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Teacher Guide: Money and Pricing Problems

Learn to solve real-world word problems involving money, prices, discounts, and making change.

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For Teachers

Learning Objectives
  • Calculate total cost when purchasing multiple items at given prices
  • Determine the amount of change to receive from a purchase
  • Apply percentage discounts to find sale prices
  • Calculate and compare unit prices to determine the best value
  • Solve multi-step money problems involving tax and discounts
Prerequisites
  • • Addition and subtraction with decimals
  • • Multiplication and division with decimals
  • • Understanding of percentages and how to convert them to decimals
  • • Basic understanding of what discounts and taxes are
Discussion Starters
  • 1. When have you needed to calculate if you had enough money for something?
  • 2. Why do stores sometimes price items at 9.99 dollars instead of 10.00 dollars?
  • 3. How do you decide which size of a product is the best deal?
  • 4. What mistakes could happen if a cashier calculates change incorrectly?
Common Misconceptions

A bigger discount percentage always means a lower final price

Remediation: Compare: 50% off a 20 dollar item (10 dollars) vs 20% off a 100 dollar item (80 dollars). The actual prices matter, not just the percentage.

The larger package is always the better value

Remediation: Calculate unit prices to compare. Sometimes smaller packages are on sale or have a better price per unit.

You can add percentages directly (20% off + 10% off = 30% off)

Remediation: Successive discounts multiply, not add. 20% off then 10% off means 0.80×0.90=0.720.80 \times 0.90 = 0.72, which is 28% off total, not 30%.

Differentiation Ideas

For Struggling Students:

  • • Start with whole dollar amounts before introducing decimals
  • • Provide visual models like play money or tape diagrams
  • • Use familiar contexts like buying school supplies or snacks

For On-Level Students:

  • • Work with realistic prices including cents
  • • Include single discount or tax calculations
  • • Compare two options to find the better deal

For Advanced Students:

  • • Solve problems with multiple discounts applied sequentially
  • • Calculate tips and split bills among multiple people
  • • Analyze when buying in bulk saves money versus when it doesn't
Standards Alignment
  • 6.NS.B.3 (CCSS.MATH.CONTENT.6.NS.B.3)

    Fluently add, subtract, multiply, and divide multi-digit decimals using standard algorithms

  • 6.RP.A.3b (CCSS.MATH.CONTENT.6.RP.A.3.B)

    Solve unit rate problems including those involving unit pricing

  • 7.RP.A.3 (CCSS.MATH.CONTENT.7.RP.A.3)

    Use proportional relationships to solve multistep ratio and percent problems

Lesson Resources
  • activityGrocery Store Simulation

    Students plan a shopping trip with a budget and calculate totals

  • worksheetDiscount Detective

    Find the best deals by comparing original and sale prices

  • gameCash Register Challenge

    Practice making correct change quickly

Lesson Content

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

Definition

Money and pricing problems are word problems that involve real-world situations with money. These problems require you to:
  • Calculate totals: Add up the cost of multiple items
  • Find change: Subtract the purchase amount from the payment
  • Apply discounts: Calculate sale prices using percentages
  • Determine unit prices: Find the cost per single item or unit
The key to solving money problems is:
  1. 1.Read carefully to identify what you're finding
  2. 2.Identify the operation (add, subtract, multiply, or divide)
  3. 3.Set up the equation with the correct values
  4. 4.Calculate and check your answer makes sense

Worked Examples

Emma buys 3 notebooks at 4.50 dollars each and 2 pens at 1.75 dollars each. What is her total cost?
1

Calculate the cost of notebooks

3×4.50=13.503 \times 4.50 = 13.50 dollars → 13.50 dollars for notebooks
2

Calculate the cost of pens

2×1.75=3.502 \times 1.75 = 3.50 dollars → 3.50 dollars for pens
3

Add both amounts

13.50+3.50=17.0013.50 + 3.50 = 17.00 dollars → Total: 17.00 dollars

Common Mistakes

Forgetting to multiply quantity times price

Why it's wrong: When buying multiple items, students sometimes just add the price once instead of multiplying.

Correct: If you buy 4 items at 3 dollars each, the cost is 4×3=124 \times 3 = 12 dollars, not just 3 dollars.

Subtracting discount percentage from price instead of calculating the actual discount

Why it's wrong: A 20% discount on 50 dollars is not 50 - 20 = 30 dollars.

Correct: First calculate: 50×0.20=1050 \times 0.20 = 10 dollars discount. Then: 50−10=4050 - 10 = 40 dollars.

Confusing which number to divide when finding unit price

Why it's wrong: To find price per item, some students divide items by price instead of price by items.

