As you know from my earlier posts that there are two things I really like about math.
1. Relevance to life
2. Formulas
I have always been more drawn to algebra and those types of math problems. I have never been a big fan of geometry (Yes, I know! You get it! I don't really like geometry!) But if you really break down geometry, you do indeed get the two things I like about math. Relevance and formulas. You can try to argue against it, but geometry is very relevant in our everyday lives. You want to know how much will fit into a container? Guess what you are doing geometry! My husband and I are going to buying some river rock to finish off some landscaping in our yard. Yup, you guessed it geometry. No, you say, that is measuring, that is not triangles and trapezoids. Wrong again. Measuring goes hand in hand with shapes and you got it, geometry!
Measuring can be easy if you just learn a few equivalences. For example how nice is it if you are cooking and you want to make another half batch of something, knowing how much you need to add can really save you a lot of time and waste.
Here are some examples of some equivalences:
1 yard = 3 feet
1 mile = 1,760 yards = 5,280 feet
1 sq foot = 144 square inches
1 pint = 2 cups
1 quart = 2 pints
1 gallon = 4 quarts
1 pound = 16 ounces
Here is a little video on measurement.
Monday, July 25, 2011
1510 Week 6
What is a rational number?
I look at the above question and I think, "It's a..um...it's a number that is.....you know....rational. That makes sense." The definition according to the book "Mathematics for Elementary School Teachers" is "the quotient of a pair of integers (a/b, b is not equal to 0) that can be represented by a fraction or a decimal."
Like most math definitions, I think it sounds a bit more complicated than it really is. So I took to Google. What is a rational number? One site stated that it is any number that can be written as a simple fraction. Well that makes sense. I found this video on youtube that really helps clarify this.
Another real life math example...I love it!
So I do find this area of math pretty easy to understand. Understanding the meaning behind the math really helps solidify it is my mind. I guess that is the "Why?" Ok, so moving on to adding or subtracting rational numbers, like a decimal. It seems so "elementary" but I sometimes forget the basics behind the "easy" math because of the convenience of calculators. My current job is a banker. I work with numbers all day long. I NEVER use a piece of paper and pencil to figure out a deposit or interest, or a payment etc. I use the computer or a calculator. Can I do it without, sure. But, I don't want to make a mistake or take too long. Let's test my skills. Honest, no calculator.
56.45
+82.67
139.12
YES! I can do it. I know where to carry the decimal because there are only 2 places. Now let's try a little harder one and see how I do.
45.88769
+ 23.882
69.76969
Got it! Whew. I will be honest, I was a little nervous because the decimals are not the same and I promised to use only my mad skills. All I did was added 2 zeros to the end to get my answer.
45.88769
+23.88200
I have to say, throughout this experience of recording my thoughts and what I have learned during his math course, I still get a smile when I get the answer right. Even if it is "easy". Come on, let's celebrate the right answer!
Another area I feel like I feel I should celebrate my understanding is adding and subtracting fractions and mixed fractions. Another "Duh." section, you say? . But, come on! How many really remember how to do it. I will tell you, I took my Praxis test (pretest for elementary teachers) and failed the math portion. Yup. I told myself no kidding you failed! When was the last time I added fractions?! Or did simple geometry on my own?! Too long. Well, I am retaking it now! You see what I have learned.....
3/4 + 2/3 = 17/12 or 1 5/12
(Little smile). I will leave you with this song by Tom Lehrer.
I look at the above question and I think, "It's a..um...it's a number that is.....you know....rational. That makes sense." The definition according to the book "Mathematics for Elementary School Teachers" is "the quotient of a pair of integers (a/b, b is not equal to 0) that can be represented by a fraction or a decimal."
Like most math definitions, I think it sounds a bit more complicated than it really is. So I took to Google. What is a rational number? One site stated that it is any number that can be written as a simple fraction. Well that makes sense. I found this video on youtube that really helps clarify this.
Another real life math example...I love it!
So I do find this area of math pretty easy to understand. Understanding the meaning behind the math really helps solidify it is my mind. I guess that is the "Why?" Ok, so moving on to adding or subtracting rational numbers, like a decimal. It seems so "elementary" but I sometimes forget the basics behind the "easy" math because of the convenience of calculators. My current job is a banker. I work with numbers all day long. I NEVER use a piece of paper and pencil to figure out a deposit or interest, or a payment etc. I use the computer or a calculator. Can I do it without, sure. But, I don't want to make a mistake or take too long. Let's test my skills. Honest, no calculator.
