Generalizing Patterns: Table Tiles

Mathematical goals

This lesson unit is intended to help you assess how well students are able to identify linear and quadratic relationships in a realistic context: the number of tiles of different types needed for a range of square tabletops. In particular, this unit aims to identify and help students who have difficulties:

  • Choosing an appropriate, systematic way to collect and organize data.
  • Examining the data and looking for patterns; finding invariance and covariance in the numbers of different types of tile.
  • Generalizing using numerical, geometrical or algebraic structure.
  • Describing and explaining findings clearly and effectively.


The unit is structured in the following way:

  • Before the lesson, students attempt the task individually. You then review their work and formulate questions for students to answer in order for them to improve their work.
  • At the start of the lesson, students work individually to answer your questions.
  • Next, they work collaboratively, in small groups, to produce a better joint solution than those they produced alone. In the same small groups, students critique examples of other students’ work.
  • In a whole-class discussion, students explain and compare the approaches seen and used.
  • Finally, students reflect on their work and their learning.

Materials required

  • Each student will need the Table Tiles task, a copy of the Grid Paper and a copy of the How Did You Work? questionnaire.
  • Each small group of students will need a copy of the Grid Paper and the Sample Responses to Discuss.
  • There is a projector resource to help you with the whole-class discussions.

Time needed:

15 minutes before the lesson, a 1-hour lesson, and 10 minutes in a follow-up lesson. All timings are approximate. Exact timings will depend on the needs of the class.