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# Renovate a Park by Applying Radicals and Formulas

Lesson 6 of 11

## Objective: SWBAT to solve geometric formulas, some involving squares, and square roots to determine certain dimensions to build a park using their algebra skills.

#### Warm Up

*10 min*

This Warm Up is intended to take about 15 minutes for students to complete and for me to review. I spend extra time on this Warm Up to make sure that students can work with basic geometric shape formulas to be successful in this lesson. The goal of this Warm Up, lesson, and unit is to create students that are strong problem solving on their own, and able to apply formulas with and without radicals.

Number one in the Warm Up has students find the area and perimeter of an Equilateral Triangle. I also demonstrate in the review a second formula for the area of an equilateral triangle, and introduce the formulas of the 30-60-90 degree triangle.

In the second problem, the students have to find the area and circumference of a circle given the radius. Then given an area for the circle, students have to determine the radius and the Circumference.

I demonstrate reviewing part of the Warm up in the video below:

#### Resources

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This section is an Introduction to the activity to Renovate a Park. I hand one copy of the Introduction to each student. I have a student read the introduction in which the students are asked by the Mayor to do three renovations in the Park:

- Build a triangular eating deck
- Build a full-size baseball field
- Resurface the basketball court

After reading the instructions, I have the students work independently on finding the dimensions of the triangular deck. Students are required to answer the questions within the activity, and label their diagrams.

The students use the length of the side of an equilateral triangle to find:

- the altitude or height
- the perimeter of the deck
- the area of half of the deck
- the area of the entire deck.

The key is listed in the resource section.

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#### Partner Work

*30 min*

After students have completed the introduction activity of finding the area of the triangular deck and answering the questions from the introduction, I allow them to work with their table partner. Part II has the students find specific dimensions of a baseball field given 90 feet for each side of the infield.

Students have to find:

- the distance from home to second base
- the perimeter of one half of the infield
- the area of one half of the infield
- the perimeter of the whole infield
- the area of the whole infiel

The final problem of the activity, Part III, is finding the dimensions of a basketball court given certain measurements in feet. The diagram shown is an example of a NBA size court. The students have to find:

- the area of the whole court
- the perimeter of the whole court
- the area of half-court
- the perimeter of half court
- the area encompassed by the three point line

Number five requires the student(s) to find the area of the large semi-circle and the rectangle that you can form where it connects to the straight line segments. Several students struggled with this problem. I have the students hand in the Park activity for me to assess, and then I demonstrate Number 5 for them. I show part of that demonstration below in the video.

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#### Summary

*5 min*

The purpose of the Summary Activity is for students to summarize what they had difficulties with and reflect on the work that they have done. These were multi-step problems that students had to persevere (MP1) through. There were some students that struggled specifically on the dimensions of the basketball court. It was more difficult for the students to read the basketball floor plan, than writing in the measurements on the other two diagrams.

This intend for this closure activity to only take about 5 minutes for students to reflect on their work and complete. Most of the students stated that the basketball court would be more expensive to resurface because of the materials and labor. The baseball field takes a lot of labor, but they felt the materials were cheaper.

#### Resources

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- UNIT 1: Introduction to Functions
- UNIT 2: Expressions, Equations, and Inequalities
- UNIT 3: Linear Functions
- UNIT 4: Systems of Equations
- UNIT 5: Radical Expressions, Equations, and Rational Exponents
- UNIT 6: Exponential Functions
- UNIT 7: Polynomial Operations and Applications
- UNIT 8: Quadratic Functions
- UNIT 9: Statistics

- LESSON 1: Introduction to Radicals
- LESSON 2: Apply the Pythagorean Theorem to a Broken Telephone Pole and an Isosceles Right Triangle.
- LESSON 3: The Pythagorean Theorem and the Distance Formula
- LESSON 4: Finding the Distance or the Midpoint of a Line Segment on the Coordinate Plane
- LESSON 5: Tailgating and Solving Radical Equations
- LESSON 6: Renovate a Park by Applying Radicals and Formulas
- LESSON 7: Add and Subtract Radical Expressions
- LESSON 8: Gallery Walk of Application Problems Involving Radicals
- LESSON 9: Multiplying Radical Expressions
- LESSON 10: Dividing Radicals Made Easy Through the History of Rationalizing
- LESSON 11: Simplify and Rewrite Radicals as Rational Exponents and Vice Versa.