F1. Financial Decisions
Specific Expectations
Financial Decisions
F1.1
identify a past or current financial situation and explain how it can inform financial decisions, by applying an understanding of the context of the situation and related mathematical knowledge
- financial situations that students may identify:
- systemic, current, or historical events and issues, or economic shifts, that happen at a global, national, local, or individual level
- considerations for understanding the context of the situation to inform financial decisions:
- What factors contribute to a financial situation?
- Who does the financial situation affect?
- What factors contribute to a financial decision?
- Who has the ability to make decisions as a result of the situation?
- Who is affected by the decisions?
- What are the impacts of the decisions?
- What aspect of mathematics is helpful in order to understand the situation and the decisions that might be made?
- related mathematical knowledge:
- proportional reasoning
- operation sense
- linear and non-linear relations
- graphical analysis
- data analysis
Teachers can:
- facilitate students’ sharing of the financial situations they are exploring, in a safe, supportive, and inclusive environment that is free of judgement and respects family, community, and cultural expectations, practices, and perspectives;
- be flexible and create space for discussions based on authentic and relevant opportunities as they emerge from current social issues;
- ensure that all examples of financial situations discussed, although authentic and connected to students’ realities, are generalized or fictionalized and free of judgement;
- provide students with access to a variety of print and digital resources to research financial situations;
- support students in making connections between the financial situations they are exploring and mathematical concepts they are learning throughout the course.
- What are some past or current financial situations, events, or issues that have had an impact on your local communities, country, or the world at large?
- What factors contributed to this financial situation and who does/did it affect?
- What are some of the impacts of this situation and the decisions around it?
- What sources could you use to gather more information about the context of the situation?
- What mathematics could you use to better understand this situation and its impact?
- What mathematics would you need to learn more about to better understand this situation and its impact?
Have students brainstorm financial situations and then, in groups or with a partner, choose a situation to discuss more thoroughly. Ask them to identify what mathematical concepts would be helpful in understanding the situation and the decisions that might be made. (See the Examples for questions that students might consider in their discussion.)
F1.2
identify financial situations that involve appreciation and depreciation, and use associated graphs to answer related questions
- financial situations that involve appreciation or depreciation of assets over time:
- the purchase, ownership, or sale of:
- collectibles
- electronic goods
- vehicles
- real estate
- stocks and other investments
- the purchase, ownership, or sale of:
Teachers can:
- compile a list of relevant student-generated examples through class discussions about goods or assets that appreciate and depreciate;
- ensure that the examples are authentic and relevant to students’ lives, by drawing from topics generated by students;
- provide opportunities for students to:
- interpret graphs that show appreciation or depreciation, including identifying possible causes for the trends, making predictions about future trends, and discussing possible implications;
- make connections to characteristics of linear and non-linear relationships, including exponential relationships, such as increasing and decreasing trends and rates of change when interpreting graphs (see C3.1).
- What are some examples of assets that appreciate or depreciate?
- What might affect the rate at which an asset appreciates or depreciates?
- What causes some assets to appreciate while others depreciate?
- Given a graph showing appreciation and depreciation rates, identify the following:
- What variables are involved? What is being measured on the vertical axis? On the horizontal axis?
- During what time period(s) is the value increasing or decreasing quickly?
- At what point has the value of the item dropped to half the original value or increased to double the original value?
- What might have caused the change in value at a given time and how might this affect the people involved?
- How does the depreciation or appreciation of [a given item] compare to the depreciation or appreciation of [another given item]?
- Why do you think a business or non-profit organization has to take into account the depreciation of its assets when it does year-end accounting?
Have students brainstorm examples of assets that appreciate or depreciate, including those that might experience a short-term appreciation due to a current trend (e.g., trading cards, trends started on social media). Show students graphs or provide them with data to graph depicting the appreciation and depreciation of assets identified during the brainstorming session and have them identify what they notice and what questions they might still have about each of the graphs.
Show students a graph comparing the depreciation of two different vehicles, such as the graph below.
Ask students:
- What variables are represented on each of the axes?
- Why might one vehicle depreciate at a different rate than the other?
- When (after how many years) is each vehicle worth less than half its original value?
- Why might it be helpful to understand how vehicles depreciate?
- Could a vehicle ever appreciate in value?
Have them choose a vehicle they are curious about, look up the depreciation rate for that vehicle, and then compare the rate with that of a vehicle chosen by a classmate.
Have students investigate an item they think has appreciated or depreciated over time. Ask: Did the value of this item appreciate or depreciate as you expected? Have students find or create a graph to show how the value has changed.
Have students write code to analyse the value of an item over time for different rates of appreciation. The following is an example of pseudocode that determines the value of an item that appreciates at a given rate for each period of time and graphs the results. Have students alter the code for a situation involving depreciation, and have them consider which items appreciate or depreciate in value.
| costOfItem = 0.00 |
| timePeriod = 0 |
| appreciationRate = 0.00 |
| output “Enter the cost of an item.” |
| store user input as costOfItem |
| plot point (timePeriod, costOfItem) |
| output “Enter the rate of appreciation as a percentage.” |
| store user input as appreciationRate |
| while appreciationRate < 1 |
| output “Enter the rate of appreciation as a number greater than 1.” |
| store user input as appreciationRate |
| repeat until timePeriod = 10 |
| timePeriod = timePeriod + 1 |
| costOfItem = costOfItem * (1 + appreciationRate/100) |
| plot point (timePeriod, costOfItem) |
Pseudocode does not represent a specific programming language. It can be adapted to work with a variety of programming languages and/or environments.
