Do Hybrid Cars Pay for Themselves?

The Situation:

Your family wants to buy a new Toyota Camry LE and is considering buying the hybrid version if the money saved on gas will be enough to pay the extra cost of the hybrid.

The Challenge:

How many years will it take from saved gas money to pay for the extra cost for a hybrid?

Information that May be Helpful:

Below is important information about the Camry LE and Hybrid Camry LE

Below is information on average miles driven by age group (for the purposes of this activity, please use the average for all groups).

Below is a picture of the price sign for a local gas station.

What problem(s) are you trying to figure out?

What do you already know from the problem? What do you need to know to solve the problem?

What is your conclusion? How did you reach that conclusion? How do you know your conclusion is correct?

How Much Does a 100x100 Five Guys Cheeseburger Cost?

The Situation:

Five Guys Burgers and Fries ordinarily sells hamburgers, cheeseburgers (two beef patties and two slices of cheese) and little hamburgers and cheeseburgers (a single beef patty and a single slice of cheese). While they don’t advertise it, they have a secret menu which includes a burger where you can order as many extra beef patties and cheese slices as you like. The prices and nutrition information are not listed though. The most common orders are 3x3’s (read as “three by three”) and 4x4’s (read as “four by four) that contain three and four layers of beef and cheese, respectively. However some people have ordered 20x20’s and even a 100x100 (pictured below).

The Challenge:

How much would a 100x100 cost?

Information that may be Helpful:

The picture below shows the menu from Five Guys Burgers and Fries.

The picture below shows a cheeseburger from Five Guys Burgers and Fries.

The picture below shows a 20x20 from Five Guys Burgers and Fries.

The picture below shows a 100x100 from Five Guys Burgers and Fries.

What problem(s) are you trying to figure out?

What do you already know from the problem? What do you need to know to solve the problem?

What is your conclusion? How did you reach that conclusion? How do you know your conclusion is correct?

Which Bed, Bath & Beyond coupon should you use?

The Situation:

Bed, Bath & Beyond frequently sends out two different coupons to its customers. One coupon is “20% on single item” and the other coupon is “$5 off any purchase of $15 or more.”

The Challenge:

Which coupon will save you the most money?

Questions to Answer:

Will both coupons always save you the same amount of money?

How can we tell which coupons will save us more money?

Information that May be Helpful:

You may be able to figure this out without knowing what items to purchase. If you are struggling, consider using the following items from Bed, Bath & Beyond to help determine which coupon will save you the most money.

What problem(s) are you trying to figure out?

What do you already know from the problem? What do you need to know to solve the problem?

What is your conclusion? How did you reach that conclusion?

How Much Purple Ribbon Will You Need?

The Situation:

You are making a wedding like pictured above (the ribbon does wrap all the way around each layer). You need to purchase ribbon at the fabric store to wrap around the cake.

The Challenge:

How much purple ribbon do you need to buy?

Questions to Answer:

What length of ribbon will you need to decorate the cake exactly as pictured above?

Information that May be Helpful:

Below is an overhead view of the cake with the scale used for drawing it.

What problem(s) are you trying to figure out?

What do you already know from the problem? What do you need to know to solve the problem?

What is your conclusion? How did you reach that conclusion?

How Much Would a Coin Carpet Cost?

The Situation:

You are looking for a unique way to cover the floor of your house, so you decide to create a “coin carpet”.

The Challenge:

Which coin will create the cheapest “carpet”?

Questions to Answer:

If you were going to carpet the living room pictured below, with a single kind of coin, which would be the cheapest option?

Information that May be Helpful:

The table below provides some information about the different types of US coins that you could use to “carpet” your room. (Remember: 1 inch is approximately equal to 25.4 cm)

The arrangement of the coins is pictured below. They will be touching edge to edge.

What problem(s) are you trying to figure out?

What do you already know from the problem? What do you need to know to solve the problem?

What is your conclusion? How did you reach that conclusion?

Is Gas Cheaper with a Credit Card or Cash?

The Situation:

Some gas stations charge lower prices for customers who pay with cash instead of credit cards. Some credit cards give a cash back rebate for purchasing gas with their credit card.

The Challenge:

Is gas cheaper with a credit card or cash?

Questions to Answer:

Should you pay for your gas with cash or a credit card?

Information that May be Helpful:

Below is a picture of a gas station sign including their cash and credit prices.

Below is information about how the credit card company rebate program works.

What problem(s) are you trying to figure out?

What do you already know from the problem? What do you need to know to solve the problem?

What is your conclusion? How did you reach that conclusion? How do you know your conclusion is correct?