Manitoba

M Measurement

• M.1 Develop spatial sense and proportional reasoning.

  • M.1.1 Solve problems that involve linear measurement, using:

    • M.1.1.1 SI and imperial units of measure

      • Convert rates and measurements: metric units (10-W.2)
      • Convert rates and measurements: imperial units of length (10-W.4)
      • Unit prices with imperial length conversions (10-W.6)
      • Imperial mixed units of length (10-W.7)
      • Perimeter (10-Y.3)

    • M.1.1.2 estimation strategies

      • Estimate metric measurements (10-W.1)
      • Estimate imperial measurements of length (10-W.3)

    • M.1.1.3 measurement strategies.

  • M.1.2 Apply proportional reasoning to problems that involve conversions between SI and imperial units of measure.

    • Convert between metric and imperial units of length (10-W.8)

  • M.1.3 Solve problems, using SI and imperial units, that involve the surface area and volume of 3-D objects, including:

    • M.1.3.1 right cones

      • Surface area of pyramids and cones (10-Z.6)
      • Volume of pyramids and cones (10-Z.8)

    • M.1.3.2 right cylinders

      • Surface area of prisms and cylinders (10-Z.5)
      • Volume of prisms and cylinders (10-Z.7)

    • M.1.3.3 right prisms

      • Surface area of prisms and cylinders (10-Z.5)
      • Volume of prisms and cylinders (10-Z.7)

    • M.1.3.4 right pyramids

      • Surface area of pyramids and cones (10-Z.6)
      • Volume of pyramids and cones (10-Z.8)

    • M.1.3.5 spheres.

      • Surface area and volume of spheres (10-Z.9)

  • M.1.4 Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles.

    • Trigonometric ratios: sin, cos and tan (10-EE.1)
    • Find trigonometric functions of special angles (10-EE.3)
    • Find trigonometric functions using a calculator (10-EE.4)
    • Inverses of trigonometric functions (10-EE.5)
    • Trigonometric ratios: find a side length (10-EE.6)
    • Trigonometric ratios: find an angle measure (10-EE.7)
    • Solve a right triangle (10-EE.8)

A Algebra and Number

• A.1 Develop algebraic reasoning and number sense.

  • A.1.1 Demonstrate an understanding of factors of whole numbers by determining the:

    • A.1.1.1 prime factors

      • Prime factorization (10-A.2)

    • A.1.1.2 greatest common factor

      • Greatest common factor (10-A.3)
      • GCF and LCM: word problems (10-A.5)

    • A.1.1.3 least common multiple

      • Least common multiple (10-A.4)
      • GCF and LCM: word problems (10-A.5)

    • A.1.1.4 square root

      • Square roots (10-A.6)

    • A.1.1.5 cube root.

      • Cube roots (10-A.7)

  • A.1.2 Demonstrate an understanding of irrational numbers by:

    • A.1.2.1 representing, identifying and simplifying irrational numbers

      • Classify rational and irrational numbers (10-A.8)

    • A.1.2.2 ordering irrational numbers

  • A.1.3 Demonstrate an understanding of powers with integral and rational exponents.

    • Exponents with integer bases (10-B.1)
    • Exponents with decimal and fractional bases (10-B.2)
    • Negative exponents (10-B.3)
    • Multiplication with exponents (10-B.4)
    • Division with exponents (10-B.5)
    • Multiplication and division with exponents (10-B.6)
    • Power rule (10-B.7)
    • Evaluate expressions using properties of exponents (10-B.8)
    • Evaluate rational exponents (10-E.1)
    • Multiplication with rational exponents (10-E.2)
    • Division with rational exponents (10-E.3)
    • Power rule with rational exponents (10-E.4)
    • Simplify expressions involving rational exponents I (10-E.5)
    • Simplify expressions involving rational exponents II (10-E.6)

  • A.1.4 Demonstrate an understanding of the multiplication of polynomial expressions (limited to monomials, binomials and trinomials), concretely, pictorially and symbolically.

    • Multiply a polynomial by a monomial (10-O.6)
    • Multiply two polynomials using algebra tiles (10-O.7)
    • Multiply two binomials (10-O.8)
    • Multiply two binomials: special cases (10-O.9)
    • Multiply polynomials (10-O.10)

  • A.1.5 Demonstrate an understanding of common factors and trinomial factoring, concretely, pictorially and symbolically.

    • GCF of monomials (10-P.1)
    • Factor out a monomial (10-P.2)
    • Factor quadratics with leading coefficient 1 (10-P.3)
    • Factor quadratics with other leading coefficients (10-P.4)
    • Factor quadratics using algebra tiles (10-P.5)
    • Factor quadratics: special cases (10-P.6)
    • Factor by grouping (10-P.7)
    • Factor polynomials (10-P.8)

R Relations and Functions

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

  • R.1.1 Interpret and explain the relationships among data, graphs and situations.

