Develop a rubric or other scoring schema for the assessment of the research and presentation.

]]> Collect primary or secondary data (quantitative or qualitative) related to the topic.

]]> 111673 Assess the accuracy, reliability, and relevance of the primary or secondary data (quantitative/qualitative) collected by:

identifying examples of bias and points of view
identifying and describing the data collection methods
determining whether or not the data are relevant
determining whether or not the data are consistent with information obtained from other sources on the same topic.

]]> 111674 Interpret data, using statistical methods if applicable.

]]> 111675 Identify controversial issues, if any, and present multiple sides of the issues with supporting data.

]]> 111676 Organize and create a presentation (oral, written, multimedia, etc.) of the research findings and conclusions.

]]> 111677

analyzing conjectures

analyzing spatial puzzles and games

providing conjectures

solving problems.

]]> 111672

proofs NOT be limited to the two column proof style

analysis and conjectures related to spatial puzzles and games be incorporated throughout the course.

]]> Make conjectures by observing patterns and identifying properties, and justify the reasoning.

]]> 111680 Provide examples of how inductive reasoning might lead to false conclusions.

]]> 111681 Critique the following statement “Decisions can be made and actions taken based upon inductive reasoning”.

]]> 111682 Identify situations relevant to self, family, or community involving inductive and/or deductive reasoning.

]]> 111683 Prove algebraic number relationships, such as divisibility rules, number properties, mental mathematics strategies, or algebraic number tricks using deductive reasoning.

]]> 111684 Prove conjectures using deductive reasoning.

]]> 111685 Analyze an argument for its validity.

]]> 111686 Identify errors in proofs that lead to incorrect conclusions (e.g., a proof that ends with 2 = 1).

]]> 111687 Solve situational questions that involve inductive or deductive reasoning.

]]> 111688 Determine, explain, and verify strategies for solving puzzles or winning games, such as:

guess and check
analyze a pattern
make a systematic list
create a drawing or model
eliminate possibilities
solve simpler problems
work backward.

]]> 111689 Create a variation of a puzzle or a game, and describe a strategy for solving the puzzle or winning the game.

]]> 111690

rates

scale diagrams

scale factor

area

surface area

volume.

]]> 111679 Identify and describe situations relevant to one’s self, family, or community that involve proportional reasoning.

]]> Create non-symbolic representations for rates, including pictures and graphs.

]]> 111693 Describe situations in which a given rate might occur.

]]> 111694 Explain the meaning of rates given in context, such as the arts, commerce, the environment, medicine, or recreation.

]]> 111695 Solve situational questions that require the use of proportional reasoning, including those that involve the isolation of a variable.

]]> 111696 Analyze situations in which unit rates can be determined and suggest reasons why the rates would or would not be used to make decisions in each situation (i.e., are other factors in the situation outweighing the importance of the mathematical calculations?).

]]> 111697 Explain, using examples, the relationship between the slope of a graph and a rate.

]]> 111698 Identify and explain the effect of factors within given situations that could influence a particular rate.

]]> 111699 Solve situational questions involving rates, including unit rates.

]]> 111700 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.

]]> 111701 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.

]]> 111702 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).

]]> 111703 Solve situational problems involving scale diagrams of 2-D shapes and 3-D objects.

]]> 111704 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.

]]> 111705 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.

]]> 111706 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.

]]> 111707 Solve situational questions that involve scale factors, areas, surface areas, and volumes, including ones that require the manipulation of formulas.

]]> 111708

deriving proofs based on theorems and postulates about congruent triangles

solving problems.

]]> 111692 Identify and describe situations relevant to self, family, or community that involve parallel lines cut by transversals.

]]> 111711 Develop, generalize, explain, apply, and prove relationships between pairs of angles formed by transversals and parallel lines, with and without the use of technology.

]]> 111712 Prove and apply the relationship relating the sum of the angles in a triangle.

]]> 111713 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.

]]> 111714 Apply knowledge of angles formed by parallel lines and transversals to identify and correct errors in a given proof.

]]> 111715 Explore and verify whether or not the angles formed by non-parallel lines and transversals create the same angle relationships as those created by parallel lines and transversals.

