Think back to when you were in math class as a kid. Did you enjoy it, did you not? Did you feel challenged or did you feel confused? Did you feel like you were going to use the math you were learning or did you wonder how this was ever going to apply to real life? Here at Mathnasium of Cherry Hills, we recognize that not all math is something that can be literally applied to real life scenarios, and to tell you the truth, practical application is not always the reason we teach math. Math is taught and done for some practical application, but it’s also taught as a means to develop your mind into thinking more expansively in general. It’s like exercise for your brain. Despite that some math is really just practiced to expand your mind and move into more advanced concepts, there is math you learned in school that you do use all the time, whether you realize it or not. Want an example? Fractions. In this blog, we are specifically talking about fractions and how we use them, what they are and ways to help move past the struggle with them.
The easiest way to describe a fraction in adult is a number that represents a whole number that has been divided into parts. For example, if you have a pizza and you cut it into 8 equal slices, 1 of those slices can be written and represented as 1/8 of the total pizza. Same goes with a group of items. Say like you have 4 apples and you give 3 to other members of your family, the apples you gave away can be represented at 3/4. Some of the daily uses of fractions for us adults are when shopping. Think of 1/2 off sales. Other uses are for filling gas tanks, using tools or cooking/baking. Think of all the times you use measuring cups when cooking and what they say on them – 1/2, 1/3, 1/4 of a whole cup. We honestly use them all the time!
However, describing fractions to younger people can be tricky. Many kids mix up the tops (numerators) and bottoms (denominators) of fractions because they don’t understand what they mean when it comes to the whole of a number and it is surprising difficult to explain fractions to kids, unless you’re a teacher or tutor and you’re used to breaking down hard concepts for developing minds. When working with young students, one of the first forays in approaching fractions is to explain the concept of half. How much is half? What exactly does it mean? Show me a visual of half? Are all ways to start explaining what half is, without them knowing what the word half is already. Using real life examples of what they have had to share in their life can be helpful. They have likely had to share fruit snacks or a cookie in their lives. They understand that when they share that cookie equally, the two pieces should be the same size. Building on that, if half is two parts of the cookie that are the same size, then thirds is three parts that are the same size. This is the very basic concept of fractions for little ones.
The next step in understanding fractions is how to represent them by the top and bottom numbers. Let’s start with the bottom number, known as a denominator. You’ll notice the word “nom” is in the word deNOMinator. Nom is another word for name in Latin. You can then refer to the denominator as the “name” of the fraction. Anyway, the denominator tells you how many parts the whole is divided into and what you should call these parts. When you see an eight in the denominator of a fraction, it means you have broken something into eight equal parts. In this instance, you could call those eight parts “eighths.” Now let’s shift focus to the top number, known as the numerator. The numerator is the number that tells you how many parts you have. So, using the same denominator as above, eight, say like you have five parts. This would be written as 5/8. Congratulations, you officially have five out of the eight equal parts.
After being able to read and understand what a numerator and denominator mean, the next step is being able to add and subtract them. The first rule of thumb in adding and subtracting fractions if that you have to have a common denominator, meaning, the bottom number has to be the same. Remember, the denominator is the name of the fraction. If you buy five apples, then you buy two more apples, you have bought seven apples altogether. 5/apples + 2/apples = 5/apples. But, if you buy five apples and two bananas, you can’t add them as the same thing, because they aren’t the same thing. There is no such thing as a banapple! You cannot subtract or add things with different names, thus different denominators. You must think of denominators as names and not a number and you must find a common name. So, say like we have one half plus one third (1/2 + 1/3) the closest common name is sixths 1/2 becomes 3/6 and 1/3 becomes 2/6. All numbers on the bottom are the same – apples – and we can add them. This looks like 3/6 + 2/6 = 5/6. Consider this a small free lesson from Mathnasium of Cherry Hills.
We could go further into reducing, multiplying and dividing fractions but we’ll leave it as the basics for now. We teach those concepts in a similar way as the example above with the overall goal being to help students master them. We want math myth dragons slayed and fear conquered. If your child needs help slaying those math myth dragons, give us a call for an assessment. We’d love to help your child get back on track and make sure they are numerically fluent to handle fractions and beyond!
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