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Area in the Coordinate Plane (easy)

  • 9-12 grade

Lesson Description:

The students figure out the area of the region created by ball position, Nao player's position, and the goal posts. The positions have coordinates on the field.


 

Standards Covered

CCSS.MATH.CONTENT.HSG.GPE.B.7

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.*

CCSS.MATH.PRACTICE.MP1

Make sense of problems and persevere in solving them.

CCSS.MATH.PRACTICE.MP3

Construct viable arguments and critique the reasoning of others.

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.

image description

Lesson Modules


Teaching Tips:

Have students work in a group and encourage them to discuss the questions with their team members. 

Have students answer the question individually. 

Share the poll result and have a quick class discussion(lesson than 5 minutes) around the norms. Lead the discussion toward to the next module where the students will explore strategies to find the area of the triangle.

Look at the image and think about the questions below.

  • Can you explain what's happening?
  • What does the red triangle represent? 
  • Can you calculate the area of the red triangle?

 

 



What information do you need to figure out the area of the region? Type your answer only in one word.

 


Teaching Tips:

Give students a limited time for this module. The students can try to solve the challenge individually or in a small group. 

The potential strategies that students might use:

  1. counting the unit (1 by 1) square and estimate the area visually.
  2. using the formula {latexinline{\frac{1}{2} \cdot base \cdot height}latexinline}
  3. subtracting right triangles from a rectangle. 

While the students are working on this module, monitor who is working on which strategy. At the end of this module, have students present their strategy and reason why they chose it. 

Make a connection between different strategies and discuss the cons. & pros. of using each strategy. The goal of this presentation is to lead the students to use the distance between two points and apply the area of triangle formula. 

Play with the interactive tool below. Click on the box next to "Goal Line" text and follow the next steps. 




How can you calculate the are of the triangle? Type your key word for your strategy using only one word.



Estimate the area of the triangular region. Type your answer using only a number.


Share how you did what you did to the class. You can see what other students approached the same problem with different ways. Think of cons. and pros. of each strategy. 


Teaching Tips:

First, make sure you use Adobe Acrobat, if you don't have the program in your computer, download Adobe Acrobat.

Print out the soccer field, selecting the option Poster to see the multiple pages. 

Place the multiple pages together in order on a flat surface such as a floor or a table. Use tapes to paste and create a soccer field.

Use the list of questions and ask students to find the area of the region where the ball can travel to score the goal. The first answering team will get to chance to control NAO to kick the ball. 


Before proceeding with the physical robot, familiarize yourself with the Robot anc choregraphe interface. Take a moment to explore its features and understand how to connect and disconnect the robot properly. Remember, a proper disconnection is crucial to avoid waiting times or unnecessary reboots.

Now, let's add a fun twist! Make the simulation and get ready to make NAO score some goals!!!



Teaching Tips:

If time is allowed, use this bonus challenge for students to understand that if two triangles have the same base and height, they have the same area. 

Compare the areas of the two regions below:


               


Which triangle has the bigger area, left or right one?
  • Left Triangle
  • Right Triangle
  • Both triangles have the same area.
  • Cannot determined with the given information.


Teaching Tips:

Have students mark the self-reporting scores and answer the in-depth questions. You can access to the answers from the dashboard. 

You've learned how to use coordinates to compute areas of a triangle. Check how much you understand each concept and answer the questions below. 

I understand the concept of distance between a point and a line
  • Not at all
  • Not really
  • Kind of understood
  • Pretty much understood
  • Totally got it

Explain how you can find the shortest distance between the ball position and the goal line.

I understand the concept of distance between two points
  • Not at all
  • Not really
  • Kind of understood
  • Pretty much understood
  • Totally got it

Explain how you can use Pythagorean Theorem to conclude the distance formula.