If I had to give this post a subtitle, it would be... "And Why the Schools Do It Wrong." It isn't because the teachers are bad (just as homeschooling parents aren't bad teachers), but it's the way things are done. The "system" doesn't work.
For example... Typically a kid learns a new concept in class, and is then sent home with practice problems to work. If he did every single problem wrong at home, he won't find out until the next day (if he's lucky), right before the teacher moves on to the next concept. This makes no sense.
The reason one on one education is superior to classroom teaching is because the teacher is available for immediate feedback. If a child doesn't do something correctly or misunderstands a concept, the teacher sees it, corrects it, and the child is back on the path. Well, usually...
Because a lot of parents use the same school system to teach their kids at home, their kids are not benefiting from the one one one instruction in the best way. If your child is doing 20 problems on his own and then you are grading it later, you have just wasted your child's time if he didn't work the problems correctly. And he has just re-enforced the incorrect method to solve the problems. I actually figured this out through working with my own kids. For one full year, I worked with both of my kids every day, with every problem. If they had 20 problems to work, we did them on the white board together. So if they got stumped, I was there to guide their thinking correctly. They were never able to "think wrong" and think they were right. I was able to stop and re-teach a concept if necessary, or explain it in a different way.
When my kids hit 6th and 7th grades, I decided to give Teaching Textbooks (TT) a try. I love teaching math, but it was getting overwhelming. The TT method works really well. They learn a concept, and then do some practice problems (as well as review problems). If they miss the practice problem, they know right away. Additionally, they can click a button to learn how to work a problem correctly. I love this.
If you use a different curriculum but have a lot of kids and not enough time, an alternative is to allow your kids to have the answers to their problems so they can self check as they go. You can't do this with younger kids, but you will know when your kid has reached the age where this will work.
The way to teach math is by providing immediate feedback, one problem at a time. Whether you do it, or the computer does it, or the answer sheet does it, a kid needs to know if he's on the right track WHILE he's on it. Following a system at home that doesn't work for the public schools is probably creating unnecessary frustration in your home.
Showing posts with label teaching math concepts. Show all posts
Showing posts with label teaching math concepts. Show all posts
Wednesday, January 28, 2015
Friday, September 5, 2014
Common Core Propaganda
Today in my facebook feed, there were FIVE references (so far) to this same "Common Core" video. Attached were numerous (sometimes thousands!) of comments about how Common Core math is dumbing down our kids, how this method is stupid, how people can't believe our kids are being taught this, etc. The funny thing is, all these "Common Core" math concept videos are just showing what kids have been learning for AGES and it's sad that parents have had no clue what their kids have been taught.
Before I go further and lose all my anti Common Core folks, I *am* against Common Core, simply for the fact that it is 100% about federal control of our schools. Even if they included in Common Core curriculum everything I agree with (didn't happen BEFORE Common Core, probably isn't happening now), I would be against federal control of our schools. I am against a federal agency tracking my children and keeping records of everything they say, do, or believe from the day they set foot in a school. Additionally, even if I agreed with everything included in the Common Core curriculum, what about when they change something? Am I supposed to believe that someone who doesn't even live in the same community knows what's best for my children?
That said, I believe the videos and pictures going around against "Common Core" are doing us all a disservice. First, they are improperly blaming Common Core for methods that have been used for years. Common Core did not invent any new way of doing anything! It simply took methods of teaching concepts that were already being used. Second, they are distracting us from the real problem, which I stated above, the federal takeover of schools. Here is the video that is making its rounds this week:
Now... most of the comments against this method are, "Why can't our poor, coddled kids just learn to memorize the facts like we had to?!" This is just a plain ignorant statement. As I've stated before in another post, people want to be so against Common Core, they don't really even pay attention to what's going on in the math, or they immediately "don't understand it." Either I'm just WAY better at math than most Americans, or having a teaching degree and learning numerous methods of teaching math allows me to see what they do not.
