Appendix D: Assessment and Evaluation - Samples
Sample 4: Essentials of Mathematics 10

Topic: Wages, Salaries, and Expenses

Prescribed Learning Outcomes:

Problem Solving

It is expected that students will:

• solve problems that involve a specific content area
• solve problems that involve more than one content area
• solve problems that involve mathematics within other disciplines
• analyze problems and identify the significant elements
• demonstrate the ability to work individually and cooperatively to solve problems
• 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

Wages, Salaries and Expenses

It is expected that students will:

• calculate hours worked and gross pay
• calculate net income using deduction tables with different pay periods
• calculate changes in income
• develop a budget that matches predicted income

Unit Focus

The overall goal of the unit was to familiarize students with the use of budgets to more effectively manage income. Assessment required students to demonstrate their ability to read and comprehend problems whose components contained income calculations, deduction estimation, changes in income, and budget creation.

Planning the Unit

To develop the unit, the teacher:

• determined the overall goals of the unit
• identified the related IRP outcomes to be targeted in the unit
• identified the prerequisite knowledge and skills students needed to achieve the targeted outcomes included in this unit, and planned for review
• looked for ways to connect students' learning with other desirable outcomes, including those associated with students' attitudes
• looked for ways to encourage students' understanding of the ways in which practical problems are solved mathematically
• planned a variety of integrated instructional and assessment activities to help students achieve identified outcomes
• determined criteria with which to evaluate students' learning for marking and reporting purposes. Whenever appropriate, the teacher involved the students in setting evaluation criteria.
• developed with students a rubric that would be used to mark the unit project and its presentation. The development of the rubric's criteria as done as early as possible and with the purpose of promoting the students understanding of the work that they were expected to accomplish.

The Unit

Recalling, Reviewing and Extending Relevant Concepts

• To review and evaluate students' understanding of calculations of hours worked, the teacher presented a 24-hour clock scenario and had students fill out time cards indicating the times they arrived and left work. The teacher then had students calculate the hours worked per shift. The teacher gradually introduced time sheets involving split shifts and overtime to the students. The teacher then added the concept of calculating gross pay using a calculator.

Peer Assessment - Students were encouraged to check a partner's calculations of both time spent at work and calculations of gross pay.

Assessment Strategies - the teacher assessed the student's development of completing time sheets and finding gross pay. The teacher viewed the student's work and gave feedback on the appropriateness of their representations.

Creating a Budget

• The teacher had students research jobs that they might expect to have upon completion of high school. Students found the hourly pay associated with one particular job of their choice. As the students considered the job opportunities available to them, the teacher encouraged students to consider the type of lifestyle they would expect to have given their career choice.
• The teacher then had students assume a typical week and asked them to calculate their gross income for that week. Using deduction tables provided by the teacher, the student then calculated take home pay.
• The students were asked to consider typical weekly expenses. Using budget tables provided to them, the students estimated expenses such as rent, utilities, food, telephone, and transportation costs. The total estimated weekly expenses were calculated and checked with a partner.
• With the teacher's guidance, the students then reconciled their calculated take home pay with their estimated expenses and produced an acceptable budget.
• The teacher asked students to create a new budget based on a 10% increase in income that resulted from a student taking extra training or education.

Teacher Review - As student understanding of ways in which income could be managed grew, initiating retirement or education savings plans was discussed. In as much as possible students were asked to apply their learning to new a variety of practical financial problems.

Peer, Small Group, and Teacher Assessment - Students were asked at various developmental stages to report their concepts in a small group setting. Members of the group were asked to provide feedback to the reporter.

The teacher created an environment that encouraged students to participate fully in the development of individual budgets, goal setting and planning.

The demonstration of student's abilities to meet the prescribed learning outcomes was encouraged by reporting on the student's individual ability to use appropriate strategies to estimate and produce realistic and workable budgets. Students were also required to effectively communicate how they arrived at their estimates and what their goals were as well as how their goals affected their budgets.

Using Performance Activities in Instruction

To help students understand various ways of creating viable budgets, students were asked to experiment with making changes to a budget and seeing what effect that had on the complete picture. For example, students were asked to find the effect of buying a car on their ability to save. Other students were asked to find the effect of working overtime on their budgets. Students were asked to comment on the effect of a windfall such as a cash gift or income tax refund on their budget. Some students were able to use spreadsheets to more effectively manage their data and consider changes.

Defining the Criteria

Mathematical Thinking

To what extend do students:

• demonstrate an ability to fill in time sheets and find gross pay.
• use deduction tables to find net pay
• calculate the net effect of pay rate changes
• create rationalized budgets

Unit Test

Students were given a carefully constructed test that initially required them to show an understanding of time sheets, and how to find net and gross pay. Students were then required to show how a time sheet could be used to estimate average weekly take home pay, given access to deduction tables. Students were given a list of expenses for an individual whose time sheet was provided. Students were then assessed on their ability to create a workable budget for that individual.

Self Assessment

Students' assessment of their understanding of the budgeting process included a written explanation of how they would go about creating a budget, given an hourly pay rate and access to typical housing costs and other expenses.

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Revised: September 2001

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