Correct: Unit price = Total price divided by number of items. For 6 dollars for 3 items: 6÷3=26 \div 3 = 2 dollars per item.

Adding tax before calculating discounts

Why it's wrong: Tax should be calculated on the final price after any discounts are applied.

Correct: First apply the discount, then calculate tax on the discounted price.

Why It Matters

Money problems are some of the most practical math skills you'll ever learn:
  • Shopping: Calculate if you have enough money, find the best deals
  • Budgeting: Plan your spending for allowance, events, or trips
  • Jobs: Count earnings, calculate tips, manage a cash register
  • Comparison shopping: Determine which size or brand is the better value
  • Saving goals: Figure out how long it takes to save for something you want
Every time you buy something, tip at a restaurant, or save for a goal, you're using money math!

Real World Applications

Shopping with a Budget

When shopping with limited money, you need to track your running total to stay within budget.

Example:

You have 25 dollars. A shirt costs 12.99 dollars and socks cost 5.49 dollars. Your total is 12.99+5.49=18.4812.99 + 5.49 = 18.48 dollars, leaving you 25−18.48=6.5225 - 18.48 = 6.52 dollars.

1Try It Yourself

You have 40 dollars to spend at the bookstore. You want to buy a book for 14.95 dollars and a journal for 8.50 dollars.

How much money will you have left?

Step 1: Write the mathematical expression

Calculate: 40 - (14.95 + 8.50)

Comparing Store Prices

Smart shoppers compare unit prices to find the best deal, especially when packages come in different sizes.

Example:

Store A sells 6 apples for 3.00 dollars (0.50 dollars each). Store B sells 8 apples for 3.60 dollars (0.45 dollars each). Store B has the better price per apple.

2Try It Yourself

A 500ml bottle of shampoo costs 4.50 dollars. A 750ml bottle costs 6.00 dollars.

Which bottle has the better price per ml?

Step 1: Choose the right answer

Compare the unit prices: which statement is true?

Restaurant Bills and Tips

When dining out, you need to calculate tips based on the bill amount and sometimes split costs with friends.

Example:

A meal costs 32 dollars. A 15% tip is 32×0.15=4.8032 \times 0.15 = 4.80 dollars. Total with tip: 32+4.80=36.8032 + 4.80 = 36.80 dollars.

3Try It Yourself

Your dinner bill is 45 dollars. You want to leave a 20% tip.

What is the total amount you will pay?

Step 1: Write the mathematical expression

Calculate: 45 + (45 x 0.20)

Key Takeaways

  • 1Read money problems carefully to identify what you need to find (total, change, discount, unit price)
  • 2Total cost = quantity multiplied by price per item, then add all items together
  • 3Change = payment amount minus purchase amount
  • 4Discount amount = original price multiplied by discount percentage as a decimal
  • 5Sale price = original price minus discount amount (or original price multiplied by remaining percentage)
  • 6Unit price = total price divided by number of items (useful for comparing values)
  • 7Always check your answer makes sense - change should be less than payment, sales price should be less than original

Frequently Asked Questions

How do I convert a percentage to a decimal for calculations?

Divide the percentage by 100. For example, 25% becomes 25÷100=0.2525 \div 100 = 0.25. Then multiply by this decimal.

Should I calculate tax before or after a discount?

Always apply discounts first, then calculate tax on the discounted price. This gives you the correct final total.

How do I know which size is a better deal?

Calculate the unit price (price per item or per unit of measurement) for each size. The lower unit price is the better deal.

Glossary

Unit price
The cost of one item or one unit of measurement (e.g., price per ounce or per item)
Discount
A reduction from the original price, often expressed as a percentage
Sale price
The reduced price after a discount is applied
Subtotal
The sum of all items before tax or additional fees are added
Sales tax
A percentage added to purchases that goes to the government
Change
The money returned when you pay more than the exact purchase amount

Formula Card

Total Cost

Total=Quantity×Price per item\text{Total} = \text{Quantity} \times \text{Price per item}

Multiply the number of items by the price of each item

Change

Change=Payment−Total Cost\text{Change} = \text{Payment} - \text{Total Cost}

Subtract what you owe from what you paid

Discount Amount

Discount=Original Price×Discount Rate\text{Discount} = \text{Original Price} \times \text{Discount Rate}

Convert percentage to decimal and multiply

Sale Price

Sale Price=Original−Discount\text{Sale Price} = \text{Original} - \text{Discount}

Subtract the discount from the original price

Unit Price

Unit Price=Total PriceNumber of Items\text{Unit Price} = \frac{\text{Total Price}}{\text{Number of Items}}

Divide total cost by quantity to compare values

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