Number patterns: seating guests at a wedding feast
Push tables together for a wedding feast, spot the pattern in the number of seats, and write the rule for any number of tables.
Core concept
In short: Add tables to a banquet and find the rule for how many chairs you need.
When each step adds the same amount a, the nth term of the pattern is an + b
Topic: Patterns and sequences
At a wedding feast, square tables are pushed together in a long row. One table seats 4: one guest on each side. Two tables seat 6, three seat 8: each extra table adds 2 seats, because the seats at the joins disappear. The pattern 4, 6, 8, 10, … goes up by the same amount each time, so it has a rule: seats = 2 × tables + 2, written 2n + 2 for n tables. With the rule we can find the seats for 10 tables, or the tables needed for 30 guests, without drawing them all.
What you will learn
- Continue a number pattern and find its constant difference.
- Write the nth term of a pattern as an + b.
- Use the rule to answer questions in both directions.
Before you start
- Times tables and simple expressions such as 2n.
Materials
- Square tiles or matchsticks to model the tables
Equipment
- Squared paper
Procedure
- Tap − or + to change the number of tables; tap the chip for square tables in a row, long tables in a row or tables set apart.
- Read the table of values and the difference between seats.
- Find the seats for 10 square tables in a row, and the tables needed for 30 guests.
- Record 10 tables set apart, and the fewest long tables that seat 50 guests.
How this simulation is simplified
- One guest sits on each side of a square table; a long table seats 2 on each long side.