Newfoundland and Labrador

1 Inductive and Deductive Reasoning

• 1.NL Number and Logic

  • 1.NL1 Analyze and prove conjectures, using inductive and deductive reasoning, to solve problems.

    • 1.NL1.1 Make conjectures by observing patterns and identifying properties, and justify the reasoning.

    • 1.NL1.2 Explain why inductive reasoning may lead to a false conjecture.

    • 1.NL1.3 Determine if a given argument is valid, and justify the reasoning.

      • Truth values (11-W.4)
      • Conditionals (11-W.5)
      • Converses, inverses and contrapositives (11-W.7)

    • 1.NL1.4 Provide and explain a counterexample to disprove a given conjecture.

      • Counterexamples (11-W.2)

    • 1.NL1.5 Prove a conjecture, using deductive reasoning (not limited to two column proofs).

      • Proofs involving angles (11-T.4)
      • Proofs involving parallel lines I (11-T.5)
      • Proofs involving parallel lines II (11-T.6)
      • Proofs involving triangles I (11-T.13)
      • Proofs involving triangles II (11-T.14)

    • 1.NL1.6 Prove algebraic and number relationships such as divisibility rules, number properties, mental mathematics strategies or algebraic number tricks.

    • 1.NL1.7 Compare, using examples, inductive and deductive reasoning.

    • 1.NL1.8 Identify errors in a given proof; e.g., a proof that ends with 2 = 1.

    • 1.NL1.9 Solve a contextual problem that involves inductive or deductive reasoning.

      • Solve problems involving corresponding parts (11-T.2)
      • Truth tables (11-W.3)
      • Negations (11-W.6)

  • 1.NL2 Analyze puzzles and games that involve spatial reasoning, using problem-solving strategies.

    • 1.NL2.1 Determine, explain and verify a strategy to solve a puzzle or to win a game; e.g.,

      • 1.NL2.1.a guess and check

      • 1.NL2.1.b look for a pattern

      • 1.NL2.1.c make a systematic list

      • 1.NL2.1.d draw or model

      • 1.NL2.1.e eliminate possibilities

      • 1.NL2.1.f simplify the original problem

      • 1.NL2.1.g work backward

      • 1.NL2.1.h develop alternative approaches

    • 1.NL2.2 Create a variation on a puzzle or a game, and describe a strategy for solving the puzzle or winning the game.

2 Mathematics Inquiry

• 2.RP Mathematics Research Project

  • 2.RP1 Research and give a presentation on a historical or current event, or an area of interest that involves mathematics.

    • 2.RP1.1 Collect primary or secondary data (statistical or informational) related to the topic.

    • 2.RP1.2 Assess the accuracy, reliability and relevance of the primary or secondary data collected by:

      • 2.RP1.2.a identifying examples of bias and points of view

        • Identify biased samples (12-AA.1)

      • 2.RP1.2.b identifying and describing the data collection methods

      • 2.RP1.2.c determining if the data is relevant

      • 2.RP1.2.d determining if the data is consistent with information obtained from other sources on the same topic.

    • 2.RP1.3 Interpret data, using statistical methods if applicable.

      • Mean, median, mode and range (10-HH.1)
      • Quartiles (10-HH.2)
      • Variance and standard deviation (12-AA.2)
      • Identify an outlier (12-AA.3)
      • Identify an outlier and describe the effect of removing it (12-AA.4)

    • 2.RP1.4 Identify controversial issues, if any, and present multiple sides of the issues with supporting data.

    • 2.RP1.5 Organize and present the research project, with or without technology.

3 Properties of Angles and Triangles

• 3.G Geometry

  • 3.G1 Derive proofs that involve the properties of angles and triangles.

    • 3.G1.1 Generalize, using inductive reasoning, the relationships between pairs of angles formed by transversals and parallel lines, with or without technology.

      • Transversal of parallel lines (9-E.9)

    • 3.G1.2 Verify, with examples, that if lines are not parallel, the angle properties do not apply.