The method in the video has been around for ages. While that problem in particular is simple, use the same concept for a harder problem and it allows kids (and adults) to do mental math without writing anything down. For instance, if you need to add 59 + 13, can you see how looking at it like 60 + 12 is much easier to solve in your head? You would be using the same concept as in the video. Of course, anytime you first teach a new concept you use simple numbers like 9 + 6. And to the people who have said, (and I can't believe they did), "Well after they wrote all that down, I've already come up with the answer because I've memorized the fact," you are missing the point. This is not taught so that kids don't have to memorize "the nines." It's taught so they can do these things in their heads and NOT write anything down. Writing it down is how the method is taught, which is pretty useful for the visual learners, eh?
This video was clearly on a news program and is going viral on facebook. This makes me realize that it's possible that these "examples of Common Core" are now being used to make us forget what really IS wrong with Common Core. It's a sort of propaganda...a smoke screen if you will. Also known as a red herring, or wild goose chase. Don't fall for this. Don't start thinking that if we just remove a few "crazy math" teaching methods, Common Core will be okay. It's also bringing out all the parents whose kids were already attending failing public schools, as if Common Core is the reason they are failing (remember "No Child Left Behind"?)! Schools were already dumbing down our kids before Common Core, and NOW they have a problem. I guess that's a good thing. Nothing wrong with being more aware, but don't prove that your own school dumbed you down by falling for the wrong reasons.
As a side note, I have noticed that my Libertarian friends see the real issue with Common Core, my Republican friends share "I can't believe this new Common Core math!" memes to the point they go viral, and Democrats are largely silent. I'm going to leave you with that and let you think about it a minute.
Is it really about our kids, or politics?
Before I go further and lose all my anti Common Core folks, I *am* against Common Core, simply for the fact that it is 100% about federal control of our schools. Even if they included in Common Core curriculum everything I agree with (didn't happen BEFORE Common Core, probably isn't happening now), I would be against federal control of our schools. I am against a federal agency tracking my children and keeping records of everything they say, do, or believe from the day they set foot in a school. Additionally, even if I agreed with everything included in the Common Core curriculum, what about when they change something? Am I supposed to believe that someone who doesn't even live in the same community knows what's best for my children?
That said, I believe the videos and pictures going around against "Common Core" are doing us all a disservice. First, they are improperly blaming Common Core for methods that have been used for years. Common Core did not invent any new way of doing anything! It simply took methods of teaching concepts that were already being used. Second, they are distracting us from the real problem, which I stated above, the federal takeover of schools. Here is the video that is making its rounds this week:
Now... most of the comments against this method are, "Why can't our poor, coddled kids just learn to memorize the facts like we had to?!" This is just a plain ignorant statement. As I've stated before in another post, people want to be so against Common Core, they don't really even pay attention to what's going on in the math, or they immediately "don't understand it." Either I'm just WAY better at math than most Americans, or having a teaching degree and learning numerous methods of teaching math allows me to see what they do not.
The method in the video has been around for ages. While that problem in particular is simple, use the same concept for a harder problem and it allows kids (and adults) to do mental math without writing anything down. For instance, if you need to add 59 + 13, can you see how looking at it like 60 + 12 is much easier to solve in your head? You would be using the same concept as in the video. Of course, anytime you first teach a new concept you use simple numbers like 9 + 6. And to the people who have said, (and I can't believe they did), "Well after they wrote all that down, I've already come up with the answer because I've memorized the fact," you are missing the point. This is not taught so that kids don't have to memorize "the nines." It's taught so they can do these things in their heads and NOT write anything down. Writing it down is how the method is taught, which is pretty useful for the visual learners, eh?
This video was clearly on a news program and is going viral on facebook. This makes me realize that it's possible that these "examples of Common Core" are now being used to make us forget what really IS wrong with Common Core. It's a sort of propaganda...a smoke screen if you will. Also known as a red herring, or wild goose chase. Don't fall for this. Don't start thinking that if we just remove a few "crazy math" teaching methods, Common Core will be okay. It's also bringing out all the parents whose kids were already attending failing public schools, as if Common Core is the reason they are failing (remember "No Child Left Behind"?)! Schools were already dumbing down our kids before Common Core, and NOW they have a problem. I guess that's a good thing. Nothing wrong with being more aware, but don't prove that your own school dumbed you down by falling for the wrong reasons.
