Math patterns example 1 | Applying mathematical reasoning | Pre-Algebra | Khan Academy

Summary

The video script explores seating arrangements at tables, demonstrating how many people can be seated as more tables are added end-to-end. It begins with a single table seating six, then explains that adding a second table increases capacity to ten, as one end is no longer usable. The pattern continues, with each additional table adding four more seats, totaling 14 for three tables. The explanation clarifies that the increase is due to the usable ends of the new table. The script encourages viewers to predict seating for more tables based on this pattern.

Takeaways

• 😀 A single table can accommodate six people: one at each short end and two at each long end.
• 🔄 When tables are joined end to end, the space at the ends where they touch is no longer usable for seating.
• 🔢 The seating capacity increases by four people with each additional table.
• 📈 The pattern observed is that the number of people that can be seated is 4 more than the previous number of tables.
• 🧩 The first table allows for six people, the second for ten, and the third for fourteen, following the pattern.
• 💡 The increase in seating capacity is due to the addition of four new seats from the new table, as one end is taken by a person moving from the previous table.
• 📚 The seating pattern can be visualized by imagining real people moving and rearranging as tables are added.
• 📉 The usable ends of the tables are crucial in determining the seating capacity as they are the only places where new people can be added.
• 🔎 By understanding the pattern, one can predict the seating capacity for any number of tables without needing to draw diagrams.
• 📝 The formula derived from the pattern is that the total number of people that can be seated is the number of tables multiplied by four plus two.

Q & A

How many people can be seated at a single table according to the script?

A single table can seat six people: one at each short end and two at each long end.

What happens when two tables are placed end to end?

When two tables are placed end to end, one person can no longer sit at the joint, so the total number of people that can be seated is reduced to 10.

How many people can be seated when three tables are placed end to end?

With three tables placed end to end, 14 people can be seated.

What is the pattern observed when adding more tables to the setup?

The pattern observed is that for each additional table, four more people can be seated.

Why is there a reduction in the number of people that can be seated when tables are joined?

The reduction occurs because the person at the usable end of the previous table moves to the new end, leaving one less space at the joint where the tables meet.

How does the script illustrate the seating arrangement with real people?

The script uses a blue person to represent someone who insists on sitting at the end of a table, and a purple person to represent new people who can be seated when a new table is added.

What is the seating capacity for four tables placed end to end?

With four tables placed end to end, the seating capacity is 18 people.

What is the seating capacity for five tables placed end to end?

With five tables placed end to end, the seating capacity is 22 people.

How can one calculate the seating capacity for any number of tables placed end to end?

To calculate the seating capacity for any number of tables, start with 6 (the capacity of one table) and add 4 for each additional table.

What does the script suggest about the relationship between the number of tables and the number of people seated?

The script suggests a direct proportionality where the number of people seated increases by four for each additional table.

How does the script use color to differentiate between the people being seated?

The script uses blue for the person who moves to the new end of the table and a unique color (purple in the script) for the new people who can be seated with the addition of a new table.