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!

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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.

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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.

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In my math class we had to draw a regular hexagon and a regular decagon. In order to do this we had to use a protractor, which allowed us to make equal angles and straight sides. First, we determined the central angle of the shape. Central angle = 360/number of sides; therefore, to find the central angle of a hexagon we divided 360 by 6. 60 degrees is the central angle. This means that every line we draw in the hexagon must be drawn at a 60 degree angle. The picture below is the worksheet that includes the drawings of a regular hexagon and a regular decagon.

As well as finding the central angle, it is helpful if you find the vertex angle. Vertex angle = 180 – central angle. I have highlighted the vertex angle in the worksheet above. This helps to determine the degrees of every angle in the shape. If you were to draw a regular decagon you must find the central angle first (360/10 = 36 degrees). Once you have the central angle you can find the vertex angle (180-36 = 144 degrees). Understanding how to find the central angle and vertex angle can help you determine any angle of a shape; I think these two formulas are great to know!

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Adding and subtracting numbers focuses on the accuracy of the answer. The number with the least amount of decimal places is the “winning” number. For example if we are adding 5.36+2.2, the “winning” number is 2.2 because it has the least amount of decimal places. The answer to this problem is 7.56, but since we need to have 1 decimal place the answer is 7.6. In the picture below I have provided an example of a subtraction problem.

Multiplying and dividing numbers focuses on the least number of significant digits. Instead of looking at the amount of decimal places, we look at the whole number and count the amount of significant numbers; therefore, the “winning” number is the number with the least amount of significant digits. The solution to the problem should be rounded to the same amount of numbers as the “winning” number. For example if we are multiplying 82.1×3.2, the “winning” number is 3.2 because it only has 2 significant digits. In the picture above I have included a division problem and some tricky problems dealing with zeroes. I think with effort and determination anyone can understand the rules and differences between adding and subtracting numbers compared to multiplying and dividing!

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Irrational numbers cannot be written in a ratio; therefore, it can be hard to determine what a number is equal to. In the picture above I have given an example of an irrational number. Nonrepeating decimals are an example of irrational numbers. 8.08008000800008… is an example because there are no repeats in the numbers.

Rational and irrational numbers are both real numbers. There are also non-real numbers; these numbers are usually not learned until higher grade levels, but they do exist. An example of a non-real number is the square root of -4. Having a negative number under a square root is a sign that the number you are dealing with is non-real. This is a good tip to know if you have to categorize numbers into different groups. I experienced this while I was working on a worksheet in my math class. Understanding the difference between real and non-real numbers helped me on my worksheet and can help you too!

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Understanding the “easy 10%” method can help you figure out other percentages. If something in 30% off, you need to find 10% off of the item, then multiply it by 3. An example of this could be if an item costs $25.00 and it is 30% off. We can start by finding 10% of the item which is $2.50, then multiply that by 3; this will equal $7.50. I think percentages are very important to learn because they are common in our lives. Everytime we shop we can use percentages to figure out our discounts, coupons, and the total of our purchase!

Another way to look at percentages is by using percent charts. If we are taking 50% of 200, we can set up a 10×10 grid with each unit equalling 2. By setting the grid up like this we are essentially multiplying 2×100 which makes 200. In order to get 50% of this grid we would fill in 50 units. In this case 50 units would equal 100 because each unit is equal to 2. This example is drawn in the picture provided.

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There are also irrational numbers which are not in the diagram above. They are kind of in their own circle. These numbers are nonrepeating decimals that do not terminate and have no pattern. An example of an irrational number is the square root of 2. This number does not come to an end (not terminating) and has no pattern. If you type the square root of 2 into a calculator you will get something like 1.414213562 and it continues on and on. Clearly, you can see that this is an irrational number.

Adding and subtracting decimals are very similar concepts. In order to add and subtract numbers you need to line up the decimals in the problem. An example of adding two decimal numbers is 1.2+2.4. If we line up the decimal numbers it will be 3.6. Subtracting two decimal numbers like 3.6-2.1 uses the same method. You need to line up the decimals and subtract the numbers; therefore, the answer is 1.5. Lining up the decimal numbers can be hard if the numbers are super long. A great way to eliminate this problem is by lining up your decimal numbers on graph paper. I think this is a great tip that may create less confusion!

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The United States separates numbers with commas every third number: 5,853,567.75; however, many other places around the world separate their numbers with spaces and use a comma the way the United States uses the decimal point like this 5 853 597,75. I think this is a very interesting fact! Another thing I learned is that the number 0.0000000009 is easier to read if we put spaces every third number: 0.000 000 000 9. If we put spaces it does not mean anything different; it is just to help us count the zeros or read the number easier. These are great tips to keep in mind while working with decimals.

As you can see from the decimal table, decimals can be written in many ways; essentially a decimal is a fraction. I say this because 0.732 is 732/1000 and can be written as 732 thousandths. Another example of this is 0.20 is 20/100 and can be written as 20 hundredths. No matter the decimal number it can always be written as a fraction which may be easier for some people. You can also look at a decimal by expanding it. If we look back at the decimal 0.732 we can break it down into three parts 0.732=0.7+0.03+0.002. This can also be written as 732/1000=7/10+30/100+200/1000. Decimals are very versatile which allows for many different strategies to understand them better!

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Another great way to help gain an understanding of fractions is by using fraction bars. Fraction bars are rectangular shaped pieces of paper that are divided up into different amounts. The different amounts are the fractions that the shape equals. For example, I have 5 different fraction bars: twelfths, sixths, fourths, thirds, and halves. The rectangles that represent twelfths are divided into 12 sections; the rectangles that represent sixths are divided into 6 sections, and so on. These are great tools to work out fraction problems. Finding a fraction between 2/6 and 3/6 is easier with fraction bars. This may sound easy, but it is hard to figure out if you do not have a good understanding of fractions. Let’s use fraction bars to help us out; for starters we will need a 2/6 fraction bar and a 3/6 fraction bar. If we set these fractions bars side by side, we can easily see that 5/12 is between both 2/6 and 3/6. I found this by looking for a fraction bar that was in between 2/6 and 3/6.

When dealing with whole numbers and fractions, it is easier to set them up into improper fractions. To set up an improper fraction you need to multiply the denominator by the whole number and add the numerator. We do this because we are essentially looking for a common denominator. An example of this is 4 1/2, we start with 2(denominator) x 4(whole number) = 8, then we add 1 (numerator) = 9/2. 9/2 is an improper fraction because the numerator is larger than the denominator. We can also find the improper fraction by finding the common denominator. 4 1/2 can also be written as 4/1 + 1/2; in order to find the common denominator we need to multiply the 4 by 2. Once this is done we can add the two fractions together which gives us the sum of 9/2. This idea is helpful when adding and subtracting fractions: 1 2/3 = 5/3 – 1/3= 4/3. Take your time to learn fractions because I think it is a great tool that we can use in our daily lives.

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