    • Relations: convert between tables, graphs, mappings and lists of points (10-J.1)
    • Find values using function graphs (10-J.6)
    • Complete a function table from a graph (10-J.9)
    • Complete a function table from an equation (10-J.10)
    • Interpret the graph of a function: word problems (10-J.11)
    • Slope-intercept form: write an equation from a table (10-L.9)
    • Slope-intercept form: write an equation from a word problem (10-L.10)
    • Complete a table and graph a linear function (10-L.12)

  • R.1.2 Demonstrate an understanding of relations and functions.

    • Identify independent and dependent variables (10-J.3)
    • Identify functions (10-J.4)
    • Identify functions: vertical line test (10-J.5)
    • Evaluate a function (10-J.7)
    • Evaluate a function: plug in an expression (10-J.8)
    • Identify linear functions (10-L.1)

  • R.1.3 Demonstrate an understanding of slope with respect to:

    • R.1.3.1 rise and run

      • Find the slope from two points (10-L.3)

    • R.1.3.2 line segments and lines

      • Find the slope of a graph (10-L.2)
      • Slope-intercept form: find the slope and y-intercept (10-L.5)

    • R.1.3.3 rate of change

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

    • R.1.3.4 parallel lines

      • Slopes of parallel and perpendicular lines (10-L.22)

    • R.1.3.5 perpendicular lines.

      • Slopes of parallel and perpendicular lines (10-L.22)

  • R.1.4 Describe and represent linear relations, using:

    • R.1.4.1 words

      • Slope-intercept form: write an equation from a word problem (10-L.10)
      • Write linear functions to solve word problems (10-L.11)

    • R.1.4.2 ordered pairs

      • Interpret the graph of a function: word problems (10-J.11)

    • R.1.4.3 tables of values

    • R.1.4.4 graphs

      • Complete a table and graph a linear function (10-L.12)

    • R.1.4.5 equations.

      • Slope-intercept form: write an equation from a graph (10-L.7)
      • Slope-intercept form: write an equation (10-L.8)
      • Slope-intercept form: write an equation from a table (10-L.9)
      • Slope-intercept form: write an equation from a word problem (10-L.10)

  • R.1.5 Determine the characteristics of the graphs of linear relations, including the:

    • R.1.5.1 intercepts

      • Slope-intercept form: find the slope and y-intercept (10-L.5)
      • Standard form: find x- and y-intercepts (10-L.15)

    • R.1.5.2 slope

      • Find the slope of a graph (10-L.2)
      • Slope-intercept form: find the slope and y-intercept (10-L.5)

    • R.1.5.3 domain

    • R.1.5.4 range.

  • R.1.6 Relate linear relations expressed in:

    • R.1.6.1 slope–intercept form (y = mx + b) to their graphs.

      • Slope-intercept form: find the slope and y-intercept (10-L.5)
      • Slope-intercept form: graph an equation (10-L.6)
      • Slope-intercept form: write an equation from a graph (10-L.7)
      • Slope-intercept form: write an equation (10-L.8)

    • R.1.6.2 general form (Ax + By + C = 0) to their graphs.

      • Write equations in standard form (10-L.14)
      • Standard form: find x- and y-intercepts (10-L.15)
      • Standard form: graph an equation (10-L.16)

    • R.1.6.3 slope–point form (y – y? = m(x – x?)) to their graphs.

      • Point-slope form: graph an equation (10-L.19)
      • Point-slope form: write an equation (10-L.20)
      • Point-slope form: write an equation from a graph (10-L.21)

  • R.1.7 Determine the equation of a linear relation, given:

    • R.1.7.1 a graph to solve problems.

      • Slope-intercept form: write an equation from a graph (10-L.7)
      • Point-slope form: write an equation from a graph (10-L.21)

    • R.1.7.2 a point and the slope to solve problems.

      • Slope-intercept form: write an equation (10-L.8)
      • Point-slope form: write an equation (10-L.20)

    • R.1.7.3 two points to solve problems.

    • R.1.7.4 a point and the equation of a parallel or perpendicular line to solve problems.

      • Write an equation for a parallel or perpendicular line (10-L.23)

  • R.1.8 Represent a linear function, using function notation.

    • Slope-intercept form: write an equation from a table (10-L.9)

  • R.1.9 Solve problems that involve systems of linear equations in two variables, graphically and algebraically.

    • Is (x, y) a solution to the system of equations? (10-M.1)
    • Solve a system of equations by graphing (10-M.2)
    • Solve a system of equations by graphing: word problems (10-M.3)
    • Find the number of solutions to a system of equations by graphing (10-M.4)
    • Find the number of solutions to a system of equations (10-M.5)
    • Classify a system of equations by graphing (10-M.6)
    • Classify a system of equations (10-M.7)
    • Solve a system of equations using substitution (10-M.8)
    • Solve a system of equations using substitution: word problems (10-M.9)
    • Solve a system of equations using elimination (10-M.10)
    • Solve a system of equations using elimination: word problems (10-M.11)
    • Solve a system of equations using any method (10-M.12)
    • Solve a system of equations using any method: word problems (10-M.13)