Which Peanuts Are The Best Deal?

 
You are going to a baseball game and you love to eat salted peanuts while watching the game.  You know that you can buy peanuts there, but you know it is cheaper to bring your own.  When you go to the grocery store to buy some, you see two choices: $3.59 for a 20 oz bag of salted peanuts or $2.59 per pound for loose salted peanuts.
 

• Which peanuts are the better deal?

 

These questions may be useful in helping students down the problem solving path:

• What information would be useful in figuring this out?
• What assumptions are we making?
• What is a guess for which peanuts are a better deal?

 

While the loose peanuts are always going to be cheaper (the loose peanuts are about $0.16/oz vs about $0.18/oz for the bagged peanuts) there are a variety of correct ways to explain how they reached that answer.  For example, students could:

• find the cost per ounce of both peanuts
• find the cost per pound of both peanuts
• find out how much 20 oz of the bulk peanuts costs and compare that to the 20 oz bag of peanuts

The key will be for students to be able “mak[e] plausible arguments that take into account the context from which the data arose.” (Standard for Mathematical Practice 3)

I have no problem with students using a calculator with this problem.  Not only is this a tool we would use in real life and supported by Standard for Mathematical Practice 5, but the sad reality is that if students do not understand the math content, the calculator is not going to help them.
 

• Prices of bulk peanuts and bags of peanuts:

 

• CCSS 6.RP.2 – Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”
• CCSS 6.RP.3 – Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

 

• Grocery store photo