F. Financial Literacy · Financial Decisions: Interest, Borrowing, Appreciation, Depreciation and Budgets

Budgets Displayed in Different Ways

F1.4 A1About 65 minutes

Learning goals

I can read a budget shown as a table, a circle graph, a bar graph or a spreadsheet.
I can convert between dollar amounts, percents of income and circle-graph angles.
I can convert a budget between weekly, bi-weekly, monthly and yearly amounts.
I can compare a budget with actual spending and spot categories that are over or under.

Words to know

budget
A plan for how income will be spent and saved over a period of time.

balanced budget
A budget where planned spending and saving add up exactly to income.

fixed expense
A cost that stays the same each month, such as rent or a phone plan.

variable expense
A cost that changes from month to month, such as food or entertainment.

variance
Actual amount − budgeted amount. A positive variance on an expense means overspending.

circle graph (pie chart)
A graph that shows parts of a whole. Each sector's angle = percent × 360°.

bi-weekly
Every two weeks: 26 times a year. (Semi-monthly means twice a month: 24 times a year.)

Remember from Grade 8

In Grade 8 you kept budgets balanced, spread irregular costs across months, and tracked income and spending with ledgers, spreadsheets and apps. In Grade 9, expectation F1.4 asks you to modify budgets displayed in various ways when circumstances change, and to give reasons for the changes. Before you can modify a budget, you need to read it fluently in any form. That is today's lesson. The next lesson is about changing it.

Meet Jordan

Jordan is 19, works as a first-year apprentice and shares an apartment with a friend. Jordan's take-home pay is about $3 000 a month (an example amount). Here is Jordan's budget in four different displays.

Category	Monthly amount	Percent of income
Rent & utilities	$1 050	35%
Phone & internet	$90	3%
Food	$450	15%
Debt payment	$210	7%
Transportation	$300	10%
Clothing & other	$240	8%
Savings	$300	10%
Personal & fun	$360	12%
Total	$3 000	100%

Display 1: a table. Percent = amount ÷ income × 100%. A balanced budget totals 100% of income.

Display 2: a circle graph. It shows at a glance that rent and utilities take the biggest share (35%). Each sector's angle is its percent × 360°.

Worked example

Example 1: From table to circle graph

Find the angle of each sector for Jordan's circle graph.

Angle = percent × 360°.
Rent: 0.35 × 360° = 126°. Food: 0.15 × 360° = 54°.
Transportation and savings: 0.10 × 360° = 36° each.
Personal: 0.12 × 360° = 43.2°. Clothing: 0.08 × 360° = 28.8°. Debt: 0.07 × 360° = 25.2°. Phone: 0.03 × 360° = 10.8°.
Check: 126 + 54 + 36 + 36 + 43.2 + 28.8 + 25.2 + 10.8 = 360°. ✓

The angles add to 360°, just as the percents add to 100%.

Display 3: a spreadsheet

A spreadsheet keeps the math up to date. If the amounts are in B2 to B9:

Total income or total budget: =SUM(B2:B9) in B10
Percent for row 2: =B2/$B$10 (formatted as a percent), copied down
Angle for row 2: **=B2/$B$10360*
Variance (actual in C2): =C2-B2

Change any amount and every percent, angle and total updates automatically.

Display 4: budget vs. actual on a bar graph

A budget is a plan. At the end of the month, compare it with what actually happened. In March, Jordan spent $520 on food (budget $450), $410 on personal and fun (budget $360) and only $120 on clothing and other (budget $240).

Display 4: a double bar graph. Where the second bar is taller, Jordan spent more than planned (food, personal). Where it is shorter, Jordan spent less (clothing).

Worked example

Example 2: Find the variances

Use the bar graph. Find the variance for food, personal and clothing. Is Jordan's month still balanced?

Food: 520 − 450 = +$70 (over budget).
Personal and fun: 410 − 360 = +$50 (over budget).
Clothing and other: 120 − 240 = −$120 (under budget).
Total variance: 70 + 50 − 120 = $0.

Jordan overspent on food and fun by $120 but underspent on clothing by $120, so the month still balanced. That is luck, not a plan: next month clothing might be needed.

Worked example

Example 3: Change the time period

Jordan's food budget is $450 a month. Write it as a yearly, weekly and bi-weekly amount.

