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Decimals

The best way to first begin to teach decimals is to teach by the means of money. Since children are often exposed to the dealings of money, they are more accepting of the idea of decimals in this way. They also see the relevancy in learning this, thus making them try a bit harder to understand the subject. When you can get a topic to somehow relate to the student’s life, then they are more likely to really enjoy learning, and that is really the goal. We want the students to learn, but to make sure they do so, they need to enjoy it in some way. Decimals can be tricky, and teachers need to be careful when teaching this subject. Being very clear is key. To begin with we need to show the students what places are where, and what they are called. So, doing something like 1.234, and point out that from the right of the decimal it goes tenths, hundredths, and then thousandths. Then somehow making
sure the student has practice with this everyday in order to be certain they remember it.

The best way to first begin to teach decimals is to teach by the means of money. Since children are often exposed to the dealings of money, they are more accepting of the idea of decimals in this way. They also see the relevancy in learning this, thus making them try a bit harder to understand the subject. When you can get a topic to somehow relate to the students life, then they are more likely to really enjoy learning, and that is really the goal. We want the students to learn, but to make sure they do so, they need to enjoy it in some way. Decimals can be tricky, and teachers need to be careful when teaching this subject. Being very clear is key. To begin with we need to show the students what places are where, and what they are called. So, doing something like 1.234, and point out that from the right of the decimal it goes tenths, hundredths, and then thousandths. Then somehow making sure the student has practice with this everyday in order to be certain they remember it.

Here is a website that explains how to divide decimals by decimals, which I found pretty interesting…  http://homeschoolmath.blogspot.com/2010/02/dividing-decimals-by-decimals.html

Add a comment July 18, 2010
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Adding and subtracting fractions is something I had to try and help students understand when I spent time in a fourth grade classroom. A lot of students were not able to recognize when they could just add or when they had to change the denominator. Other students would not even know what numbers they are adding together. It was frustrating for not only the students, but for me and the teacher as well.

A lot of times students will often just add the two numerators together and the two denominators. This is something teachers really need to grind into their brains, that just adding across is totally wrong.  After they are aware of that deal, it is just getting them to understand what you do to the bottom you have to do to the top. Something that I noticed that helps is making the student rewrite the problem with the new denominator, because it helps them see what they are actually doing. It is not a great idea to rely on fourth graders doing math in their heads, always make them write it out. It just makes it easier for everyone.

Here is an example of how adding fractions with different denominators could be done…

It was just amazing how much this help students understand how to add fractions. So, I guess we should all try and pay attention to the little things in teaching.

Add a comment July 16, 2010
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Yum!

Understanding fractions and being able to recognize their decimals is very important. We see and need to use fractions in everyday life almost all the time. A lot of polls and surveys show their results in percentages or fractions, and it would be difficult to understand what that actually means, if you didn’t understand fractions. Or, for example, you are reading an article, and it says like 5/8’s of the country feels one way on a subject, but if you don’t know fractions, you probably wouldn’t be able to tell if that was a good thing, bad thing, or just kind of in the middle. The sharing method is probably the most common and one of the most effective methods in teaching children to learn fractions. Like when you have a Hershey’s chocolate bar, and you’re splitting it up amongst friends, but I’d rather show it through cake!

Cake is a great and tasty way to show fractions. The first step would be to bake a cake. Then after it is all baked, and you have people over, you need to count and see how many people would like a slice of cake. After you know that, then you can slice the cake. Say there are eight people at the party including yourself, then you slice the cake into eight pieces. From then on, is when you can teach the child about fractions. When a slice is pulled off the cake, you can ask how much of the cake is missing and how much is there, which is 1/8 and 7/8. This is a great way to practice, and you can even show how 4/8 of the cake is the same as 1/2 of the cake. This is an effective way in teaching, especially if you refuse to give the child cake until they answer all your questions correctly. Haha.

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Dragons

Once upon a time there was a crazy mathematics dragon. The Dragon’s name was Magnets. Magnets was a terrifying dragon, he often stole people from the village of Slope. These townspeople were very frightened of the dragon, but refused to answer his request of teaching math to the village. They believed since the dragon was bad and he liked math, that they too would turn bad if they began studying math. So, every month the dragon would steal one person from the town, and they had not seen these people since. Some townspeople would speak of their bravery in approaching the dragon’s den, and that they would see the glowing eyes of the dragon, and hear screams of his victims. These villagers would tell stories of the dragon cursing their fellow villagers, tearing them from limb to limb, and even light them on fire. But nobody knew the truth, because the ones who got close enough to see inside the dragon’s den, was not seen in the town again.

