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Skills available for Saskatchewan grade 11 math curriculum

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

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

  • 11.FM20.2.a Make conjectures by observing patterns and identifying properties, and justify the reasoning.

  • 11.FM20.2.b Provide examples of how inductive reasoning might lead to false conclusions.

  • 11.FM20.2.c Critique the following statement "Decisions can be made and actions taken based upon inductive reasoning."

  • 11.FM20.2.d Identify situations relevant to self, family, or community involving inductive and/or deductive reasoning.

  • 11.FM20.2.e Prove algebraic number relationships, such as divisibility rules, number properties, mental mathematics strategies, or algebraic number tricks using deductive reasoning.

  • 11.FM20.2.f Prove conjectures using deductive reasoning.

  • 11.FM20.2.g Analyze an argument for its validity.

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

  • 11.FM20.2.i Solve situational questions that involve inductive or deductive reasoning.

  • 11.FM20.2.j Determine, explain, and verify strategies for solving puzzles or winning games, such as:

    • 11.FM20.2.j.1 guess and check

    • 11.FM20.2.j.2 analyze a pattern

    • 11.FM20.2.j.3 make a systematic list

    • 11.FM20.2.j.4 create a drawing or model

    • 11.FM20.2.j.5 eliminate possibilities

    • 11.FM20.2.j.6 solve simpler problems

    • 11.FM20.2.j.7 work backward.

  • 11.FM20.2.k Create a variation of a puzzle or a game, and describe a strategy for solving the puzzle or winning the game.

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

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

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

  • 11.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.

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

  • 11.FM20.4.d Generalize, using inductive reasoning, a rule for the relationship between the sum of the interior angles and the number of sides (n) in a polygon, with or without technology.

  • 11.FM20.4.e Apply knowledge of angles formed by parallel lines and transversals to identify and correct errors in a given proof.

  • 11.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.

  • 11.FM20.4.g Solve situational problems that involve:

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

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

  • 11.FM20.5.a Identify and describe situations relevant to self, family, or community that involve triangles without a right angle.

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

  • 11.FM20.5.c Draw diagrams to represent situations in which the cosine law or sine law could be used to solve a question.

  • 11.FM20.5.d Explain the steps in a given proof of the sine law or cosine law.

  • 11.FM20.5.e Illustrate and explain how one, two, or no triangles could be possible for a given set of measurements for two side lengths and the non-included angle in a proposed triangle.

  • 11.FM20.5.f Develop, generalize, explain, and apply strategies for determining the number of solutions possible to a situation involving the ambiguous case.

  • 11.FM20.5.g Solve situational questions involving triangles without a right angle.

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

  • 11.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.

  • 11.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.

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

  • 11.M20.6.d Critique the statement "Every set of data will correspond to a normal distribution."

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

  • 11.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.

  • 11.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.

  • 11.M20.6.h Solve situational questions that involve the interpretation of standard deviations to make decisions.

  • 11.M20.6.i Determine, with or without technology, and explain the meaning of the z-score for a given value in a normally distributed data set.

  • 11.M20.6.j Pose and solve situational questions relevant to self, family, or community that involve normal distributions and z-scores.

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

  • 11.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.

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

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

  • 11.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.

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

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

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

  • 11.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.

  • 11.FM20.8.c Develop, generalize, explain, and apply strategies for verifying solutions to systems of linear inequalities, including the use of test points.

  • 11.FM20.8.d Explain, using examples, the meaning of the shaded region in the graphical solution of a system of linear inequalities.

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

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

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

11.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.