]]> 111716 Solve situational problems that involve:

angles, parallel lines, and transversals
angles, non-parallel lines, and transversals
angles in triangles
angles in polygons.

]]> 111717 Develop, generalize, explain, and apply strategies for constructing parallel lines.

]]> 111718 111710 Identify and describe situations relevant to self, family, or community that involve triangles without a right angle.

]]> 111721 Develop, generalize, explain, and apply strategies for determining angles or side lengths of triangles without a right angle.

]]> 111722 Draw diagrams to represent situations in which the cosine law or sine law could be used to solve a question.

]]> 111723 Explain the steps in a given proof of the sine law or cosine law.

]]> 111724 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.

]]> 111725 Develop, generalize, explain, and apply strategies for determining the number of solutions possible to a situation involving the ambiguous case.

]]> 111726 Solve situational questions involving triangles without a right angle.

]]> 111727 111720 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.

]]> Explain the meaning and purpose of the properties of a normal curve, including mean, median, mode, standard deviation, symmetry, and area under the curve.

]]> 111730 Calculate, using technology, the population standard deviation of a data set.

]]> 111731 Critique the statement “Every set of data will correspond to a normal distribution”.

]]> 111732 Analyze a data set to determine if it approximates a normal distribution.

]]> 111733 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.

]]> 111734 Explain, using examples that represent multiple perspectives, the application of standard deviation for making decisions in situations such as warranties, insurance, or opinion polls.

]]> 111735 Solve situational questions that involve the interpretation of standard deviations to make decisions.

]]> 111736 Determine, with or without technology, and explain the meaning of the z-score for a given value in a normally distributed data set.

]]> 111737 Pose and solve situational questions relevant to self, family, or community that involve normal distributions and z-scores.

]]> 111738

confidence intervals

confidence levels

margin of error.

]]> 111729 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.

]]> 111741 Explain how confidence levels, margins of error, and confidence intervals can be impacted by the size of the random sample used.

]]> 111742 Make inferences and decisions with justification about a population from sample data using confidence intervals.

]]> 111743 Provide and critique examples from print or electronic media in which confidence intervals and confidence levels are used to support a particular position.

]]> 111744 Support a position or decision relevant to self, family, or community by analyzing statistical data, as well as considering other factors.

]]> 111745 111740 Identify situations relevant to self, family, or community which could be described using a system of linear inequalities in two variables.

]]> Develop, generalize, explain, and apply strategies for graphing and solving systems of linear inequalities, including justification of the choice of solid or broken lines.

]]> 111748 Develop, generalize, explain, and apply strategies for verifying solutions to systems of linear inequalities, including the use of test points.

]]> 111749 Explain, using examples, the meaning of the shaded region in the graphical solution of a system of linear inequalities.

]]> 111750 Write a system of linear inequalities for a given graph.

]]> 111751 Match optimization questions and the graphs of sets of linear inequalities.

]]> 111752 Apply knowledge of graphing of systems of linear inequalities and linear programming to solve optimization questions.

]]> 111753

vertex

intercepts

domain and range

axis of symmetry.

]]> 111747 Identify situations and objects relevant to self, family, or community which could be described using a quadratic function.

]]> 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.

]]> 111756 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.

]]> 111757 Explain, using examples, why the graph of a quadratic function may have zero, one, or two x-intercepts.

]]> 111758 Write a quadratic equation in factored form given the zeros of a corresponding quadratic function or the x-intercepts of a corresponding quadratic function.

]]> 111759 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.

]]> 111760 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.

]]> 111761 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.

]]> 111762 Generalize about and explain the effects on the graph of a quadratic function when the values for a, p, and q are changed.

]]> 111763 Develop, generalize, explain, and apply strategies for determining the domain and range of a quadratic function.

]]> 111764 Explain what the domain and range of a quadratic function tell about the situation that the quadratic function models.

]]> 111765 Develop, generalize, explain, and apply strategies for sketching the graph of a quadratic function.

]]> 111766 Solve situational questions involving the characteristics and graphs of quadratic functions.

]]> 111767 Critique the statement “Any function that can be written in the form $y = a(x - p)^2 + q$ will have a parabolic graph.”

]]> 111768