56.45
+82.67
139.12
YES! I can do it. I know where to carry the decimal because there are only 2 places. Now let's try a little harder one and see how I do.
45.88769
+ 23.882
69.76969
Got it! Whew. I will be honest, I was a little nervous because the decimals are not the same and I promised to use only my mad skills. All I did was added 2 zeros to the end to get my answer.
45.88769
+23.88200
I have to say, throughout this experience of recording my thoughts and what I have learned during his math course, I still get a smile when I get the answer right. Even if it is "easy". Come on, let's celebrate the right answer!
Another area I feel like I feel I should celebrate my understanding is adding and subtracting fractions and mixed fractions. Another "Duh." section, you say? . But, come on! How many really remember how to do it. I will tell you, I took my Praxis test (pretest for elementary teachers) and failed the math portion. Yup. I told myself no kidding you failed! When was the last time I added fractions?! Or did simple geometry on my own?! Too long. Well, I am retaking it now! You see what I have learned.....
3/4 + 2/3 = 17/12 or 1 5/12
(Little smile). I will leave you with this song by Tom Lehrer.
Tuesday, July 12, 2011
1512 Week 5
Geometry, Geometry and more Geometry. Sigh.
Let's face it, I am not excited about geometry. Instead of talking about geometry this week, I am going to talk about staying excited as a teacher. Even when I don't really like the subject.
So......how do you make it fun? I think hands on is a great way to make it fun. So have the students draw geometric shapes like triangles, sort shapes and draw reflections. A favorite website of mine is Enchanted Learning http://www.enchantedlearning.com/math/geometry/shapes/ this site gives worksheets on many different subjects. I just love it.
Games are another way to make geometry fun. Brain pop is a great resource for games and interactive quizzes that help the class work together as a team. http://www.brainpop.com/math/geometryandmeasurement/
I also think making it relevant to students will help to make it more fun. Use colors and music and draw in the excitement. And be a little silly. It is okay!
Let's face it, I am not excited about geometry. Instead of talking about geometry this week, I am going to talk about staying excited as a teacher. Even when I don't really like the subject.
So......how do you make it fun? I think hands on is a great way to make it fun. So have the students draw geometric shapes like triangles, sort shapes and draw reflections. A favorite website of mine is Enchanted Learning http://www.enchantedlearning.com/math/geometry/shapes/ this site gives worksheets on many different subjects. I just love it.
Games are another way to make geometry fun. Brain pop is a great resource for games and interactive quizzes that help the class work together as a team. http://www.brainpop.com/math/geometryandmeasurement/
I also think making it relevant to students will help to make it more fun. Use colors and music and draw in the excitement. And be a little silly. It is okay!
1510 Week 5
Homework is not the answer!
Okay, so there is definitely real value in doing homework. As the old saying goes, practice makes perfect, right? Well, I was reading the blog called "Let's Play Math" authored by Denise. As I read the posts, one follower stated that with the use of new techniques and strategies in math, the parents are the ones learning the homework while trying to help their children with their homework. Denise responded with yes, and that is why at a young age, she is not a fan of homework.
I thought that was very interesting. I thought about earlier discussions we had with learning new math strategies and how parents and teachers are so used to learning one way, it can be a challenge to "get on board" with new the new ways. The new ways of learning math should be taught and mastered in the classroom. I do think the biggest challenge with this is time. But time cannot be a barrier to better or at the very least different ways of understanding things like algebra.
One of the strategies young students are using to learning about addition, subtraction and multiplication is by using bar diagrams. I think bar diagrams give a clear understanding of numbers and relationships. The blogger, Denise, gives a nice explanation of what a bar diagram is. She says imagine legos lines up. You have the whole part and the parts that make up the whole.
There is a website that is used for practice of this technique and helps make learning fun by using an interactive game. The link is http://www.thinkingblocks.com/ThinkingBlocks_AS/TB_AS_Main.html
Denise also references a book called Mr Poppers Penguins. This book uses word problems and the bar diagram to solve them. Here is a sample: Mr Popper had 78 fish. The penguins ate 40 of them. How many fish did Mr Popper have left? The problems start out easy and get harder. I think by having a clear understanding of the relationship between numbers helps to make the harder problems using multiplication and division easier.