F1.3
compare the effects that different interest rates, lengths of borrowing time, ways in which interest is calculated, and amounts of down payments have on the overall costs associated with purchasing goods or services, using appropriate tools
- ways in which interest is calculated:
- simple interest
- compound interest
- different compounding periods, such as weekly, monthly, biannually, or annually
- tools:
- spreadsheets
- graphing tools
- coding
- online financial calculators
Teachers can:
- facilitate a class discussion, using authentic and accessible contexts, about how changing different variables might affect overall costs of a purchase, then have students complete a numerical analysis;
- incorporate contexts from previous grades such as loans, credit cards, or lines of credit;
- create opportunities for students to engage in estimation and make conjectures before calculating the actual values, then have them compare their estimations with the results and reflect on the reasons for any differences;
- support students in using available technology and coding tools to examine how changing one variable might affect overall costs so that the focus of the learning can be on the effects of changing variables rather than on making complex calculations.
- What effect will increasing or decreasing each of the following have on the overall cost (of goods or services)?
- the interest rate
- the length of the borrowing time
- the frequency at which interest is calculated
- the amount of a down payment
- Why does increasing the length of the borrowing time increase the total cost of an item?
- How does a lower interest rate compounded monthly compare to a higher interest rate compounded annually?
Provide students with a chart similar to the one below. Have them indicate whether certain changes in variables would increase or decrease the overall cost of an item and explain why. Encourage students to use an online or handheld financial calculator to test their ideas.
| Variable | Change in variable | Effect on cost (circle one) | Explanation |
| interest rate | increase | Increase / decrease / remain the same | |
| loan term length | increase | Increase / decrease / remain the same | |
| amount of down payment | increase | Increase / decrease / remain the same |
Ask students to choose an item they might want to purchase sometime in the future (e.g., computer, gaming system, used vehicle, bicycle). Have them use a financial calculator to explore the effects of changing the conditions of a loan to purchase the item, such as the interest rate or term length.
Provide students with a sequence of code to calculate the total cost and interest paid on a loan that has interest compounded monthly. Have students alter the code to explore how changing the compounding period (e.g., compounding annually, semi-annually, weekly) would change the total cost and interest for that loan.
| amountOfLoan = 0.00 |
| borrowingTime = 0 |
| interestRate = 0.00 |
| output “Enter the amount of the loan.” |
| store user input as amountOfLoan |
| output “Enter the borrowing time for the loan in years.” |
| store user input as borrowingTime |
| output “Enter the annual interest rate as a percentage.” |
| store user input as interestRate |
| interestRate = interestRate/100 |
| compoundPeriods = borrowingTime * 12 |
| totalCost = amountOfLoan * (1 + interestRate/12)^compoundPeriods |
| totalInterest = totalCost - amountOfLoan |
| output “The total amount paid at the end of the loan would be” totalCost |
| output “The total interest paid would be” totalInterest |
Pseudocode does not represent a specific programming language. It can be adapted to work with a variety of programming languages and/or environments.
F1.4
modify budgets displayed in various ways to reflect specific changes in circumstances, and provide a rationale for the modifications
- ways of displaying a budget:
- budget template:
- circle graph:
- digital spreadsheet or software
- changes in circumstances:
- a change in income or revenue
- a change in the cost of utilities
- a change in transportation costs
- a change in operational costs
- modifying budgets:
- adjusting income or expense categories in a budget to create a balanced budget, whether for an individual, a family, an organization, a business, or a government
Teachers can:
- share examples of budgets represented in various ways;
- provide students with opportunities to work with a variety of budgets, such as those for an individual, a family, a business, an organization, a community-based non-profit organization, or a government (municipal, provincial, or federal);
- provide students with opportunities to discuss and explore various categories that might be included in a budget;
- ensure that all examples provided or discussed, although authentic and connected to students’ realities, are hypothetical and free of judgement;
- create opportunities for students to work in pairs or small groups to brainstorm how a change in circumstances might affect a budget;
- have students modify budgets and justify their modifications through discussion or in writing.
- What are some of the categories you might find on a family budget? a school team’s or club’s budget? a small business’s budget?
- In general, which categories of expenses and revenue on a budget are easier to change? Which are more difficult to change?
- What are some circumstances that would result in the need for a change in a budget?
Provide students, working in small groups, with a sample balanced budget for a family that includes realistic values for the local community. Give each group a realistic circumstance that would require a change or changes in the budget. Have the group work collaboratively to adjust the budget to keep it balanced and then share their changes and rationale with the class. Note: Ensure that all examples provided or discussed, although authentic and connected to students’ lives, are hypothetical and free of judgement.
Show students the budget for a division of the local municipal government (e.g., Parks and Recreation). Pose a scenario that is relevant to the current local situation (e.g., community members would like an outdoor skating rink) and have students discuss how the budget could be modified based on this scenario.
Provide students with a budget for a school trip in the form of a circle graph. Have them consider how the budget would need to be changed for a variety of circumstances, such as:
- an increase in transportation costs
- a decrease in the number of people coming on the trip
- a donation from a community organization to help fund the trip
