Year 8 Interactive Maths - Second Edition

## Problem Solving Unit

### Problem 15.1  Modelling the Number of Sleepers

Sleepers can be used to divide a garden into separate beds as shown in the following diagrams:

1.  One garden bed requires 4 sleepers, two garden beds require 7 sleepers, three garden beds require 10 sleepers and four garden beds require 13 sleepers.
a.  How many sleepers are required for 5 garden beds?
b.  How many sleepers are required for 6 garden beds?
c.  How many sleepers are required for 7 garden beds?

2.  Let b represent the number of garden beds and s the number of sleepers.
a.  Complete the following table:

b.  In mathematics, patterns in numbers are often used to discover a rule for finding the next number.  When we look for a pattern in numbers, we try to look at each number and find out how it relates to other numbers.  This enables us to state a rule in words and then write it algebraically.  By observing the pattern in the above table, find the relationship that exists between b and s.

3.  Draw a graph of s against b.

4.  How many pieces of sleepers would be needed for 100 garden beds?

5.  How many pieces of sleepers would be needed for 1000 garden beds?

### Problem 15.2  Modelling the Number of Chairs

Chairs can be arranged to surround tables as shown in the following diagrams:

1.  From the diagrams above, we notice that 8 chairs can surround one table and 10 chairs can surround two tables.  Draw a similar diagram to work out how many chairs can be arranged to surround 3 tables?

2.  Let t represent the number of tables and c the number of chairs.  Complete the following table.

3.  In mathematics, patterns in numbers are often used to discover a rule for finding the next number.  When we look for a pattern in numbers, we try to look at each number and find out how it is related to other numbers.  This enables us to state a rule in words and then write it algebraically.  By observing the pattern in the above table, find the relationship that exists between t and c.

4.  Draw a graph of c against t.

5.  How many chairs can be arranged to surround 15 tables?

6.  How many chairs can be arranged to surround 20 tables?