Newfoundland and Labrador

Measurement

• Develop spatial sense and proportional reasoning

  • 10.M1 Solve problems that involve linear measurement, using:

    • 10.M1.A SI and imperial units of measure

      • Perimeter (10-Y.3)

    • 10.M1.B estimation strategies

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

    • 10.M1.C measurement strategies.

    • 10.M1.1 Provide referents for linear measurements, including millimetre, centimetre, metre, kilometre, inch, foot, yard and mile, and explain the choices.

    • 10.M1.2 Compare SI and imperial units, using referents.

    • 10.M1.3 Estimate a linear measure, using a referent, and explain the process used.

    • 10.M1.4 Justify the choice of units used for determining a measurement in a problem solving context.

    • 10.M1.5 Solve problems that involve linear measure, using instruments such as rulers, calipers or tape measures.

    • 10.M1.6 Describe and explain a personal strategy used to determine a linear measurement; e.g., circumference of a bottle, length of a curve, perimeter of the base of an irregular 3-D object.

  • 10.M2 Apply proportional reasoning to problems that involve conversions between SI and imperial units of measure.

    • 10.M2.1 Using proportional reasoning, convert a measurement within or between SI and imperial systems.

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

    • 10.M2.2 Solve a problem that involves the conversion of units within or between SI and imperial units.

      • Imperial mixed units of length (10-W.7)
      • Scale drawings: word problems (10-W.9)

    • 10.M2.3 Verify, using unit analysis, a conversion within or between SI and imperial systems, and explain the conversion.

    • 10.M2.4 Justify, using mental mathematics, the reasonableness of a solution to a conversion problem.

  • 10.M3 Solve problems, using SI and imperial units, that involve the surface area and volume of 3-D objects, including:

    • 10.M3.A right cones

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

    • 10.M3.B right cylinders

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

    • 10.M3.C right prisms

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

    • 10.M3.D right pyramids

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

    • 10.M3.E spheres.

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

    • 10.M3.1 Sketch a diagram to represent a problem that involves surface area or volume.

    • 10.M3.2 Determine the surface area of a right cone, right cylinder, right prism, or a right pyramid, using an object or its labelled diagram.

      • Surface area of prisms and cylinders (10-Z.5)
      • Surface area of pyramids and cones (10-Z.6)

    • 10.M3.3 Determine an unknown dimension of a right cone, right cylinder, right prism, or right pyrmaid, given the object's surface area and the remaining dimensions.

      • Surface area of prisms and cylinders (10-Z.5)
      • Surface area of pyramids and cones (10-Z.6)

    • 10.M3.4 Determine the volume of a right cone, right cylinder, right prism, or a right pyramid using an object or its labelled diagram.

      • Volume of prisms and cylinders (10-Z.7)
      • Volume of pyramids and cones (10-Z.8)

    • 10.M3.5 Describe the relationship between the volumes of:

      • 10.M3.5.a right cones and right cylinders with the same base and height

      • 10.M3.5.b right pyramids and right prisms with the same base and height.

    • 10.M3.6 Determine an unknown dimension of a right cone, right cylinder, right prism, or right pyramid, given the object's volume and the remaining dimensions.

      • Volume of prisms and cylinders (10-Z.7)
      • Volume of pyramids and cones (10-Z.8)

    • 10.M3.7 Determine the surface area and volume of a sphere, using an object or its labelled diagram.

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

    • 10.M3.8 Determine an unknown dimension of a sphere, given the object's surface area and the remaining dimensions.

    • 10.M3.9 Solve a problem that involves surface area or volume, using an object or its labelled diagram of a composite 3-D object.

Trigonometry

• Develop spatial sense and proportional reasoning

  • 10.M4 Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles.

    • 10.M4.1 Identify the hypotenuse of a right triangle and the opposite and adjacent sides for a given acute angle in the triangle.

    • 10.M4.2 Explain the relationships between similar right triangles and the definitions of the primary trigonometric ratios.

    • 10.M4.3 Use the primary trigonometric ratios to determine the measure of a missing angle in a right triangle.

      • Inverses of trigonometric functions (10-EE.5)
      • Trigonometric ratios: find an angle measure (10-EE.7)

    • 10.M4.4 Use the primary trigonometric ratios to determine the length of a missing side in a right triangle.

