For my weekly, I decided to focus on area and found many ways to do a single problem that will be very important in teaching kids because of their different forms of learning. First I worked on thinking of all the possible ways to see a shape and find area by figuring geometrical formulas and visually moving pieces of the shapes around. In a classroom, there is going to be many different learning styles and I need to be able to work with each one to teach math in a way that everyone learns to understand. I decided to work with the two shapes below to figure area and different ways to see and solve a single problem so I can use this technique in the classroom.
To find the area of the triangle below, I would teach students to count the number of full squares inside the shape and find there to be 10 and then see that there are half squares. These five triangles add up to 2 and 1/2 squares or 2.5 which equals 12 and 1/2 or 12.5.
10+1/2+1/2+1/2+1/2+1/2= 12 and 1/2 10+.5+.5+.5+.5+.5= 12.5
Area could also be found using the geometry formula for a triangle, A=1/2bh or Area=1/2base x height. To solve this you would count the base which is five across and the height which is also five and plug them into the formula.
A=1/2(5)x(5) A= 1/2 x 25 A= 12.5 or 12 and 1/2
To find the area of the parallelogram, I solved it similar to the triangle by counting the amount which is 30 whole squares in the middle. Then figure if you cut off the triangles on each side and add them together it forms a rectangle that is 3 x 5 which has an area of 15, (A=bh) and then you would add it to 30 to equal 45. The area could also be done the same way by using the formula of A=1/2bh on each side triangle.
10+1/2+1/2+1/2+1/2+1/2= 12 and 1/2 10+.5+.5+.5+.5+.5= 12.5
Area could also be found using the geometry formula for a triangle, A=1/2bh or Area=1/2base x height. To solve this you would count the base which is five across and the height which is also five and plug them into the formula.
A=1/2(5)x(5) A= 1/2 x 25 A= 12.5 or 12 and 1/2
To find the area of the parallelogram, I solved it similar to the triangle by counting the amount which is 30 whole squares in the middle. Then figure if you cut off the triangles on each side and add them together it forms a rectangle that is 3 x 5 which has an area of 15, (A=bh) and then you would add it to 30 to equal 45. The area could also be done the same way by using the formula of A=1/2bh on each side triangle.
To compare the methods used to find the area of the two shapes, I found that to work with any shapes you can use a mathematical formula, or just visually count squares. Some kids may find it easier visually, to put the half squares to together and then count the total area and others work better with the area formulas. In a classroom, I think that it is so important to teach concepts in many different ways because it is difficult to make math click with every student. By using different methods, kids can learn in their own style and it is good to provide different ways to approach a math problem so kids can form new ways of thinking. By forming those skills, students can use the abilities in math problems throughout their lives.
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