#### 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.

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

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

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

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

#### 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.

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

#### 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.

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

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

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

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.

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.

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).

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

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.

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.

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.

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

#### 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.

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.

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

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.

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

#### 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.

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.

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

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

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

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.

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.

#### 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.

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

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

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.

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

#### 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.

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.

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

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

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

#### 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.

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.

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.

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

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.

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.

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.

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.

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

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

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.?

Correlation last revised: 9/16/2020

This correlation lists the recommended Gizmos for this province's curriculum standards. Click any Gizmo title below for more information.