Lesson objective: Apply understanding of irrational square roots to solve a real-life problem.

This lesson provides an opportunity for students to apply their knowledge and understanding of estimating irrational square roots to a real-life situation. Students are asked to determine whether Mr. Nelson has enough materials to build a fence around three sides of his yard, given the area of the yard and the length of the fence Mr. Nelson can construct.

Students will use the Key Concept, which states that because we can find find the area of squares given the side length, we should be able to find the side length of a square given the area. This requires finding a number which, multiplied by itself, gives the area. Some of those numbers cannot be expressed as the ratio of integers, and are called "irrational" numbers.

Students will use their skills to estimate an irrational square root.

Students engage in Mathematical Practice 6 (attend to precision) as they attempt to discover an accurate estimation of the square root of 10,890, then multiply it by three to find the total length of the fence that is needed.

**Key vocabulary: **

- irrational number
- square root