Appendix D: Assessment and Evaluation - Samples
Sample 5: Essentials of Mathematics 11

Topic: Owning and Operating a Vehicle

Prescribed Learning Outcomes:

Problem Solving

It is expected that students will:

• analyse problems and identify the significant elements
• develop specific skills in selecting and using an appropriate problem-solving strategy or combination of strategies chosen from, but not restricted to, the following:
• guess and check
• look for a pattern
• make a systematic list
• make and use a drawing or model
• eliminate possibilities
• work backward
• simplify the original problem
• develop alternative original approaches
• analyse keywords
• determine that their solutions are correct and reasonable
• clearly communicate a solution to a problem and the process used to solve it
• use appropriate technology to assist in problem solving

Owning and Operating a Vehicle

It is expected that students will:

• solve problems involving the acquisition and operation of a vehicle including
• renting
• leasing
• buying
• licensing
• insuring
• operating (e.g., fuel and oil)
• maintaining (e.g., repairs, tune-ups)

In addition to these outcomes, the teacher assessed students' attitudes, group work, and communication skills.

Unit Focus

The teacher's overall goal for this unit was to help students develop mathematical tools to calculate and analyse the costs associated with acquiring and operating a vehicle. To introduce and reinforce new concepts, the teacher provided concrete examples and guided practice, and prompted discussions of real-world applications. The teacher designed activities to assess students' application of concepts, mathematical thinking, and problem-solving and communication skills.

Planning the Unit

To develop the unit, the teacher:

• identified the prescribed learning outcomes for this unit
• examined the specific prerequisite knowledge and skills needed to achieve these outcomes
• determined which prerequisites were already in place and which should be reviewed
• looked for ways to connect students' learning to other desirable learning outcomes, including those associated with problem solving, communication skills, and attitudes
• identified criteria to evaluate students' learning
• designated assessment that was an integral part of the instructional process

The Unit

Leasing and Buying Vehicles

• Students were given advertisements taken from newspapers and magazines that displayed the costs of leasing vehicles. Working as a class, students identified monthly costs, fixed costs (e.g., down-payments, security payments, levies, taxes) and special costs ( e.g., mileage costs)
• The teacher presented students with different scenarios for leasing vehicles (e.g., length of leases, driving over the allowable mileage limit, paying different down-payments) and asked the class to calculate the costs of leasing in each scenario.
• The class then found advertisements for vehicles that could be appealing to younger consumers. The teacher asked students to:
• present the cost of leasing the vehicle for a set amount of time
• find a cost of leasing that could be used to compare to other forms of transportation
• determine how much of a personal budget leasing a vehicle would consume
• The teacher used the same process to develop students' understanding of purchasing a vehicle. The teacher and students investigated how the purchase price of a vehicle is not actually the amount of money paid for a vehicle, unless it was paid for in cash.
• Students worked with spreadsheets and programmable calculator lists to discover that monthly payments consisted of finance charges and reductions to the principle amount of the loan. To help the students' understanding, the teacher assigned students to use spreadsheet templates to calculate the interest paid in paying off a loan.
• When students had more of an understanding of the nature of loans, the teacher guided them to discover how the length of loan, the size of the monthly payments and the interest rates affected the total paid on a loan
• A loan manager from a credit institution was invited in to discuss the advantages and disadvantages of leasing and purchasing, and then worked together to compile pertinent points.
• Teacher guided students in a discussion on a costs and benefits of extended warranty.

Licensing and Insuring

• The teacher, using pamphlets supplied by an insurance broker, worked with students to help them:
• learn basic insurance terminology (e.g., basic coverage, liability, third-party, no-fault, comprehensive, safe driver discount)
• calculate basic and optional insurance costs
• When students had a firm understanding of insurance costs, the teacher guided them to discover how different vehicles had different insurance requirements and costs. The teacher had students research why some vehicles had higher insurance and license costs, and how these costs could affect purchasing decisions.
• Students worked with the teacher to calculate safe-driving discounts, and then worked independently on a number of application problems based on years of safe driving.

