Manitoba

M Measurement

• M.1 Develop spatial sense and proportional reasoning.

  • M.1.1 Solve problems that involve the application of rates.

    • Slope-intercept form: write an equation from a word problem (10-L.10)
    • Unit rates (11-A.1)
    • Solve linear equations: word problems (11-B.2)

  • M.1.2 Solve problems that involve scale diagrams, using proportional reasoning.

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

  • M.1.3 Demonstrate an understanding of the relationships among scale factors, areas, surface areas and volumes of similar 2-D shapes and 3-D objects.

    • Area and perimeter of similar figures (11-R.10)
    • Introduction to similar solids (11-S.10)
    • Surface area and volume of similar solids (11-S.11)
    • Identify similar figures (11-V.1)
    • Similarity ratios (11-V.2)
    • Similarity statements (11-V.3)
    • 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)
    • Similarity rules for triangles (11-V.7)
    • Similar triangles and similarity transformations (11-V.8)
    • Similarity of circles (11-V.9)
    • Areas of similar figures (11-V.11)

G Geometry

• G.1 Develop spatial sense.

  • G.1.1 Derive proofs that involve the properties of angles and triangles.

    • 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)

  • G.1.2 Solve problems that involve the properties of angles and 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)

  • G.1.3 Solve problems that involve the cosine law and the sine law, including the ambiguous case.

    • 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)

LR Logical Reasoning

• LR.1 Develop logical reasoning.

  • LR.1.1 Analyze and prove conjectures, using inductive and deductive reasoning, to solve problems.

    • Identify hypotheses and conclusions (11-W.1)
    • Counterexamples (11-W.2)
    • Truth tables (11-W.3)
    • Truth values (11-W.4)
    • Conditionals (11-W.5)
    • Negations (11-W.6)
    • Converses, inverses and contrapositives (11-W.7)
    • Biconditionals (11-W.8)

  • LR.1.2 Analyze puzzles and games that involve spatial reasoning, using problem-solving strategies.

S Statistics

• S.1 Develop statistical reasoning.

  • S.1.1 Demonstrate an understanding of normal distribution, including:

    • S.1.1.1 standard deviation

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

    • S.1.1.2 z-scores.

      • Find z-values (12-Z.14)

  • S.1.2 Interpret statistical data, using:

    • S.1.2.1 confidence intervals

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

    • S.1.2.2 confidence levels

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

    • S.1.2.3 margin of error.

R Relations and Functions

• R.1 Develop algebraic and graphical reasoning through the study of relations.

  • R.1.1 Model and solve problems that involve systems of linear inequalities in two variables.

    • Is (x, y) a solution to the system of inequalities? (11-F.1)
    • Find the vertices of a solution set (11-F.3)
    • Linear programming (11-F.4)

  • R.1.2 Demonstrate an understanding of the characteristics of quadratic functions, including:

    • R.1.2.1 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)

    • R.1.2.2 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)

    • R.1.2.3 domain and range

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

    • R.1.2.4 axis of symmetry.

      • Find the axis of symmetry of a parabola (11-I.3)

MRP Mathematics Research Project

• MRP.1 Develop an appreciation of the role of mathematics in society.

  • MRP.1.1 Research and give a presentation on a historical event or an area of interest that involves mathematics.