Almost the whole town feared Magnets and his unknown wrath, but there was one exception. A little girl named Numeratora, but everyone called her Numy for short. Numy was different in this town filled of fear for she was a brave and strong-willed being. She mostly kept to herself, she often sat alone for days on end studying and learning everything she can. Her curiosity got the better of her, and she even read the books that were forbidden, but she wanted to understand everything. It was then when she learned about mathematics, and its potential increase the well-being of the town and its people. So, she went to the town to share her new found knowledge, but they would not listen. They felt she spoke a different language, and they screamed she was Magnets’s worshiper. They decided that she should be the one taken from the dragon that month, so they tied her up and left her in the middle of the field.

Night fell upon the town, and Magnet tore out of his den appearing to be going on a tangent. Magnet flew over the town, but stopped when he saw Numy. He glided down to her, and with a sad look on his face, he scooped her up. Numy was not afraid of this dragon, and she was already planning her escape. They finally reached his den, and he set her down. And before a word was spoken, Magnet cut the ties on Numy. Her eyes were filled with shock for how kind the dragon was being.

Then Magnet spoke, “Everything that you might think that happens here isn’t true. I am not here to harm you, or harm anyone actually. I never wanted that, but it is true that I have not let any of the other villagers return to their homes, but that is because they did not pass my test. I am hoping that you will, are you ready?” Numy was surprised, but she would not refuse such a task she believed would be easy, “I am ready.” The dragon smiled. “Alright, well this isn’t any normal test, but a mathematics test! Here is your first question. If I have been taking only one person each month for the past six months, and continue to do that for the next three, how many people will I have taken?” Although Numy has only studied math very recently, and not in depth, she still answered very quickly. “Easy. You are really just saying that if you take one person per month, and there are nine months, which is six added to three, then the number of people would be the same as the number of months. So, you would have taken nine people all together.”

Magnets was so surprised for no one has even got the first half of his test before, but he was very happy at the same time. Magnets continued, “Correct, now if you get the next question right, you will free all of the other villagers. Here it is, if I took 5 people every month for five months, and I returned one fifth of the villagers after the fifth month, how many villagers would I still have?” Numy was a little concerned at her lack of practice of math problems, but would never give up, “Well, if you took five people every month, that would be 5+5+5+5+5, or 5×5, which is 25 people. And one fifth of the 25 villagers, would be the same as 25x(1/5) or 25/5, and that would be 5 villagers. But you said how many would you still have, so I need to subtract 5 from 25, which is 20! You would have 20 villagers still!” Magnets jaw dropped, he never imagined that a little girl would pass his test. “You have passed my test, and I am very pleased. You must understand the importance of math, and hopefully you will be able to teach your fellow villagers of its importance.” Numy shook her head and explained that is why she ended up tied and left in the field. Magnets smiled again, “Well, you will not be the only one explaining the importance of math.” At that moment the other villagers that were captured came walking out. Numy was told they were forced to study and learn mathematics by the dragon, they had become experts in the matter of months from his teachings. They left Magnets’s den, and showed the town what they could do.

And that is how the expert mathematicians of the world came to be, and it is the dragons who we need to thank. The end.

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Numbers

Numbers are either positive or negative with the exception of zero, which means all numbers have a sign. I made a little picture in paint that I thought was just silly, but it helps in restating my point…

I came across a web page that really explains different ways in showing how to deal with negative numbers. http://www.themathpage.com/Alg/signed-numbers.htm#parts This site brings up a really good point in teaching children, as long as they remember the signs, when doing a problem like 5-8. When a child first looks at a problem like this, they might think it would be impossible to ever do something like this. But if they understand subtraction, then they could switch the problem around. So the new problem would be, 8-5. The child should then recognize the answer is three, and because they switched the numbers around, which is the same as switching the signs of the number, instead of the answer being 3, it would be (-3). This is a cool method in teaching students an easier way of subtracting, and allowing them to practice sign changes at the same time.

The number line method in approaching problems like these is also a wonderful way to teach. I personally never learned in that way before, but seeing it now I can really appreciate it. This is a visual method for the child that I believe is better than the take-away method. The number line is a good way to lean children into seeing math equations, and just knowing how to do it. Overall I think it is great to know all the methods, because not all people learn in the same ways.

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Tricky

Even though not all math will be encountered in every job, but doesn’t mean you shouldn’t learn it, or give up on the subject all together. I have previously taken calculus in high school, and in the last fall semester at MCC, and I am pretty sure that I will not be finding derivatives teaching elementary students. However, I do not regret taking the class, and besides who is to say it won’t be important to know in the future.

