Teacher Guide: Commission

Learn how salespeople earn commission: find the commission, total earnings with a base salary, the commission rate, the sales needed for a target income and tiered commission.

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10 questions on Percentages. Students join with a name, you see everyone's score.

For Teachers

Learning Objectives

Calculate commission as commission rate times sales
Find total earnings from a base salary plus commission
Find the commission rate from the commission and the sales
Find the sales needed to reach a target income
Calculate tiered commission and compare two job offers

Prerequisites

• Introduction to Percentages: writing percents as decimals
• Finding Percent of a Number: multiplying the whole by the rate
• Percent Equation: part = rate × whole
• Solving one-step equations with multiplication and division

Discussion Starters

1. Would you rather have a high base salary and a low commission rate, or the opposite? Why?
2. Why might a store pay its staff commission instead of only a fixed wage?
3. A real estate agent earns 3% of a house price. Why might the agent not keep all of that money?
4. Two job offers pay the same at 30,000 dollars of sales. What does that tell you about lower and higher sales?
5. Is tiered commission fair to new salespeople? What would you change?

Common Misconceptions

Students multiply by the percent number (3) instead of the decimal (0.03)

Remediation: Ask for an estimate first: can the commission be bigger than the sales? Practice turning every rate into a decimal before any multiplication, and check with 1% of the sales.

Students apply the highest tier rate to all the sales

Remediation: Use the tape diagram: color the first 10,000 and the part above it differently and calculate each piece on its own before adding.

Students divide the whole target income by the rate when finding the sales needed

Remediation: Have them say in words where each dollar comes from: the base salary is paid anyway, so only the rest must come from commission. Always check the answer by putting it back into the earnings formula.

Differentiation Ideas

For Struggling Students:

• Start with rates like 1%, 5% and 10% that are easy to find mentally
• Give a fill-in table with columns: sales, rate as decimal, commission, base, total
• Use the bar chart to read earnings before calculating them

For On-Level Students:

• Mix problems that ask for the commission, the total, the rate and the sales needed
• Solve tiered commission problems with two tiers
• Compare two job offers at a given sales level

For Advanced Students:

• Find the break-even sales of two offers by solving an equation
• Design a three-tier commission plan and test it on several sales amounts
• Find the sales needed for a target income under a tiered plan

Standards Alignment

7.RP.A.3 (CCSS.MATH.CONTENT.7.RP.A.3)
Use proportional relationships to solve multistep ratio and percent problems, including gratuities and commissions
7.EE.B.3 (CCSS.MATH.CONTENT.7.EE.B.3)
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form
6.RP.A.3.C (CCSS.MATH.CONTENT.6.RP.A.3.C)
Find a percent of a quantity as a rate per 100; solve problems involving finding the whole, given a part and the percent

Lesson Resources

visualEarnings Bar Chart
Total earnings at five sales levels for a base salary of 1,500 plus 4% commission
visualTiered Commission Tape
A tape diagram splitting 15,000 of sales into the 5% tier and the 8% tier
activityWhich Job Would You Take?
Pairs compare two sales job offers at different sales levels and find the break-even point
worksheetCommission Word Problems
Real estate, car sales and shop problems: commission, total earnings, rates and sales targets

Lesson Content

Everything students see: definition, examples, common mistakes, applications. Tap to open.

Definition

A commission is money a salesperson earns as a percent of what they sell. The percent is called the commission rate.

Commission is the percent equation you already know,

\text{part} = \text{rate} \times \text{whole}

, where the whole is the sales and the part is the commission:

\text{Commission} = \text{Commission rate} \times \text{Sales}

Many jobs pay a fixed base salary plus commission:

\text{Total earnings} = \text{Base salary} + \text{Commission rate} \times \text{Sales}

Example: a shop assistant earns 1,500 dollars a month plus 4% of sales. With sales of 10,000 dollars the commission is

0.04 \times 10{,}000 = 400

dollars, so the total is

1{,}500 + 400 = 1{,}900

dollars.

Always write the rate as a decimal before you multiply:

4\% = 0.04

Worked Examples

A real estate agent sells a house for 250,000 dollars. Her commission rate is 3%. How much commission does she earn?

Write the rate as a decimal

$3\% = \frac{3}{100} = 0.03$

Multiply the rate by the sales

$0.03 \times 250{,}000 = 7{,}500$

Check with 1%

$1\%$ of $250{,}000$ is $2{,}500$ , and $3 \times 2{,}500 = 7{,}500$ → Same answer

Answer: The agent earns a commission of 7,500 dollars.

Common Mistakes

Multiplying by the percent number: $3 \times 250{,}000 = 750{,}000$

Why it's wrong: 3% means 3 out of 100, not 3 whole times. The commission can never be bigger than the sales.

Correct: Write the rate as a decimal first: $0.03 \times 250{,}000 = 7{,}500$

Giving only the commission when the question asks for total earnings

Why it's wrong: Total earnings include the base salary. The commission is only the extra part.

Correct: Total earnings = base salary + commission: $1{,}800 + 1{,}200 = 3{,}000$

Using the higher tier rate on all sales: $0.08 \times 15{,}000 = 1{,}200$

Why it's wrong: In tiered commission each rate applies only to its own part of the sales.