    • 3.G1.3 Prove, using deductive reasoning, properties of angles formed by transversals and parallel lines, including the sum of the angles in a triangle.

      • Proofs involving angles (11-T.4)
      • Proofs involving parallel lines I (11-T.5)
      • Proofs involving parallel lines II (11-T.6)
      • Triangle Angle-Sum Theorem (11-U.2)

    • 3.G1.4 Identify and correct errors in a given proof of a property that involves angles.

    • 3.G1.5 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.

      • Interior angles of polygons (9-E.8)

    • 3.G1.6 Prove, using deductive reasoning, that two triangles are congruent.

      • SSS and SAS Theorems (11-T.7)
      • ASA and AAS Theorems (11-T.8)
      • SSS, SAS, ASA and AAS Theorems (11-T.9)
      • SSS Theorem in the coordinate plane (11-T.10)

  • 3.G2 Solve problems that involve properties of angles and triangles.

    • 3.G2.1 Construct parallel lines, given a compass or a protractor, and explain the strategy used.

    • 3.G2.2 Determine the measures of angles in a diagram that includes parallel lines, angles and triangles, and justify the reasoning.

      • Transversal of parallel lines (9-E.9)
      • Solve problems involving corresponding parts (11-T.2)
      • Congruency in isosceles and equilateral triangles (11-T.11)
      • Triangle Angle-Sum Theorem (11-U.2)

    • 3.G2.3 Determine if lines are parallel given the measure of an angle at each intersection formed by the lines and a transversal.

      • Proofs involving parallel lines I (11-T.5)
      • Proofs involving parallel lines II (11-T.6)

    • 3.G2.4 Identify and correct errors in a given solution to a problem that involves the measures of angles.

    • 3.G2.5 Solve a contextual problem that involves angles or triangles.

      • Pythagorean Theorem (11-P.1)
      • Converse of the Pythagorean theorem (11-P.2)
      • Pythagorean Inequality Theorems (11-P.3)
      • Special right triangles (11-P.4)
      • Trigonometric ratios: sin, cos and tan (11-Q.1)
      • Trigonometric ratios: csc, sec and cot (11-Q.2)
      • Sin, cos and tan of special angles (11-Q.5)
      • Csc, sec and cot of special angles (11-Q.6)
      • Trigonometric ratios: find a side length (11-Q.12)
      • Trigonometric ratios: find an angle measure (11-Q.13)
      • Solve a right triangle (11-Q.14)
      • Congruence statements and corresponding parts (11-T.1)
      • Solve problems involving corresponding parts (11-T.2)
      • Identify congruent figures (11-T.3)
      • Congruency in isosceles and equilateral triangles (11-T.11)
      • Classify triangles (11-U.1)
      • Triangle Angle-Sum Theorem (11-U.2)
      • Midsegments of triangles (11-U.3)
      • Triangles and bisectors (11-U.4)
      • Identify medians, altitudes, angle bisectors and perpendicular bisectors (11-U.5)
      • Angle-side relationships in triangles (11-U.6)
      • Triangle Inequality Theorem (11-U.7)
      • Triangle Proportionality Theorem (11-V.10)

• 3.NL Number and Logic

  • 3.NL2 Analyze puzzles and games that involve spatial reasoning, using problem-solving strategies.

    • 3.NL2.1 Determine, explain and verify a strategy to solve a puzzle or to win a game; e.g., guess and check; look for a pattern; make a systematic list; draw or model; eliminate possibilities; simplify the original problem; work backward; develop alternative approaches.

    • 3.NL2.2 Create a variation on a puzzle or a game, and describe a strategy for solving the puzzle or winning the game.

4 Acute Triangle Trigonometry

• 4.G Geometry

  • 4.G3 Solve problems that involve the cosine law and the sine law, excluding the ambiguous case.