Here is a humorous math clip showing different understandings.
Okay, so there is definitely real value in doing homework. As the old saying goes, practice makes perfect, right? Well, I was reading the blog called "Let's Play Math" authored by Denise. As I read the posts, one follower stated that with the use of new techniques and strategies in math, the parents are the ones learning the homework while trying to help their children with their homework. Denise responded with yes, and that is why at a young age, she is not a fan of homework.
I thought that was very interesting. I thought about earlier discussions we had with learning new math strategies and how parents and teachers are so used to learning one way, it can be a challenge to "get on board" with new the new ways. The new ways of learning math should be taught and mastered in the classroom. I do think the biggest challenge with this is time. But time cannot be a barrier to better or at the very least different ways of understanding things like algebra.
One of the strategies young students are using to learning about addition, subtraction and multiplication is by using bar diagrams. I think bar diagrams give a clear understanding of numbers and relationships. The blogger, Denise, gives a nice explanation of what a bar diagram is. She says imagine legos lines up. You have the whole part and the parts that make up the whole.
There is a website that is used for practice of this technique and helps make learning fun by using an interactive game. The link is http://www.thinkingblocks.com/ThinkingBlocks_AS/TB_AS_Main.html
Denise also references a book called Mr Poppers Penguins. This book uses word problems and the bar diagram to solve them. Here is a sample: Mr Popper had 78 fish. The penguins ate 40 of them. How many fish did Mr Popper have left? The problems start out easy and get harder. I think by having a clear understanding of the relationship between numbers helps to make the harder problems using multiplication and division easier.
Here is a humorous math clip showing different understandings.
Tuesday, July 5, 2011
1510 Week 4
Finally a topic I like! Factoring. Sorry! Love it! Yes, at times it can be a bit tedious, but I really like it. I am not sure if I really like it because I like it, or if I like it because I actually get it. It might be a little of both. This was a subject that took a lot of notebook paper and well, determination. I had to do a lot of figuring things out.
The think that really helped me through this area was the "rules". If you want to see if a number is divisible by 2, just follow the rule. Does 7 go into 65734 evenly? Follow the rules. Here is an example:
56743
Is it divisible by 2? Well, you could start some long division or grab your calculator. OR ask yourself this question. Is the last digit even? Nope. Well, guess what? The rule says if it does not end in an even number it is not divisible by 2. Go ahead, try it.....
Here is another one....Is it divisible by 3? Add it up! 5+6+7+4+3=25. 3 does not go into 25 evenly. So no it is not divisible by 3.
Last one, is it divisible by 6? Well, if it not divisible by 2 AND 3, then it is not divisible by 6.
Come on......it's too easy and I like it.
Here is a little song from youtube.
The think that really helped me through this area was the "rules". If you want to see if a number is divisible by 2, just follow the rule. Does 7 go into 65734 evenly? Follow the rules. Here is an example:
56743
Is it divisible by 2? Well, you could start some long division or grab your calculator. OR ask yourself this question. Is the last digit even? Nope. Well, guess what? The rule says if it does not end in an even number it is not divisible by 2. Go ahead, try it.....
Here is another one....Is it divisible by 3? Add it up! 5+6+7+4+3=25. 3 does not go into 25 evenly. So no it is not divisible by 3.
Last one, is it divisible by 6? Well, if it not divisible by 2 AND 3, then it is not divisible by 6.
Come on......it's too easy and I like it.
Here is a little song from youtube.
1512 Week 4
G-E-O-M-E-T-R-Y
When I think about geometry, I don't instantly think about angles, lines and shapes. I think about middle school. No, not teaching it, but living it. Awkwardly, racing down the the hall from a locker that was way too far away only to realize I was hustling for mmmaaath. No, worse. I was hustling for Geometry. So, I read the cover of my book again to make sure I was still in elementary math, I nodded my head and reminded myself, "Oh that's right, these kids learn way more than I did in elementary math. So, I dug in. The topics weren't too bad and I actually got a flood of memories back, lines, dots, angles and the Pythagorean theorem....yeah...I can do this!
HOLD THE PHONE.
