Category Archives: Area

Breaking Down a Story Problem

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Story problems can become frustrating if you do not understand what the problem is asking. I had a story problem in my math text-book for homework that I had to walk through step by step in order to fully understand it. The problem was broken into four parts: a, b, c, and d. Part a involved converting the units into liters of water; part b involved dividing the volume; part c involved division of a given volume; part d involved finding perimeter. Looking back on the problem gives me a different perspective because now I realized it is a great problem. It has many different parts which makes you think critically about the problem and how to find the answer. I have provided the story problem below and how I worked through it!

The story problem stated: the number of fish that can be put in an aquarium depends on the amount of water the tank holds, the size of the fish, and the capacity of the pump and filter system (Mathematics for Elementary Teachers Text book ninth edition). The picture from the story problem is above.

Part a states: How many liters of water will this tank hold? I found the volume of the tank with the formula V = Area of base x h. (50cm x 25 cm) x 30 cm = 37500 cm cubed. Once I found the volume in cubic centimeters, I converted it to liters. Since 1 cubic centimeter is equivalent to an mL, I did that first. Once I had the problem in mL it was easy to find liters because there are 1000 mL in a liter; therefore, the answer is 37.5 liters.

Part b states: The recommended number of tropical fish for this tank is 30. How many cubic centimeters of space would each fish have? This was pretty easy because all I did was divide the volume (37500) by 30 fish which equals 1250 cubic centimeters.

Part c states: Goldfish need more space and oxygen than tropical fish. Goldfish that are about 5 centimeters long require 3000 cubic centimeters of water. How many goldfish could live in this tank? For this I divided the volume (37500 cubic centimeters) by the required 3000 cubic centimeters of water; this comes out to about 12 goldfish.
 
Part d states: How many square centimeters of glass are needed for this tank if there is glass on all sides except the top? This question is simply asking for the surface area; therefore I found the area of all the shapes and added them together. (2 x 25 x 30) + (50 x 25) + (2 x 30 x 50) = 5750 cm squared.
 
With patience and effort any story problem can be solved!

Discovering Volume

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Understanding volume can be a tricky topic because it is easy to get it confused with area and perimeter. There are some main things that can help you understand volume. First, you want to make sure that all of the dimensions are labeled in cubic units. For example, if you have a triangular prism with sides measured in centimeters, you want the answer to be in cubic centimeters. Secondly, there are separate formulas to find the volume of a prism and the volume of a pyramid. Thirdly, you want to know the shape or 3 dimensional object you are dealing with because that will help you to determine the formula you need to use. Let’s look at some examples!

The formula for a prism is V = Area of base x height of prism. A prism is a three-dimensional shape with two parallel bases that are the same. In the picture below I have drawn a right prism. The base in this case is the square; therefore, area = length x width (3cm x 3cm = 9cm squared). Once we find the area of the base, we need to multiply it by the height of the prism (5 cm). The answer to the example is 45cm cubed because 45 cm cubed = 9 cm squared x 5 cm.

The formula for a pyramid is V = 1/3 x Area of base x height of pyramid. A pyramid is a three-dimensional shape with one base of any shape with sides all meeting at one point. In the picture above I have drawn a triangular pyramid. The one base in the pyramid is a triangle; therefore, area = 1/2 length x height (1/2 x 4 cm x 8 cm= 16 cm squared). Once we find the area of the base, we need to multiply it by the height of the pyramid which in the example is 10 cm. Lastly, we multiply the whole answer by 1/3. The answer to the example is about 53.3 cm cubed. The descriptions above can help clear up any confusion, and help to explain the two different formulas for volume of a prism and the volume of a pyramid.

Having Fun in Math Class

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Today in math class I presented an activity. I had the class divide into groups of two, and each group was given a shape; there were squares, triangles, and rectangles. The measurements of the sides were labeled to help find the area and perimeter of each shape. One person in each group was in charge of finding the perimeter, and the other person had to find the area. I did have a formula sheet under the projector to help if the students got stuck on a problem. The class did a great job with area and perimeter and understood how to find the solutions. Before the activity, we discussed circumference and diameter.

We went on a circle scavenger hunt! This was fun because we grouped into partners and went around the college measuring circles. Each group had a ruler, pencil, piece of string, and a worksheet. To measure circumference we wrapped the string around the circle and measured the length of the string with the ruler. After we found the circumference, we found the diameter. This was done by placing the string on one side of the circle’s face and measuring the length across. Some objects that my partner and I found were a master lock, door knob, and elevator button. The scavenger hunt was fun and productive because it helped me understand how to find the circumference and diameter of a circle.

Although the scavenger hunt was productive and helped me understand the meaning of circumference and diameter of a circle, there is a formula for circumference. Circumference = ∏ x diameter or ∏ x 2radius. (∏=pie) Radius can be found by taking half of the diameter. If you have a circle with a diameter of 2, you can multiply it by ∏ and get 6.28; therefore, 6.28 is the circumference of your circle. If you have a circle with a radius of 3, you can multiply it by 2 then multiply it by ∏ and get 18.85; therefore, 18.85 is the circumference of your circle. I have included a picture of these two problems below to clear up any confusion you may have.