As a side note, I have noticed that my Libertarian friends see the real issue with Common Core, my Republican friends share "I can't believe this new Common Core math!" memes to the point they go viral, and Democrats are largely silent. I'm going to leave you with that and let you think about it a minute.
Is it really about our kids, or politics?
Friday, February 14, 2014
Students Who Don't Like Math
I can't even believe I'm writing this. Raised in a family of math geniuses, it is hard to admit that the words, "I hate math!" ever fell from my child's mouth. They did. I was shocked.
When my son was in kindergarten I remember working on math with him and how he would sometimes come to an answer really quickly. He wasn't guessing, but he knew the answer. I asked him how he got the answer and he couldn't tell me. This drove me nuts. I learned in college that children should grow up learning how to communicate about math, and here I was, his kindergarten teacher and I was a total failure! Why couldn't he tell me?!
Now my son is 12 and over the years I've realized that sometimes the "experts" were wrong. While I couldn't figure out my son's methods, I didn't necessarily have to understand it in order to teach him. At this point, he is figuring out the answers much quicker than me. And still, he does a LOT of it in his head.
Usually I heard, "I hate math," when something got a little hard and required extra brain power. Sometimes kids are lazy and just don't want to do math RIGHT NOW. Adults are the same way, aren't we? But what if your kid NEVER likes math? What do you do then?
First, don't ever tell your child that you were bad at or did not like math. They will grow up thinking they will be the same way. If you have already done this, undo it. Get excited about math and act like it's all the rage. If your kid looks at you funny or asks you what's wrong, just say you have discovered how much fun math is and work the problems with him. If you had mediocre math teachers, it's possible that looking at math from your adult perspective will make the work easier to understand. If you are still intimidated by the numbers and calculations, make sure to enlist some help in the math area. There are lots of videos online that can help you both. You don't have to know everything all the time, you just have to have a learning spirit and excitement about working with numbers.
Second, figure out what your child really doesn't like. It could be that he is really struggling with a certain concept. Just because addition was a piece of cake doesn't mean subtraction is going to come easy. Help him climb the obstacles rather than struggle, fall, and give up. Imagine coming to a difficult concept, realizing there are only more difficult concepts behind it in the future. Not fun. Most kids like riddles or puzzles. I've always viewed each math problem as a riddle to figure out. If you are excited, even if your child is struggling, he will plow through if he has your help. The benefit of schooling at home is you can spend as much time as you need to get the concept down. Don't rush it! Let him get comfortable with a concept before jumping to the next "obstacle."
Third, make math fun. Some things are just going to be work, like learning math facts. For this, we use xtramath.org. Try to take something your child enjoys and incorporate it into math. Now that my son is older, we try to see who can come up with the answer first. There are some things I will never beat him on, but other things I can. He gets a kick out of the times he beats me, and works harder to beat me on the others. If you don't have a competitive kid, this won't work. But maybe he is very active and likes jumping on the rebounder, bouncing on a ball, or getting M&Ms. Yes, bribery works, too! You know your kid, figure out what works and make math the most fun subject of the day. If you are really creative, make a treasure hunt, lasting over the course of a week. Each day's assignment provides another clue. Each clue takes him to the next location of the "riddles" to solve, eventually leading to the treasure. I bet he will want to start with math each day!
Your child will learn to like math if you provide the environment that makes math exciting. That doesn't mean that he will be good at it, but it will be easier when he is willing to do the work. Although we have met our own obstacles, I don't think my son will ever say he hates math again. However, we are just in pre-algebra now and I've still got high school to go so I'm not going to hold my breath! Good luck teaching parents, and have fun!