      • Trigonometric ratios: sin, cos and tan (10-EE.1)
      • Trigonometric ratios: csc, sec and cot (10-EE.2)
      • Find trigonometric functions using a calculator (10-EE.4)
      • Trigonometric ratios: find a side length (10-EE.6)

    • 10.M4.5 Solve a problem that involves indirect and direct measurement, using the trigonometric ratios, the Pythagorean theorem and measurement instruments such as a clinometer or metre stick.

    • 10.M4.6 Solve right triangles.

      • Solve a right triangle (10-EE.8)

    • 10.M4.7 Solve a problem that involves one or more right triangles by applying the primary trigonometric ratios or the Pythagorean theorem.

      • Pythagorean Theorem (10-DD.1)
      • Special right triangles (10-DD.4)
      • Solve a right triangle (10-EE.8)

Roots and Powers

• Develop algebraic reasoning and number sense

  • 10.AN1 Demonstrate an understanding of factors of whole numbers by determining the:

    • 10.AN1.A prime factors

      • Prime factorization (10-A.2)

    • 10.AN1.B greatest common factor

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

    • 10.AN1.C least common multiple

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

    • 10.AN1.D square root

      • Square roots (10-A.6)

    • 10.AN1.E cube root.

      • Cube roots (10-A.7)

    • 10.AN1.1 Determine the prime factors of a whole number.

      • Prime factorization (10-A.2)

    • 10.AN1.2 Explain why the numbers 0 and 1 have no prime factors.

    • 10.AN1.3 Determine, using a variety of strategies, the greatest common factor or least common multiple of a set of whole numbers, and explain the process.

      • Greatest common factor (10-A.3)
      • Least common multiple (10-A.4)

    • 10.AN1.4 Solve problems that involve prime factors, greatest common factors, least common multiples, square roots or cube roots.

      • GCF and LCM: word problems (10-A.5)

    • 10.AN1.5 Determine, concretely, whether a given whole number is a perfect square, a perfect cube or neither.

    • 10.AN1.6 Determine, using a variety of strategies, the square root of a perfect square, and explain the process.

      • Square roots (10-A.6)

    • 10.AN1.7 Determine, using a variety of strategies, the cube root of a perfect cube, and explain the process.

      • Cube roots (10-A.7)

  • 10.AN2 Demonstrate an understanding of irrational numbers by:

    • 10.AN2.A representing, identifying and simplifying irrational numbers

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

    • 10.AN2.B ordering irrational numbers.

    • 10.AN2.1 Explain, using examples, the meaning of the index of a radical.

    • 10.AN2.2 Sort a set of numbers into rational and irrational numbers.

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

    • 10.AN2.3 Represent using a graphic organizer, the relationship among the subsets of the real numbers (natural, whole, integer, rational, irrational).

      • Compare rational numbers (9-A.2)

    • 10.AN2.4 Determine an approximate value of a given irrational number.

    • 10.AN2.5 Approximate the locations of irrational numbers on a number line, using a variety of strategies, and explain the reasoning.

    • 10.AN2.6 Order a set of irrational numbers on a number line.

    • 10.AN2.7 Express a radical as a mixed radical in simplest form (limited to numerical radicands).

      • Simplify radical expressions (10-D.1)

    • 10.AN2.8 Express a mixed radical as an entire radical (limited to numerical radicands).

  • 10.AN3 Demonstrate an understanding of powers with integral and rational exponents.

    • 10.AN3.1 Explain, using patterns, why a to the m/n = (ⁿ√a)to the m squared, a ≠ 0

    • 10.AN3.2 Express powers with rational exponents as radicals and vice versa.

    • 10.AN3.4 Explain, using patterns, why a^-n = 1/aⁿ, a ≠ 0

    • 10.AN3.5 Apply the exponent laws:

      • 10.AN3.5.a (a to the m power) (aⁿ) = a to the m + n power

        • Multiplication with exponents (10-B.4)
        • Multiplication with rational exponents (10-E.2)

      • 10.AN3.5.b (a to the m power) ÷ (aⁿ) = a to the m-n power

        • Division with exponents (10-B.5)
        • Division with rational exponents (10-E.3)

      • 10.AN3.5.c (a to the m power)ⁿ = a to the mn power

        • Power rule (10-B.7)
        • Power rule with rational exponents (10-E.4)

      • 10.AN3.5.d (ab)to the m power = a to the m power b to the m power

      • 10.AN3.5.e (a/b)ⁿ = aⁿ/bⁿ, b ≠ 0 to expressions with rational and variable bases and integral and rational exponents, and explain the reasoning.

