### Course Outline

Mathematics Essentials 10 is a graduation level high school mathematics course. Students will explore the following topics:

- Earning and Purchasing
- Banking
- Measurement
- Geometry
- Transportation and Travel
- Probability

#### Earning and Purchasing

- understand purchasing power.
- determine the renumeration for chosen occupations, including salary and benefits, and evaluate it in terms of purchasing power and living standards.
- solve problems involving various ways that an employee can be paid using calculators or appropriate software.
- explain the difference between gross pay and net pay, and describe possible payroll deductions.
- calculate gross pay and net pay for given situations.
- read and apply payroll deduction tables.
- identify the information and documents required for filing a personal income tax return, and explain why they are required (optional).
- describe the effects on personal spending habits of the frequency of pay period.
- estimate and calculate the unit prices of comparable items to determine the best buy.
- explain indirect and direct forms of taxation.
- solve problems involving the estimation and calculation of provincial and federal sales taxes.
- estimate and calculate selling price, discounts, and taxes.
- provide the correct change for an amount offered and minimize the number of coins/bills.
- select amounts to offer for a given charge to minimize the number of coins/bills received in the change.
- identify and explain the advantages and disadvantages of various plans to make purchases.
- identify, calculate, and compare the interest costs involved in making purchases under various plans.
- make decisions regarding the purchase of costly items by identifying and ranking criteria for the comparison of possible choices.
- make decisions regarding the payment options for purchases.
- identify various incentives to make purchases.
- estimate and calculate the price in Canadian funds of items bought in or ordered from another country.

#### Banking

- understand transactions such as depositing, transferring and withdrawing money, writing cheques and withdrawing money.
- understand how interest is calculated by a bank.
- calculate simple and compound interest.
- recognize patterns in tables where simple interest has been calculated.

#### Measurement

- demonstrate a working knowledge of the metric system and imperial system.
- measure lengths accurately, using metric system and the imperial system.
- estimate distances in metric units and in imperial units by applying personal referents.
- estimate capacities in metric units by applying personal referents.
- estimate, with reasonable accuracy, large numbers that are illustrated visually and explain the strategies used.
- recognize and apply the patterns in the metric system.
- recognize and apply the common fraction patterns found on an Imperial ruler.
- recognize and find equivalencies among common fractions and percent.
- compare and order common fractions and percent.
- rename common fractions.
- round rational numbers and percent in contexts.

#### Geometry

- identify the first 5 regular polygons and understand basic properties (# of sides, lines of symmetry, and definitions of geometric terms).
- describe and apply translations, reflections, rotations, and dilatations as they relate to symmetry and design, with the aid of technology.
- determine (through investigations, using concrete materials and technology) the characteristics of shapes that will tile the plane with a reflecting pattern.
- create designs involving tiling patterns (e.g., Escher-type designs, wallpaper or fabric designs), using technology (e.g., dynamic geometry software, design or drawing software).
- analyse the geometric aspects of logos and design.
- create a personal logo, using the mathematics of symmetry, translations, reflections, rotations, or dilations, with the aid of technology.

#### Transportation and Travel

- describe the procedures and costs involved in obtaining a driver’s license.
- describe the costs if failing to operate a vehicle responsibly.
- calculate the fixed and variable costs involved in owning and operating a vehicle.
- compare the procedures, costs, advantages, and disadvantages involved in buying a new versus a used vehicle.
- explain the factors and costs involved in insuring a vehicle.
- make personal decisions regarding the best form of transportation.
- compare the costs involved in buying versus leasing the same new vehicle.
- compare the costs of owning or leasing and maintaining vehicle with the costs of other forms of transportation.
- complete a project involving the purchase or lease of a new vehicle or the purchase of a used vehicle, including the cost of insurance.

#### Probability

- express probabilities of simple events as the number of favourable outcomes divided by the total number of outcomes.
- express probabilities as fractions, decimals, and percent, and interpret probabilities expressed in each of these forms.
- predict and describe the results obtained in carrying out probability experiments related to familiar situations involving chance.
- compare predicted and experimental results for familiar situations involving chance, using technology to extend the number of experimental trials.
- simulate familiar situations involving chance and explain the choice of simulation
- interpret information about probabilities to assist in making informed decisions in a variety of situations.
- interpret and assess probabilistic information used in the media and in common conversation.

**Updated August 24, 2021**