Correct: Split the sales: $0.05 \times 10{,}000 + 0.08 \times 5{,}000 = 500 + 400 = 900$

Forgetting to subtract the base salary when finding the sales needed: $\frac{2{,}500}{0.05} = 50{,}000$

Why it's wrong: Only the part of the income above the base salary has to come from commission.

Correct: First subtract: $2{,}500 - 1{,}200 = 1{,}300$ , then $\frac{1{,}300}{0.05} = 26{,}000$

Why It Matters

Commission decides the income of millions of people:

Real estate agents often earn 2% to 3% of the price of every house they sell
Car salespeople usually get a base salary plus a percent of each car sold
Shop assistants in electronics or fashion stores often earn a small percent on top of their wage
Job offers in sales are hard to compare without math: is 2,000 dollars plus 3% better than 1,400 dollars plus 5%?

Once you can work with commission, you can check a paycheck, set a sales goal and decide which job offer really pays more.

Real World Applications

Real Estate Agents

When a house is sold, the agent who helped sell it is paid a percent of the selling price.

Example:

On a 400,000 dollar apartment with a 2% commission, the agent earns $0.02 \times 400{,}000 = 8{,}000$ dollars.

1Try It Yourself

An agent sells a house for 320,000 dollars. Her commission rate is 2.5%.

How much commission does she earn, in dollars?

Step 1: Write the mathematical expression

Multiply the selling price by the rate as a decimal:

Comparing Job Offers at a Car Dealership

Sales jobs often mix a fixed base salary with commission. A higher base is safer, a higher rate pays more when sales are good.

Example:

Offer A pays 2,000 dollars plus 3%, offer B pays 1,400 dollars plus 5%. They pay the same when $0.02 \times \text{sales} = 600$ , so at sales of 30,000 dollars. Above that, offer B pays more.

2Try It Yourself

Offer A: 2,000 dollars a month plus 3% of sales. Offer B: 1,400 dollars a month plus 5% of sales. You expect to sell 40,000 dollars a month.

How many dollars more per month does the better offer pay?

Step 1: Write the mathematical expression

Subtract the total of offer A from the total of offer B:

A Shop Assistant's Sales Goal

Shop assistants who earn commission often set a monthly sales target so they reach the income they need.

Example:

With a base of 1,500 dollars and 4% commission, sales of 20,000 dollars give $1{,}500 + 800 = 2{,}300$ dollars (see the bar chart).

3Try It Yourself

A shop assistant earns 1,500 dollars a month plus 4% commission. She wants to earn 1,900 dollars this month.

How much must she sell, in dollars?

Step 1: Write the mathematical expression

Divide the commission she needs by the rate:

Key Takeaways

1Commission = commission rate × sales, the percent equation with the sales as the whole
2Always write the rate as a decimal before multiplying: $3\% = 0.03$ , $2.5\% = 0.025$
3Total earnings = base salary + commission
4Commission rate = commission ÷ sales, then multiply by 100 to get a percent
5Sales needed = (target income - base salary) ÷ rate
6Tiered commission: apply each rate only to its own part of the sales, then add the parts

Frequently Asked Questions

Is commission the same as a bonus?

Not quite. Commission is tied to each sale and grows with every dollar sold. A bonus is usually a fixed extra amount paid for reaching a goal.

Can a commission rate be more than 100%?

No. That would mean the salesperson earns more than the price of what was sold. Real rates are usually between 1% and 20%.

Why do some companies use tiered commission?

To reward strong sellers. A higher rate above a certain amount makes every extra sale worth more, so salespeople are motivated to sell beyond the first tier.

How do I know which job offer is better?

Compute the total earnings of each offer for the sales you expect. You can also find the break-even sales, where both offers pay the same: below it the higher base salary wins, above it the higher rate wins.

Glossary

Commission: Money earned as a percent of the sales a person makes
Commission rate: The percent of the sales paid as commission, for example 3%
Sales: The total value of what the salesperson sold, the whole in the percent equation
Base salary: A fixed amount paid no matter how much is sold
Total earnings: Base salary plus commission
Tiered commission: A system where different rates apply to different parts of the sales, for example 5% up to 10,000 and 8% above

Formula Card

Commission

\text{Commission} = \text{rate} \times \text{sales}

Write the rate as a decimal first

Total earnings

\text{Earnings} = \text{base salary} + \text{rate} \times \text{sales}

Fixed pay plus commission

Commission rate

\text{rate} = \frac{\text{commission}}{\text{sales}}

Multiply by 100 to write it as a percent

Sales needed

\text{sales} = \frac{\text{target} - \text{base salary}}{\text{rate}}

Sales that give a target income

Teacher Guide: Commission

Use this lesson with your class

For Teachers

For Struggling Students:

For On-Level Students:

For Advanced Students:

Lesson Content

Definition

Worked Examples

Common Mistakes

Why It Matters

Real World Applications

Real Estate Agents

Comparing Job Offers at a Car Dealership

A Shop Assistant's Sales Goal

Key Takeaways

Frequently Asked Questions

Glossary

Formula Card

Commission

Total earnings

Commission rate

Sales needed

More in This Topic

Introduction to Percentages

Finding Percent of a Number

Percent Increase and Decrease

Percent Proportion