High School Block:

Geometry, Measurement and Finance 10

Geometry, Measurement and Finance 10 provides foundations for further study in mathematics and along mathematics pathways, and includes concepts in geometry and measurement, and develops financial literacy. Learners will relate the properties and principles of lines and angles; compare and apply systems of measurement; apply financial literacy concepts to personal financial decisions and wellness; apply formulae to solve problems. Learners will enact and apply prior Mathematics K-9 knowledge, and personal financial decision-making and wellness knowledge from Personal Wellness 6-8 curriculum. Geometry, Measurement and Finance 10 is the final compulsive mathematics course in New Brunswick.

Topics include Pythagorean Theorem; polygons; angles; trigonometric ratios; metric and imperial systems of measurement; surface area and volume; unit pricing; currency exchange; income (gross and net pay); credit cards; loans; interest.

Mathematics 9 is recommended before enrolling in Geometry, Measurement and Finance 10.

For Educators:

CONTEXTS AND CONCEPTS

Synthesis

Strategies

  • Using algorithms, mental procedures, technology/tools, and other strategies
  • Determining appropriate units of measure and precision
  • 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
  • Deriving, manipulating, and applying formulae
  • Using calculators
  • Modeling and using simulations
  • Extrapolation and interpolation
  • Using area tiles
  • Order and angle of rotation
  • Working with line and rotational symmetry
  • Calculate gross and net pay and determine deductions
  • Calculate interest and transactions

Fluency

  • Conversion between formats, representations, and equivalents of numbers
  • Ways to present information/data
  • Similarity
  • Scale
  • Calculating unit price
  • Working with complementary and supplementary angles
  • Working with transversals and pairs of congruent and supplementary angles
  • Système International d’Unités (SI)
  • Imperial system of measurement

Communication

  • Using variable terms and constant terms
  • Using coefficients, exponents, powers, and bases
  • Using terms income, wage, piecework, salary, and commission
  • Using terms principal, interest rate, simple interest, term, compound interest, and compounding period
  • Using terms credit, down payment, finance charge, charge for purchase, cash advance, principal amount, amortization period, line of credit, and overdraft protection
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GRADE 10

Strand: Patterns and Relations

Big Idea: Algebra

Skill Descriptor: Solve contextual problems that require the manipulation and application of formulae.

Global Competencies: CM, CTPS

Achievement Indicators:

  • Apply formulae that do, and do not, require manipulation
  • Explain, using algebraic rules, why different forms of the same formula are equivalent
  • Create formulae
  • Identify and correct errors in solutions to problems that involve a formula

Strand: Number

Big Idea: Financial Applications

Skill Descriptor: Solve problems that involve unit pricing and currency exchange using proportional reasoning.

Global Competencies: CM, CTPS, ICE, SASM

Achievement Indicators:

  • Calculate and compare unit prices and relative costs of goods and services
  • Identify and evaluate purchasing choices and explain in terms of cost and other factors
  • Identify and calculate different sales promotion techniques
  • Calculate the percentage change of the original price when applying discounts, taxes, and tips
  • Solve currency exchange problems using proportional reasoning, charts, tables or formulas
  • Explain the meaning of the difference between the selling and purchasing rates for currency exchange
  • Explain how to estimate the cost of items in Canadian currency while in other nations, and justify the importance of the skill

Skill Descriptor: Apply the understanding of income to calculate gross pay and net pay.

Global Competencies: CM, CTPS, ICE, SASM

Achievement Indicators:

  • Identify and describe the contexts of different methods of earning income
  • Describe the advantages and disadvantages of given methods of earning income
  • Calculate, in decimal form, from a time schedule, total time worked in hours and minutes
  • Calculate time worked from different types of schedules
  • Calculate gross pay from different methods of earning income
  • Explain the difference between gross pay and net pay
  • Calculate the Canadian Pension Plan (CPP), Employment Insurance (EI) and Income Tax deductions for given gross pay
  • Calculate net pay when given non-taxable deductions
  • Identify and explain errors in solutions to problems that involve gross or net pay

Skill Descriptor: Apply the understanding of financial institution services used to access and manage personal finances.

Global Competencies: CM, CTPS, ICE, SASM

Achievement Indicators:

  • Describe the type of banking services available from various financial institutions
  • Identify the type of banking account that best meets the needs for given sets of criteria
  • Identify and explain various service charges
  • Describe the types of online banking services
  • Describe the advantages and disadvantages of types of digital transactions
  • Describe ways that ensure the security of personal financial information

Skill Descriptor: Apply the understanding of simple and compound interest.

