High School Block:

Number, Relations and Functions 10

Number, Relations, and Functions 10 provides foundations for more complex mathematical reasoning and/or calculus and includes number properties, algebra, and functions. Learners will analyze numbers and model factoring; graph and describe relationships between variables; analyze functions; apply understanding of systems of linear equations to solve problems. Learners will enact and apply prior Mathematics K-9 knowledge. This course develops pathways to further studies in mathematics and/or preparatory skills for calculus.

Topics include prime factors; common factors; square and cube roots; irrational numbers; integral and rational exponents; polynomial expressions; trinomial factoring; linear relations and functions; slope; distance formula; and midpoint formula.

Mathematics 9 is recommended before enrolling in Number, Relations and Functions 10.

For Educators: Number, Relations and Functions 10 Companion Document

CONTEXTS AND CONCEPTS

Synthesis

Strategies

  • Using algorithms, mental procedures, technology/tools, and other strategies
  • Using the most efficient strategies
  • Determining the reasonableness of the answer and explaining thinking
  • Verifying solutions with substitution
  • Simplifying
  • Comparing

Processes

  • Deriving mathematical rules and algorithms
  • Using calculators
  • Modeling and using simulations
  • Working with exponent laws
  • Extrapolation and interpolation
  • Using area tiles
  • Determining domain and range
  • Prime factorization
  • Derive distance and midpoint formulae

Fluency

  • Conversion between formats, representations, and equivalents of numbers
  • Ways to present information/data
  • Similarity
  • Working with factors, prime factors, greatest common factors, least common multiples, perfect squares, and perfect cubes

Communication

  • Continuous and discrete data
  • Using variable terms and constant terms
  • Using coefficients, integral and rational exponents, powers, and bases
  • Working with irrational and rational numbers
  • Polynomial expressions
  • Using degrees of terms and degrees of polynomials
  • Using titles, labels for axes, values
  • Using the terms natural, whole, and real numbers, and integers
  • Using the terms radicand, index, numerical coefficient, entire and mixed radical
  • Using the terms function and relation
  • Express intercepts
  • General form
  • Slope-intercept form
  • Slope-point form
  • Function notation
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GRADE 10

Strand: Number

Big Idea: Number Sense

Skill Descriptor: Use prime factorization to solve problems.

Global Competencies: CTPS

Achievement Indicators:

  • Determine the prime factors of whole numbers
  • Express numbers as products of their primes
  • Justify why zero and one are not prime numbers
  • Determine the greatest common factor or least common multiple of sets of whole numbers with and without technology
  • Determine whether given whole numbers are perfect “nths”
  • Determine the root of numbers
  • Model situations and their solutions using prime factorization

Skill Descriptor: Analyze irrational numbers.

Global Competencies: CTPS

Achievement Indicators:

  • Classify numbers into their subset(s) by their number properties
  • Identify the parts of radical expressions
  • Approximate the values of irrational numbers
  • Order sets of irrational numbers on number lines
  • Convert between entire and mixed radical forms (limited to numerical radicands)

Big Idea: Algebra

Skill Descriptor: Apply exponent laws to integral and rational components.

Global Competencies: CTPS

Achievement Indicators:

  • Express values with negative and positive exponents
  • Express values with rational exponents and radicals
  • Convert between radical form and exponential form using exponent laws
  • Simplify expressions involving exponent laws or radicals
  • Evaluate exponential expressions with numerical bases
  • Convert between exponential and radical forms
  • Simplify radical and exponential expressions

Skill Descriptor: Multiply polynomial expressions symbolically.

Global Competencies: CTPS

Achievement Indicators:

  • Model the multiplication of polynomials
  • Verify polynomial products
  • Simplify the products of polynomials
  • Justify strategies for multiplication of polynomials

Skill Descriptor: Express polynomials as a product of its factors symbolically.

Global Competencies: CTPS

Achievement Indicators:

  • Determine the greatest common factor of polynomial expressions
  • Model the factoring of polynomials
  • Factor difference of squares
  • Verify the factors of polynomials
  • Justify strategies used to factor trinomials

Strand: Relations and Functions

Big Idea: Algebraic and Graphical Reasoning

Skill Descriptor: Describe the relationships among data, graphs and situations.

Global Competencies: CTPS

Achievement Indicators:

  • Graph sets of data
  • Sketch graphs for given situations
  • Describe the domain and range of relations
  • Classify data as discrete or continuous
  • Describe possible situations for a given graphs

Skill Descriptor: Apply the understanding of relations and functions.

Global Competencies: CTPS

Achievement Indicators:

  • Identify functions from given sets of relations
  • Justify a strategy for determining if a relation is a function

Skill Descriptor: Solve problems involving the rate of change of linear relations.

Global Competencies: CTPS

Achievement Indicators:

  • Classify slopes of line segments as positive, negative, zero or
    undefined
  • Calculate the slopes of line segments
  • Prove that the slopes of line segments are constant
  • Describe the properties of horizontal and vertical lines
  • Identify rate of change for given situations
  • Draw lines given their slope and a point on the lines
  • Determine another point on lines given the slope and a point on the lines
  • Describe the properties of parallel and perpendicular lines

Skill Descriptor: Describe and represent linear relations.

Global Competencies: CTPS

Achievement Indicators:

  • Identify independent and dependent variables in a variety of contexts
  • Justify if relations are linear or non-linear
  • Match corresponding representations of linear relations

Skill Descriptor: Determine the characteristics of linear relations.

Global Competencies: CTPS

Achievement Indicators:

  • Determine the intercepts of linear relations
  • Determine the slope of linear relations from given equations
  • Express the domain and range of linear relations using a variety of notations
  • Solve problems involving the characteristics of linear relations

Skill Descriptor: Relate linear equations to their graphs.

Global Competencies: CTPS

Achievement Indicators:

  • Justify a strategy for graphing linear equations in given forms
  • Graph linear relations from equations
  • Convert between equivalent linear forms
  • Match sets of linear relations to their graphs

Skill Descriptor: Determine the equation that models a linear relation.

Global Competencies: CTPS

Achievement Indicators:

  • Determine the equations of linear relations in slope-intercept form (graphs; data sets; contexts; parallel/perpendicular lines)
  • Determine the equations of linear relations in slope-point form (graphs; data sets; contexts; parallel/perpendicular lines)
  • Determine the equations of the line of best fit from scatter plots
  • Solve problems using the equations of linear relations

Skill Descriptor: Determine the characteristics of a line segment.

Global Competencies: CTPS

Achievement Indicators:

  • Determine the distance between two points on a Cartesian plane
  • Determine the midpoint of a line segment given the endpoints of the segment
  • Determine an endpoint of a line segment, given the other endpoint and the midpoint
  • Solve problems involving distance between two points or midpoint of a line segment

Skill Descriptor: Analyze functions using function notation.

Global Competencies: CTPS

Achievement Indicators:

  • Express functions as an equation with two variables and in function notation
  • Determine range values given domain values for functions
  • Determine domain values given range values for functions
  • Sketch graphs of linear functions expressed in function notation

Skill Descriptor: Solve problems that involve systems of linear equations.

Global Competencies: CM, CTPS, ICE

Achievement Indicators:

  • Model situations using systems of linear equations
  • Relate systems of linear equations to the context of the problems
  • Determine solutions of systems of linear equations graphically and algebraically
  • Verify solutions of systems of linear equations algebraically
  • Explain the meaning of the point of intersection given contexts
  • Justify why systems of equations may have no solution, one solution or an infinite number of solutions
  • Justify strategies to solve systems of linear equations
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