Lesson objective: Apply knowledge of representing functional relationships in the form of tables and graphs to solve a tiling pattern problem.

This lesson provides an opportunity for students to apply their knowledge and understanding of linear and nonlinear functions to a real-life situation. Pairs of students are asked to create a visual pattern that represents a linear or nonlinear functional relationship to give to a partner, so that the partner can create a table or graph of the relationship. The student pairs also create a graph and table for the "answer key." As an extension, the partner may try to write a general rule for the functional relationship. Alternatively, teachers may assign the pattern from the task introduction video, and have pairs of students create tables or graphs to answer the questions from the task introduction video. Students who would like a challenge can write a rule for the pattern in the task introduction video.

Key Concept students will use:

- Nonlinear functions can be represented by tables, graphs, equations, and written descriptions.

Skills students will use:

- Qualitatively describe functional relationships. (Grade 8 Unit 6)
- Write a rule for a linear function. (Grade 8, Unit 7)
- Create a graph of a functional relationship. (Grade 8, Unit 6)

Students engage in Mathematical Practice MP.4 (model with mathematics) as they create tables, graphs, and equations to help them figure out how many tiles they need for their pattern.

**Key vocabulary: **

- linear
- nonlinear
- relationship
- sealant

**Special materials needed:**

- graph paper
- rectangular tile pieces may be helpful