    • 4.G3.1 Draw a diagram to represent a problem that involves the sine law or the cosine law.

    • 4.G3.2 Solve a contextual problem that requires the use of the sine law (excluding the ambiguous case) or the cosine law, and explain the reasoning.

      • Law of Sines (11-Q.15)
      • Law of Cosines (11-Q.16)
      • Solve a triangle (11-Q.17)
      • Area of a triangle: Law of Sines (11-Q.19)

    • 4.G3.3 Solve a contextual problem that involves more than one triangle.

• 4.NL Number and Logic

  • 4.NL2 Analyze puzzles and games that involve spatial reasoning, using problem-solving strategies.

    • 4.NL2.1 Determine, explain and verify a strategy to solve a puzzle or to win a game; e.g., guess and check; look for a pattern; make a systematic list; draw or model; eliminate possibilities; simplify the original problem; work backward; develop alternative approaches.

    • 4.NL2.3 Identify and correct errors in a solution to a puzzle or in a strategy for winning a game.

5 Radicals

• 5.NL Number and Logic

  • 5.NL3 Solve problems that involve operations on radicals and radical expressions with numerical and variable radicands (limited to square roots).

    • 5.NL3.1 Express a mixed radical with a numerical radicand as an entire radical.

    • 5.NL3.2 Compare and order radical expressions with numerical radicands.

    • 5.NL3.3 Express an entire radical with a numerical radicand as a mixed radical.

      • Simplify radical expressions (10-D.1)

    • 5.NL3.4 Identify values of the variable for which the radical expression is defined.

    • 5.NL3.5 Express an entire radical with a variable radicand as a mixed radical.

      • Simplify radical expressions with variables I (11-K.5)
      • Simplify radical expressions with variables II (11-K.6)

    • 5.NL3.6 Perform one or more operations to simplify radical expressions with numerical or variable radicands.

      • Multiply radical expressions (11-K.7)
      • Divide radical expressions (11-K.8)
      • Add and subtract radical expressions (11-K.9)
      • Simplify radical expressions using the distributive property (11-K.10)

    • 5.NL3.7 Rationalize the monomial denominator of a radical expression.

      • Divide radical expressions (11-K.8)

  • 5.NL4 Solve problems that involve radical equations (limited to square roots or cube roots).

    • 5.NL4.1 Determine any restrictions on values for the variable in a radical equation.

    • 5.NL4.2 Determine, algebraically, the roots of a radical equation, and explain the process used to solve the equation.

      • Solve radical equations (11-K.13)

    • 5.NL4.3 Verify, by substitution, that the values determined in solving a radical equation are roots of the equation.

    • 5.NL4.4 Explain why some roots determined in solving a radical equation are extraneous.

    • 5.NL4.5 Solve problems by modelling a situation with a radical equation and solving the equation.

  • 5.NL2 Analyze puzzles and games that involve spatial reasoning, using problem-solving strategies.

    • 5.NL2.1 Determine, explain and verify a strategy to solve a puzzle or to win a game; e.g.,

      • 5.NL2.1.a guess and check

      • 5.NL2.1.b look for a pattern

      • 5.NL2.1.c make a systematic list

      • 5.NL2.1.d draw or model

      • 5.NL2.1.e eliminate possibilities

      • 5.NL2.1.f simplify the original problem

      • 5.NL2.1.g work backward

      • 5.NL2.1.h develop alternative approaches.

    • 5.NL2.3 Identify and correct errors in a solution to a puzzle or in a strategy for winning a game.

6 Statistical Reasoning

• 6.S Statistics

  • 6.S1 Demonstrate an understanding of normal distribution, including:

    • 6.S1.a standard deviation

      • Variance and standard deviation (10-HH.5)
      • Variance and standard deviation (12-AA.2)

    • 6.S1.b z –scores.

      • Find z-values (12-Z.14)

    • 6.S1.1 Use dispersion to describe the differences between two sets of data.