When my son was in kindergarten I remember working on math with him and how he would sometimes come to an answer really quickly. He wasn't guessing, but he knew the answer. I asked him how he got the answer and he couldn't tell me. This drove me nuts. I learned in college that children should grow up learning how to communicate about math, and here I was, his kindergarten teacher and I was a total failure! Why couldn't he tell me?!
Now my son is 12 and over the years I've realized that sometimes the "experts" were wrong. While I couldn't figure out my son's methods, I didn't necessarily have to understand it in order to teach him. At this point, he is figuring out the answers much quicker than me. And still, he does a LOT of it in his head.
Usually I heard, "I hate math," when something got a little hard and required extra brain power. Sometimes kids are lazy and just don't want to do math RIGHT NOW. Adults are the same way, aren't we? But what if your kid NEVER likes math? What do you do then?
First, don't ever tell your child that you were bad at or did not like math. They will grow up thinking they will be the same way. If you have already done this, undo it. Get excited about math and act like it's all the rage. If your kid looks at you funny or asks you what's wrong, just say you have discovered how much fun math is and work the problems with him. If you had mediocre math teachers, it's possible that looking at math from your adult perspective will make the work easier to understand. If you are still intimidated by the numbers and calculations, make sure to enlist some help in the math area. There are lots of videos online that can help you both. You don't have to know everything all the time, you just have to have a learning spirit and excitement about working with numbers.
Second, figure out what your child really doesn't like. It could be that he is really struggling with a certain concept. Just because addition was a piece of cake doesn't mean subtraction is going to come easy. Help him climb the obstacles rather than struggle, fall, and give up. Imagine coming to a difficult concept, realizing there are only more difficult concepts behind it in the future. Not fun. Most kids like riddles or puzzles. I've always viewed each math problem as a riddle to figure out. If you are excited, even if your child is struggling, he will plow through if he has your help. The benefit of schooling at home is you can spend as much time as you need to get the concept down. Don't rush it! Let him get comfortable with a concept before jumping to the next "obstacle."
Third, make math fun. Some things are just going to be work, like learning math facts. For this, we use xtramath.org. Try to take something your child enjoys and incorporate it into math. Now that my son is older, we try to see who can come up with the answer first. There are some things I will never beat him on, but other things I can. He gets a kick out of the times he beats me, and works harder to beat me on the others. If you don't have a competitive kid, this won't work. But maybe he is very active and likes jumping on the rebounder, bouncing on a ball, or getting M&Ms. Yes, bribery works, too! You know your kid, figure out what works and make math the most fun subject of the day. If you are really creative, make a treasure hunt, lasting over the course of a week. Each day's assignment provides another clue. Each clue takes him to the next location of the "riddles" to solve, eventually leading to the treasure. I bet he will want to start with math each day!
Your child will learn to like math if you provide the environment that makes math exciting. That doesn't mean that he will be good at it, but it will be easier when he is willing to do the work. Although we have met our own obstacles, I don't think my son will ever say he hates math again. However, we are just in pre-algebra now and I've still got high school to go so I'm not going to hold my breath! Good luck teaching parents, and have fun!
Tuesday, January 8, 2013
Algebra Teaching Tool
A great teaching tool for teaching algebraic concepts is called Hands-On Equations. I was trained in using this system in 1994 when I taught 6th grade math. Years later, I purchased my own system to help my stepdaughter who struggled with algebra. Then I used it for my son a couple of years ago when he was 9. We were just working on some math today and a word problem came up that was best solved using an algebraic equation. My son got a worried look on his face, and I decided to re-write the equation using the Hands-On Equations "pawns." He got it immediately. I suggest this system to ALL parents, whether they are homeschooling or not. You can start it as young as 3rd grade, and there is no upper age limit, so if you struggled with algebra yourself, it might help you re-learn (or learn) it. You can learn more about the system at the Hands-On Equations website. I was able to use just the Learning System for $34.95, but I did have previous training in it. You may or may not need to purchase more in order to really understand how to use the system. I would say that the worse you are in math, the more you may need to purchase. But, if you are determined, you should be able to use just the system I purchased. (The more broke we are, the more determined we must become!)