Yearly: 450 × 12 = $5 400.
Weekly: 5 400 ÷ 52 ≈ $103.85. (Do not divide the monthly amount by 4, because most months are a bit more than 4 weeks.)
Bi-weekly: 5 400 ÷ 26 ≈ $207.69.

$5 400 a year, about $103.85 a week, or about $207.69 every two weeks.

Watch out for misleading displays

A bar graph whose vertical axis does not start at 0 can make small differences look huge.
A circle graph shows percents, not dollars: 35% of $3 000 ($1 050) is very different from 35% of $2 000 ($700).
Monthly and bi-weekly pay are not the same: 26 bi-weekly paycheques a year means two months each year have three paycheques.

Hands-on activity

Display a real budget three ways

You need: your own allowance or job income (or a made-up budget for a young adult in your community), paper, coloured pencils, a protractor, and a spreadsheet if you have one.

Write a balanced monthly budget with at least 6 categories in a table.
Add a percent column. Check that it adds to 100%.
Draw a circle graph: find each angle (percent × 360°) and measure it with a protractor.
Track one week of real spending, multiply by 52 and divide by 12 to estimate a month, and draw a budget vs. actual bar graph.
Write two sentences about what each display shows best.

Model answer: a Grade 9 student with $200 a month: savings $60 (30%, 108°), food out $50 (25%, 90°), transit $40 (20%, 72°), gifts $20 (10%, 36°), games $20 (10%, 36°), other $10 (5%, 18°). The circle graph shows the shares best; the bar graph shows over- and under-spending best.

Just for fun

Why was the circle graph so calm about the budget? Because it knew everything would add up to 100% in the end.

Your turn

What percent of Jordan's $3 000 income is rent and utilities ($1 050)?

What is the circle-graph angle for food (15%)?

A circle-graph sector has an angle of 72°. Income is $2 500 a month. What amount does it represent?

In the budget vs. actual graph, which categories are over budget, and by how much?

Write a spreadsheet formula for the percent in C2 if the amount is in B2 and the total is in B10.

Jordan saves $300 a month. What percent is that, and how much is saved in a year?

Write Jordan's $3 000 monthly income as a weekly amount.

More practice: warm-up

What percent of $3 000 is $300?

How many degrees is 25% of a circle?

In a balanced budget, what do all the categories add up to?

Find 3% of $3 000.

Which display best shows parts of a whole?

More practice: on your own

Convert a $90 monthly phone bill into a yearly amount and a bi-weekly amount.

A sector in a budget circle graph is 43.2°. What percent is it? If income is $3 000, how many dollars?

Jordan underspent on clothing by $120 in March. Give two sensible things Jordan could do with that $120 next month, and a reason for each.

Which of Jordan's categories are mostly needs? What percent of income do they add up to?

A bar graph of spending has a vertical axis from $400 to $550. Food is $520 and the budget is $450. Why might the graph be misleading?

Challenge

Jordan's and Sam's circle graphs both show rent as 35%. Jordan earns $3 000 a month and Sam earns $2 000. Do they pay the same rent? What does this show about circle graphs?

Write a spreadsheet formula for D2 that shows "over" if actual (C2) is more than budget (B2), and "ok" otherwise. What does it show for food?

Jordan is actually paid $1 384.62 every two weeks. Show that this is about $3 000 a month on average, and explain why some months feel richer.

Check your understanding

Quiz

A budget item is $600 of a $2 400 income. What percent is it?

What is the circle-graph angle for 20% of a budget?

Budget for food $450, actual $520. What is the variance?

Which spreadsheet formula finds the percent for row 2 when the total is in B10?

A monthly cost is $450. About what is it per week?

Two circle graphs both show savings as 10%. What can you conclude?

For parents and teachers

Big idea: F1.4 asks students to modify budgets displayed in various ways and to justify the changes. This lesson makes sure students can read and convert between the displays (tables, circle graphs, bar graphs, spreadsheets) and time periods. The next lesson focuses on making and justifying changes. It also draws on data skills (circle and bar graphs) from the Data strand.

Common difficulties:

Dividing a monthly amount by 4 to get a weekly amount. Use × 12 ÷ 52.
Reading a circle graph as dollars. It shows percents of a total.
Forgetting the absolute reference ($B$10) in spreadsheet formulas.

How to help: If you are comfortable, show your teen a simplified version of a household budget (rounded or made-up numbers are fine) and ask them to turn it into a circle graph or a spreadsheet. Ask: "Which display makes it easiest to see where the money goes?"