    • 6.S1.2 Create frequency tables and graphs from a set of data.

    • 6.S1.3 Explain, using examples, the meaning of standard deviation.

    • 6.S1.4 Calculate, using technology, the population standard deviation of a data set.

    • 6.S1.5 Solve a contextual problem that involves the interpretation of standard deviation.

    • 6.S1.6 Explain, using examples, the properties of a normal curve, including the mean, median, mode, standard deviation, symmetry and area under the curve.

    • 6.S1.7 Determine if a data set approximates a normal distribution and explain the reasoning.

    • 6.S1.8 Compare the properties of two or more normally distributed data sets.

    • 6.S1.9 Solve a contextual problem that involves normal distribution.

      • Find probabilities using the normal distribution (11-Y.14)
      • Find probabilities using the normal distribution I (12-Z.12)
      • Use normal distributions to approximate binomial distributions (12-Z.18)

    • 6.S1.10 Determine, with or without technology, and explain the z-score for a given value in a normally distributed data set.

      • Find z-values (12-Z.14)

    • 6.S1.11 Explain, using examples representing multiple perspectives, the application of standard deviation for making decisions in situations such as warranties, insurance or opinion polls.

  • 6.S2 Interpret statistical data, using:

    • 6.S2.a confidence intervals

      • Interpret confidence intervals for population means (12-AA.14)

    • 6.S2.b confidence levels

      • Interpret confidence intervals for population means (12-AA.14)

    • 6.S2.c margin of error.

    • 6.S2.1 Explain, using examples, the significance of a confidence interval, margin of error or confidence level.

    • 6.S2.2 Explain, using examples, how confidence levels, margin of error and confidence intervals may vary depending on the size of the random sample.

    • 6.S2.3 Make inferences about a population from sample data, using confidence intervals, and explain the reasoning.

      • Interpret confidence intervals for population means (12-AA.14)

    • 6.S2.4 Provide examples from print or electronic media in which confidence intervals and confidence levels are used to support a particular position.

    • 6.S2.5 Interpret and explain confidence intervals and margin of error, using examples found in print or electronic media.

    • 6.S2.6 Support a position by analyzing statistical data presented in the media.

7 Quadratic Functions

• 7.RF Relations and Functions

  • 7.RF1 Demonstrate an understanding of the characteristics of quadratic functions, including:

    • 7.RF1.a vertex

      • Characteristics of quadratic functions (11-H.1)
      • Graph quadratic functions in vertex form (11-H.4)
      • Find the vertex of a parabola (11-I.2)
      • Write equations of parabolas in vertex form from graphs (11-I.4)
      • Write equations of parabolas in vertex form using properties (11-I.5)
      • Graph parabolas (11-I.6)

    • 7.RF1.b intercepts

      • Factor quadratics (11-G.2)
      • Find a quadratic function (11-H.3)
      • Solve a quadratic equation using the zero product property (11-H.7)
      • Solve a quadratic equation by factoring (11-H.8)

    • 7.RF1.c domain and range

      • Complete a function table: quadratic functions (11-H.2)

    • 7.RF1.d axis of symmetry.

      • Characteristics of quadratic functions (11-H.1)
      • Find the axis of symmetry of a parabola (11-I.3)

    • 7.RF1.1 Determine the characteristics of a quadratic function (y = ax² + bx + c, a ≠0) through manipulation of the parameters a, b and c.

      • Characteristics of quadratic functions (11-H.1)
      • Match quadratic functions and graphs (11-H.5)

    • 7.RF1.2 Determine, with or without technology, the coordinates of the vertex of the graph of a quadratic function.

      • Characteristics of quadratic functions (11-H.1)
      • Graph quadratic functions in vertex form (11-H.4)
      • Find the vertex of a parabola (11-I.2)
      • Graph parabolas (11-I.6)

    • 7.RF1.3 Determine the coordinates of the vertex of the graph of a quadratic function, given the equation of the function and the axis of symmetry, and determine if the y-coordinate of the vertex is a maximum or a minimum value.

