Grocery Store Mathlete Challenge! (7.RP.3)

Mission Briefing: Becoming a Smart Shopper!

Welcome, Mathlete! Today, your mission is to conquer the grocery store using your amazing math skills! We're going to explore how percentages, ratios, and unit prices help us make smart choices and save money. This is all about Common Core Standard 7.RP.A.3: Using proportional relationships to solve multistep ratio and percent problems.

Part 1: What's the Real Deal? Unit Pricing Power! (Approx. 20 minutes)

Imagine you see two bottles of orange juice. One is bigger, but also more expensive. How do you know which one is the better deal? That's where unit price comes in! The unit price tells you the cost per unit of measure (like per ounce, per pound, per item).

Formula: Unit Price = Total Price / Total Units (e.g., ounces, pounds, count)

Activity 1: Unit Price Detective

1. Grab your grocery ads or open an online grocery store page.
2. Find 3 different items that come in at least two different sizes (e.g., a small box of cereal vs. a large box, a can of beans vs. a larger can).
3. For each item and its different sizes:
   • Note down the total price and the total quantity (e.g., 10 oz, 32 oz).
   • Calculate the unit price for each size. (Example: Cereal A is $3.00 for 10 oz. Unit price = $3.00 / 10 oz = $0.30 per ounce. Cereal B is $4.80 for 16 oz. Unit price = $4.80 / 16 oz = $0.30 per ounce. In this example, they are the same, but often one is a better deal!)
   • Which size is the better buy based on the unit price?
4. Record your findings on a piece of paper or in your notebook. Title it "Unit Price Detective Work."

Discussion: Why is it important to look at the unit price instead of just the total price?

Part 2: Sale Away! Calculating Discounts (Approx. 20 minutes)

Everyone loves a sale! But how much are you actually saving? Let's practice calculating discounts.

Remember: A percentage is just a part of 100. So, 20% off means you save $20 for every $100, or $0.20 for every $1.00.

To find the discount amount: Discount Amount = Original Price × (Percent Discount / 100)

To find the sale price: Sale Price = Original Price - Discount Amount

Alternatively, to find the sale price directly: If an item is 20% off, you pay 100% - 20% = 80% of the price. So, Sale Price = Original Price × ((100 - Percent Discount) / 100)

Activity 2: Discount Decoder

1. Look through your grocery ads for items that are on sale with a percentage off (e.g., "25% off all sodas," "15% off frozen pizzas").
2. Choose 3-5 items. For each item:
   • Note the original price and the percentage discount.
   • Calculate the discount amount.
   • Calculate the sale price.
3. Show your work! Example: A bag of chips is originally $4.00 and is 25% off.
   • Discount Amount: $4.00 × (25/100) = $4.00 × 0.25 = $1.00
   • Sale Price: $4.00 - $1.00 = $3.00 (OR $4.00 × (75/100) = $4.00 × 0.75 = $3.00)

Part 3: The Tax Man Cometh (Understanding Sales Tax) (Approx. 15 minutes)

In many places, you have to pay sales tax on certain items. Sales tax is also a percentage of the item's price.

To find the sales tax amount: Sales Tax Amount = Price of Item(s) × (Sales Tax Rate / 100)

To find the total cost: Total Cost = Price of Item(s) + Sales Tax Amount

Let's assume a local sales tax rate of 6% for this activity (you can use your actual local rate if you know it and if it applies to food - some places exempt food from sales tax. For this exercise, we will pretend all food items are taxed).

Activity 3: Tax Time!

1. Imagine you are buying the following items (use prices from your ads, or make reasonable ones up if needed):
   • A box of cookies: $3.50
   • A bottle of juice (after a 10% discount from an original price of $3.00): $2.70
   • A bag of apples: $5.00
2. Calculate the subtotal (the total cost of all items before tax).
3. Calculate the sales tax amount on the subtotal using a 6% tax rate.
4. Calculate the final total cost including sales tax.

Part 4: The Grand Shopping Spree Challenge! (Approx. 25 minutes)

Now it's time to put it all together! You have a budget of $25.00 and a shopping list. Your goal is to buy everything on the list (or suitable alternatives if you can't find the exact item), get the best deals possible by comparing unit prices and using sales, and stay within your budget, including a 5% sales tax on your total purchase.

Your Shopping List:

• 1 box of your favorite cereal
• 1 gallon of milk (or two half-gallons if it's a better deal based on unit price)
• 1 loaf of bread
• 1 jar of peanut butter
• 1 bag of fruit (e.g., apples, oranges, bananas - aim for about 2 lbs)
• 1 treat of your choice (under $3 before tax and any discounts)

Instructions:

1. Use your grocery ads or online store. For each item on the list:
   • Find at least two options if possible (different brands, sizes).
   • Calculate and compare unit prices to choose the best value.
   • Note if any of your chosen items are on sale and calculate the sale price.
2. Create a detailed "receipt":
   • List each item, its original price, any discount applied, and the final price for that item.
   • Calculate your subtotal (total cost of all items after discounts but before tax).
   • Check: Is your subtotal allowing you to stay under $25 after tax? If not, you might need to make different choices (e.g., a cheaper brand, a smaller size if the unit price is still good).
   • Calculate the 5% sales tax on your subtotal.
   • Calculate your final grand total.
   • How much money do you have left from your $25 budget? Or did you go over?

Wrap-up & Reflection (5 minutes)

• What was the most challenging part of this "shopping trip"?
• What strategy did you find most helpful for saving money (unit prices, sales)?
• How can you use these math skills in real-life grocery shopping?

Great job, Grocery Store Mathlete! You've shown that math is incredibly useful in everyday life!