Preschoolers and kindergarteners learn geometry. Huh? Why? Well a found a really short video that shows you exactly why. This video is from youtube and is actually from Sesame Street. Yes, Sesame Street teaches geometry!
This little demonstration shows that geometry is indeed relevant and also everywhere! If I think about making a pizza and making sure I cut it correctly to give enough pieces and even pieces. That is geometry. I bought a house a few years back and needed a really tall ladder to be able to paint an area on my vaulted ceiling, all the ladders I was choosing were coming up short. Maybe a little geometry would have helped me to figure out the right size to make sure I could safely reach all the spots I needed to reach. Another area I see geometry used in in art. Oh yes, art. If you think about sketching what is the first thing you do? You start with lines and shapes.
These are just small examples of everyday life. I have to say, since I have mentioned this before. I am a formula lover. I like to know what to use when. Geometry is full of formulas. So I guess geometry isn't so scary after all. And more importantly it is very important for even young children to learn.
When I think about geometry, I don't instantly think about angles, lines and shapes. I think about middle school. No, not teaching it, but living it. Awkwardly, racing down the the hall from a locker that was way too far away only to realize I was hustling for mmmaaath. No, worse. I was hustling for Geometry. So, I read the cover of my book again to make sure I was still in elementary math, I nodded my head and reminded myself, "Oh that's right, these kids learn way more than I did in elementary math. So, I dug in. The topics weren't too bad and I actually got a flood of memories back, lines, dots, angles and the Pythagorean theorem....yeah...I can do this!
HOLD THE PHONE.
Preschoolers and kindergarteners learn geometry. Huh? Why? Well a found a really short video that shows you exactly why. This video is from youtube and is actually from Sesame Street. Yes, Sesame Street teaches geometry!
This little demonstration shows that geometry is indeed relevant and also everywhere! If I think about making a pizza and making sure I cut it correctly to give enough pieces and even pieces. That is geometry. I bought a house a few years back and needed a really tall ladder to be able to paint an area on my vaulted ceiling, all the ladders I was choosing were coming up short. Maybe a little geometry would have helped me to figure out the right size to make sure I could safely reach all the spots I needed to reach. Another area I see geometry used in in art. Oh yes, art. If you think about sketching what is the first thing you do? You start with lines and shapes.
These are just small examples of everyday life. I have to say, since I have mentioned this before. I am a formula lover. I like to know what to use when. Geometry is full of formulas. So I guess geometry isn't so scary after all. And more importantly it is very important for even young children to learn.
Monday, June 27, 2011
1512 Week 3
I am leaving this week a bit frustrated. I find probabilities to be rather confusing. It leads me to ask one question. Do elementary students really do these problems? I am thinking it must be geared more towards middle school. Then again maybe I am just trying to make myself feel better for not getting it.
Now, don't get my wrong. I get the importance of probabilities. I think they are an everyday tool, I just think in my head there must be an easier way. I think this is part of my problem though. There isn't a formula you "always" use. It is based on the question. Does it or doesn't it? Regardless, I need more practice and probably should have put in some extra time to try to gain a better understanding of it. And for the students that get this: KUDOS to you!
Since I do like formulas, I am going to focus on one. The definition of odds.
Odds in favor: A = P(A)
1- P(A)
Odds against: A = 1- P(A)
P(A)
These formulas are easy to use and if only they applied to most probability questions, we would be in business.
I found this video on youtube that is called the Monty Hall Problem and discusses the probability of opening a door to win a car and what your strategy should be. It gives the mathematical reasoning behind the choice. It's interesting.
Now, don't get my wrong. I get the importance of probabilities. I think they are an everyday tool, I just think in my head there must be an easier way. I think this is part of my problem though. There isn't a formula you "always" use. It is based on the question. Does it or doesn't it? Regardless, I need more practice and probably should have put in some extra time to try to gain a better understanding of it. And for the students that get this: KUDOS to you!
Since I do like formulas, I am going to focus on one. The definition of odds.
Odds in favor: A = P(A)
1- P(A)
Odds against: A = 1- P(A)
P(A)
These formulas are easy to use and if only they applied to most probability questions, we would be in business.
I found this video on youtube that is called the Monty Hall Problem and discusses the probability of opening a door to win a car and what your strategy should be. It gives the mathematical reasoning behind the choice. It's interesting.
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