      • Characteristics of quadratic functions (11-H.1)
      • Graph quadratic functions in vertex form (11-H.4)
      • Find the vertex of a parabola (11-I.2)
      • Graph parabolas (11-I.6)

    • 7.RF1.4 Determine the equation of the axis of symmetry of the graph of a quadratic function using the x-intercepts of the graph.

      • Characteristics of quadratic functions (11-H.1)
      • Find the axis of symmetry of a parabola (11-I.3)

    • 7.RF1.5 Sketch the graph of a quadratic function.

      • Graph quadratic functions in vertex form (11-H.4)
      • Graph parabolas (11-I.6)

    • 7.RF1.6 Determine the domain and range of a quadratic function.

      • Complete a function table: quadratic functions (11-H.2)

    • 7.RF1.7 Determine the characteristics of a quadratic function (y = a(x - h)²+ k, a ≠0) through manipulation of the parameters h and k.

      • Characteristics of quadratic functions (11-H.1)

    • 7.RF1.8 Determine the quadratic function given the characteristics of its graph.

      • Characteristics of quadratic functions (11-H.1)
      • Match quadratic functions and graphs (11-H.5)

    • 7.RF1.9 Solve a contextual problem that involves the characteristics of a quadratic function.

  • 7.RF2 Solve problems that involve quadratic equations.

    • 7.RF2.1 Determine, with or without technology, the intercepts of the graph of a quadratic function.

      • Factor quadratics (11-G.2)
      • Find a quadratic function (11-H.3)
      • Solve a quadratic equation using the zero product property (11-H.7)
      • Solve a quadratic equation by factoring (11-H.8)

    • 7.RF2.2 Express a quadratic equation in factored form, given the zeros of the corresponding quadratic function or the x-intercepts of the graph of the function.

• 7.NL Number and Logic

  • 7.NL2 Analyze puzzles and games that involve spatial reasoning, using problem-solving strategies.

    • 7.NL2.1 Determine, explain and verify a strategy to solve a puzzle or to win a game; e.g.,

      • 7.NL2.1.a guess and check

      • 7.NL2.1.b look for a pattern

      • 7.NL2.1.c make a systematic list

      • 7.NL2.1.d draw or model

      • 7.NL2.1.e eliminate possibilities

      • 7.NL2.1.f simplify the original problem

      • 7.NL2.1.g work backward

      • 7.NL2.1.h develop alternative approaches

8 Quadratic Equations

• 8.RF Relations and Functions

  • 8.RF2 Solve problems that involve quadratic equations.

    • 8.RF2.1 Determine, with or without technology, the intercepts of the graph of a quadratic function.

      • Factor quadratics (11-G.2)
      • Find a quadratic function (11-H.3)
      • Solve a quadratic equation using the zero product property (11-H.7)
      • Solve a quadratic equation by factoring (11-H.8)

    • 8.RF2.2 Express a quadratic equation in factored form, given the zeros of the corresponding quadratic function or the x-intercepts of the graph of the function.

    • 8.RF2.3 Explain the relationships among the roots of an equation, the zeros of the corresponding function, and the x-intercepts of the graph of the function.

    • 8.RF2.4 Explain, using examples, why the graph of a quadratic function may have zero, one or two x-intercepts.

    • 8.RF2.5 Determine, by factoring, the roots of a quadratic equation, and verify by substitution.

      • Factor quadratics (11-G.2)
      • Factor quadratics using algebra tiles (11-G.3)
      • Find a quadratic function (11-H.3)
      • Solve a quadratic equation using the zero product property (11-H.7)
      • Solve a quadratic equation by factoring (11-H.8)

    • 8.RF2.6 Determine, using the quadratic formula, the roots of a quadratic equation.

      • Solve a quadratic equation using the quadratic formula (11-H.11)

    • 8.RF2.7 Solve a contextual problem by modelling a situation with a quadratic equation and solving the equation.