    • 10.AN3.6 Identify and correct errors in a simplification of an expression that involves powers.

Factors and Products

• Develop algebraic reasoning and number sense

  • 10.AN4 Demonstrate an understanding of the multiplication of polynomial expressions (limited to monomials, binomials and trinomials), concretely, pictorially and symbolically.

    • 10.AN4.1 Explain, using examples, the relationship between the multiplication of binomials and the multiplication of two digit numbers.

    • 10.AN4.2 Model the multiplication of two given binomials, concretely or pictorially, and record the process symbolically.

      • Multiply two binomials (10-O.8)
      • Multiply two binomials: special cases (10-O.9)

    • 10.AN4.3 Relate the multiplication of two binomial expressions to an area model.

      • Multiply two polynomials using algebra tiles (10-O.7)

    • 10.AN4.4 Multiply two polynomials symbolically, and combine like terms in the product.

      • Multiply polynomials (10-O.10)

    • 10.AN4.5 Verify a polynomial product by substituting numbers for the variables.

    • 10.AN4.6 Generalize and explain a strategy for multiplication of polynomials.

    • 10.AN4.7 Identify and explain errors in a solution for a polynomial multiplication.

  • 10.AN5 Demonstrate an understanding of common factors and trinomial factoring, concretely, pictorially and symbolically.

    • 10.AN5.1 Explain, using examples, the relationship between multiplication and factoring of polynomials.

    • 10.AN5.2 Express a polynomial as a product of its factors.

      • 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: special cases (10-P.6)

    • 10.AN5.3 Determine the common factors in the terms of a polynomial, and express the polynomial in factored form, concretely, pictorially and symbolically.

      • 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)

    • 10.AN5.4 Factor a polynomial and verify by multiplying the factors.

    • 10.AN5.5 Model the factoring of a trinomial, concretely or pictorially, and record the process symbolically.

      • Factor quadratics using algebra tiles (10-P.5)

    • 10.AN5.6 Identify and explain errors in a polynomial factorization.

    • 10.AN5.7 Factor a polynomial that is a difference of squares, and explain why it is a special case of trinomial factoring where b=0.

      • Factor quadratics: special cases (10-P.6)

Relations and Functions

• Develop algebraic and graphical reasoning through the study of relations

  • 10.RF1 Interpret and explain the relationships among data, graphs and situations.

    • 10.RF1.1 Describe a possible situation for a given graph.

    • 10.RF1.2 Sketch a possible graph for a given situation.

    • 10.RF1.3 Explain why data points should or should not be connected on the graph for a given situation.

    • 10.RF1.4 Graph, with or without technology, a set of data, and determine the domain and range.

      • Relations: convert between tables, graphs, mappings and lists of points (10-J.1)

    • 10.RF1.5 Determine, and express in a variety of ways, the domain and range of a graph, a set of ordered pairs or a table of values.

      • Domain and range of relations (10-J.2)

  • 10.RF2 Demonstrate an understanding of relations and functions.

    • 10.RF2.1 Represent a relation in a variety of ways.

      • Relations: convert between tables, graphs, mappings and lists of points (10-J.1)

    • 10.RF2.2 Identify independent and dependent variables in a given context.

      • Identify independent and dependent variables (10-J.3)

    • 10.RF2.3 Determine if a set of ordered pairs represents a function.

      • Identify functions (10-J.4)

    • 10.RF2.4 Explain, using examples, why some relations are not functions but all functions are relations.

    • 10.RF2.5 Sort a set of graphs as functions or non-functions.

      • Identify functions: vertical line test (10-J.5)

    • 10.RF2.6 Generalize and explain rules for determining whether graphs and sets of ordered pairs represent functions.