Operating and Maintaining

• Students were given examples of real-life scenarios of operating a vehicle (e.g., 24,000 km of driving in one year). Working as a class, students estimated the costs of operating a vehicle (e.g., gas and oil), and converted the cost to cost per kilometre.
• Using supplied material on maintenance intervals, the class worked to develop a chart of the costs of operating the vehicle based on:
• tire life and replacement costs
• tune-ups and oil changes
• insurance and license costs

Applying Concepts in Other Curriculum Areas

• The teacher demonstrated to the class how personal loans and mortgages were calculated and applied in similar fashion to automobile purchase loans. The students then used spreadsheet templates to calculate various mortgages.

Defining the Criteria

Mathematical Thinking

To what extend do students:

• demonstrate an understanding in the difference of monthly costs and fixed costs in a lease
• demonstrate facility in solving loans (e.g., time, total paid, interest costs) using templates or appropriate technology
• demonstrate facility in solving application problems involving insurance requirements and safe-driver discounts
• demonstrate facility in estimating operating costs per year or per kilometre

Attitudes

To what extend do students:

• approach problem situations with confidence
• show a willingness to persevere in solving difficult problems
• show flexibility in using available resources (e.g., calculators, Internet, outside expertise, help from other students or the teacher )
• contribute to class discussions and problem solving sessions

Group Skills

To what extent do students:

• communicate ideas clearly and efficiently
• work with other students in whole-class and small-group discussions to build on ideas and reinforce understanding
• present logical arguments to support their conclusions
• listen to the ideas of other students and respond appropriately

Assessing and Evaluating Performance

Observing and Questioning

The teacher assessed students' understanding, attitudes, and group skills informally throughout the unit.

The teacher:

• observed students as they participated in class and small-group activities, taking note of behaviour that indicated whether they were achieving the criteria established for the unit
• asked questions to assess students' understanding of the central concepts
• moved through the class, observing students' work, encouraging their efforts, and listening to comments as they worked in small groups. (The teacher knew students were involved in the unit when they made comments such as "Maybe we should try ..." or "I wonder what would happen if ...")

Journal Entries

The teacher had students paste in their mathematical workbooks examples of leasing and purchasing vehicles. Students used these examples to create problems for other students within small groups to solve. (Each group had to be able to solve the challenges it designed.) The teacher reviewed the work created by each group and evaluated the complexity and appropriateness of the problems as an indication of students' understanding of the concepts included in the unit.

Lease or Purchase Project

Students chose a vehicle from an advertisement that featured a lease and purchase plan. The students calculated the total cost of leasing and buying including all hidden costs and taxes. Students worked on deciding whether leasing or purchasing was preferable, and were encouraged to express their answers in cents per kilometre.

A loan manager from a credit institution was invited to the class to show students how to complete a loan application, as well as discuss the implications of leasing, buying new and buying used.

Students and the teacher perused the finished projects, and worked together to find discrepancies in the projects. Students were assigned points on a scale of 1 to 5 for each of the following criteria:

Summary Sheets

Prior to instruction, the teacher gave students summary sheets designed to provide a reference and study guide for future use. Students could use one sheet for comparing the costs of mandatory and optional insurance and licensing costs including:

• mandatory basic coverage
• third-party coverage
• collision
• comprehensive
• safe driving discount
• other features of coverage (e.g., loss of vehicle costs, medical)

Another summary sheet could contain costs of leasing and purchasing including:

• down payment
• damage and security costs
• battery and tire levies
• transportation and dealer preparation costs
• options
• provincial and federal taxes
• tune-ups and maintenance costs
• extended warranty

The teacher assigned marks on the summary sheets based on the clarity, thoroughness and accuracy of students' responses. Written feedback was provided, and students were given the opportunity to make corrections and resubmit their sheets for improved grades.

Solving Problems

The teacher used a performance scale to evaluate students' abilities to solve problems and present their conclusions.

Previous Page Next Page

Revised: September 2001

  BC Ministry of Education Home Page