition and Subtraction of Functions
General Form of a Rational Function

FM20.9.n: Critique the statement ?Any function that can be written in the form y = a(x ? p)² + q will have a parabolic graph.?

Addition and Subtraction of Functions
Parabolas
Translating and Scaling Functions
Zap It! Game