You have a big birthday party coming up soon. You invited 16 people for the occasion.  The problem is, you haven’t gotten cupcakes yet. While considering the number of cupcakes to buy, your rule is each person attending (including yourself) must have 2 cupcakes each. Assuming that each person you invite will come and have their 2 cupcakes, how many cupcakes should you buy to hold true to your rule (2 cupcakes for everyone)?

This problem can be manipulated in many ways. For instance, what if you wanted each person to have 3 cupcakes? 5? We can let the number of cupcakes you are buying to be y and the number of cupcakes per  person be x and create an equation for the number of cupcakes you should buy for your party (n) and the number of cupcakes per person (x).

Now you are having second thoughts. Instead of yourself having the same number of cupcakes as everyone else, you want to have one more (so you would have x+1 cupcakes and everyone else would have x). How would this change your equation above? Create a new equation demonstrating this new rule with the same variables.

Now that you have established how to manipulate the equation based on changing information, you want to create an equation for future parties that you host showing the amount of cupcakes (or other food items) you need to have based on: the number of food item you want for each person, the number of people that will be there, and the amount (if any) more you want to have for yourself. Let these variables be x, y, and z respectively and the number of food items you need be the variable n. Create a brand new equation given these variables for the number of food items you need.

At times, it can be very difficult to engage math students in a classroom. Story problems are somewhat recommended because they can bring relevance from the students’ lives into a math problem. What preceded is an extended story problem involving something that all students will love: food. Along with the problem, the picture should make students’ mouths water. This problem should be relevant to almost all students and possibly give them some party planning advice.

The Common Core State Standard this problem is aligned with is HSA.CED.A.2:
Create equations in two or more variables to represent relationships between quantities.