9 Proportional Reasoning

• 9.G Geometry

  • 9.M1 Solve problems that involve the application of rates.

    • 9.M1.1 Interpret rates in a given context, such as the arts, commerce, the environment, medicine or recreation.

    • 9.M1.2 Determine and compare rates and unit rates.

      • Unit rates (11-A.1)

    • 9.M1.3 Make and justify a decision, using rates.

      • Unit prices with imperial length conversions (10-W.6)

    • 9.M1.4 Draw a graph to represent a rate.

    • 9.M1.5 Explain, using examples, the relationship between the slope of a graph and a rate.

      • Find the constant of variation (10-K.2)

    • 9.M1.6 Describe a context for a given rate or unit rate.

    • 9.M1.7 Identify and explain factors that influence a rate in a given context.

    • 9.M1.8 Solve a contextual problem that involves rates or unit rates.

      • Unit rates (11-A.1)

    • 9.M1.9 Solve a rate problem that requires the isolation of a variable.

  • 9.M2 Solve problems that involve scale diagrams, using proportional reasoning.

    • 9.M2.1 Explain, using examples, how scale diagrams are used to model a 2-D shape.

    • 9.M2.2 Determine, using proportional reasoning, an unknown dimension of a 2-D shape, given a scale diagram or model.

      • Side lengths and angle measures in similar figures (11-V.4)
      • Similar triangles and indirect measurement (11-V.5)
      • Triangle Proportionality Theorem (11-V.10)

    • 9.M2.3 Determine, using proportional reasoning, the scale factor, given one dimension of a 2-D shape, and its representation.

      • Dilations: scale factor and classification (10-FF.15)
      • Similar triangles and similarity transformations (11-V.8)

    • 9.M2.4 Draw, with or without technology, a scale diagram of a given 2-D shape, according to a specified scale factor (enlargement or reduction).

      • Similar triangles and similarity transformations (11-V.8)

    • 9.M2.5 Solve a contextual problem that involves a scale diagram.

      • Scale drawings: word problems (11-A.2)

    • 9.M2.6 Explain, using examples, how scale diagrams are used to model a 3-D object.

    • 9.M2.7 Determine, using proportional reasoning, the scale factor, given one dimension of a 3-D object, and its representation.

    • 9.M2.8 Determine, using proportional reasoning, an unknown dimension of a 3-D object, given a scale diagram or model.

      • Introduction to similar solids (11-S.10)

  • 9.M3 Demonstrate an understanding of the relationships among scale factors, areas, surface areas and volumes of similar 2-D shapes and 3-D objects.

    • 9.M3.1 Explain, using examples, the effect of a change in the scale factor on the area of a 2-D shape.

      • Area and perimeter of similar figures (11-R.10)
      • Areas of similar figures (11-V.11)

    • 9.M3.2 Determine the area of a 2-D shape, given the scale diagram, and justify the reasonableness of the result.

      • Areas of similar figures (11-V.11)

    • 9.M3.3 Solve a spatial problem that requires the manipulation of formulas.

      • Area and perimeter of similar figures (11-R.10)
      • Surface area and volume of similar solids (11-S.11)
      • Side lengths and angle measures in similar figures (11-V.4)
      • Similar triangles and indirect measurement (11-V.5)
      • Perimeters of similar figures (11-V.6)
      • Areas of similar figures (11-V.11)

    • 9.M3.4 Solve a contextual problem that involves the relationships among scale factors, areas and volumes.

      • Scale drawings: word problems (11-A.2)

    • 9.M3.5 Explain, using examples, the effect of a change in the scale factor on the surface area and volume of a 3-D object.

      • Surface area and volume of similar solids (11-S.11)

    • 9.M3.6 Determine the surface area and volume of a 3-D object, given the scale diagram, and justify the reasonableness.

      • Surface area and volume of similar solids (11-S.11)