# Produce and Prices

Develop your students’ proportional reasoning skills—and their facility with decimal operations—with this grocery store receipt challenge:

### Challenges

1. What is the total “balance due” on this grocery store receipt?
2. How many total pounds of yellow bananas were purchased?
3. What is the cost per pound of milk chocolate honeycomb?

### Setting

The receipt shown above is from a recent trip to a local grocery store. This particular purchase includes several items which are doled out on a price-per-item or price-per-pound basis, making this a great problem for wrestling with proportional reasoning and operations with rational numbers in decimal form. The image is information-dense (and not particularly visually stimulating), so it will be important to allow students to become familiar with the receipt before they’re pushed to answer any specific questions. The “noticing” part of the Math Forum’s Noticing and Wondering (video link) may be useful here.

### Lesson Notes

Display the masked receipt image with a projector. Ask students to write down several things they notice. After a few moments, gather responses and record them in writing (chalkboard, whiteboard, laptop/projector… whatever your preferred style).

Once students have become familiar with the content and structure of the receipt, distribute the receipt handout (available below under “Resources”). For this task, it’s important that students have an opportunity to show at least some of their work directly on (or immediately next to) the receipt.

The rest of the lesson unfolds as a series of “find what’s missing” challenges.

##### Item 1

This first item on the receipt is what originally sparked the lesson idea. I’ve been on the lookout for proportional reasoning challenges in everyday life, and the “this-many-at-this-rate” item certainly caught my attention. The challenge here for students is not too difficult, and an ideal start to the task. If green onions are 2 for \$1.00, how much would you have to pay for 1? (Note: If I could travel back in time, I would add another 2 (or maybe 6) green onions to the order.)

##### Item 2

The next item offers a noticeably greater challenge. At this point, teachers will have to decide whether to allow students the use of calculators. I would recommend against it in this lesson, as it would rob students of a valuable opportunity to develop their proficiency with decimal operations in a real world context. That being said, a calculator-infused version of this lesson still holds considerable value for students as they determine which operations are necessary at each stage.

##### Item(s) 3

When determining the overall cost, students don’t need to do anything with this portion of the receipt. The mushrooms are pre-packaged and have a fixed price of \$2.99, and the main question (total balance due) doesn’t require the weight of the bananas, only their total price.

Later, when students turn their attention back to the bananas, they’ll find themselves with the greatest computational challenge of the task: dividing 3.13 and 1.96 each by 0.69. Be on the lookout for multiple approaches. Many students will divide first and then add. Others may add first and then divide. This opens up a great opportunity to discuss equivalent expressions involving fractions.

##### Item(s) 4

No mysteries here, though the prices add helpful context to the other masked values on the receipt.

##### Item 5

Last but not least: milk chocolate honeycomb. Here we have one final twist, as the weight and total price are known, but the unit rate is not. Once more, students are presented with a division-with-decimals problem (as well as an opportunity to round to the nearest hundredth).

##### The Total

As students reach the end of the receipt, they should have all of the “ingredients” necessary to find the total. If they have not rounded their quotients from earlier to the nearest penny, now would be a great time to do so, as it will simplify the process of adding to find the balance due (and will more accurately reflect what happens in store).

##### The Reveal

When it’s time, reveal the unmasked receipt:

### Extensions

1. Create an imaginary receipt with the same items (with different weights/amounts) that comes to a total of exactly \$50.00.
2. Sales tax does not apply to any of the items on this receipt. Suppose instead that sales tax of 8% is applied to three of the items, and that the new total for the receipt is \$32.36. Which items were taxed?

### Standards

• CCSS 7.RP.A
Analyze proportional relationships and use them to solve real-world and mathematical problems.
• CCSS 6.RP.A
Understand ratio concepts and use ratio reasoning to solve problems.
• CCSS 5.NBT.A
Understand the place value system.
• CCSS 5.NBT.B
Perform operations with multi-digit whole numbers and with decimals to hundredths.

### Shout Outs

Katie Reneau, who provided feedback on an early draft of this lesson.