Lesson objective: Apply understanding of irrational numbers as actual distances to solve a real-world problem.

This lesson provides an opportunity for students to apply their knowledge and understanding of irrational numbers to a real-life situation. Students are asked to decide which jet engine compartment a compressor fan will fit into, and make a case for why they agree with the mechanic who chose the same engine they did.

Key Concept students will use:

- Irrational numbers are measures of lengths, and therefore can be located a distance from 0 on the number line.

Skills students will use:

- Perform operations using irrational numbers
- Solve equations of the form \(x^2 = p\)
- Solve a two-step equation (Grade 7, Unit 7)
- Find radius or diameter of a circle given the area (Grade 7, Unit 11)

Students engage in Mathematical Practice 3** **(construct viable arguments and critique the reasoning of others) as they defend their process and decisions to round or truncate irrational numbers to solve the problem.

**Key vocabulary: **

- Area
- Diameter
- Irrational number
- Pi
- Radius

**Special Materials: **