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# Course: BOX V2Application of Quadratics

• Intermediate

### Lesson Description:

Student will use a quadcopter to calculate the area of school campus so they can figure out where to place more benches and chairs for lunch break. The students will identify the relationships between the height of the quadcopter and the area the camera attached to the quadcopter can see.

## Standards Covered

### CCSS.MATH.CONTENT.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

### CCSS.MATH.CONTENT.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

### CCSS.MATH.CONTENT.HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

### CCSS.MATH.CONTENT.HSG.SRT.A.1

Verify experimentally the properties of dilations given by a center and a scale factor:

### CCSS.MATH.CONTENT.HSG.SRT.A.1.B

The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

### CCSS.MATH.CONTENT.HSG.SRT.A.3

Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

### CCSS.MATH.PRACTICE.MP1

Make sense of problems and persevere in solving them.

### CCSS.MATH.PRACTICE.MP2

Reason abstractly and quantitatively.

### CCSS.MATH.PRACTICE.MP4

Model with mathematics.

### CCSS.MATH.PRACTICE.MP5

Use appropriate tools strategically.

### CCSS.MATH.PRACTICE.MP6

Attend to precision.

### CCSS.MATH.PRACTICE.MP7

Look for and make use of structure.

## Teaching Tips:

Show the video to the class and help students to see the connection between the camera view (top right corner of the screen) and the height of the quadcopter. Repeat the video as needed.

Have students answer the question. Tell them their answer should be only in one word. If their answer includes a space, the system won't recognize their answer.

Share the answers as a word cloud and have a quick discussion with the class about the question. Make sure the students understand the key topics: as the quadcopter flies up/down, the camera sees different areas. The students will later figure out the relationships and write a quadratic equation.

Watch the video. Pay attention to the screen on the top right. It shows what the camera is seeing. Can you tell as the quadcopter is flying up, the camera sees more area?

What information do you need to figure out the area of a certain sector of the campus by using a quadcopter? Write your answer in only one word.

## Teaching Tips:

Have students play with the interactive tool. Help them to focus on the relationships between the height of the quadcopter and the area of the region the camera can see.

Once they explore with the interactive tool, have the students in small groups, depending on the number of computers you have in the class ( a group of 3 or 4 is recommended).

Show how to create a point on the x-y grid in.

There are two ways:

1. click on the       icon in the toolbar and click on the grid-in, OR
2. click on the "Input..." area to directly type the coordinates.

Have students plot the data they collected from the interactive tool.

Ask students to find the pattern/relationship between the height of the quadcopter and the area of the region that the camera can see.

There is a camera attached to the bottom of the quadcopter (blue dot). The camera can see the square region under it. Move the quadcopter up and down to see how the area changes.

With your group members, find the relationships between the height of the quadcopter and the area of the region that the camera can see. Show the patterns/relationships by using the tool below.

## Teaching Tips:

This activity helps students to apply the knowledge and skills they learned on their school campus.

Help all the students understand the task/mission of this challenge. They will come up with a proposal to the board members. You can facilitate the class like the TV show, "Shark Tank" -- each group present their proposal in front of the panels and have to answer the questions within a short time (1 or 2 minutes). In this way, the students have to summarize their ideas and deliver the message to the audience in a very clear way.

Robot simulation

Choose the height for the quadcopter to fly and click [RUN] button. You can also [RANDOMIZE] the camera view angles.

To make the quadcopter come back to the ground, click [LAND] button.

### HEIGHT:

• Rotate View
• Move Camera
• Zoom In

Now that you played with the simulation, you will go out from the building and have a quadcopter fly.

### Campus Re-design Challenge

You realized that students in your school are not hanging out in the outdoor area on campus.

You, as a designer, want to propose a solution to the board members and they will support the budgets you need.

You took a survey of the students and many said they would spend more time in the outdoor area of the campus if there were more benches. Work with your team members and come up with a design that serves as many students as possible yet it is designed very user-friendly. For example, you cannot just place benches on the campus without considering how the benches are used and how the people move around them, and how much extra space they need.

Work with your team members and come up with your design proposal. To convince the board members, you should explain how your design serves school community better and it still is very easy to use.

## Teaching Tips:

Give the students a quiet time. Have the students answer the questions individually. Encourage them to be honest in answering the questions. You have access to the responses in the dashboard.

Have a quiet individual time to answer the following questions. Be honest in answering the questions. No one will judge but your feedback will be used for better planning the future lessons.

I can identify AA similar triangles

• Not at all
• Not really
• Kind of understood
• Pretty much understood
• Totally got it

Explain how you can estimate the height of the quadcopter in order the camera to see the area of the campus.

I can create equations in one or more variables to represent relationships between quantities

• Not at all
• Not really
• Kind of understood
• Pretty much understood
• Totally got it

Explain how you can calculate the area of the region that the camera can see.