Tables and chairs 0 Overview Using this Resource Connecting to the Curriculum Marking Student Responses Working with Students Further Resources This task is about spatial patterns and rules. A room has tables that are shaped like this. Each table can seat 5 people. Here is a picture of 3 tables in a row. Question 1Change answer a) Six tables are put together in one long row (as above). a) Six tables are put together in one long row (as above). How many people could be seated? people Question 1Change answer b) 35 people needed to be seated in one long line of tables (arranged as above). b) 35 people needed to be seated in one long line of tables (arranged as above). How many tables would be needed? tables Question 2Change answer c) Write a rule to work out the number of people that could be seated in a long row of any number of tables. c) Write a rule to work out the number of people that could be seated in a long row of any number of tables. Rule: Task administration: This task is completed with pencil and paper or online with some auto-marking. Level: 4 Curriculum info: Maths, Number and Algebra, Patterns and relationships Keywords: spatial patterns, functional rules Description of task: Students answer two questions about the number of seats available as more tables are added to a row, and state a rule for the pattern. Learning Progression FrameworksThis resource can provide evidence of learning associated with Patterns and relationships, sets 5-6 within the Mathematics Learning Progressions Frameworks.Read more about the Learning Progressions Frameworks. Answers/responses: Y8 (04/1997) Y9 (04/1997) a) 20 moderate moderate b) 11 difficult difficult c) "Multiply the number of tables by 3 and add 2' (3n + 2). Also accept: 5 + 3 (n - 1) ["5 seats with 1 table with 3 more for each subsequent table"]. 5n - 2 (n - 1) ["5 seats per table minus 2 seats each time tables are put together"]. very difficult difficult Diagnostic and formative information: Common error Likely calculation Likely misconception a) 22 30 11 × 2 6 × 5 Calculate twice the number of people at 3 tables. 5 people at each table rather than an extra 3. b) 7 35 ÷ 5 5 people at each table rather than an extra 3. c) 5 per table - 5 people at each table rather than an extra 3. Diamond patterns II Matchstick patterns III Building square patterns Supermarket patterns Diamond patterns III Matchstick patterns Building patterns L Patterns Grid triangles