School is back and middle school students are getting comfortable with some math topics that will help them out right now, but also in the future as they move up to high school math. One such topic is percentages, and another that is closely linked and just as important is percentage ratios. These topics tie in with our recent article on probability and statistics, so be sure to go back to our blog and read that article.
If you haven’t yet read that article, don’t worry, we won’t leave you lost and unable to understand this one. Let’s quickly look back at the key points from our most recent blog article to see how percentages play a key role in our understanding and ability to express statistics and probabilities.
Percentages, Statistics, and Probability
If you read that article, you’ll know that statistics and probability rely heavily on percentages. In math class and in online math classes, students will be expected to use percentages to describe data distributions when solving statistics problems. One example would be calculating the percentage of students who passed their math exam before summer.
Similarly, percentages are used when calculating probabilities, such as the odds of rolling any particular number on a six-sided unbiased die. As you will remember from previous blog articles, this probability is 1-in-6, which can be difficult to understand and visualize until we turn it into a percentage (16.67%).
Clearly, percentages and percentage ratios are fundamental mathematical concepts that every student must learn in class and during individual tutoring sessions. Let’s go deeper into these topics and see just how vital they are to a well-rounded math education.
Understanding Percentages
Percentages are everywhere in our world. From the discounted items on sale to our scores on tests in school, we simply can’t avoid percentages, and we don’t want to. As a method of expressing part of something in relation to the whole itself, percentages are invaluable. We usually represent them as a fraction out of 100, which may appear a bit abstract to middle school math students, but wrapping your head around this concept isn’t too hard with a little imagination.
Let’s pretend you want to buy a brand new game console and when you get to the shop, you see a sign that says ‘30% OFF’. This means you will only have to pay 70% of the original price of the console, not a bad deal! On the other hand, let’s imagine there is no discount and you also have no money to buy the console. If you agree to borrow the money to buy the console from your brother and he wants you to pay 5% interest, you will ultimately pay 105% of the original price for the console.
As we can see from these examples, percentages are extremely useful when we want to estimate expenses, compare certain prices, or express one portion of an object in relation to its whole.
Percentage Ratios
Now that we understand percentages, we need to get to know a closely linked topic: percentage ratios. This concept involves comparing two different percentages to better understand the relationship between them. Percentage ratios are key to more advanced statistical analysis, as well as being very useful when we are dealing with comparisons.
Let’s take a look at an example. We want to conduct a survey where we ask every student in the school if they would prefer to wear school uniforms or not. 75% of students say no, while 25% say yes. Now imagine we want to express this result by relating the percentages to each other. We know that 75 is three times as big as 25. Therefore, we can express the results in the ratio 3:1. When we see the results written like this, it is much easier to understand the result, and in turn, draw conclusions from it.
Visual Representation
Being able to visualize numbers, data, and other information relating to mathematics is a powerful ability. Visual representation of percentages makes a potentially complicated concept clearer, and if we want people to understand percentages and percentage ratios, utilizing visuals can be very rewarding.
Let’s say we want to show an audience how our school day is divided in terms of each class and break times. We could share an image of a pie chart with individual slices representing each class and additional slices to show the time spent on breaks between classes. This pie chart would instantly allow audience members to see if any classes are dominating everyone’s time if everyone is getting enough time outside between classes, or if any subject has been lost in the shuffle and needs more focus.
At Online Math Center
At OMC, children get the opportunity to get ahead of their math class and are matched with teachers who have the experience and time to focus on that child’s specific needs. Nowhere else will you find comprehensive individual math tutoring lessons that are tailored to your child’s needs, whether they want to plug gaps in their knowledge, prepare for the Math SAT or a math competition, or simply improve their math grades.
Contact OMC today and turn your child’s math struggles into math success.