Also, if you do get the system and then have questions, they will answer them for you, and I will, too!
Also, if you do get the system and then have questions, they will answer them for you, and I will, too!
Wednesday, December 26, 2012
Teaching Metric Conversions
This is a great way to teach metric conversions to your child. Study the board first, then I'll explain.
First, the mnemonic device...King Henry Doesn't [usually] Drink Chocolate Milk. You can use the same one, or have your child make up one s/he remembers. Each of these stands for a prefix as you can see in red. The [unit] can be gram, meter, or liter, depending on the conversion they are asked to solve.
You can see one problem in green, and how it is solved on the chart. We want to know how many kg is 200g? So we go to our chart and start at "g," because it is our base unit. We need to end up at kg, because that is what we are converting to. We jump from one prefix to the next, until we arrive at the unit we need (kg in this case). We jumped 3 to the left. Therefore, we will move our decimal 3 places to the left. As you can see in the drawing, we end up with .200 kg or .2 kg.
In the blue, we want to convert 3m to mm. Again, we start at our base unit, m, and jump until we end up at mm (3 times). We jumped to the right, so our decimal will move 3 places to the right.
Kids will ask...What is hecto? What is deka? What is deci? The truth is, they don't need to know these. Tell them what each prefix stands for, but realize that they will NEVER be asked to convert to these, because we simply don't use them. They are really just place holders. If they leave them out of the chart, they won't jump enough...so while they need to know they exist, they will never use these prefixes. This chart will help them "see" why they are moving the decimal and they will learn pretty quickly how many jumps it is to go all the way from kilo to milli (6) or vice versa (still 6!)
If you have struggled with metric conversions and have some anxiety about teaching them to your child, sit down and make this chart for yourself and then work some problems out. Use this as a TOOL to go along with your child's textbook, which will go more in depth with how the metric system is based on tens, etc. You know your child better than anyone, but I suggest using this chart ONLY with one unit at first, probably meters. Have your child understand how it works first, and THEN say, "Hey, guess what...it works for grams and liters, too!" Trying all three in the beginning is probably too much if you are working with a 3rd or 4th grader. Older kids are less rigid and can assimilate easier with different units.
If you have any questions, please ask!
Here is another great conversion tool!
You can see one problem in green, and how it is solved on the chart. We want to know how many kg is 200g? So we go to our chart and start at "g," because it is our base unit. We need to end up at kg, because that is what we are converting to. We jump from one prefix to the next, until we arrive at the unit we need (kg in this case). We jumped 3 to the left. Therefore, we will move our decimal 3 places to the left. As you can see in the drawing, we end up with .200 kg or .2 kg.
In the blue, we want to convert 3m to mm. Again, we start at our base unit, m, and jump until we end up at mm (3 times). We jumped to the right, so our decimal will move 3 places to the right.
Kids will ask...What is hecto? What is deka? What is deci? The truth is, they don't need to know these. Tell them what each prefix stands for, but realize that they will NEVER be asked to convert to these, because we simply don't use them. They are really just place holders. If they leave them out of the chart, they won't jump enough...so while they need to know they exist, they will never use these prefixes. This chart will help them "see" why they are moving the decimal and they will learn pretty quickly how many jumps it is to go all the way from kilo to milli (6) or vice versa (still 6!)
If you have struggled with metric conversions and have some anxiety about teaching them to your child, sit down and make this chart for yourself and then work some problems out. Use this as a TOOL to go along with your child's textbook, which will go more in depth with how the metric system is based on tens, etc. You know your child better than anyone, but I suggest using this chart ONLY with one unit at first, probably meters. Have your child understand how it works first, and THEN say, "Hey, guess what...it works for grams and liters, too!" Trying all three in the beginning is probably too much if you are working with a 3rd or 4th grader. Older kids are less rigid and can assimilate easier with different units.
If you have any questions, please ask!
Here is another great conversion tool!