Global Competencies: CM, CTPS, ICE, SASM

Achievement Indicators:

  • Solve simple interest problems with and without manipulating a formula
  • Explain the difference between simple and compound interest
  • Solve problems by applying the compound interest formula:
  • A = P (1 + (r ⁄ n))nt
  • Explain the effect of different compounding periods on calculations of compound interest

Skill Descriptor: Apply the understanding of credit options.

Global Competencies: CTPS, ICE, SASM

Achievement Indicators:

  • Compare advantages and disadvantages of different types of credit options
  • Explore and make informed decisions related to the use of credit
  • Solve problems involving credit cards or loans, and sales promotions

Strand: Shape and Space

Big Idea: Trigonometry

Skill Descriptor: Apply the understanding of primary trigonometric ratios.

Global Competencies: CTPS

Achievement Indicators:

  • Show that the ratios of the length of any two sides are equal for specified acute angles in sets of similar right triangles
  • Generalize a formula for the primary trig ratios
  • Solve problems using the primary trigonometric ratios that involve context or application for side lengths and angles
  • Determine if solutions to problems that involve primary trigonometric ratios are reasonable

Big Idea: Geometry

Skill Descriptor: Apply the understanding of the Pythagorean theorem.

Global Competencies: CM, CTPS

Achievement Indicators:

  • Verify the Pythagorean Theorem
  • Describe historical and contemporary applications of the Pythagorean Theorem
  • Determine if given triangles are right triangles, using the Pythagorean Theorem
  • Explain how side length ratio can be used to prove a triangle is a right triangle
  • Apply Pythagorean triples to determine if corners are square (90o)
  • Solve problems using the Pythagorean Theorem

Skill Descriptor: Apply the understanding of angle relationships between parallel, perpendicular and transversal lines.

Global Competencies: CTPS

Achievement Indicators:

  • Justify lines as perpendicular, parallel or neither
  • Illustrate and label complementary and supplementary angles
  • Identify and correct errors involving sets of angles that are not complementary or supplementary
  • Identify and name pairs of angles formed by parallel lines and transversals
  • Identify problems from given sets where angle relationships can be applied
  • Solve problems that determine the measures of angles involving parallel lines and transversals

Skill Descriptor: Apply the understanding of angles by drawing, replicating and constructing, bisecting, and solving problems.

Global Competencies: CTPS

Achievement Indicators:

  • Identify angles with various measures
  • Estimate the measure of given angles, using 30°, 45°, 60°, 90° and 180° as referent angles
  • Sketch angles based on referent angles
  • Measure angles in various orientations
  • Replicate and bisect angles precisely using a variety of methods

Big Idea: Measurement

Skill Descriptor: Describe the relationships of base units within Système International (SI) measurements.

Global Competencies: CTPS

Achievement Indicators:

  • Identify the base units of measurement in the SI system
  • Identify contexts that involve SI system measurements
  • Explore the relationships between and match the prefixes used for SI units of measurement within the base ten system
  • Demonstrate how and why decimals are used in converting between SI measurements
  • Convert between SI units

Skill Descriptor: Describe the relationships of units within Imperial System measurements.

Global Competencies: CTPS

Achievement Indicators:

  • Identify the units of measurement in the Imperial system
  • Identify contexts that involve Imperial system measurements
  • Explore the relationships between and sort Imperial units of measurement
  • Convert between Imperial units

Skill Descriptor: Solve problems using linear SI and Imperial measurements and verify solutions.

Global Competencies: CM, CTPS

Achievement Indicators:

  • Provide reasonable referents for linear measurements
  • Identify SI and Imperial units that are of similar magnitude (but not equivalent)
  • Justify estimates for a linear measurement
  • Justify choices of units used when determining linear measurements
  • Use linear measurement instruments
  • Describe and explain personal strategies used to determine complex linear measurements
  • Convert between SI and Imperial Systems
  • Identify and explain errors in SI and Imperial conversions
  • Evaluate the reasonableness of solutions to a conversion problems

Skill Descriptor: Solve problems that involve area using SI and Imperial measurements and verify the solutions.

Global Competencies: CTPS

Achievement Indicators:

  • Provide reasonable referents for area measurements
  • Justify estimates for area measurements
  • Justify the choice of units used when determining area measurements
  • Estimate area using square grids
  • Convert between squared units
  • Apply formulae for determining area of regular, composite, and irregular 2D shapes, including circles

Skill Descriptor: Solve problems involving 3D objects using surface area and volume SI and Imperial measurements and verify the solutions.

Global Competencies: CTPS

Achievement Indicators:

  • Visually represent and label surface area and volume of 3D objects
  • Determine surface area and volume of 3D objects
  • Solve for a single unknown dimension for surface area and volume problems that do and do not require manipulation
  • Solve surface area and volume problems that involve composite 3D objects
  • Describe the relationship between 3D objects that have the same base and height but different shapes.
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