Lesson objective: Solve mathematical problems that connect algebraic representations to a geometric pattern.

This lesson provides an opportunity for students to apply their knowledge and understanding of equivalent expressions to a mathematical situation. Students are asked to draw the next figure in the pattern, identify the number of dots in Figure ten, and write (at least) one algebraic expression that represents the number of dots in Figure *n*.

Key Concept students will use:

- Equivalent expressions have the same value.

Skills students will use:

- Writing expressions based on a given situation.
- Evaluating an expression at a given value of the variable.
- Identifying equivalent expressions as expressions that have the same value.

Students engage in Mathematical Practice 4 (model with mathematics) as they write algebraic expressions to represent the nth term of a pattern. Students use dot patterns to make sense of the numeric change in a sequence. The use of dot patterns allows students to loosely connect the numeric sequence with a familiar tool, the area model.

**Key vocabulary: **

- dot pattern
- Figure n
- nth term

**Special materials needed:**

- Application task handout (optional)