Teaching Conversions to the Right Brained Child
Right brained children work better when they can see things in pictures. When converting from one unit of measure to another, this image will help ALL children remember, but especially right-brained children who might not remember it otherwise.
This image "says" that 1 gallon = 4 qts. 1 qt = 2 pts. 1 pt. = 2 cups, etc. Quick...how many pints in a gallon? How many cups in a gallon? How many cups in 4 gallons? All can be solved quickly by using this picture. Kids might have 2-3 days of unit conversions before moving on to something else. If they draw this 2-3 times, they will remember it on their own, and eventually, will be able to see it in their heads.
On a test, such as a state assessment, they cannot bring this in with them, but they can jot it down real quick when a conversion problem pops up. Now if you remember, there might be 2-3 of these on the whole test. Why bother to teach them this for just a couple of answers? Well, I've needed this info in real life...so it IS one of those things that is helpful to just know.
On a test, such as a state assessment, they cannot bring this in with them, but they can jot it down real quick when a conversion problem pops up. Now if you remember, there might be 2-3 of these on the whole test. Why bother to teach them this for just a couple of answers? Well, I've needed this info in real life...so it IS one of those things that is helpful to just know.
Tuesday, January 4, 2011
How many cubic feet is my washer?
I always enjoy the, "I get to use the math I learned in junior high!" moments because I can use these examples one day when my kids ask, "Why do I have to learn this?!" Here is a great use of measurement, formulas, and figuring out volume...
My washing machine broke. It is over 20 years old, so I decided it was probably time to start looking for a new one. I looked them up online and kept seeing how many cubic feet the new ones were. Well, how can I know how big that is if I don't know the cubic feet of my current washer? Hmmmm.... So I googled, "How many cubic feet is XXX washer?" I had written down the model number, serial number, brand and anything else I might need off the washer so I could find the information online. But what I found instead was (GASP!) how to calculate your cubic feet. Not only did I have to know what pi was, I needed to use the ol' formula A=pi (r squared). THEN I had to multiply the area by the height of the drum, to satisfy the formula V = pi (radius squared) (height) or V= pi X r^2 X h . But it doesn't end there! I measured in inches and ended up with the volume in cubic inches. In order to compare to the new washers, I needed to know how many cubic feet it was.
There are 12 inches in 1 foot, 144 (or 12x12) square inches in 1 square foot, 1728 (or 12x12x12) cubic inches in 1 cubic foot. So to find how many cubic feet you have, divide the number you got in inches by 1728. Then, you will know how many cubic feet your washer is in. Do yourself a favor and write it with permanent marker somewhere on the machine! It might come in handy at some point.
My washing machine broke. It is over 20 years old, so I decided it was probably time to start looking for a new one. I looked them up online and kept seeing how many cubic feet the new ones were. Well, how can I know how big that is if I don't know the cubic feet of my current washer? Hmmmm.... So I googled, "How many cubic feet is XXX washer?" I had written down the model number, serial number, brand and anything else I might need off the washer so I could find the information online. But what I found instead was (GASP!) how to calculate your cubic feet. Not only did I have to know what pi was, I needed to use the ol' formula A=pi (r squared). THEN I had to multiply the area by the height of the drum, to satisfy the formula V = pi (radius squared) (height) or V= pi X r^2 X h . But it doesn't end there! I measured in inches and ended up with the volume in cubic inches. In order to compare to the new washers, I needed to know how many cubic feet it was.
There are 12 inches in 1 foot, 144 (or 12x12) square inches in 1 square foot, 1728 (or 12x12x12) cubic inches in 1 cubic foot. So to find how many cubic feet you have, divide the number you got in inches by 1728. Then, you will know how many cubic feet your washer is in. Do yourself a favor and write it with permanent marker somewhere on the machine! It might come in handy at some point.
Figuring this out was an eye opener to me of the things we could ask children to figure out that will help them use what they are learning in math. My 4th grader isn't quite at the point of doing this, but one day... and I can't wait to show him! If you have other "using math" ideas, please share them!
