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4 a Draw the next two shapes in this spatial pattern.

b Copy and complete the table. Planks are vertical and horizontal.

Number of fence sections 1 2 3 4 5

Number of planks required c Describe a rule connecting the number of planks required to the number of fence sections produced. d Use your rule to predict how many planks would be required to make 20 fence sections. PROBLEM-SOLVING a Draw a table of results showing the relationship between the number of tables in a row and the number of students that can sit at the tables. Include results for up to five tables in a row b Describe a rule that connects the number of tables placed in a straight row to the number of students that can sit around the tables. c The room allows seven tables to be arranged in a straight line. How many students can sit around the tables? d There are 65 students in Grade 6 at North Park Primary School. Mrs Greene would like to arrange the tables in one straight line for an outside picnic lunch. How many tables will she need? a Complete a table of values relating length of spa and number of tiles required, for values up to and including a spa of length 6 units. b Describe a rule that connects the number of tiles required for the length of the spa. c The largest spa manufactured is 15 units long. How many tiles would be required to pave around its perimeter? d A paving company has only 30 tiles left. What is the largest spa they would be able to tile around?

5 At North Park Primary School, the classrooms have trapezium-shaped tables. Mrs Greene arranges her classroom’s tables in straight lines, as shown.

6 The number of tiles required to pave around a spa is related to the size of the spa. The approach is to use large tiles that are the same size as that of the smallest spa.

A spa of length 1 unit requires 8 tiles to pave around its perimeter, whereas a spa of length 4 units requires 14 tiles to pave around its perimeter.