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Mathematics

Multiple Ways To Teach a Concept – Area of a Rectangle and Tessellation

Multiple Ways To Teach a Concept – Area of a Rectangle and Tessellation

Concept #1 Example Problem
Area of a Rectangle Find the area of a rectangle whose length is 4 inches and width is 3 inches.
Video link found Online Video Link you created
https://www.youtube.com/watch?v=W2QjnsiFpNY https://youtu.be/L2nkeDG9nVA
Solving the problem using the Online video method Solving the problem using your own video method
To solve the area of a rectangle whose width is 3 inches and length is 4 inches, we begin by writing the formula.

 

 

A = L × W

= 4 × 3

= 12 inches2

We will use the counting method to solve the problem. We will count the number of cubes within the rectangle. Therefore, we will first draw a rectangle of 3 inches by 4 inches, then count the cubes within the rectangle.

       
       
       

Let’s draw a rectangle with three rows and four columns, as shown below:

 

 

 

After drawing a rectangle and making cubes within it, count the number of cubes within the rectangle, which equals 12. Since we are finding the area, we will add squared units.

Therefore, the area of the rectangle = 12 inches2.

 

Concept #2 Example Problem
Tessellation

 

 Does a pentagon tessellate?
Video link  found Online Video Link you created
https://www.youtube.com/watch?v=FRwiszRJN_s https://youtu.be/27JvlnTuVx8
Solving the problem using the Online video method Solving the problem using your own video method
A tessellation is made when a shape is repeated several times to cover a plane or surface without leaving any overlaps or gaps.

For example, in the video link above, a square polygon covers a space without leaving gaps, while a pentagon covers a plane but leaves a gap, and its interior angles do not add up to 360 degrees (CK-12 Foundations, 2015). Therefore, a pentagon is considered a non-tessellation polygon.

Tessellation has several uses, like when building walls, ceilings, and floors. In addition, they are used in art to design ceramics, clothing, and stained glass windows. For polygons, when two or more polygons meet at the same point or the vertex, the internal angle must add up to 3600 for them to tessellate.

For example, a square polygon will tessellate like this: when square one is joined to squares 2, 3, and 4 at the center, they form 3600 because a square forms an angle of 900 at every corner.

Square 1 Square 2
Square 3 Square 4

 

When all 4 ninety-degree angles are added, they add up to 360, confirming that a square polygon tessellates because when two or more squares meet at the vertex, the internal angles add up to 360.

 A pentagon is a polygon with five sides whose internal angles are 1080 each. So, when we join three or more polygons, the sum of the internal angles does not add up to 360 degrees; therefore, it does not tessellate, while that of a square will tessellate because the interior angle of a square is 900. Therefore, without adding, we just multiply the 90 degrees by four (the number of joined squares) to get 3600, confirming that a square tessellate. However, a pentagon does not because when one interior angle is multiplied by the number of joined pentagons, they add up to 3240, not 3600.

References

CK-12 Foundations. (2015). Tessellations: Examples (Geometry Concepts). Youtube https://www.youtube.com/watch?v=FRwiszRJN_s.

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Question 

Multiple Ways To Teach a Concept - Area of a Rectangle and Tessellation

Multiple Ways To Teach a Concept – Area of a Rectangle and Tessellation

Assessment Description
Creating videos allows teachers to save hours of repetitive teaching. Students also thrive if they can view a concept multiple times. It is important as a teacher that you can create short videos for your students to help them through the class.

Directions:

Use the tables below to do the following:

  • Select two concepts that were covered in Topics 3 and 4 of the course. Then, select one example problem for each concept you selected.
  • Search the internet to find a video that teaches each of your selected concepts.
  • Create your own videos that teach the concepts in a different way than the videos you found on the internet. (You will need to upload your video to a video-sharing site that provides a link that you can paste below. Your video should not be “searchable” within the video-sharing site. If you upload your video to YouTube, select the “unlisted” option, so it is not searchable. Ensure that others can access and view your linked video prior to submitting it to the LMS.)
  • Solve your selected example problem twice, using the method employed in the video you found online, and using the method employed in the video you created. (Please show all work. (Hint: If you solve the problem on a piece of paper, just take a picture and copy and paste it to the Word document. You do not have to type to solve the answer.)