  • 10.RF4 Describe and represent linear relations, using:

    • 10.RF4.A words

      • Slope-intercept form: find the slope and y-intercept (10-L.5)
      • Compare linear functions: graphs, tables and equations (10-L.13)
      • Linear functions over unit intervals (10-S.4)

    • 10.RF4.B ordered pairs

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

    • 10.RF4.C table of values

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

    • 10.RF4.D graphs

      • Interpret the graph of a function: word problems (10-J.11)
      • Graph a proportional relationship (10-K.3)
      • Find the slope of a graph (10-L.2)
      • Slope-intercept form: graph an equation (10-L.6)
      • Complete a table and graph a linear function (10-L.12)
      • Standard form: graph an equation (10-L.16)
      • Point-slope form: graph an equation (10-L.19)

    • 10.RF4.E 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)
      • Write linear functions to solve word problems (10-L.11)
      • Write equations in standard form (10-L.14)
      • Point-slope form: write an equation (10-L.20)
      • Point-slope form: write an equation from a graph (10-L.21)

    • 10.RF4.1 Match corresponding representations of linear relations.

    • 10.RF4.2 Determine whether a table of values or a set of ordered pairs represents a linear relation, and explain why or why not.

      • Identify linear functions (10-L.1)

    • 10.RF4.3 Determine whether a graph represents a linear relation, and explain why or why not.

      • Identify linear functions (10-L.1)

    • 10.RF4.4 Draw a graph given a set of ordered pairs and determine whether the relationship between the variables is linear.

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

    • 10.RF4.5 Determine whether an equation represents a linear relation, and explain why or why not.

      • Identify linear functions (10-L.1)

  • 10.RF5 Determine the characteristics of the graphs of linear relations, including the:

    • 10.RF5.A intercepts

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

    • 10.RF5.B rate of change

      • Find the constant of variation (10-K.2)
      • Find the slope of a graph (10-L.2)
      • Find the slope from two points (10-L.3)
      • Slope-intercept form: find the slope and y-intercept (10-L.5)

    • 10.RF5.C domain

    • 10.RF5.D range.

    • 10.RF5.1 Determine the rate of change of the graph of a linear relation.

      • Find the constant of variation (10-K.2)
      • Find the slope of a graph (10-L.2)

    • 10.RF5.2 Determine the intercepts of the graph of a linear relation, and state the intercepts as values or ordered pairs.

    • 10.RF5.3 Determine the domain and range of the graph of a linear relation.

    • 10.RF5.4 Identify the graph that corresponds to a given rate of change and vertical intercept.

    • 10.RF5.5 Identify the rate of change and vertical intercept that correspond to a given graph.

    • 10.RF5.6 Solve a contextual problem that involves intercepts, rate of change, domain or range of a linear relation.

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

    • 10.RF5.7 Sketch a linear relation that has one intercept, two intercepts or an infinite number of intercepts.

      • Graph a proportional relationship (10-K.3)
      • Slope-intercept form: graph an equation (10-L.6)
      • Complete a table and graph a linear function (10-L.12)
      • Standard form: graph an equation (10-L.16)
      • Graph a horizontal or vertical line (10-L.18)
      • Point-slope form: graph an equation (10-L.19)

  • 10.RF8 Represent a linear function, using function notation.

    • 10.RF8.1 Express the equation of a linear function in two variables, using function notation.

    • 10.RF8.2 Express an equation given in function notation as a linear function in two variables.

    • 10.RF8.2 Express an equation given in function notation as a linear function in two variables.

    • 10.RF8.3 Determine the related range value, given a domain value for a linear function; e.g., If f(x)=3x-2, determine f(-1).

    • 10.RF8.4 Determine the related domain value, given a range value for a linear function; e.g., If g(t)=7+t, determine t so that g(t)=15.

    • 10.RF8.5 Sketch the graph of a linear function expressed in function notation.

Linear Functions

• Develop algebraic and graphical reasoning through the study of relations

  • 10.RF3 Demonstrate an understanding of slope with respect to:

    • 10.RF3.A rise and run

      • Find the slope of a graph (10-L.2)

    • 10.RF3.B line segments and lines

      • Find the slope of a graph (10-L.2)

    • 10.RF3.C rate of change

      • Find the constant of variation (10-K.2)
      • Find the slope from two points (10-L.3)

    • 10.RF3.D parallel lines

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

    • 10.RF3.E perpendicular lines.

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

    • 10.RF3.1 Determine the slope of a line segment by measuring or calculating the rise and run.

      • Find the constant of variation (10-K.2)
      • Find the slope of a graph (10-L.2)

    • 10.RF3.2 Classify lines in a given set as having positive or negative slopes.

    • 10.RF3.3 Explain the meaning of the slope of a horizontal or vertical line.

    • 10.RF3.4 Draw a line, given its slope and a point on the line.