P.S. My washer was 2.5 cubic feet!
Tuesday, April 8, 2008
How much trash do we generate per day?
Yesterday for school, we calculated how much trash our family of three generates per day. We collected our trash for three days. Since some days have little trash, and other days have more, I wanted to get a better idea of where we stood. (We did discuss "high trash" weeks like birthdays and Christmas when we have boxes and wrapping paper, etc.) But on average, we generate about one pound each day.
My children are 5 (and 5 months) and 6 (and 11 months). I am exact with their ages, because if they were in school, there is NO WAY this problem would be put in front of them. First, I asked how to figure out how much trash we generated in one day if we know how much trash we generated in 3 days. They kind of threw around some close ideas, so I drew an illustration that worked out their thoughts more concretely. "What if I took each piece in the trash and cut it into three equal pieces. I would put each piece into a pile, and have three piles when I'm done. Would you say that I split the trash into three even stacks, representing the three days? And would one stack represent the trash we would generate in one day?" Their eyes began to light up. Since we had already talked about fractions, they quickly recognized that we had split the trash into thirds.
I then drew a circle on a paper and said, "this circle represents the three days worth of trash that we collected. How can I divide the "trash" to help me figure out the amount generated in one day?"
"Divide it into three equal parts."
I tried my best at making "thirds" and it was at least sufficient. I then showed how I can not only divide a circle into thirds, or the trash into thirds, but a number into thirds (division- a new concept). They now know that we generate one pound per day.
"How many do we generate in a week?" To which my FIVE year-old responded, "Seven." Sign her up for MIT, folks!
She new the answer was 7, but did not know how to explain why. So I let her brother think and verbalize. I then explained how you could add 1+1+1+1+1+1+1 to get 7, or you could say "1 TIMES 7." I knew they got it once we needed to know how many pounds we generate in a month, and used "30" as the number of days per month.
When we started working on the number of pounds per year, I first was going to use the result from our monthly figure, but my 6 year old helped me realize something when he said, "figure out how many days there are in a year and times that..." It occurred to me that he was dead on. Since there are not 30 days in every month, you cannot simply multiply that result by 12. You need to go back to the daily amount and multiply it by 365 for the most accurate result.
There was never any reason for them to know how many days there are in a year, but they know now!
This is a great example of the many concepts taught in one activity. And this was part of "science," not math! It also shows that children understand much more than we give them credit for. I've mentioned this often in my blog, but in case you are a new reader, my daughter isn't even supposed to be in kindergarten yet, according to her birthday. And here she is at home, dividing, multiplying, and problem solving!
My children are 5 (and 5 months) and 6 (and 11 months). I am exact with their ages, because if they were in school, there is NO WAY this problem would be put in front of them. First, I asked how to figure out how much trash we generated in one day if we know how much trash we generated in 3 days. They kind of threw around some close ideas, so I drew an illustration that worked out their thoughts more concretely. "What if I took each piece in the trash and cut it into three equal pieces. I would put each piece into a pile, and have three piles when I'm done. Would you say that I split the trash into three even stacks, representing the three days? And would one stack represent the trash we would generate in one day?" Their eyes began to light up. Since we had already talked about fractions, they quickly recognized that we had split the trash into thirds.
I then drew a circle on a paper and said, "this circle represents the three days worth of trash that we collected. How can I divide the "trash" to help me figure out the amount generated in one day?"
"Divide it into three equal parts."
I tried my best at making "thirds" and it was at least sufficient. I then showed how I can not only divide a circle into thirds, or the trash into thirds, but a number into thirds (division- a new concept). They now know that we generate one pound per day.
"How many do we generate in a week?" To which my FIVE year-old responded, "Seven." Sign her up for MIT, folks!
She new the answer was 7, but did not know how to explain why. So I let her brother think and verbalize. I then explained how you could add 1+1+1+1+1+1+1 to get 7, or you could say "1 TIMES 7." I knew they got it once we needed to know how many pounds we generate in a month, and used "30" as the number of days per month.
