In your journal, you identified careers that involve irrational numbers. You brainstormed or researched jobs that use pi or Euler's number to do their work.

Question

Imagine that your friend loves to plan parties, and he wants to be an event planner someday. He does not think he needs to know how to find a number between two rational numbers. He also says he will never use pi again in his life after math class. You think of some of the tasks he might need to do as an event planner:

Decide how many cakes to order when a party could have as few as 50 people and as many as 100 people.
Choose a round table that is the correct size to fit six people.
Make a prediction about how much to budget for the decorations at a party when the customer is still deciding between $10 floral arrangements and $30 floral arrangements.
In your post, explain to your friend how he will use the skill of finding a number between two rational numbers in his dream career:

Choose one of the examples from the list above, and represent the example with a mathematical statement.
Summarize to your friend why he will need both rational and irrational numbers as an event planner.
Then read two of your peers' messages to their friends. Respond to two of your peers:

For each message, add one more example of how you believe an event planner needs the skill of finding a number between two rational numbers.
Post a detailed response to the Numbers Between Rational Numbers prompt. Then respond to two classmates' posts.

Participate in the discussion to learn more about using rational and irrational numbers when planning an event.

Conversations Start a new conversation within this discussion.

Answer 1

Hey [Friend's Name],

I know you love party planning and are set on your dream of becoming an event planner, but I think you might be underestimating the importance of rational and irrational numbers in your future career. Let’s look at one of the examples you mentioned—deciding how many cakes to order for a party.

Mathematical Statement:
Let’s say you anticipate that the number of guests could realistically be anywhere between 50 and 100 people. If you know each cake serves about 12 slices, you might use an equation like this:

Number of cakes needed = (number of people) / (slices per cake)
If you expect a party of 75 people, you'd calculate:

Number of cakes needed = 75 / 12 ≈ 6.25 cakes

In this case, finding a number between two rational numbers (in this case, 50 and 100) helps you understand how many cakes you should round up or down for ordering—most likely to 7 cakes since we can’t order a fraction of a cake.

Why You’ll Need Both Rational and Irrational Numbers:
As an event planner, you'll regularly deal with situations where both rational and irrational numbers come into play. For example:

1. Rational Numbers: These will help you manage budgets, and figure out seating arrangements, guest counts, and item quantities—all discrete things that can be expressed as whole numbers or fractions. You’ll often need to balance your expenses between fixed costs (like venue rentals) and variable costs (like food per guest).

2. Irrational Numbers: You might not think it, but irrational numbers like π (pi) could pop up when planning table sizes, round table placements, or decor arrangements. For instance, if you’re determining how much fabric is needed to drape a round table or setting up a dance floor with rounded corners, you end up needing the area or circumference calculations involving pi.

In conclusion, embracing both types of numbers will enhance your planning efficiency and accuracy. So don’t dismiss those math skills – they will definitely come in handy!

New Example:
You might also need to estimate the amount of space needed for a buffet table. If guests will be fashionably spaced apart, you could calculate how many tables to place based on the distance between them. If you estimate that two tables need to be spaced between 5 and 10 feet apart, using the average or to find a number between those measurements will ensure you have enough space without overcrowding.

Looking forward to hearing your thoughts!

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Responses to Two Classmates

Response to Classmate 1:
Great point about the decorations! It’s so true that understanding the budget based on varying floral options can drastically impact the event's theme. As an additional example, consider the layout for seating arrangements at a wedding. If table sizes vary between 4 to 10 people per table, you’ll need to find the right number of tables required to accommodate an exact midpoint guest count. If the total number of guests is anywhere between, say, 80 and 120, recognizing a number between those rational numbers can help optimize the seating arrangement.

Response to Classmate 2:
I agree with your example about finding venue spaces! It's invaluable to use rational and irrational numbers in space planning, like determining the area for dance areas and seating layouts. Another case in point could be calculating catering quantities based on different menu items. If you are planning a menu for a range of guests, estimating between two numbers—for example, 50 and 150 spicy appetizers—will help you find the right amount to order, all while keeping food waste low.

Let’s keep the conversation going!