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# Gallery Walk of Application Problems Involving Radicals

Lesson 8 of 11

## Objective: SWBAT use their problem solving skills to solve problems with radicals with different pieces of given information.

*50 minutes*

#### Warm Up

*10 min*

This Warm Up is intended to take about 10 minutes. I will not assess this Warm Up. I have purposely chosen two problems that may give my students difficulty. The level of challenge in this Warm Up will help students in the next activity, when we work on Posters in small groups of 4-5 students.

The problems on the posters are meant to reinforce applying adding and subtracting radicals learned in the previous lesson. However, one of the problems on poster five requires some knowledge of multiplying or squaring radicals using the Pythagorean Theorem. Therefore, the problems I select for this Warm Up should help them get started on the problem.

I model reviewing the Warm Up below in the video:

#### Resources

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#### Poster Activity

*30 min*

After reviewing the Warm Up, I start randomly numbering heads for the Poster Activity. I count to 4 or 5 before starting over , depending on the number of students in the class. For a class of 30, I need six groups, so I count to 5. Like numbers are grouped together, and I have to be careful of students not going to the correct group. Students spend about 4 minutes at each poster before I instruct them to the number that follows. The group at poster six, moves to one.

A goal of this activity is for students to learn from each other, while working in collaborative groups. Each group will rotate from one problem to the next about every four minutes. I number heads for this activity from one to four or five depending on the number of students in class. Like numbers are placed in the same group.

There are six posters that each group will rotate between.

- Poster 1 asks, "Which one does not belong?" Three of the expressions when completely simplified equals twelve square root of six minus twenty-nine square root of two. Expression number three does not belong because it is given as twenty-nine square root of two minus twelve square root of six.
- Poster 2 requires students to simplify two radical terms to like radicals and completely simplify.
- Poster 3 requires students to simplify three radical expressions. Two of the terms combine because they are like radicals when simplified, and the third one is not when completely simplified.
- Poster 4 requires students to find the perimeter of a rectangle given the width and length are radical expressions.
- Poster 5 begins with the problem that I model in the Warm Up, using Pythagorean Theorem. After the side of the third side of the triangle is found, students are instructed to find the perimeter of the triangle.
- Poster 6 is a multi-step problem. Students first have to evaluate the distance a person can see from two different heights. Then the students are are instructed to find the difference of those distances.

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#### Gallery Walk

*10 min*

After the Poster Activity, Students walk around and observe the posters for the last five minutes of class on a **Gallery Walk**. I ask students to complete a Reflection sheet as they are walking around that they hand in to me. I want to see what problems that they had difficulty on, and what problems that they were more confident.

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Hello,

I have a clarifying question. As the students go from poster to poster are they recording their answers on the poster or in their notebooks?

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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.