When we started working on the number of pounds per year, I first was going to use the result from our monthly figure, but my 6 year old helped me realize something when he said, "figure out how many days there are in a year and times that..." It occurred to me that he was dead on. Since there are not 30 days in every month, you cannot simply multiply that result by 12. You need to go back to the daily amount and multiply it by 365 for the most accurate result.
There was never any reason for them to know how many days there are in a year, but they know now!
This is a great example of the many concepts taught in one activity. And this was part of "science," not math! It also shows that children understand much more than we give them credit for. I've mentioned this often in my blog, but in case you are a new reader, my daughter isn't even supposed to be in kindergarten yet, according to her birthday. And here she is at home, dividing, multiplying, and problem solving!
Friday, January 25, 2008
Counting by Fives
This is an activity that my son enjoyed a lot, so I thought I would share. We started using this when he was five years old, doing kindergarten work. He could count by fives perfectly, but I wanted to make sure that he could recognize the numbers as well. I printed out the numbers 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100 fairly large on cardstock paper. I then cut them into little squares. I gave them to him all mixed up, and had him put them in the correct order. For beginning learners, you can start with half of the numbers, and then add the second half once your child gets those down. I cannot stress how helpful this is when learning about money, and counting nickels! We coincidentally did this shortly before the "nickels" section in his time and money book came up.
We also used the same concept with recognizing the months and days of the week. Simple enough, and it's fun, too!
Thursday, August 16, 2007
Algebra for Four Year Olds
A few days ago, I was sitting in McDonald's with my children, waiting for them to finish eating. Out of boredom, I developed a great little game that they have enjoyed playing. I put my hand behind my back and said, "I have 3 fingers up behind my back, and two up here (holding two up). How many do I have up all together?" My four year old looked at both of her hands under the table and set them up and counted. "Five!"
The game continued and I actually saw right there in McDonald's, my four year old "get" counting on. She finally stopped counting ALL of the fingers and started with one number and then counted on the rest. After a while, I asked questions like, "If I have 5 fingers up behind my back, and I need to have 8 fingers up, how many do I need to put up on this hand?" And of course, they both got these every time.
Now, my daughter will be five in three months. Because she has a November birthday, she does not meet the cut off for starting kindergarten this year. She is learning to read, she is figuring out missing addend problems, and her skills test all showed that she is on a 5-6 year old level (that was at age 3). Imagine if I were depending on public schools to educate my child! Not only would I have to make her wait an entire year, I know that kids coming out of our local kindergarten are not even reading. After having taught my son to read last year, I just can't imagine why children are not reading out of kindergarten! Even an average child should be able to read to a degree.
Anyway, we still play the game everyday, and my daughter loves asking ME "finger problems!" She has figured out that she has to check to make sure I'm right! And yes, we will be doing kindergarten this year, because unlike the school system, I have common sense!
P.S. I almost forgot. One of the problems I gave was to see how my son would handle it. I said, "I have 100 fingers up behind my back, and 5 up here. How many do I have up?" He answered 105, but then I asked him, "HOW can I have 100 fingers up behind my back?!" We all got a laugh out of that!
Friday, July 6, 2007
It's JUST a Geoboard!
Last week we were at the school supply store and I remembered reading about a geoboard in the next week's lessons when I saw one in the midst of the math supplies. I thought, "It's jut a board with some nails in it!" and put it down. Then I noticed it was ONLY $3.95 or so and figured we might use it at some point, so I added it to my pile. I didn't get the colored rubber bands because we had perfectly good rubber bands at home!
I put it with the school stuff and the next time we did school, brought it out with the lesson materials. Before I even had to say anything, my 6 year old was adding rubberbands and creating a design. Before we finished school he was fighting over it with my 4 year old. They LOVED this thing! He played with it all day, and then, get THIS: he put it under his pillow at bed time! Here is one of the designs that he created. He also took the picture! He made countless designs that day, and I bet if I look, it is still under his pillow. Here is a great resource for geoboard lessons.
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