One concept that everyone should understand is graphs. Graphing is very common in a lot of jobs. It is a great way to visually see how a company is running, estimating for the future, showing the efficiency of a product, and many other things. My physical science instructor last semester showed my class the value of not speeding on the highway, using a graph. He proved to us that to receive maximum fuel efficiency we have to drive around 65 mph, depending on the type of car, and that speeding will just cause a loss in gas, and only seconds gained in time. I drive slower on the highway now, because my instructor knows how to graph equations, and understand what it meant.

Graphing can be a wonderful tool in helping people to understand a point. However, there are people who become masters at making something bad look good, by changing how the graph looks. It is important to read what each axis represents, and look at how they are numbered. It is easy to be fooled. I came across a political blog that tells people how to make a graph ‘say what you want.’   Here is the link… http://www.politicalmathblog.com/?p=401

I guess the message is to be suspicious of all graphs, especially when it comes to politics.  ;-]

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disjointed

Wouldn’t it be neat if we could separate and organize everything that has taken place in our lives? It would make looking at the events and people who have molded us to who we are today so much easier. If only life was that simple. There are a lot of events or people in our lives that we don’t fully understand, and to categorize them would be nearly impossible. Organizing numbers is much simpler. Numbers are organized with sets, which can be described, listed, or placed in a Venn diagram.

I will try using sets with my past boyfriends…

All real boyfriends:  {Alex, Andrew, Jess, Kris, Nick, Steven}

Boyfriends that treated me right: {Andrew, Steven}

Boyfriends I definitely should not have dated: {Jess, Kris}

‘Boyfriends that treated me right’ and ‘boyfriends I definitely should not have dated’ are both subsets for ‘All real boyfriends’ since each element belongs to that set. If everyone managed their lives according to how we organized numbers, then we would have a much weirder world, but probably a much more detailed one.

Maybe we should spend some more time managing our lives, because this Venn diagram really depicts teens today…

…I guess I need to make a Twitter.  😉

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Velociraptors

Motivation is one of the main issues with students today. Who would want to study or do their homework when there is the internet to explore, or millions of television channels to surf? More students are slacking off, and teachers struggle to find ways to get them interested again. A plan needs to be developed for students to have a better education. If only there was some way, like if they needed to learn to survive.

http://xkcd.com/135/

If we were under a velociraptor attack or a zombie apocalypse, and learning math was the only way to stay alive, then students would be math geniuses. But hopefully it won’t come to something that drastic for students to finally gain some interest in learning. But maybe students would enjoy math a little bit more with problems like the ones in the comic. Just a little silliness could be all it takes.

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A Bunny’s Tail

…In Math Class

Sneakers was a little bunny, curious to the wide world around him. He attends post-bunny school to even further his knowledge, every day. He loved the smell of books and freshly sharpened pencils, so he always arrived to class early. Not that it did any good, because his teacher was always running late. The whole class had to listen every single day about the teacher’s adventures chasing after some girl in an obnoxious blue dress. But Sneakers was not interested in any of these frivolous things, he only wanted to learn. He had recently picked up a math book. Now math was not a subject that bunnies were very fond of, and they could not imagine why they would ever need it. The first day of his math class, he dreaded it, like all of the other bunnies did, but it wasn’t what he had expected.

The class was about learning how to solve problems. Sneakers could not have imagined that he would learn so much in such little time. He started thinking about his opinion of math before, and realized that it was the other bunnies that made math out to be a difficult and useless subject, because it had become such a frequent idea over the years. But Sneakers saw the beauty that can be found in math. He saw math all around his bunny community, that no one else seem to notice. Sneakers practiced his math every day in common activities. Sneakers gathered yummy apples. He gave half of them to his neighbor, then 8 apples to his friend, Hoppy, half of the remaining apples to his mother, and kept 3 for himself. Sneakers then thought about how he would figure out. He decided that drawing a picture would help, so he tried it, but he couldn’t do it. But he didn’t give up! He visualized what the problem looked like…

From looking at the problem this way, he realized he just needed to solve it backwards. He first had to solve to find half the apples. So, ( half apples – 8 ) / 2 =3, Sneakers thought the easiest way to do this was by guessing, and plugging numbers in for the half apples. He found that 14 solves this part of the problem, and since he wanted to find how many were at the beginning, he just doubled the number, and found that he had gathered 28 apples total. But thinking back, he found that it would have been just as easy to multiply 3 by 2, add 8, then multiply that number by 2, and it gives you the same answer, in just a different way. Sneakers enjoyed his lesson in problem solving, and decided at that he would do his best to let the other bunnies know how fun math could be!

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