      • Point-slope form: graph an equation (10-L.19)

    • 10.RF3.5 Determine another point on a line, given the slope and a point on the line.

      • Find a missing coordinate using slope (10-L.4)

    • 10.RF3.6 Explain why the slope of a line can be determined by using any two points on that line.

    • 10.RF3.7 Explain, using examples, slope as a rate of change.

    • 10.RF3.8 Solve a contextual problem involving slope.

    • 10.RF3.9 Generalize and apply a rule for determining whether two lines are parallel or perpendicular.

  • 10.RF6 Relate linear relations expressed in:

    • 10.RF6.A slope-intercept form y = mx + b

      • Slope-intercept form: graph an equation (10-L.6)
      • Slope-intercept form: write an equation from a graph (10-L.7)

    • 10.RF6.B general form Ax + By + C = 0

      • Standard form: graph an equation (10-L.16)

    • 10.RF6.C slope-point form y – y₁ = m(x–x₁) to their graphs.

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

    • 10.RF6.1 Express a linear relation in different forms, and compare their graphs.

      • Compare linear functions: graphs, tables and equations (10-L.13)

    • 10.RF6.2 Generalize and explain strategies for graphing a linear relation in slope-intercept, general or slope-point form.

    • 10.RF6.3 Graph, with and without technology, a linear relation given in slope-intercept, general or slope-point form, and explain the strategy used to create the graph.

      • Graph a proportional relationship (10-K.3)
      • Slope-intercept form: graph an equation (10-L.6)
      • Standard form: graph an equation (10-L.16)
      • Point-slope form: graph an equation (10-L.19)

    • 10.RF6.4 Match a set of linear relations to their graphs.

    • 10.RF6.5 Rewrite a linear relation in either slope-intercept or general form.

    • 10.RF6.6 Identify equivalent linear relations from a set of linear relations.

  • 10.RF7 Determine the equation of a linear relation, given:

    • 10.RF7.A a graph

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

    • 10.RF7.B a point and the slope

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

    • 10.RF7.C two points

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

    • 10.RF7.D 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)

    • 10.RF7.1 Determine the slope and y-intercept of a given linear relation from its graph, and write the equation in the form y = mx + b.

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

    • 10.RF7.2 Write the equation of a linear relation, given its slope and the coordinates of a point on the line, and explain the reasoning.

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

    • 10.RF7.3 Write the equation of a linear relation, given the coordinates of two points on the line, and explain the reasoning.

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

    • 10.RF7.4 Graph linear data generated from a context, and write the equation of the resulting line.

    • 10.RF7.5 Solve a problem, using the equation of a linear relation.

      • Write linear functions to solve word problems (10-L.11)
      • Find the distance between a point and a line (10-L.24)
      • Find the distance between two parallel lines (10-L.25)

    • 10.RF7.6 Write the equation of a linear relation, given the coordinates of a point on the line and the equation of a parallel or perpendicular line, and explain the reasoning.

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

Systems of Linear Equations

• Develop algebraic and graphical reasoning through the study of relations

  • 10.RF9 Solve problems that involve systems of linear equations in two variables, graphically and algebraically.

    • 10.RF9.1 Model a situation, using a system of linear equations.

    • 10.RF9.2 Relate a system of linear equations to the context of a problem.

      • Solve a system of equations by graphing: word problems (10-M.3)
      • Solve a system of equations using substitution: word problems (10-M.9)
      • Solve a system of equations using elimination: word problems (10-M.11)
      • Solve a system of equations using any method: word problems (10-M.13)

    • 10.RF9.3 Explain the meaning of the point of intersection of a system of linear equations.

    • 10.RF9.4 Determine and verify the solution of a system of linear equations graphically, with and without technology.

      • 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)

    • 10.RF9.5 Solve a problem that involves a system of linear equations.

      • Solve a system of equations by graphing: word problems (10-M.3)
      • Solve a system of equations using substitution: word problems (10-M.9)
      • Solve a system of equations using elimination: word problems (10-M.11)
      • Solve a system of equations using any method: word problems (10-M.13)

    • 10.RF9.6 Determine and verify the solution of a system of linear equations algebraically.

      • 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)

    • 10.RF9.7 Explain a strategy to solve a system of linear equations.

    • 10.RF9.8 Explain, using examples, why a system of equations may have no solution, one solution or an infinite number of solutions.