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Problem Solving for the 21st Century: Built for the TEKS

Buying Plastic Plates

The Webster family is planning a barbecue for one hundred people. The Webster family needs one plastic plate for each person at the barbecue. The Stop and Shop store and Market Place Store both sell plastic plates in packages of fifteen for five dollars and forty-eight cents per package. How many packages of plastic plates does the Webster family need to buy?

Packages of plastic plates are on sale for one-half off the regular price at the Stop and Shop store. Packages of plastic plates are on sale for buy one, get one free at the Market Place store. Which store is offering the better buy for plastic plates? Show all your mathematical thinking.

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instructional
Unit of Study:
TEKS Covered in This Unit:
  • 5.3D
  • 5.3E
  • 5.3F
  • 5.3G
Mathematical Process Standards:
  • 5.1A
  • 5.1A

    Apply mathematics to problems arising in everyday life, society, and the workplace.

  • 5.1B
  • 5.1B

    Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.

  • 5.1C
  • 5.1C

    Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.

  • 5.1E
  • 5.1E

    The student is expected to create and use representations to organize, record, and communicate mathematical ideas.

  • 5.1G
  • 5.1G

    Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

View all Grade 5 tasks

More Accessible Version

The Webster family is planning a barbecue for one hundred people. The Webster family needs one plastic plate for each person at the barbecue. The Stop and Shop store sells plastic plates in packages of fifteen for five dollars and ninety-nine cents per package. How many packages of plastic plates does the Webster family need to buy? What is the cost of plates for the barbecue? Show all your mathematical thinking.

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More Challenging Version

The Webster family is planning a barbecue for one hundred people. The Webster family needs one plastic plate for each person at the barbecue. The Stop and Shop store and Market Place Store both sell plastic plates in packages of fifteen for five dollars and forty-eight cents per package. How many packages of plastic plates does the Webster family need to buy?

Packages of plastic plates are on sale for one-half off the regular price at the Stop and Shop store. Packages of plastic plates are on sale for buy one, get one free at the Market Place store. Which store is offering the better buy for plastic plates?

The Market Place store will sell certain items in bulk. If you buy the plates in cartons of four packages of plates, the store will discount the full carton $2.00. You may only buy full cartons. They will not split cartons for this extra savings. Would buying this way save the family money at the sale price? Show all your mathematical thinking.

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Plan

Underlying Mathematical Concepts

  • Add/Multiply/Divide decimals to hundredths
  • Money notation
  • Comparing costs

Possible Problem-Solving Strategies

  • Model (manipulatives)
  • Diagram/Key
  • Table
  • Number line

Formal Mathematical Language and Symbolic Notation

  • Model
  • Diagram/Key
  • Table
  • Number line
  • Multiple
  • Fraction (1/2)
  • Cost
  • Pattern
  • Greater than (>)/Less than (<)
  • Most/Least
  • Total/Sum/Product
  • Equivalent/Equal to
  • Rule (15 • p = t, $5.48 • p = c)
  • Graph
  • Division
  • Quotient
  • Multiplication
  • Per
  • Percent (50%)
  • Decimal (0.5)
  • Variables
  • Whole number
  • Place value (ones, tens, tenths, hundredths)

A student may independently select a printed number line, number chart, ten frames, graph paper, etc. as they work on a task.

Download printable resources for student representations.

Suggested Materials

Engagement Image:

Teachers may project the image below to launch this task for their students, define nouns, promote discussion, access prior knowledge, and inspire engagement and problem solving.

Click image to enlarge

Task-Specific Evidence

This task requires students to multiply and divide decimals to hundredths and compare the resulting products/quotients.

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Printer-Friendly Exemplars Rubric

Possible Solutions

  • Task Solution (active tab)
  • More Accessible Solution
  • More Challenging Solution
Task Solution

The Webster family needs to buy 7 packages of plastic plates. Stop and Shop is offering the better buy.

More Accessible Solution

The Webster family needs to buy 7 packages of plastic plates, for a cost of $41.93.

More Challenging Solution

See the solution to the original version of the task. No, buying in bulk at the sale price will not save the family money.

Possible Connections

Below are some examples of mathematical connections. Your students may discover some that are not on this list.

  • Patterns: Packages +1, People +15, Cost +$5.48.
  • Rules: 15 • p = t; $5.48 • p = c (p is packages, t is total plates, c is total cost).
  • You will end up with an extra package of 15 plates with the buy one, get one free deal.
  • You spend $2.74 less at Market Place than Stop and Shop.
  • `sf(1/2)` off is 0.5, or 50% the regular cost.
  • There are 5 extra plates.
  • The number of people are multiples of 15.
  • Relate to a similar task and state a math link.
  • Graph the data in the tables comparing costs at the 2 stores.
  • Find the cost of plates for more people/packages.

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